# Common Core State Standards

StandardDescription of StandardCorresponding Floor Mat
K.CC Counting and CardinalityKnow number names and the count sequence
CC.K.CC.1Count to 100 by ones and by tens.Add/Subtract Mat
Hop by Tens Mat
Hopscotch for Threes Mat
CC.K.CC.2Count forward beginning from a given number within the known sequence (instead of having to begin at 1).Add/Subtract Mat
Hopscotch for Threes Mat
CC.K.CC.3Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).Skip Counting by 2s Mat
Hopscotch for Threes Mat
K.CC Counting and CardinalityCount to tell the number of objects.
CC.K.CC.4Understand the relationship between numbers and quantities; connect counting to cardinality.Add/Subtract Mat
Hopscotch for Threes Mat
CC.K.CC.4aWhen counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.Skip Counting by 2s Mat
Hopscotch for Threes Mat
CC.K.CC.4bUnderstand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.Skip Counting by 2s Mat
Hopscotch for Threes Mat
CC.K.CC.4cUnderstand that each successive number name refers to a quantity that is one larger.Skip Counting by 2s Mat
Hopscotch for Threes Mat
CC.K.CC.5Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.Skip Counting by 2s Mat
Hopscotch for Threes Mat
K.CC Counting and CardinalityCompare numbers.
CC.K.CC.6Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. (Include groups with up to ten objects.)Skip Counting by 2s Mat
CC.K.CC.7Compare two numbers between 1 and 10 presented as written numerals.Number Line 1-10 Floor Mat
K.OA Operations and Algebraic ThinkingUnderstand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
CC.K.OA.1Represent addition and subtraction with objects, fingers, mental images, drawings (drawings need not show details, but should show the mathematics in the problem), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.Skip Counting by 2s Mat
CC.K.OA.2Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.Skip Counting by 2s Mat
Number Line 1-10 Floor Mat
CC.K.OA.3Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).Number Line 1-10 Floor Mat
CC.K.OA.4For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.Number Line 1-10 Floor Mat
CC.K.OA.5Fluently add and subtract within 5.Number Line 1-10 Floor Mat
K.NBT Number and Operations in Base TenWork with numbers 11–19 to gain foundations for place value.
CC.K.NBT.1Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.Place Value Mat (P1)
Skip Counting by 2s Mat
K.MD Measurement and Data
Describe and compare measurable attributes.
CC.K.MD.1Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.Attribute Word Mat
CC.K.MD.2Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.
K.MD Measurement and Data
Classify objects and count the number of objects in each category.
CC.K.MD.3Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. (Limit category counts to be less than or equal to 10.)Skip Counting by 2s Mat
Number Line 1-10 Floor Mat
K.G Geometry
Identify and describe shapes (squares circles triangles rectangles hexagons cubes cones cylinders and spheres).
CC.K.G.1Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.My First Shapes Hop
CC.K.G.2Correctly name shapes regardless of their orientations or overall size.My First Shapes Hop
Geometric Shapes Hop
CC.K.G.3Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).My First Shapes Hop
K.G Geometry
Analyze, compare, create, and compose shapes.
CC.K.G.4Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length).My First Shapes Hop
CC.K.G.5Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.My First Shapes Hop
CC.K.G.6Compose simple shapes to form larger shapes. For example, "can you join these two triangles with full sides touching to make a rectangle?”My First Shapes Hop

StandardDescription of StandardCorresponding Floor Mat
1.OA Operations and Algebraic ThinkingRepresent and solve problems involving addition and subtraction.
CC.1.OA.1Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.Skip Counting by 2s Mat
CC.1.OA.2Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.Skip Counting by 2s Mat
1.OA Operations and Algebraic ThinkingUnderstand and apply properties of operations and the relationship between addition and subtraction.
CC.1.OA.3Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) (Students need not use formal terms for these properties.)Skip Counting by 2s Mat
Hopscotch for Threes Mat
CC.1.OA.4Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8.Skip Counting by 2s Mat
1.OA Operations and Algebraic ThinkingAdd and subtract within 20.
CC.1.OA.5Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).Skip Counting by 2s Mat
CC.1.OA.6Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).Skip Counting by 2s Mat
1.OA Operations and Algebraic ThinkingWork with addition and subtraction equations.
CC.1.OA.7Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.Skip Counting by 2s Mat
CC.1.OA.8Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ＿ – 3, 6 + 6 = ＿.Skip Counting by 2s Mat
1.NBT Number and Operations in Base TenExtend the counting sequence.
CC.1.NBT.1Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.Add/Subtract Mat
1.NBT Number and Operations in Base TenUnderstand place value.
CC.1.NBT.2Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:Place Value Mat (P1)
CC.1.NBT.2a10 can be thought of as a bundle of ten ones — called a “ten.”Place Value Mat (P1)
CC.1.NBT.2bThe numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. Place Value Mat (P1)
CC.1.NBT.2cThe numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).Place Value Mat (P1)
CC.1.NBT.3Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.Place Value Mat (P1)
1.NBT Number and Operations in Base TenUse place value understanding and properties of operations to add and subtract.
CC.1.NBT.4Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.Add/Subtract Mat
CC.1.NBT.5Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.Add/Subtract Mat
CC.1.NBT.6Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.Add/Subtract Mat
1.MD Measurement and DataMeasure lengths indirectly and by iterating length units.
CC.1.MD.1Order three objects by length; compare the lengths of two objects indirectly by using a third object.
CC.1.MD.2Measure lengths indirectly and by iterating length units. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.
1.MD Measurement and DataTell and write time.
CC.1.MD.3Tell and write time in hours and half-hours using analog and digital clocks.Clock Hop
1.MD Measurement and DataRepresent and interpret data.
CC.1.MD.4Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.
1.G GeometryReason with shapes and their attributes.
CC.1.G.1Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); for a wide variety of shapes; build and draw shapes to possess defining attributes.Geometric Shapes Hop
CC.1.G.2Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names such as “right rectangular prism.”)
CC.1.G.3Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.Unit Circle Hop Mat
Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
Equivalent Fraction Hop Floor Mat

StandardDescription of StandardCorresponding Floor Mat
2.OA Operations and Algebraic ThinkingRepresent and solve problems involving addition and subtraction.
CC.2.OA.1Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.Add/Subtract Floor Mat
2.OA Operations and Algebraic ThinkingAdd and subtract within 20.
CC.2.OA.2Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.Skip Counting by 2s Mat
Hopscotch For Threes Mat
2.OA Operations and Algebraic ThinkingWork with equal groups of objects to gain foundations for multiplication.
CC.2.OA.3Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.Skip Counting by 2s Mat
CC.2.OA.4Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
2. NBT Number and Operations in Base TenUnderstand place value.
CC.2.NBT.1Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:Place Value Mat (P1)
CC.2.NBT.1a100 can be thought of as a bundle of ten tens — called a “hundred.”
Place Value Mat (P1)
Hopping by 100s Mat
CC.2.NBT.1bThe numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).Place Value Mat (P1)
Hopping by 100s Mat
CC.2.NBT.2CC.2.NBT.2 Understand place value. Count within 1000; skip-count by 5s, 10s, and 100s.Place Value Mat (P1)
Hopping by 100s Mat
CC.2.NBT.3CC.2.NBT.3 Understand place value. Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.Place Value Mat (P1)
CC.2.NBT.4CC.2.NBT.4 Understand place value. Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.Place Value Mat (P1)
2. NBT Number and Operations in Base TenUse place value understanding and properties of operations to add and subtract.
CC.2.NBT.5Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.Place Value Mat (P1)
CC.2.NBT.6Add up to four two-digit numbers using strategies based on place value and properties of operations.Place Value Mat (P1)
CC.2.NBT.7Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.Place Value Mat (P1)
CC.2.NBT.8Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.Place Value Mat (P1)
CC.2.NBT.9Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.)Place Value Mat (P1)
2.MD Measurement and DataMeasure and estimate lengths in standard units.
CC.2.MD.1Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.Measurement Hop
CC.2.MD.2Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.Measurement Hop
CC.2.MD.3Estimate lengths using units of inches, feet, centimeters, and meters.Measurement Hop
CC.2.MD.4Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.Measurement Hop
2.MD Measurement and DataRelate addition and subtraction to length.
CC.2.MD.5Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.Add/Subtract Mat
CC.2.MD.6Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, … , and represent whole-number sums and differences within 100 on a number line diagram.Add/Subtract Mat
2.MD Measurement and DataWork with time and money.
CC.2.MD.7Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.Clock Hopa
CC.2.MD.8Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using \$ (dollars) and ¢ (cents) symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?Dollar Hop
Money Hop
Represent and interpret data.
CC.2.MD.9Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.Cartesian Coordinate Hop
CC.2.MD.10Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.Cartesian Coordinate Hop
2.G GeometryReason with shapes and their attributes.
CC.2.G.1Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. (Sizes are compared directly or visually, not compared by measuring.)Geometric Shapes Hop
CC.2.G.2Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.Equivalent Fraction Hop
CC.2.G.3Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.Unit Circle Hop Mat
Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
Equivalent Fraction Hop Floor Mat

StandardDescription of StandardCorresponding Floor Mat
CC.4.OA.1Use the four operations with whole numbers to solve problems. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.Skip Counting Mats Set
Factor Fun Hop
CC.4.OA.2Use the four operations with whole numbers to solve problems. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.Multiplication Hop
CC.4.OA.3Use the four operations with whole numbers to solve problems. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.Add/Subtract Floor Mat
Operations Floor Mat
Geometric Shapes Hop
Multiplication Hop
CC.4.OA.4Gain familiarity with factors and multiples. Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.Multiplication Hop
Factor Fun Hop
CC.4.OA.5Generate and analyze patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.Corresponding Floor Mat
CC.4.NBT.1Generalize place value understanding for multi-digit whole numbers. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)Place Value Mats
CC.4.NBT.2Generalize place value understanding for multi-digit whole numbers. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)Add/Subtract Floor Mat
Operations Floor Mat
CC.4.NBT.3Generalize place value understanding for multi-digit whole numbers. Use place value understanding to round multi-digit whole numbers to any place. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)Place Value - Decimals (P3)
CC.4.NBT.4Use place value understanding and properties of operations to perform multi-digit arithmetic. Fluently add and subtract multi-digit whole numbers using the standard algorithm. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.)Add/Subtract Floor Mat
CC.4.NBT.5Use place value understanding and properties of operations to perform multi-digit arithmetic. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.)Skip Counting Mats Set
Multiplication Hop
CC.4.NBT.6Use place value understanding and properties of operations to perform multi-digit arithmetic. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.)Skip Counting Mats Set
CC.4.NF.1Extend understanding of fraction equivalence and ordering. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
Equivalent Fraction Hop Floor Mat
CC.4.NF.2Extend understanding of fraction equivalence and ordering. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
Equivalent Fraction Hop Floor Mat
CC.4.NF.3Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
Equivalent Fraction Hop Floor Mat
CC.4.NF.3aUnderstand addition and subtraction of fractions as joining and separating parts referring to the same whole.Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
Equivalent Fraction Hop Floor Mat
CC.4.NF.3bDecompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
Equivalent Fraction Hop Floor Mat
CC.4.NF.3cAdd and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
Equivalent Fraction Hop Floor Mat
CC.4.NF.3dSolve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
Equivalent Fraction Hop Floor Mat
CC.4.NF.4Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
CC.4.NF.4aUnderstand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
CC.4.NF.4bUnderstand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
CC.4.NF.4cSolve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
CC.4.NF.5Understand decimal notation for fractions, and compare decimal fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100 and add 3/10 + 4/100 = 34/100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)Fraction, Decimal, and Percentage Hops
Place Value Hop - Decimals (P3)
CC.4.NF.6Understand decimal notation for fractions, and compare decimal fractions. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length as 0.62 meters; locate 0.62 on a number line diagram. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)Fraction, Decimal, and Percentage Hops
Place Value Hop - Decimals (P3)
CC.4.NF.7Understand decimal notation for fractions, and compare decimal fractions. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons comparisons are valid only when two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)Fraction, Decimal, and Percentage Hops
Place Value Hop - Decimals (P3)
Operations Floor Mat
CC.4.MD.1Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example: Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ….Measurement Hop
Clock Hop
CC.4.MD.2Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.Measurement Hop
Clock Hop
Dollar Hop
Money Hop
CC.4.MD.3Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
CC.4.MD.4Represent and interpret data. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
CC.4.MD.5Geometric measurement: understand concepts of angle and measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:Angle Hop Mat
CC.4.MD.5aAn angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.Unit Circle Hop Mat
CC.4.MD.5bAn angle that turns through n one-degree angles is said to have an angle measure of n degrees.Unit Circle Hop Mat
CC.4.MD.6Geometric measurement: understand concepts of angle and measure angles. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.Unit Circle Hop Mat
CC.4.MD.7Geometric measurement: understand concepts of angle and measure angles. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.Unit Circle Hop Mat
CC.4.G.1Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.Angle Hop Mat
CC.4.G.2Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.Angle Hop Mat
CC.4.G.3Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.Angle Hop Mat

StandardDescription of StandardCorresponding Floor Mat
CC.4.OA.1Use the four operations with whole numbers to solve problems. Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.Skip Counting Mats Set
Factor Fun Hop
CC.4.OA.2Use the four operations with whole numbers to solve problems. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.Multiplication Hop
CC.4.OA.3Use the four operations with whole numbers to solve problems. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.Add/Subtract Floor Mat
Operations Floor Mat
Geometric Shapes Hop
Multiplication Hop
CC.4.OA.4Gain familiarity with factors and multiples. Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.Multiplication Hop
Factor Fun Hop
CC.4.OA.5Generate and analyze patterns. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.Corresponding Floor Mat
CC.4.NBT.1Generalize place value understanding for multi-digit whole numbers. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)Place Value Mats
CC.4.NBT.2Generalize place value understanding for multi-digit whole numbers. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)Add/Subtract Floor Mat
Operations Floor Mat
CC.4.NBT.3Generalize place value understanding for multi-digit whole numbers. Use place value understanding to round multi-digit whole numbers to any place. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)Place Value - Decimals (P3)
CC.4.NBT.4Use place value understanding and properties of operations to perform multi-digit arithmetic. Fluently add and subtract multi-digit whole numbers using the standard algorithm. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.)Add/Subtract Floor Mat
CC.4.NBT.5Use place value understanding and properties of operations to perform multi-digit arithmetic. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.)Skip Counting Mats Set
Multiplication Hop
CC.4.NBT.6Use place value understanding and properties of operations to perform multi-digit arithmetic. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000. A range of algorithms may be used.)Skip Counting Mats Set
CC.4.NF.1Extend understanding of fraction equivalence and ordering. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
Equivalent Fraction Hop Floor Mat
CC.4.NF.2Extend understanding of fraction equivalence and ordering. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
Equivalent Fraction Hop Floor Mat
CC.4.NF.3Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
Equivalent Fraction Hop Floor Mat
CC.4.NF.3aUnderstand addition and subtraction of fractions as joining and separating parts referring to the same whole.Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
Equivalent Fraction Hop Floor Mat
CC.4.NF.3bDecompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
Equivalent Fraction Hop Floor Mat
CC.4.NF.3cAdd and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
Equivalent Fraction Hop Floor Mat
CC.4.NF.3dSolve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
Equivalent Fraction Hop Floor Mat
CC.4.NF.4Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
CC.4.NF.4aUnderstand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
CC.4.NF.4bUnderstand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
CC.4.NF.4cSolve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
CC.4.NF.5Understand decimal notation for fractions, and compare decimal fractions. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100 and add 3/10 + 4/100 = 34/100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)Fraction, Decimal, and Percentage Hops
Place Value Hop - Decimals (P3)
CC.4.NF.6Understand decimal notation for fractions, and compare decimal fractions. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length as 0.62 meters; locate 0.62 on a number line diagram. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)Fraction, Decimal, and Percentage Hops
Place Value Hop - Decimals (P3)
CC.4.NF.7Understand decimal notation for fractions, and compare decimal fractions. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons comparisons are valid only when two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)Fraction, Decimal, and Percentage Hops
Place Value Hop - Decimals (P3)
Operations Floor Mat
CC.4.MD.1Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example: Know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ….Measurement Hop
Clock Hop
CC.4.MD.2Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.Measurement Hop
Clock Hop
Dollar Hop
Money Hop
CC.4.MD.3Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
CC.4.MD.4Represent and interpret data. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
CC.4.MD.5Geometric measurement: understand concepts of angle and measure angles. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:Angle Hop Mat
CC.4.MD.5aAn angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.Unit Circle Hop Mat
CC.4.MD.5bAn angle that turns through n one-degree angles is said to have an angle measure of n degrees.Unit Circle Hop Mat
CC.4.MD.6Geometric measurement: understand concepts of angle and measure angles. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.Unit Circle Hop Mat
CC.4.MD.7Geometric measurement: understand concepts of angle and measure angles. Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.Unit Circle Hop Mat
CC.4.G.1Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.Angle Hop Mat
CC.4.G.2Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.Angle Hop Mat
CC.4.G.3Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.Angle Hop Mat

StandardDescription of StandardCorresponding Floor Mat
CC.5.OA.1Write and interpret numerical expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.PEMDAS Hop
CC.5.OA.2Write and interpret numerical expressions. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.PEMDAS Hop
CC.5.OA.3Analyze patterns and relationships. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.Cartesian Coordinate Hop
CC.5.NBT.1Understand the place value system. Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.Place Value Hop - Decimals (P3)
CC.5.NBT.2Understand the place value system. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10.Place Value Hop - Decimals (P3)
CC.5.NBT.3Understand the place value system. Read, write, and compare decimals to thousandths.Place Value Hop - Decimals (P3)
CC.5.NBT.3aRead and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).Place Value Hop - Decimals (P3)
PEMDAS Hop
CC.5.NBT.3bCompare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.Place Value Hop - Decimals (P3)
PEMDAS Hop
CC.5.NBT.4Understand the place value system. Use place value understanding to round decimals to any place.Place Value Hop - Decimals (P3)
CC.5.NBT.5Perform operations with multi-digit whole numbers and with decimals to hundredths. Fluently multiply multi-digit whole numbers using the standard algorithm.Place Value Hop - Decimals (P3)
Skip Counting Mat Set
CC.5.NBT.6Perform operations with multi-digit whole numbers and with decimals to hundredths. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.Place Value Hop - Decimals (P3)
Skip Counting Mat Set
CC.5.NBT.7Perform operations with multi-digit whole numbers and with decimals to hundredths. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.Place Value Hop - Decimals (P3)
Skip Counting Mat Set
CC.5.NF.1Use equivalent fractions as a strategy to add and subtract fractions. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
CC.5.NF.2Use equivalent fractions as a strategy to add and subtract fractions. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 by observing that 3/7 < 1/2.Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
CC.5.NF.3Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3 and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
Equivalent Fraction Hop
CC.5.NF.4Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.Skip Counting Mat Set
CC.5.NF.4aInterpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
CC.5.NF.4bFind the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
CC.5.NF.5Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Interpret multiplication as scaling (resizing) by:

-- a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

-- b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a) / (n×b) to the effect of multiplying a/b by 1.
Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
Factor Fun Hop
CC.5.NF.6Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
CC.5.NF.7Apply and extend previous understandings of multiplication and division to multiply and divide fractions. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.)Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
CC.5.NF.7aInterpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4 and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
CC.5.NF.7bInterpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5) and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
CC.5.NF.7cSolve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
CC.5.MD.1Convert like measurement units within a given measurement system. Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step real world problems.Measurement Hop
CC.5.MD.2Represent and interpret data. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.Fraction Walk (Halves/Quarters)
Fraction Walk (Thirds/Sixths)
CC.5.MD.3Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
-- a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.
-- b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
CC.5.MD.4Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
CC.5.MD.5Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.Skip Counting Mat Set
CC.5.MD.5AFind the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent three-fold whole-number products as volumes, e.g., to represent the associative property of multiplication.
CC.5.MD.5BApply the formulas V =(l)(w)(h) and V = (b)(h) for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
CC.5.MD.5CRecognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
CC.5.G.1Graph points on the coordinate plane to solve real-world and mathematical problems. Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).Cartesian Coordinate Hop
CC.5.G.2Graph points on the coordinate plane to solve real-world and mathematical problems. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.Cartesian Coordinate Hop
CC.5.G.3Classify two-dimensional figures into categories based on their properties. Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.Geometric Shapes Hop
CC.5.G.4Classify two-dimensional figures into categories based on their properties. Classify two-dimensional figures in a hierarchy based on properties.Geometric Shapes Hop

# New York Next Generation Learning Standards

StandardDescription of StandardCorresponding Floor Mat
Counting and Cardinality
NY-K.CC.1Count to 100 by ones and by tens.Add/Subtract, Hop by Tens, Hundred Number Grid
NY-K.CC.2Count to 100 by ones beginning from any given number (instead of beginning at 1).Add/Subtract, Count to 10, Hopscotch for 3's, Hundred Number Grid
NY-K.CC.3Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).Add/Subtract, Make Sums Set, Number Line 0-10 Fruits and Vegetables, Number Word Hop, Place Value Hop, Skip Counting by 2s, Open Number Line, Hundred Number Grid, Number Word Hop, Connect the Dots
NY-K.CC.4Understand the relationship between numbers and quantities up to 20; connect counting to cardinality.Ten Frame Hop, Skip Counting (all), Add/Subtract, Make Sums Set, Number Line 0-10 Fruits and Vegetables, Number Word Hop, Place Value Hop, Number line to 10, Hopscotch for 3's, Count to 10, Hundred Number Grid, Number Word Hop
NY-K.CC.4aWhen counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. (1:1 correspondence)Add/Subtract, Number Line 0-10 Fruits and Vegetables, Number Word Hop, Count to 10, Place Value Hop, Skip Counting (all), Hundred Number Grid, Number Word Hop
NY-K.CC.4bUnderstand that the last number name said tells the number of objects counted, (cardinality). The number of objects is the same regardless of their arrangement or the order in which they were counted.Add/Subtract, Number Line 0-10 Fruits and Vegetables, Number Word Hop, Count to 10, Place Value Hop, Skip Counting (all), Hundred Number Grid, Number Word Hop
NY-K.CC.4cUnderstand the concept that each successive number name refers to a quantity that is one larger.Add/Subtract, Number Line 0-10 Fruits and Vegetables, Number Word Hop, Count to 10, Place Value Hop, Skip Counting (all), Make Sums Set, Number Line to 10, Hundred Number Grid, Number Word Hop
NY-K.CC.4dUnderstand the concept of ordinal numbers (first through tenth) to describe the relative position and magnitude of whole
numbers.
Ordinal Number Hop, Open Number Line
NY-K.CC.5aAnswer counting questions using as many as 20 objects arranged in a line, a rectangular array, and a circle. Answer counting questions using as many as 10 objects in a scattered configuration.
e.g., “How many_____ are there?”
Number Line 0-10 Fruits and Vegetables, Number Word Hop, Count to 10, Place Value Hop, Number Line to 10, Number Word Hop
NY-K.CC.5bGiven a number from 1–20, count out that many objects.Skip Counting by 2's, Add/Subtract, Hundred Number Grid, Number Word Hop
NY-K.CC.6Identify whether the number of objects in one group is greater than (more than), less than (fewer than), or equal to (the same as) the number of objects in another group.
e.g., using matching and counting strategies. Note: Include groups with up to ten objects.
Skip Counting by 2s Mat, Count to 10, Make Sums Set, Number Line 0-10 Fruits and Vegetables, Place Value Hop, Hundred Number Grid
NY-K.CC.7Compare two numbers between 1 and 10 presented as written numerals.
e.g., 6 is greater than 2.
Skip Counting by 2s Mat, Count to 10, Make Sums Set, Number Line 0-10 Fruits and Vegetables, Place Value Hop, Open Number Line
Operations and Algebraic Thinking
NY-K.OA.1Represent addition and subtraction using objects, fingers, pennies, drawings, sounds, acting out situations, verbal explanations, expressions, equations or other strategies.
Note: Drawings need not show details, but should show the mathematics in the problem."
Add/Subtract, Count to 10, Number Word Hop, Place Value Hop, Whole Part and Number Bond Floor Mat, 10 Frame, Doubles Hopscotch, Hopscotch for 3's, Open Number Line
NY-K.OA.2aAdd and subtract within 10.Count to 10, Make Sums Set, Number Line 0-10 Fruits and Vegetables, Number Line to 10, Place Value, Ten Frame Hop, Whole Part and Number Bond Floor Mat, Open Number Line, Number Word Hop
NY-K.OA.2bSolve addition and subtraction word problems within 10. e.g., using objects or drawings to represent the problem.Count to 10, Make Sums Set, Number Line 0-10 Fruits and Vegetables, Number Line to 10, Place Value, Ten Frame Hop, Whole Part and Number Bond Floor Mat, Open Number Line
NY-K.OA.3Decompose numbers less than or equal to 10 into pairs in more than one way.
Record each decomposition by a drawing or equation. e.g., using objects or drawings.
Count to 10, Make Sums Set, Number Line 0-10 Fruits and Vegetables, Number Line to 10, Place Value, Ten Frame Hop, Whole Part and Number Bond Floor Mat, Open Number Line
NY-K.OA.4Find the number that makes 10 when given a number from 1 to 9.
Record the answer with a drawing or equation. e.g., using objects or drawings.
Ten Frame Hop, Make Sums Set, Number Line to 10, Place Value, Open Number Line
NY-K.OA.5Fluently add and subtract within 5.
Note: Fluency involves a mixture of just knowing some answers, knowing some answers from patterns, and knowing some answers from the use of strategies.
Count to 10, Ten Frame Hop, Whole Part and Number Bonds, Open Number Line
NY-K.OA.6Duplicate, extend, and create simple patterns using concrete objects.Add/Subtract, Hundred Number Grid
Number and Operations in Base Ten
NY-K.NBT.1Compose and decompose the numbers from 11 to 19 into ten ones and one, two, three, four, five, six, seven, eight, or nine ones.
e.g., using objects or drawings.
Skip Count by 2's, Whole Part and Number Bond Floor Mat, Place Value Hop,
Measurement and Data
NY-K.MD.1Describe measurable attributes of an object(s), such as length or weight, using appropriate vocabulary.
e.g., small, big, short, tall, empty, full, heavy, and light.
Measurement Hop, My First Shapes Hop, Attribute Word Hop
NY-K.MD.2Directly compare two objects with a common
measurable attribute and describe the difference.
Measurement Hop, My First Shapes Hop, Attribute Word Hop
NY-K.MD.3Classify objects into given categories; count the objects in each category and sort the categories by count.
Note: Limit category counts to be less than or equal to 10.
Count to 10, Attribute Word Hop
NY-K.MD.4Explore coins (pennies, nickels, dimes, and quarters) and begin identifying pennies and dimes.Money Hop Mat, Dollar Hop
Geometry
NY-K.G.1Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.My First Shapes Hop, Number Line 0-10 Fruits and Vegetables
NY-K.G.2Name shapes regardless of their orientation or overall size.My First Shapes Hop, Connect the Dots
NY-K.G.3Understand the difference between two-dimensional (lying in a plane, “flat”) and three-dimensional (“solid”) shapes.My First Shapes Hop, Connect the Dots
NY-K.G.4Analyze, compare, and sort two- and three- dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts, and other attributes.
e.g., number of sides and vertices/“corners”, or having sides of equal length.
My First Shapes Hop, Connect the Dots
NY-K.G.5Model objects in their environment by building and/or drawing shapes.
e.g., using blocks to build a simple representation in the classroom.
Note on and/or: Students should be taught to model objects by building and drawing shapes; however, when answering a question, students can choose to model the object by building or drawing the shape.
My First Shapes Hop, Connect the Dots
NY-K.G.6Compose larger shapes from simple shapes.
e.g., join two triangles to make a rectangle.
My First Shapes Hop, Connect the Dots

StandardDescription of StandardCorresponding Floor Mat
Operations and Algebraic Thinking
NY-1.OA.1Use addition and subtraction within 20 to solve one-step word problems involving situations of adding to, taking from, putting together, taking apart, and/or comparing, with unknowns in all positions.Add/Subtract, Count to Ten, Make Sums Set, Place Value Hop, Skip Count by 2's, 10 Frame Hop, Whole Part and Number Bond, Doubles Hopscotch, Hundred Number Grid
Note: Problems should be represented using objects, drawings, and equations with a symbol for the unknown number. Problems should be solved using objects or drawings, and equations.
NY-1.OA.2Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20.
e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
Add/Subtract, Skip Count by 2's, Place Value, Hundred Number Grid
NY-1.OA.3 Apply properties of operations as strategies to add and subtract.
e.g.,
• If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.)
• To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12.
Add/Subtract, Skip Count by 2's, Place Value, Hundred Number Grid
Note: Students need not use formal terms for these properties.
NY-1.OA.4Understand subtraction as an unknown- addend problem within 20. e.g., subtract 10 – 8 by finding the number that makes 10 when added to 8.Add/Subtract, Skip Count by 2's, Whole Part Number Bond, Hundred Number Grid
NY-1.OA.5Relate counting to addition and subtraction.
e.g., by counting on 2 to add 2
Add/Subtract, Count to 10, Hopscotch for 3's, Hundred Number Grid
NY-1.OA.6aAdd and subtract within 20. Use strategies such as:
• counting on;
• making ten;
• decomposing a number leading to a ten;
• using the relationship between addition and subtraction; and
• creating equivalent but easier or known sums.
Make Sums Set, Place Value Hop, Skip Counting by 2's, Ten Frame Hop, Whole Part and Number Bond, Add/Subtract, Count to Ten, Doubles Hopscotch, Hundred Number Grid
NY-1.OA.6bFluently add and subtract within 10.
Note: Fluency involves a mixture of just knowing some answers, knowing some answers from patterns, and knowing some answers from the use of strategies.
Count to 10, Make Sums Set, Number Line 0-10 Fruits and Vegetables, Number Line to 10, Place Value, Ten Frame Hop, Whole Part and Number Bond Floor Mat, Open Number Line
NY-1.OA.7Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.
e.g., Which of the following equations are true and which are false? 6 = 6 7 = 8 – 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2
NY-1.OA.8Determine the unknown whole number in an addition or subtraction equation with the unknown in all positions.
e.g., Determine the unknown number that makes the equation true in each of the equations
8 + ? = 11 ＿ – 3 = 5 6 + 6 =
Add/Subtract, Whole Part Number Bond, Hundred Number Grid
Number and Operations in Base Ten
NY-1.NBT.1Count to 120, starting at any number less than
120. In this range, read and write numerals and represent a number of objects with a written numeral.
NY-1.NBT.2Understand that the two digits of a two-digit number represent amounts of tens and ones.Place Value
NY-1.NBT.2aUnderstand 10 can be thought of as a bundle of ten ones, called a "ten".Place Value
NY-1.NBT.2bUnderstand that the numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.Place Value
NY-1.NBT.2cUnderstand that the numbers 10, 20, 30, 40,
50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight or nine tens (and 0 ones).
Hop by Tens
NY-1.NBT.3NY-1.NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.Place Value, Skip Counting by 2's, Open Number Line, Operations Hop
• a two-digit number and a one-digit number;
• a two-digit number and a multiple of 10.
Use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
Understand that in adding two-digit numbers, one adds tens and tens, ones and ones, and sometimes it is necessary to compose a ten.
Add/Subtract, Hundred Number Grid, Place Value
Relate the strategy to a written representation and explain the reasoning used.
Notes:
Students should be taught to use strategies based on place value, properties of operations, and the relationship between addition and subtraction; however, when solving any problem, students can choose any strategy.
A written representation is any way of representing a strategy using words, pictures, or numbers.
NY-1.NBT.5Given a two-digit number, mentally find 10 more or 10
less than the number, without having to count; explain the reasoning used.
Add/Subtract, Hop by Tens, Hundred Number Grid
NY-1.NBT.6Subtract multiples of 10 from multiples of 10 in the range 10-90 using
• concrete models or drawings, and
• strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
Relate the strategy used to a written representation and explain the reasoning.
Notes:
Students should be taught to use concrete models and drawings; as well as strategies based on place value, properties of operations, and the relationship between addition and subtraction. When solving any problem, students can choose to use a concrete model or a drawing. Their strategy must be based on place value, properties of operations, or the relationship between addition and subtraction.
A written representation is any way of representing a strategy using words, pictures, or numbers.
Hop by Tens, Place Value
Measurement and Data
NY-1.MD.1Order three objects by length; compare the lengths of two objects indirectly by using a third object.Measurement Hop, Open Number Line
NY-1.MD.2Measure the length of an object using same- size “length units” placed end to end with no gaps or overlaps. Express the length of an object as a whole number of “length units.”
Note: “Length units” could include cubes, paper clips, etc.
Measurement Hop
NY-1.MD.3aTell and write time in hours and half-hours using analog and digital clocks. Develop an understanding of common terms, such as, but not
limited to, o’clock and half past.
Clock Hop
NY-1.MD.3bRecognize and identify coins (penny, nickel, dime, and quarter) and their value and use the cent symbol (¢) appropriately.Money Hop Mat, Dollar Hop
NY-1.MD.3cCount a mixed collection of dimes and pennies and determine the cent value (total not to exceed 100 cents).
e.g. 3 dimes and 4 pennies is the same as 3 tens and 4 ones, which is 34 cents ( 34 ¢ )
Money Hop Mat, Dollar Hop
NY-1.MD.4Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.Number Grid
Geometry
NY-1. G.1Distinguish between defining attributes versus non-defining attributes for a wide variety of shapes. Build and/or draw shapes to possess defining attributes.
e.g.,
• A defining attribute may include, but is not limited to: triangles are closed and three-sided.
• Non-defining attributes include, but are not limited to: color, orientation, and overall size.
Note on and/or: Students should be taught to build and draw shapes to possess defining attributes; however, when answering questions, students can choose to build or draw the shape.
My First Shapes Hop, Connect the Dots
NY-1.G.2Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three- dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.
Note: Students do not need to learn formal names such as “right rectangular prism.”
My First Shapes Hop, Connect the Dots
NY-1. G.3Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of.
Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.
Fraction Walk

StandardDescription of StandardCorresponding Floor Mat
Operations and Algebraic Thinking
NY-2.OA.1aUse addition and subtraction within 100 to solve one-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.
e.g., using drawings and equations with a symbol for the unknown number to represent the problem.
Add/Subtract, Place Value, Measurement Hop, Dollar Hop, Hundred Number Grid
NY-2.OA.1b Use addition and subtraction within 100 to develop an understanding of solving two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.
e.g., using drawings and equations with a symbol for the unknown number to represent the problem.
Add/Subtract, Place Value, Measurement Hop, Dollar Hop, Hundred Number Grid
NY-2.OA.2aFluently add and subtract within 20 using mental strategies. Strategies could include:
• counting on;
• making ten;
• decomposing a number leading to a ten;
• using the relationship between addition and subtraction; and
• creating equivalent but easier or known sums.
Note: Fluency involves a mixture of just knowing some answers, knowing some answers from patterns, and knowing some answers from the use of strategies.
NY-2.OA.2b Know from memory all sums within 20 of two one-digit numbers.
Skip Counting by 2's, Add/Subtract, Count to Ten, Make Sums Set, Place Value, Hundred Number Grid
NY-2.OA.3a Determine whether a group of objects (up to 20) has an odd or even number of members.
e.g., by pairing objects or counting them by 2’s.
Skip Counting by 2's, Make Sums Set, Place Value
NY-2.OA.3bWrite an equation to express an even number as a sum of two equal addends.Doubles Hop Scotch
NY-2.OA.4NY-2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns. Write an equation to express the total as a sum of equal addends.Skip Counting by 2's, Skip Counting by 3's, Skip Counting by 4's
Number and Operations in Base Ten
NY-2.NBT.1Understand that the digits of a three-digit number represent amounts of hundreds, tens, and ones.
e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.
Place Value
NY-2.NBT.1aUnderstand 100 can be thought of as a bundle of ten tens, called a "hundred."
Place Value, Hop by Ten
NY-2.NBT.1bUnderstand the numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four,
five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones)."
Hopping by 100s, Make 100 Hop
NY-2.NBT. 2Count within 1000; skip-count by 5’s, 10’s, and 100’s.Hop by Ten, Skip Count by 5's, Add/Subtract, Clock Hop, Hundred Number Grid, Make 100 Hop, Multiplication Hop
NY-2.NBT. 3"NY-2.NBT. 3 Read and write numbers to 1000 using base- ten numerals, number names, and expanded form.
e.g., expanded form: 237 = 200 + 30 + 7"
Place Value
NY-2.NBT. 4NY-2.NBT.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.Place Value, Operations Hop
NY-2.NBT. 5"NY-2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
Notes: Students should be taught to use strategies based on place value, properties of operations, and the relationship between addition and subtraction; however, when solving any problem, students can choose any strategy."
Place Value, Add/Subtract, Hundred Number Grid
Fluency involves a mixture of just knowing some answers, knowing some answers from patterns, and knowing some answers from the use of strategies.
NY-2.NBT. 6NY-2.NBT.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.Place Value
NY-2.NBT. 7aAdd and subtract within 1000, using
• concrete models or drawings, and
• strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
Relate the strategy to a written representation.
Notes:
Students should be taught to use concrete models and drawings; as well as strategies based on place value, properties of operations, and the relationship between addition and subtraction. When solving any problem, students can choose to use a concrete model or a drawing. Their strategy must be based on place value, properties of operations, and/or the relationship between addition and subtraction.
Place Value
A written representation is any way of representing a strategy using words, pictures, or numbers.
NY-2.NBT. 7bUnderstand that in adding or subtracting up to three- digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones, and sometimes it is necessary to compose or decompose tens or hundreds.Place Value
NY-2.NBT. 8Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.Hop by Ten, Hopping by 100's
NY-2.NBT. 9Explain why addition and subtraction strategies work, using place value and the properties of operations.Place Value, Add/Subtract, Hundred Number Grid
Note: Explanations may be supported by drawings or objects.
Measurement and Data
NY-2.MD.1Measure the length of an object to the nearest whole by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.Measurement Hop
NY-2.MD.2Measure the length of an object twice, using different “length units” for the two measurements; describe how the two measurements relate to the size of the unit chosen.Measurement Hop
NY-2.MD.3Estimate lengths using units of inches, feet, centimeters, and meters.Measurement Hop
NY-2.MD.4Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard “length unit.”Measurement Hop
NY-2.MD.6Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units.
e.g., using drawings and equations with a symbol for the unknown number to represent the problem.
Measurement Hop
NY-2.MD.6Represent whole numbers as lengths from 0 on a number line with equally spaced points corresponding to the numbers
0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line.
Measurement Hop, Number Line to 10, Open Number Line
NY-2.MD.7Tell and write time from analog and digital clocks in five- minute increments, using a.m. and p.m. Develop an understanding of common terms, such as, but not limited to, quarter past, half past, and quarter to.Clock Hop
NY-2.MD.8aCount a mixed collection of coins whose sum is less than or equal to one dollar. e.g., If you have 2 quarters, 2 dimes and 3 pennies, how many cents do you have?
Dollar Hop, Money Hop
NY-2.MD.8bSolve real world and mathematical problems within one dollar involving quarters, dimes, nickels, and pennies, using the ¢ (cent) symbol appropriately.
Note: Students are not introduced to decimals, and therefore the dollar symbol, until Grade 4.
Dollar Hop, Money Hop
NY-2.MD.9Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Present the measurement data in a line plot, where the horizontal
scale is marked off in whole-number units.
Measurement Hop
NY-2.MD.10Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and
compare problems using information presented in a picture graph or a bar graph.
Number Grid
Geometry
NY-2.G.1Classify two-dimensional figures as polygons or non-polygons.My First Shapes, Geometric Shapes, Connect the Dots
NY-2.G.2Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.Equivalent Fraction, Fraction Walk Set
NY-2.G.3Partition circles and rectangles into two, three, or four equal shares. Describe the shares using the words halves, thirds, half of, a third of, etc. Describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.Equivalent Fraction, Fraction Walk Set

StandardDescription of StandardCorresponding Floor Mat
Operations and Algebraic Thinking
NY-3.OA.1Interpret products of whole numbers.
e.g., Interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. Describe a context in which a total number of objects can be expressed as 5 × 7.
Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch, Hopscotch for Threes, Hopscotch for Twos
NY-3.OA.2Interpret whole-number quotients of whole numbers.
e.g., Interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. Describe a context in which a number of shares or a number of groups can be expressed as
56 ÷ 8.
Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch, Hopscotch for Threes, Hopscotch for Twos,
NY-3.OA.3Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.
e.g., using drawings and equations with a symbol for the unknown number to represent the problem.
Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch, Hopscotch for Threes, Hopscotch for Twos,
NY-3.OA.4Determine the unknown whole number in a multiplication or division equation relating three whole numbers.
e.g., Determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ÷ 3, 6 × 6 = ?.
Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch, Hopscotch for Threes, Hopscotch for Twos,
NY-3.OA.5Apply properties of operations as strategies to multiply and divide.
e.g.,
• If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication)
• 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5
× 2 = 10, then 3 × 10 = 30. (Associative property of multiplication)
• Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property)
Note: Students need not use formal terms for these properties.
Note: A variety of representations can be used when applying the properties of operations, which may or may not include parentheses.
Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch, Hopscotch for Threes, Hopscotch for Twos,
NY-3.OA.6Understand division as an unknown-factor problem.
e.g., Find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch, Hopscotch for Threes, Hopscotch for Twos,
NY-3.OA.7aFluently solve single-digit multiplication and related divisions, using strategies such as the relationship between multiplication and division or properties of operations.
e.g., Knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8.
Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch, Hopscotch for Threes, Hopscotch for Twos,
Note: Fluency involves a mixture of just knowing some answers, knowing some answers from patterns, and knowing some answers from the use of strategies.
Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch, Hopscotch for Threes, Hopscotch for Twos,
NY-3.OA.8Solve two-step word problems posed with whole numbers and having whole-number answers using the four operations.Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch, Hopscotch for Threes, Hopscotch for Twos, Add/Subtract, Hundred Number Grid, Open Number Line, Place Value, Operations Hop
NY-3.OA.8aRepresent these problems using equations or expressions with a letter standing for the unknown quantity.
NY-3.OA.8bAssess the reasonableness of answers using mental computation and estimation strategies including rounding. Note: Two-step problems need not be represented by a single expression or equation.Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch, Hopscotch for Threes, Hopscotch for Twos, Add/Subtract, Hundred Number Grid, Open Number Line, Place Value
NY-3.OA.9Identify and extend arithmetic patterns (including patterns in the addition table or multiplication table).Add/Subtract, Hundred Number Grid, Multiplication Hop, Skip Counting Wall Banners
Number and Operations in Base Ten
NY-3.NBT.1Use place value understanding to round whole numbers to the nearest 10 or 100.Add/Subtract, Hundred Number Grid, Multiplication Hop, Hop by Tens, Hop by 100's
NY-3.NBT.2Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
Note: Students should be taught to use strategies and algorithms based on place value, properties of operations, and the relationship between addition and subtraction; however, when solving any problem, students can choose any strategy.
Note: A range of algorithms may be used.
Place Value, Add/Subtract, Hundred Number Grid
NY-3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 using strategies based on place value and properties of operations.
e.g., 9 × 80, 5 × 60
Add/Subtract, Hundred Number Grid, Multiplication Hop, Hop by Tens, Place Value
NY-3.NBT.4a Understand that the digits of a four-digit number represent amounts of thousands, hundreds, tens, and ones.
e.g., 3,245 equals 3 thousands, 2 hundreds, 4 tens, and 5 ones.
NY-3.NBT.4b Read and write four-digit numbers using base-ten numerals, number names, and expanded form.
e.g., The number 3,245 in expanded form can be written as 3,245= 3,000 + 200 + 40 + 5.
Place Value
Number and Operations - Fractions
NY-3.NF.1Understand a unit fraction, 1, is the quantity formed by 1 part when a whole is partitioned into b equal
parts.
Understand a fraction 𝑎 as the quantity formed by a parts of size 1/𝑏.
Note: Fractions are limited to those with denominators 2, 3, 4, 6, and 8."
Equivalent Fraction Hop, Fraction Walk Set
NY-3.NF.2Understand a fraction as a number on the number line; represent fractions on a number line.
Note: Fractions are limited to those with denominators 2, 3, 4, 6, and 8.
Equivalent Fraction Hop, Fraction Walk Set, Open Number Line
NY-3.NF.2aRepresent a fraction 1/𝑏 on a number line by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/𝑏 and that the endpoint of the part starting at 0 locates the number 1/𝑏 on the number line.Equivalent Fraction Hop, Fraction Walk Set, Open Number Line
NY-3.NF.2bRepresent a fraction 𝑎𝑏 on a number line by marking off a lengths 1/𝑏 from 0. Recognize that the resulting interval has size 𝑎/𝑏 and that its endpoint locates the number 𝑎/𝑏 on the number line.Equivalent Fraction Hop, Fraction Walk Set, Open Number Line
NY-3.NF.3Explain equivalence of fractions and compare fractions by reasoning about their size.
Note: Fractions are limited to those with denominators 2, 3, 4, 6, and 8.
Equivalent Fraction Hop, Fraction Walk Set, Open Number Line
NY-3.NF.3aUnderstand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.Equivalent Fraction Hop, Fraction Walk Set, Open Number Line
NY-3.NF.3bRecognize and generate equivalent fractions.
e.g. 1/2 = 2/4; 4/6 = 2/3.
Explain why the fractions are equivalent. e.g., using a visual fraction model.
Equivalent Fraction Hop, Fraction Walk Set, Open Number Line
NY-3.NF.3cExpress whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
e.g., Express 3 in the form 3 = 3/1, recognize that 6/3 = 2, and locate 4/4 and 1 at the same point on a number line.
Equivalent Fraction Hop, Fraction Walk Set, Open Number Line
NY-3.NF.3d.Compare two fractions with the same numerator or the same denominator by reasoning about their size.
Recognize that comparisons rely on the two fractions referring to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.
e.g., using a visual fraction model."
Equivalent Fraction Hop, Fraction Walk Set, Open Number Line
Measurement and Data
NY-3.MD.1Tell and write time to the nearest minute and measure time intervals in minutes. Solve one-step word problems involving addition and subtraction of time intervals in minutes.
e.g., representing the problem on a number line or other visual model. Note: This includes one-step problems that cross into a new hour.
Clock Hop
NY-3.MD.2aMeasure and estimate liquid volumes and masses of objects using grams (g), kilograms (kg), and liters (l).
Note: Does not include compound units such as cm3 and finding the geometric volume of a container.
NY-3.MD.2bAdd, subtract, multiply, or divide to solve one-step word problems involving masses or liquid volumes that are given in the same units.
e.g., using drawings (such as a beaker with a measurement scale) to represent the problem.
Note: Does not include multiplicative comparison problems involving notions of “times as much.”
NY-3.MD.3Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in a scaled picture graph or a scaled bar graph.
e.g., Draw a bar graph in which each square in the bar graph might represent 5 pets.
Number Grid
NY-3.MD.4Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in
appropriate units—whole numbers, halves, or quarters.
Measurement Hop
NY-3.MD.5Recognize area as an attribute of plane figures and understand concepts of area measurement.Number Grid, Cartesian Coordinate, Connect the Dots
NY-3.MD.5aRecognize a square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.Number Grid, Cartesian Coordinate, Connect the Dots
NY-3.MD.5bRecognize a plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.Number Grid, Cartesian Coordinate, Connect the Dots
NY-3.MD.6Measure areas by counting unit squares.
Note: Unit squares include square cm, square m, square in., square ft., and improvised units.
Number Grid, Cartesian Coordinate, Connect the Dots
NY-3.MD.7Relate area to the operations of multiplication and addition.Number Grid, Cartesian Coordinate, Multiplication Hop, Connect the Dots
NY-3.MD.7aFind the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.Number Grid, Cartesian Coordinate, Multiplication Hop, Connect the Dots
NY-3.MD.7bMultiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.Number Grid, Cartesian Coordinate, Multiplication Hop, Connect the Dots
NY-3.MD.7cUse tiling to show in a concrete case that the area of a rectangle with whole-number side length a and side length b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.Number Grid, Cartesian Coordinate, Multiplication Hop, Connect the Dots
NY-3.MD.7dRecognize area as additive. Find areas of figures composed of non-overlapping rectangles, and apply this technique to solve real world problems.
Note: Problems include no more than one unknown side length.
Number Grid, Cartesian Coordinate, Connect the Dots
NY-3.MD.8aSolve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths or finding one unknown side length given the perimeter and other side lengths.Number Grid, Cartesian Coordinate, Multiplication Hop, My First Shapes Hop, Geometric Shapes, Connect the Dots
NY-3.MD.8bIdentify rectangles with the same perimeter and different areas or with the same area and different perimeters.Number Grid, Cartesian Coordinate, Connect the Dots
Geometry
NY-3.G.1Recognize and classify polygons based on the number of sides and vertices (triangles, quadrilaterals, pentagons, and hexagons). Identify shapes that do not belong to one of the given subcategories.
Note: Include both regular and irregular polygons, however, students need not use formal terms “regular” and “irregular,” e.g., students should be able to classify an irregular pentagon as “a pentagon,” but do not need to classify it as an “irregular pentagon.”
My First Shapes Hop, Geometric Shapes, Connect the Dots
NY-3.G.2Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.
e.g., Partition a shape into 4 parts with equal area, and describe the area of each part as 1 of the area of the shape.
4
Number Grid, Cartesian Coordinate, Equivalent Fractions, Connect the Dots

StandardDescription of StandardCorresponding Floor Mat
Operations and Algebraic Thinking
NY-4.OA.1Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations.
e.g.,
• Interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 or 7 times as many as 5.
• Represent “Four times as many as eight is thirty-two” as an equation, 4 x 8 = 32.
Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch, Hopscotch for Threes, Hopscotch for Twos
NY-4.OA.2Multiply or divide to solve word problems involving multiplicative comparison, distinguishing multiplicative comparison from additive comparison. Use drawings and equations with a symbol for the unknown number to represent the problem.Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch, Hopscotch for Threes, Hopscotch for Twos
NY-4.OA.3Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted.Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch, Hopscotch for Threes, Hopscotch for Twos, Operations Hop, PEMDAS Hop
NY-4.OA.3aRepresent these problems using equations or expressions with a letter standing for the unknown quantity.Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch, Hopscotch for Threes, Hopscotch for Twos, Operations Hop
NY-4.OA.3bAssess the reasonableness of answers using mental computation and estimation strategies including rounding.Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch, Hopscotch for Threes, Hopscotch for Twos
Note: Multistep problems need not be represented by a single expression or equation.
NY-4.OA.4Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch, Hopscotch for Threes, Hopscotch for Twos, Factor Fun
NY-4.OA.5Generate a number or shape pattern that follows a given rule. Identify and informally explain apparent features of the pattern that were not explicit in the rule itself.
e.g., Given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers.
Explain informally why the numbers will continue to alternate in this way.
Add/Subtract, Hundred Number Grid, Multiplication Hop, Skip Counting Mats, Skip Counting Wall Banners, Hopscotch by Threes and Twos
Number and Operations in Base Ten
NY-4.NBT.1Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
e.g., Recognize that 70 × 10 = 700 (and, therefore,
700 ÷ 10 = 70) by applying concepts of place value, multiplication, and division.
Place Value (P2), Hopping by 100's
Note: Grade 4 expectations are limited to whole numbers less than or equal to 1,000,000.
NY-4.NBT.2aRead and write multi-digit whole numbers using base- ten numerals, number names, and expanded form.
e.g., 50,327 = 50,000 + 300 + 20 + 7
Place Value (P2)
NY-4.NBT.2bCompare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.Place Value (P2), Operations Hop
Note: Grade 4 expectations are limited to whole numbers less than or equal to 1,000,000.
NY-4.NBT.3Use place value understanding to round multi-digit whole numbers to any place.Place Value, Add/Subtract, Hundred Number Grid, Count by Tens, Hopping by 100's
Note: Grade 4 expectations are limited to whole numbers less than or equal to 1,000,000.
NY-4.NBT.4Fluently add and subtract multi-digit whole numbers using a standard algorithm.
Note: Grade 4 expectations are limited to whole numbers less than or equal to 1,000,000.
Place Value (P2)
NY-4.NBT.5Multiply a whole number of up to four digits by a
one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations.
Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Place Value (P2), PEMDAS Hop, Number Grid
Note on and/or: Students should be taught to use equations, rectangular arrays, and area models; however, when illustrating and explaining any calculation, students can choose any strategy.
Note: Grade 4 expectations are limited to whole numbers less than or equal to 1,000,000.
NY-4.NBT.6Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Notes on and/or: Students should be taught to use strategies based on place value, the properties of operations, and the relationship between multiplication and division; however, when solving any problem, students can choose any strategy. Students should be taught to use equations, rectangular arrays, and area models; however, when illustrating and explaining any calculation, students can choose any strategy.
Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch, Hopscotch for Threes, Hopscotch for Twos, Place Value, Cartesian Coordinate, Number Grid, PEMDAS Hop
Number and Operations - Fractions
NY-4.NF.1Explain why a fraction 𝑎/𝑎 is equivalent to a fraction 𝑎 × 𝑛 / 𝑏 × 𝑛 by using visual fraction models, with attention to how the number and size
of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
Note: Grade 4 expectations are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
Equivalent Fraction Hop, Fraction Walk Set, Open Number Line
NY-4.NF.2Compare two fractions with different numerators and different denominators.
Recognize that comparisons are valid only when the two fractions refer to the same whole.
e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2
Record the results of comparisons with symbols >, =, or <, and justify the conclusions.
e.g., using a visual fraction model.
Note: Grade 4 expectations are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
Equivalent Fraction Hop, Fraction Walk Set, Open Number Line, Operations Hop
NY-4.NF.3Understand a fraction 𝑎 / 𝑏 with 𝑎 > 1 as a sum of fractions 1 / 𝑏. Note: 1 / 𝑏 refers to the unit fraction for 𝑎 / 𝑏.Equivalent Fraction Hop, Fraction Walk Set, Open Number Line
NY-4.NF.3aUnderstand addition and subtraction of fractions as joining and separating parts referring to the same whole.Equivalent Fraction Hop, Fraction Walk Set, Open Number Line
NY-4.NF.3bDecompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions.
e.g., by using a visual fraction model such as, but not limited to:
Equivalent Fraction Hop, Fraction Walk Set, Open Number Line
NY-4.NF.3cAdd and subtract mixed numbers with like denominators.
e.g., replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
Equivalent Fraction Hop, Fraction Walk Set, Open Number Line, PEMDAS Hop
NY-4.NF.3dSolve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.
e.g., using visual fraction models and equations to represent the problem.
Note: Grade 4 expectations are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
Equivalent Fraction Hop, Fraction Walk Set, Open Number Line
NY-4.NF.4Apply and extend previous understandings of multiplication to multiply a whole number by a fraction.
Note: This standard refers to n groups of a fraction (where n is a whole number), e.g., 4 groups of 1/3; which lends itself to being thought about as repeated addition. In grade 5 (NY-5. NF.4) students will be multiplying a fraction by a whole number, e.g., 1/3 of 4.
Equivalent Fraction Hop, Fraction Walk Set, Open Number Line
NY-4.NF.4aUnderstand a fraction 𝑎 / 𝑏 as a multiple of 1 / 𝑏.
e.g., Use a visual fraction model to represent 5/4 as the product 5 x 1/4, recording the conclusion with the equation 5/4 = 5 x 1/4.
Equivalent Fraction Hop, Fraction Walk Set, Open Number Line
NY-4.NF.4bUnderstand a multiple of 𝑎 / 𝑏 as a multiple of 1 / 𝑏, and use this understanding to multiply a whole number by a fraction.
e.g., Use a visual fraction model to express 3 × 2/5 as 6 x 1/5, recognizing this product as 6/5, in general, n x a/b = (n x a) / b.
Equivalent Fraction Hop, Fraction Walk Set, Open Number Line
Solve word problems involving multiplication of a whole number by a fraction.
e.g., using visual fraction models and equations to represent the problem.
e.g., If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
Note: Grade 4 expectations are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
Equivalent Fraction Hop, Fraction Walk Set, Open Number Line
NY-4.NF.5Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.
e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 341/00.
Notes:
• Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.
• Grade 4 expectations are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
Equivalent Fraction Hop, Fraction Walk Set, Open Number Line
NY-4.NF.6Use decimal notation for fractions with denominators 10 or 100.
e.g.,
• Rewrite 0.62 as 62 / 100 or 62 / 100 as 0.62.
• Describe a length as 0.62 meters.
• Locate 0.62 on a number line.
Note: Grade 4 expectations are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
Fraction, Decimal, Percentage Hop
NY-4.NF.7Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions.
e.g., using a visual model.
Note: Grade 4 expectations are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
Equivalent Fraction Hop, Fraction Walk Set, Open Number Line, Operations Hop
Measurement and Data
NY-4.MD.1Know relative sizes of measurement units: ft., in.; km, m, cm
e.g.,
A foot is the length of two-dollar bills.
A meter is about the height of a kitchen counter. A kilometer is 2 ½ laps around most tracks.
Know the conversion factor and use it to convert measurements in a larger unit in terms of a smaller unit: ft., in.; km, m, cm; hr., min., sec.
e.g., Know that 1 ft. is 12 times as long as 1 in. and express the length of a 4 ft. snake as 48 in.
Given the conversion factor, convert all other measurements within a single system of measurement from a larger unit to a smaller unit.
e.g., Given the conversion factors, convert kilograms to grams, pounds to ounces, or liters to milliliters.
Record measurement equivalents in a two-column table. e.g., Generate a conversion table for feet and inches.
Measurement Hop
NY-4.MD.2Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money.Operations Hop, PEMDAS Hop
NY-4.MD.2aSolve problems involving fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit.Fractions, Decimals, Percentage Hop, Measurement Hop
NY-4.MD.2bRepresent measurement quantities using diagrams that feature a measurement scale, such as number lines. Note: Grade 4 expectations are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.Open Number Line, Number Grid
NY-4.MD.3Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
e.g., Find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
Number Grid, Cartesian Coordinate
NY-4.MD.4Make a line plot to display a data set of measurements in fractions of a unit (1/2,1/4,1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.
e.g., Given measurement data on a line plot, find and interpret the difference in length between the longest and shortest specimens in an insect collection.
Number Grid, Cartesian Coordinate
4.MD.5Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement.Angle Hop
4.MD.5aRecognize an angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1 / 360 of a circle is called a “one-degree angle,” and can be used to measure angles.Angle Hop, Unit Circle
4.MD.5bRecognize an angle that turns through n one-degree angles is said to have an angle measure of n degrees.Angle Hop, Unit Circle
NY-4.MD.6Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.Angle Hop
NY-4.MD.7Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems.
e.g., using an equation with a symbol for the unknown angle measure.
Angle Hop, Unit Circle
Geometry
NY-4.G.1Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines.
Identify these in two-dimensional figures.
Angle Hop, Number Grid, Unit Circle
NY-4.G.2aIdentify and name triangles based on angle size (right, obtuse, acute).Angle Hop, Unit Circle
NY-4.G.2bIdentify and name all quadrilaterals with 2 pairs of parallel sides as parallelograms.My First Shapes Hop, Geometric Shapes
NY-4.G.2cIdentify and name all quadrilaterals with four right angles as rectangles.My First Shapes Hop, Geometric Shapes
NY-4.G.3Recognize a line of symmetry for a two- dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts.
Identify line-symmetric figures and draw lines of symmetry.
My First Shapes Hop, Geometric Shapes

StandardDescription of StandardCorresponding Floor Mat
Operations and Algebraic Thinking
NY-5.OA.1 Apply the order of operations to evaluate numerical expressions.
e.g.,
• 6 + 8 ÷ 2
• (6 + 8) ÷ 2
Note: Exponents and nested grouping symbols are not included.
Operations Hop
NY-5.OA.2Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.
e.g., Express the calculation “add 8 and 7, then multiply by 2” as (8 + 7) × 2. Recognize that 3 × (18,932 + 921) is three times as large as 18,932 + 921, without having to calculate the indicated sum or product.
Place Value
NY-5.OA.3Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.
e.g., Given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.
Skip Counting Mats, Skip Counting Wall Banners, Cartesian Coordinate
Number and Operations in Base Ten
NY-5.NBT. 1Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1 / 10 of what it represents in the place to its left.Place Value (P1, P2, P3)
NY-5.NBT.2Use whole-number exponents to denote powers of 10. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10.Exponent Hop, Place Value
NY-5.NBT.3Read, write, and compare decimals to thousandths.Place Value (P3)
NY-5.NBT.3aRead and write decimals to thousandths using base-ten numerals, number names, and expanded form.
e.g.,
• 47.392 = 4 × 10 + 7 × 1 + 3 × 𝟏/𝟏𝟎 + 9 × 𝟏/𝟏𝟎𝟎 + 2 × 𝟏/𝟏𝟎𝟎𝟎
• 47.392 = (4 × 10) + (7 × 1) + (3 × 𝟏/𝟏𝟎 ) + (9 × 𝟏/𝟏𝟎𝟎 ) + (2 ×𝟏/𝟏𝟎𝟎𝟎)
• 47.392 = (4 × 10) + (7 × 1) + (3 × 0.1) + (9 × 0.01) + (2 × 0.001)
Place Value (P3)
NY-5.NBT.3bCompare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.Operations Hop, Place Value (P3)
NY-5.NBT.4Use place value understanding to round decimals to any place.Place Value (P3)
NY-5.NBT.5Fluently multiply multi-digit whole numbers using a standard algorithm.Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch
NY-5.NBT.6Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Notes on and/or:
• Students should be taught to use strategies based on place value, the properties of operations, and the relationship between multiplication and division; however, when solving any problem, students can choose any strategy.
• Students should be taught to use equations, rectangular arrays, and area models; however, when illustrating and explaining any calculation, students can choose any strategy.
Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch
NY-5.NBT.7Using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between operations:
• add and subtract decimals to hundredths;
• multiply and divide decimals to hundredths.
Relate the strategy to a written method and explain the reasoning used.
Notes on and/or: Students should be taught to use concrete models and drawings; as well as strategies based on place value, properties of operations, and the relationship between operations. When solving any problem, students can choose to use a concrete model or a drawing. Their strategy must be based on place value, properties of operations, or the relationship between operations.
Note: Division problems are limited to those that allow for the use of concrete models or drawings, strategies based on properties of operations, and/or the relationship between operations (e.g., 0.25 ÷ 0.05). Problems should not be so complex as to require the use of an algorithm (e.g., 0.37 ÷ 0.05).
Place Value (P3)
Number and Operations - Fractions
NY-5.NF.1Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
e.g.,
• 1/3 + 2/9 = 3/9 + 2/9 = 5/9
• 2/3 + 5/4 = 8/12 + 15/12 = 23/12
Equivalent Fraction Hop, Fraction Walk Set, Open Number Line, Fractions, Decimals, Percentage Hop
NY-5.NF.2Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators.
e.g., using visual fraction models or equations to represent the problem.
Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers.
e.g., Recognize an incorrect result 2/5 + 1/2 = 3/7 by observing that 3/7 < 1/2.
Equivalent Fraction Hop, Fraction Walk Set, Open Number Line, Fractions, Decimals, Percentage Hop
NY-5.NF.3Interpret a fraction as division of the numerator by the denominator ( 𝑎/𝑏 = a ÷ b).
e.g., Interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4.
Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.
e.g., using visual fraction models or equations to represent the problem.
e.g., If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
Equivalent Fraction Hop, Fraction Walk Set, Open Number Line, Fractions, Decimals, Percentage Hop
NY-5.NF.4Apply and extend previous understandings of multiplication to multiply a fraction by a whole number or a fraction.Equivalent Fraction Hop, Fraction Walk Set, Open Number Line, Fractions, Decimals, Percentage Hop
NY-5.NF.4aInterpret the product 𝑎/𝑏 × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b.
e.g., Use a visual fraction model to show 2/3 × 4 = 8/3, and create a story context for this equation. Do the same with 2/3 × 4/5 = 8/15 .
Equivalent Fraction Hop, Fraction Walk Set, Open Number Line, Fractions, Decimals, Percentage Hop
NY-5.NF.4bFind the area of a rectangle with fractional side lengths by tiling it with rectangles of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.Cartesian Coordinate, Number Grid
NY-5.NF.5Interpret multiplication as scaling (resizing).Cartesian Coordinate, Number Grid
NY-5.NF.5aCompare the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
e.g., In the case of 10 x 𝟏/𝟐 = 5, 5 is half of 10 and 5 is 10 times larger than 𝟏/𝟐 .
Fraction Walk Set
NY-5.NF.5bExplain why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case). Explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number. Relate the principle of fraction equivalence 𝒂/𝒃 = 𝒂/𝒃 × 𝒏/𝒏 to the effect of multiplying 𝑎𝑏 by 1.
e.g.,
Explain why 4 × 𝟑/𝟐 is greater than 4.
Explain why 4 × 𝟏/𝟐 is less than 4.
𝟏𝟑 is equivalent to 𝟐/𝟔 because 𝟏/𝟑 × 𝟐/𝟐 = 𝟐/𝟔.
Fraction Walk Set
NY-5.NF.6Solve real world problems involving multiplication of fractions and mixed numbers.
e.g., using visual fraction models or equations to represent the problem.
Equivalent Fraction Hop, Fraction Walk Set, Open Number Line, Fractions, Decimals, Percentage Hop
NY-5.NF.7Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.Equivalent Fraction Hop, Fraction Walk Set, Open Number Line, Fractions, Decimals, Percentage Hop
NY-5.NF.7aInterpret division of a unit fraction by a non-zero whole number, and compute such quotients.
e.g., Create a story context for 1/3 ÷ 4 and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 1/3 ÷ 4 = 1/12 because 1/12 × 4 = 1/3.
Open Number Line
NY-5.NF.7bInterpret division of a whole number by a unit fraction, and compute such quotients.
e.g., Create a story context for 4 ÷ 15 and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ 15 = 20 because 20 × 15 = 4.
Open Number Line
NY-5.NF.7cSolve real-world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions.
e.g., using visual fraction models and equations to represent the problem.
e.g., How much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement until grade 6
(NY-6. NS.1).
Equivalent Fraction Hop, Fraction Walk Set, Open Number Line, Fractions, Decimals, Percentage Hop
Measurement and Data
NY-5.MD.1Convert among different-sized standard measurement units within a given measurement system when the conversion factor is given. Use these conversions in solving multi-step, real world problems.
Notes: • The known conversion factors from grade 4 include ft., in.; km, m, cm; hr., min., sec. and will not be given. All other conversion factors will be given.
• Grade 5 expectations for decimal operations are limited to work with decimals to hundredths.
NY-5.MD.2Make a line plot to display a data set of measurements in fractions of a unit (1/2,1/4,1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.
e.g., Given different measurements of liquid in identical beakers, make a line plot to display the data and find the total amount of liquid in all of the beakers.
Number Grid
NY-5.MD.3Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
NY-5.MD.3aRecognize that a cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.
NY-5.MD.3bRecognize that a solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.Cubed Number
NY-5.MD.4Measure volumes by counting unit cubes, using cubic cm, cubic in., cubic ft., and improvised units
NY-5.MD.5Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.Cubed Number
NY-5.MD.5aFind the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base.
NY-5.MD.5b.Apply the formulas V = l × w × h and V = B × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
NY-5.MD.5cRecognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
Geometry
NY-5.MD.5Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
NY-5.MD.5aFind the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base.
NY-5.MD.5b.Apply the formulas V = l × w × h and V = B × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
NY-5.MD.5cRecognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

## Texas Essential Knowledge and Skills

StandardDescription of StandardCorresponding Floor Mat
111.xx.Kindergarten(b)Know number names and the count sequence.
111.xx.Kindergarten(b)(1)Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
111.xx.Kindergarten(b)(1)(A)apply mathematics to problems arising in everyday life society and the workplace;Number Line 1-10 Fruits and Vegetables
US Money Mats
Clock Hop Floor Mat
111.xx.Kindergarten(b)(1)(B)use a problem-solving model that incorporates:
- analyzing given information
- formulating a plan or strategy
- determining a solution
- justifying the solution
- and evaluating the problem-solving process and the reasonableness of the solution;
Number Line 1-10 Fruits and Vegetables
US Money Mats
Clock Hop Floor Mat
Operations Hop
111.xx.Kindergarten(b)(1)(C)select tools including:
real objects
manipulatives
paper and pencil
and technology as appropriate
and techniques including:
mental math
estimation
and number sense as appropriate
to solve problems;
111.xx.Kindergarten(b)(1)(D)communicate mathematical ideas and reasoning and their implications using multiple representations including: symbols
diagrams
graphs
and language as appropriate;
111.xx.Kindergarten(b)(1)(E)create and use representations to organize and record and communicate mathematical ideas;
111.xx.Kindergarten(b)(1)(F)analyze mathematical relationships to connect and communicate mathematical ideas;
111.xx.Kindergarten(b)(1)(G)display and explain and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
111.xx.Kindergarten(b)(2)Number and operations. The student applies mathematical process standards to understand how to represent and compare whole numbers and the relative position and magnitude of whole numbers and relationships within the numeration system. The student is expected to:
111.xx.Kindergarten(b)(2)(A)count forward and backward to at least 20 with and without objects;Number Line 1-10 Fruits and Vegetables
Skip Counting by 2s Mat
111.xx.Kindergarten(b)(2)(B)read and write and represent whole numbers from 0 to at least 20 with and without objects or pictures;Number Line 1-10 Fruits and Vegetables
Skip Counting by 2s Mat
111.xx.Kindergarten(b)(2)(C)count a set of objects up to at least 20 and demonstrate that the last number said tells the number of objects in the set regardless of their arrangement or order;Number Line 1-10 Fruits and Vegetables
Skip Counting by 2s Mat
111.xx.Kindergarten(b)(2)(D)recognize instantly the quantity of a small group of objects in organized and random arrangementsNumber Line 1-10 Fruits and Vegetables
Skip Counting by 2s Mat
111.xx.Kindergarten(b)(2)(E)generate a set using concrete and pictorial models that represents a number that is more than and less than and equal to a given number up to 20;Operations Hop
Number Line 1-10 Fruits and Vegetables
Skip Counting by 2s Mat
111.xx.Kindergarten(b)(2)(F)generate a number that is one more than or one less than another number up to at least 20;Operations Hop
Number Line 1-10 Fruits and Vegetables
Skip Counting by 2s Mat
111.xx.Kindergarten(b)(2)(G)compare sets of objects up to at least 20 in each set using comparative language;Operations Hop
Number Line 1-10 Fruits and Vegetables
Skip Counting by 2s Mat
111.xx.Kindergarten(b)(2)(H)use comparative language to describe two numbers up to 20 presented as written numerals;Operations Hop
Number Line 1-10 Fruits and Vegetables
Skip Counting by 2s Mat
111.xx.Kindergarten(b)(2)(I)compose and decompose numbers up to 10 with objects and pictures;Number Line 1-10 Fruits and Vegetables
111.xx.Kindergarten(b)(3)Number and operations. The student applies mathematical process standards to develop an understanding of addition and subtraction situations in order to solve problems. The student is expected to:
111.xx.Kindergarten(b)(3)(A)model the action of joining to represent addition and the action of separating to represent subtraction;Add/Subtract Floor Mat
Number Line 1-10
Skip Counting by 2s Mat
111.xx.Kindergarten(b)(3)(B)solve word problems using objects and drawings to find sums up to 10 and differences within 10;Add/Subtract Floor Mat
Number Line 1-10
Skip Counting by 2s Mat
111.xx.Kindergarten(b)(3)(C)explain the strategies used to solve problems involving adding and subtracting within 10 using spoken words and concrete and pictorial models and number sentences.Number Line 1-10 Fruits and Vegetables
Skip Counting by 2s Mat
111.xx.Kindergarten(b)(4)Number and operations. The student applies mathematical process standards to identify coins in order to recognize the need for monetary transactions. The student is expected to identify U.S. coins by name including pennies nickels dimes and quarters.US Money Mats
111.xx.Kindergarten(b)(5)Algebraic reasoning. The student applies mathematical process standards to identify the pattern in the number word list. The student is expected to:
111.xx.Kindergarten(b)(5)(A)recite numbers up to at least 100 by ones and tens beginning with any given number;Add/Subtract Floor Mat
Hop by Tens Mat
111.xx.Kindergarten(b)(5)(B)represent addition and subtraction with objects drawings situations verbal explanations or number sentences;Add/Subtract Floor Mat
111.xx.Kindergarten(b)(6)Geometry and measurement. The student applies mathematical process standards to analyze attributes of two-dimensional shapes and three-dimensional solids to develop generalizations about their properties. The student is expected to:
111.xx.Kindergarten(b)(6)(A)identify two-dimensional shapes including circles triangles rectangles and squares as special rectangles;My First Shapes Hop
Geometric Shapes Hop
111.xx.Kindergarten(b)(6)(B)identify three-dimensional solids including cylinders cones spheres and cubes in the real world;My First Shapes Hop
Geometric Shapes Hop
111.xx.Kindergarten(b)(6)(C)identify two-dimensional components of three-dimensional objects [such as the face of a tissue box is a rectangle];My First Shapes Hop
Geometric Shapes Hop
111.xx.Kindergarten(b)(6)(D)identify attributes of two-dimensional shapes using informal and formal geometric language interchangeably [such as number of corners or vertices and number of sides];My First Shapes Hop
Geometric Shapes Hop
111.xx.Kindergarten(b)(6)(E)classify and sort a variety of regular and irregular two- and three-dimensional figures regardless of orientation or size;My First Shapes Hop
Geometric Shapes Hop
111.xx.Kindergarten(b)(6)(F)create two-dimensional shapes using a variety of materials and drawings.My First Shapes Hop
Geometric Shapes Hop
111.xx.Kindergarten(b)(7)Geometry and measurement. The student applies mathematical process standards to directly compare measurable [measureable] attributes. The student is expected to:
111.xx.Kindergarten(b)(7)(A)give an example of a measurable attribute of a given object including length capacity and weightCartesian Coordinate Hop
any of the mats - measure any of the sides
111.xx.Kindergarten(b)(7)(B)compare two objects with a common measurable [measureable] attribute to see which object has more of/less of the attribute and describe the difference.Cartesian Coordinate Hop
any of the mats - measure any of the sides
111.xx.Kindergarten(b)(8)Data analysis. The student applies mathematical process standards to collect and organize data to make it useful for interpreting information. The student is expected to:
111.xx.Kindergarten(b)(8)(A)collect sort and organize data into two or three categories;Add/Subtract Floor Mat
111.xx.Kindergarten(b)(8)(B)use data to create real-object and picture graphs; andCartesian Coordinate Hop
111.xx.Kindergarten(b)(8)(C)draw conclusions from real-object and picture graphs.Cartesian Coordinate Hop
111.xx.Kindergarten(b)(9)Personal financial literacy. The student applies mathematical process standards to manage one's financial resources effectively for lifetime financial security. The student is expected to:
111.xx.Kindergarten(b)(9)(A)identify ways to earn income;US Money Mats
111.xx.Kindergarten(b)(9)(C)use simple skills required for jobs [such as bus driver or librarian or cashier or cook]US Money Mats
111.xx.Kindergarten(b)(9)(D)distinguish between wants and needs and identify income as a source to meet one's wants and needs.US Money Mats

StandardDescription of StandardCorresponding Floor Mat
111.xx.Grade1(b)(1)Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
111.xx.Grade1(b)(1)(A)apply mathematics to problems arising in everyday life and society and the workplaceNumber Line 1-10 Fruits and Vegetables
US Money Mats
Clock Hop Floor Mat
111.xx.Grade1(b)(1)(B)use a problem-solving model that incorporates:
analyzing given information
formulating a plan or strategy
determining a solution
justifying the solution
and evaluating the problem-solving process and the reasonableness of the solution
Number Line 1-10 Fruits and Vegetables
US Money Mats
Clock Hop Floor Mat
real objects
manipulatives
paper/pencil
and technology as appropriate
and techniques
including mental math
estimation
and number sense as appropriate
to solve problems
Number Line 1-10 Fruits and Vegetables
US Money Mats
Clock Hop Floor Mat
Operations Hop
111.xx.Grade1(b)(1)(D)communicate mathematical ideas and reasoning and their implications using multiple representations including:
symbols
diagrams
graphs
and language as appropriate
Number Line 1-10 Fruits and Vegetables
US Money Mats
Clock Hop Floor Mat
Cartesian Coordinate Hop
Operations Hop
111.xx.Grade1(b)(1)(E)create and use representations to organize and record and communicate mathematical ideas
111.xx.Grade1(b)(1)(F)analyze mathematical relationships to connect and communicate mathematical ideas
111.xx.Grade1(b)(1)(G)display and explain and justify mathematical ideas and arguments using precise mathematical language in written or oral communicationOperations Hop
111.xx.Grade1(b)(2)Number and Operations. The student applies mathematical process standards to represent and compare whole numbers and the relative position and magnitude of whole numbers and relationships within the numeration system related to place value. The student is expected to:
111.xx.Grade1(b)(2)(A)recognize instantly the quantity of structured arrangements such as seen on a die or a tenframePlace Value Hop (P1)
111.xx.Grade1(b)(2)(B)use concrete and pictorial models to compose and decompose numbers up to 120 as so many hundreds and so many tens and so many ones in more than one wayPlace Value Hop (P1)
111.xx.Grade1(b)(2)(C)use objects pictures and expanded and standard forms to represent numbers up to 120Place Value Hop (P1)
111.xx.Grade1(b)(2)(D)generate a number that is greater than or less than a given whole number up to 120Place Value Hop (P1)
Operations Hop
111.xx.Grade1(b)(2)(E)use place value to compare whole numbers to 120 using comparative languagePlace Value Hop (P1)
Operations Hop
111.xx.Grade1(b)(2)(F)order whole numbers to 120 using place value and open number lines.Place Value Hop (P1)
Operations Hop
111.xx.Grade1(b)(3)Number and Operations. The student applies mathematical process standards to develop and use strategies for whole number addition and subtraction computations in order to solve problems. The student is expected to:
111.xx.Grade1(b)(3)(A)use concrete and pictorial models to determine the sum of a multiple of ten and a one-digit number in problems up to 99Add/Subtract Floor Mat
Skip Counting by 2s Mat
111.xx.Grade1(b)(3)(B)use objects and pictorial models to solve word problems involving joining separating and comparing sets within 20 and unknowns as any one of the terms in the problem such as 2 + 4 = ?; 3 + ? = 7; and 5 = ? - 3Add/Subtract Floor Mat
Skip Counting by 2s Mat
Skip Counting by 2s Mat
111.xx.Grade1(b)(3)(D)apply basic fact strategies to add and subtract within 20 using strategies including making 10 and decomposing a number leading to a 10Add/Subtract Floor Mat
Skip Counting by 2s Mat
111.xx.Grade1(b)(3)(E)explain strategies used to solve addition and subtraction problems up to 20 using:
spoken words objects
pictorial models
and number sentences
Skip Counting by 2s Mat
111.xx.Grade1(b)(3)(F)generate and solve problem situations when given a number sentence involving addition and subtraction of numbers within 20.Add/Subtract Floor Mat
Skip Counting by 2s Mat
111.xx.Grade1(b)(4)Number and Operations. The student applies mathematical process standards to identify coins and their values and the relationships among them in order to recognize the need for monetary transactions. The student is expected to:
111.xx.Grade1(b)(4)(A)identify U.S. coins including pennies nickels dimes and quarters by value and describe the relationships between them;US Money Mats
111.xx.Grade1(b)(4)(B)write a number with the cent symbol to describe the value of a coinUS Money Mats
111.xx.Grade1(b)(4)(C)use relationships to count by twos fives and tens to determine the value of pennies nickels and dimesUS Money Mats
111.xx.Grade1(b)(5)Algebraic Reasoning. The student applies mathematical process standards to identify and apply number patterns within properties of numbers and operations in order to describe relationships. The student is expected to:
111.xx.Grade1(b)(5)(A)recite numbers forward and backward from any given number between 1 and 120Place Value Hop (P1)
111.xx.Grade1(b)(5)(B)skip count by twos fives and tens to 100Skip Counting by 2s Mat
Clock Hop Floor Mat
Hop by Tens Mat
111.xx.Grade1(b)(5)(C)skip count by twos fives and tens to determine the total number of objects up to 120 in a setSkip Counting by 2s Mat
Clock Hop Floor Mat
Hop by Tens Mat
111.xx.Grade1(b)(5)(D)use relationships to determine the number that is 10 more and 10 less than a given number up to 120Skip Counting by 2s Mat
Clock Hop Floor Mat
Hop by Tens Mat
111.xx.Grade1(b)(5)(E)represent word problems involving addition and subtraction of whole numbers to 20 using concrete and pictorial models and number sentencesSkip Counting by 2s Mat
111.xx.Grade1(b)(5)(F)understand that the equal sign represents a relationship where statements on each side of the equal sign are trueOperations Hop
Skip Counting by 2s Mat
111.xx.Grade1(b)(5)(G)determine the unknown whole number in an addition or subtraction equation when the unknown may be any one of the three or four terms in the equationAdd/Subtract Floor Mat
Skip Counting by 2s Mat
111.xx.Grade1(b)(5)(H)identify relationships between addition facts and related subtraction sentences such as 3 + 2 = 5 and 5 – 2 = 3Add/Subtract Floor Mat
Skip Counting by 2s Mat
111.xx.Grade1(b)(5)(I)apply properties of operations as strategies to add and subtract such as if 2 + 3 = 5 is known then 3 + 2 = 5.Add/Subtract Floor Mat
Skip Counting by 2s Mat
Operations Hop
111.xx.Grade1(b)(6)Geometry and Measurement. The student applies mathematical process standards to analyze attributes of two-dimensional shapes and three-dimensional solids to develop generalizations about their properties. The student is expected to:
111.xx.Grade1(b)(6)(A)classify and sort regular and irregular two-dimensional shapes based on attributes using informal geometric languageMy First Shapes Hop
Geometric Shapes Hop
111.xx.Grade1(b)(6)(B)distinguish between attributes that define a two-dimensional or three- dimensional figure such as a closed figure with three sides is a triangle or a solid with exactly six rectangular faces is a rectangular prism and attributes that do not define the shape such as orientation or colorMy First Shapes Hop
Geometric Shapes Hop
triangles
rectangles
squares as special rectangles
rhombuses
and hexagons
My First Shapes Hop
Geometric Shapes Hop
triangles
rectangles
squares as special rectangles
rhombuses
and hexagons
and describe their attributes using formal language such as vertex and side
My First Shapes Hop
Geometric Shapes Hop
spheres
cones
cylinders
rectangular prisms (including cubes)
and triangular prisms
and describe their attributes using formal language such as vertex
edge
and face
My First Shapes Hop
Geometric Shapes Hop
111.xx.Grade1(b)(6)(F)compose two-dimensional shapes by joining two three or four figures to produce a target shape in more than one way if possibleMy First Shapes Hop
Geometric Shapes Hop
111.xx.Grade1(b)(6)(G)partition two-dimensional figures such as circles and rectangles into two and four fair shares or equal parts and describe the parts using words such as “halves” “half of” “fourths” or “quarters;”My First Shapes Hop
Geometric Shapes Hop
Fraction Walk Floor Mat (Halves & Quarters)
111.xx.Grade1(b)(6)(H)identify examples and non-examples of halves and fourthsMy First Shapes Hop
Geometric Shapes Hop
Fraction Walk Floor Mat (Halves & Quarters)
111.xx.Grade1(b)(7)Geometry and Measurement. The student applies mathematical process standards to select and use units to describe length and time. The student is expected to:
111.xx.Grade1(b)(7)(A)use measuring tools such as adding machine tape or ribbon or string to measure the length of objects to reinforce the continuous nature of linear measurementAny mat - measure around the edges or objects in the mat
111.xx.Grade1(b)(7)(B)demonstrate that the length of an object is the number of same-size units of length that - when laid end-to-end with no gaps or overlaps - reach from one end of the object to the otherAny mat - measure around the edges or objects in the mat
111.xx.Grade1(b)(7)(C)measure the same object/distance with units of two different lengths and describe how and why the measurements differAny mat - measure around the edges or objects in the mat
111.xx.Grade1(b)(7)(D)describe a length to the nearest whole unit using a number and a unit such as five craft sticksAny mat - measure around the edges or objects in the mat
111.xx.Grade1(b)(7)(E)tell time to the hour and half hour using analog and digital clocksClock Hop Floor Mat
111.xx.Grade1(b)(8)Data Analysis. The student applies mathematical process standards to organize data to make it useful for interpreting information and solving problems. The student is expected to:
111.xx.Grade1(b)(8)(A)collect sort and organize data in up to three categories using models/representations such as tally marks or T-chartsCartesian Coordinate Hop
111.xx.Grade1(b)(8)(B)use data to create picture and bar-type graphsCartesian Coordinate Hop
111.xx.Grade1(b)(8)(C)draw conclusions and generate and answer questions using information from picture and bar-type graphsCartesian Coordinate Hop

StandardDescription of StandardCorresponding Floor Mat
111.xx.Grade2(b)(1)Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
111.xx.Grade2(b)(1)(A)apply mathematics to problems arising in everyday life and society and the workplaceUS Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade2(b)(1)(B)use a problem-solving model that incorporates:
analyzing given information
formulating a plan or strategy
determining a solution
justifying the solution
and evaluating the problem-solving process and the reasonableness of the solution;
US Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
real objects
manipulatives
paper/pencil
and technology as appropriate
and techniques including:
mental math
estimation
and number sense as appropriate to solve problems
US Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade2(b)(1)(D)communicate mathematical ideas and reasoning and their implications using multiple representations including:
symbols
diagrams
graphs
and language as appropriate
US Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade2(b)(1)(E)create and use representations to organize record and communicate mathematical ideasUS Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade2(b)(1)(F)analyze mathematical relationships to connect and communicate mathematical ideasUS Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade2(b)(1)(G)display and explain and justify mathematical ideas and arguments using precise mathematical language in written or oral communicationUS Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade2(b)(2)Number and Operations. The student applies mathematical process standards to understand how to represent and compare whole numbers and the relative position and magnitude of whole numbers and relationships within the numeration system related to place value. The student is expected to:
111.xx.Grade2(b)(2)(A)use concrete and pictorial models to compose and decompose numbers up to 1200 as a sum of so many thousands hundreds tens and ones in more than one wayPlace Value Hop - Millions (P2)
111.xx.Grade2(b)(2)(B)use standard and word and expanded forms to represent numbers up to 1200Place Value Hop - Millions (P2)
111.xx.Grade2(b)(2)(C)generate a number that is greater than or less than a given whole number up to 1200Place Value Hop - Millions (P2)
Operations Hop
111.xx.Grade2(b)(2)(D)use place value to compare whole numbers to 1200 using comparative language and numbers and symbols (> < or =)Place Value Hop - Millions (P2)
Operations Hop
111.xx.Grade2(b)(2)(E)locate the position of a given whole number on an open number line;Place Value Hop - Millions (P2)
Cartesian Coordinate Hop
111.xx.Grade2(b)(2)(F)name the whole number that corresponds to a specific point on a number linePlace Value Hop - Millions (P2)
Cartesian Coordinate Hop
111.xx.Grade2(b)(2)(G)order whole numbers to 1200 using place value and open number linesPlace Value Hop - Millions (P2)
Cartesian Coordinate Hop
111.xx.Grade2(b)(3)Number and Operations. The student applies mathematical process standards to recognize and represent fractional units and communicates how they are used to name parts of a whole. The student is expected to:
strips
lines
regular polygons
and circles into equal parts and name the parts including halves fourths and eighths using words such as “one-half” “three-fourths;”
Fraction Walk Floor Mats
Clock Hop Floor Mat
My First Shapes Hop
111.xx.Grade2(b)(3)(B)explain that the more fractional parts used to make a whole and the smaller the part; and the fewer the fractional parts the larger the partFraction Walk Floor Mats
111.xx.Grade2(b)(3)(C)use concrete models to count fractional parts beyond one whole using words such as “one-fourth” “two-fourths” “three-fourths” “four-fourths” “five-fourths” or “one and one-fourth” and recognize how many parts it takes to equal one whole such as four-fourths equals one wholeFraction Walk Floor Mats
111.xx.Grade2(b)(3)(D)identify examples and non-examples of halves fourths and eighthsFraction Walk Floor Mats
111.xx.Grade2(b)(4)Number and Operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve addition and subtraction problems with efficiency and accuracy. The student is expected to:
Skip Counting by 2s Mat
111.xx.Grade2(b)(4)(B)use mental strategies and flexible methods and algorithms based on knowledge of place value and equality to add and subtract two-digit numbersAdd/Subtract Floor Mat
Skip Counting by 2s Mat
Place Value Hop - Millions (P2)
111.xx.Grade2(b)(4)(C)solve one-step and multistep word problems involving addition and subtraction of two-digit numbers using a variety of strategies based on place value including algorithmsAdd/Subtract Floor Mat
Skip Counting by 2s Mat
Place Value Hop - Millions (P2)
111.xx.Grade2(b)(4)(D)generate and solve problem situations for a given mathematical number sentence involving addition and subtraction of whole numbers within 100Add/Subtract Floor Mat
Place Value Hop (P1)
111.xx.Grade2(b)(5)Number and Operations. The student applies mathematical process standards to determine the value of coins in order to solve monetary transactions. The student is expected to:
111.xx.Grade2(b)(5)(A)determine the value of a collection of coins up to one dollarUS Money Mats
111.xx.Grade2(b)(5)(B)use the cent symbol and dollar sign and the decimal point to name the value of a collection of coinsUS Money Mats
111.xx.Grade2(b)(6)Number and Operations. The student applies mathematical process standards to connect repeated addition and subtraction to multiplication and division situations that involve equal groupings and shares. The student is expected to:
111.xx.Grade2(b)(6)(A)model and create and describe contextual multiplication situations in which equivalent sets of concrete objects are joinedAdd/Subtract Floor Mat
Multiplication Hop
Skip Counting Mats Set
111.xx.Grade2(b)(6)(B)model and create and describe contextual division situations in which a set of concrete objects is separated into equivalent sets.Add/Subtract Floor Mat
Multiplication Hop
Skip Counting Mats Set
111.xx.Grade2(b)(7)Algebraic Reasoning. The student applies mathematical process standards to identify and apply number patterns within properties of numbers and operations in order to describe relationships. The student is expected to:
111.xx.Grade2(b)(7)(A)use relationships and objects to determine whether a number up to 40 is even or oddSkip Counting by 4s Mat
111.xx.Grade2(b)(7)(B)use relationships to determine the number that is 10 or 100 more or less than a given number up to 1200Add/Subtract Floor Mat
Place Value Hop - Millions (P2)
Hop by Tens Mat
Hopping by 100’s Mat
111.xx.Grade2(b)(7)(C)represent and solve addition and subtraction word problems where unknowns may be any one of the terms in the problemAdd/Subtract Floor Mat
111.xx.Grade2(b)(8)Geometry and Measurement. The student applies mathematical process standards to analyze attributes of two- and three-dimensional geometric figures to develop generalizations about their properties. The student is expected to:
111.xx.Grade2(b)(8)(A)create two-dimensional shapes based on given attributes including number of sides and verticesGeometric Shapes Hop
111.xx.Grade2(b)(8)(B)identify attributes of a quadrilateral a pentagon and an octagonGeometric Shapes Hop
spheres
cones
cylinders
rectangular prisms including cubes
and triangular prisms
and describe their attributes using formal language such as vertex and edge and face
Geometric Shapes Hop
111.xx.Grade2(b)(8)(D)classify polygons with 12 or fewer sides according to attributes including identifying the number of sides and number of verticesGeometric Shapes Hop
111.xx.Grade2(b)(8)(E)compose two-dimensional shapes and three-dimensional solids with given properties or attributes such as build a rectangle out of unit squares; build a rectangular prism out of unit cubesGeometric Shapes Hop
111.xx.Grade2(b)(8)(F)decompose two-dimensional shapes such as cutting out a square from this rectangle - dividing this shape in half - or partitioning a rectangle into identical triangles and identify the resulting geometric partsGeometric Shapes Hop
111.xx.Grade2(b)(9)Geometry and Measurement. The student applies mathematical process standards to select and use units to describe length and area and time. The student is expected to:
111.xx.Grade2(b)(9)(A)find the length of objects using concrete models for standard units of length such as the edges of inch tiles and centimeter cubesAdd/Subtract Floor Mat
111.xx.Grade2(b)(9)(B)describe the inverse relationship between the size of the unit and the number of units needed to equal the length of an object such as the longer the unit the fewer needed; the shorter the unit the more neededAdd/Subtract Floor Mat
111.xx.Grade2(b)(9)(C)represent whole numbers as distances from any given location on a number line
111.xx.Grade2(b)(9)(D)determine the length of an object to the nearest half unit using rulers or yardsticks or meter sticks or measuring tapes;Any mat - just measure the sides of any aspect of the mat.
111.xx.Grade2(b)(9)(E)determine a solution to a problem involving length including estimating lengthsAny mat - just measure the sides of any aspect of the mat.
111.xx.Grade2(b)(9)(F)use concrete models of square units to find the area of a rectangle by covering it with no gaps or overlaps and counting to find the total number of square units and describing the measurement using a number and the unit such as 24 square unitsAdd/Subtract Floor Mat
111.xx.Grade2(b)(9)(G)read and write time to the nearest five- and one-minute increments using analog and digital clocks and distinguish between a.m. and p.m.Clock Hop Floor Mat
111.xx.Grade2(b)(10)Data Analysis. The student applies mathematical process standards to organize data to make it useful for interpreting information and solving problems. The student is expected to:
111.xx.Grade2(b)(10)(A)explain that the length of a bar in a bar graph or the number of pictures in a pictograph represents the number of data points for a given categoryCartesian Coordinate Hop
111.xx.Grade2(b)(10)(B)organize a collection of data with up to four categories using pictographs and bar graphs with intervals of one or moreCartesian Coordinate Hop
111.xx.Grade2(b)(10)(C)write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of oneCartesian Coordinate Hop
111.xx.Grade2(b)(10)(D)draw conclusions and make predictions from information in a graph.Cartesian Coordinate Hop

StandardDescription of StandardCorresponding Floor Mat
111.xx.Grade3(b)(1)Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
111.xx.Grade3(b)(1)(A)apply mathematics to problems arising in everyday life and society and the workplaceUS Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade3(b)(1)(B)use a problem-solving model that incorporates:
analyzing given information
formulating a plan or strategy
determining a solution
justifying the solution
and evaluating the problem-solving process and the reasonableness of the solution
US Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
real objects
manipulatives
paper/pencil
and technology as appropriate
and techniques including:
mental math
estimation
and number sense as appropriate to solve problems
US Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade3(b)(1)(D)communicate mathematical ideas and reasoning and their implications using multiple representations including:
symbols
diagrams
graphs
and language as appropriate
US Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade3(b)(1)(E)create and use representations to organize and record and communicate mathematical ideasUS Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade3(b)(1)(F)analyze mathematical relationships to connect and communicate mathematical ideasUS Money Mats
Clock Hop Floor Mat
Operations Floor Mat
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade3(b)(1)(G)display and explain and justify mathematical ideas and arguments using precise mathematical language in written or oral communicationUS Money Mats
Clock Hop Floor Mat
Operations Hop Operations Floor Mat
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade3(b)(2)Number and Operations. The student applies mathematical process standards to represent and compare whole numbers and understand relationships related to place value. The student is expected to:
111.xx.Grade3(b)(2)(A)compose and decompose numbers to 100000 as a sum of so many ten thousands and so many thousands and so many hundreds and so many tens and so many ones in more than one way using objects and pictorial models and numbers including expanded notation as appropriatePlace Value Hop - Decimals (P3)
111.xx.Grade3(b)(2)(B)describe the mathematical relationships found in the base ten place value system through the 100000th placePlace Value Hop - Decimals (P3)
111.xx.Grade3(b)(2)(C)represent a number on a number line as being between two consecutive multiples of 10 or 100 or 1000 or 10000 and use words to describe relative size of numbers such as 'closer to' or 'is about' or 'is nearly' in order to round whole numbersPlace Value Hop - Decimals (P3)
111.xx.Grade3(b)(2)(D)compare and order whole numbers up to 100000 and represent comparisons using the symbols > or < or =Place Value Hop - Decimals (P3)
111.xx.Grade3(b)(3)Number and Operations. The student applies mathematical process standards to represent and explain fractional units. The student is expected to:
111.xx.Grade3(b)(3)(A)represent fractions greater than zero and less than or equal to one using concrete objects and pictorial models including strip diagrams and number lines with denominators of '2' '3' '4' '6' and '8'Fraction Walk Floor Mats
111.xx.Grade3(b)(3)(B)determine the corresponding fraction greater than zero and less than or equal to one with denominators of '2' '3' '4' '6' and '8' of a specified point on a number lineFraction Walk Floor Mats
111.xx.Grade3(b)(3)(C)explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole numberFraction Walk Floor Mats
111.xx.Grade3(b)(3)(D)compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/bFraction Walk Floor Mats
111.xx.Grade3(b)(3)(E)solve problems involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions with denominators of '2' '3' '4' '6' and '8' such as two children share five cookiesFraction Walk Floor Mats
111.xx.Grade3(b)(3)(F)represent equivalent fractions with denominators of '2' '3' '4' '6' and '8' using a variety of objects and pictorial models including number linesFraction Walk Floor Mats
Equivalent Fraction Hop Floor Mat
111.xx.Grade3(b)(3)(G)explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area modelFraction Walk Floor Mats
Equivalent Fraction Hop Floor Mat
111.xx.Grade3(b)(3)(H)compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols and words and objects and pictorial models such as comparing the size of pieces when sharing a candy bar equally among four people or equally among three peopleFraction Walk Floor Mats
Equivalent Fraction Hop Floor Mat
111.xx.Grade3(b)(4)Number and Operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve problems with efficiency and accuracy. The student is expected to:
111.xx.Grade3(b)(4)(A)solve one-step and multistep problems involving addition and subtraction within 1000 using strategies based on place value and properties of operations and the relationship between addition and subtraction with fluencyOperations Hop
Place Value Hop - Millions (P2)
111.xx.Grade3(b)(4)(B)use strategies including rounding to the nearest 10 or 100 and compatible numbers to estimate solutions to addition and subtraction problemsAdd/Subtract Floor Mat
Hopping by 100’s Mat
111.xx.Grade3(b)(4)(C)determine the value of a collection of coins and billsUS Money Mats
111.xx.Grade3(b)(4)(D)determine the total number of objects when equally-sized groups of objects are combined or arranged in arrays up to ten by tenSkip Counting Mats Set
111.xx.Grade3(b)(4)(E)represent multiplication facts by using a variety of approaches such as repeated addition and equal-sized groups and arrays and area models and equal jumps on a number line and skip countingSkip Counting Mats Set
Multiplication Hop
111.xx.Grade3(b)(4)(F)quickly recall facts to multiply up to ten by ten and recall the corresponding division factsSkip Counting Mats Set
Multiplication Hop
111.xx.Grade3(b)(4)(G)use strategies and algorithms including the standard algorithm to multiply a two- digit number by a one-digit number. Strategies may include:
mental math
partial products
and the commutative and associative and distributive properties
Skip Counting Mats Set
Multiplication Hop
111.xx.Grade3(b)(4)(H)determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects is shared equallySkip Counting Mats Set
Multiplication Hop
111.xx.Grade3(b)(4)(I)use divisibility rules to determine if a number is even or oddAdd/Subtract Floor Mat
111.xx.Grade3(b)(4)(J)determine a quotient using the relationship between multiplication and division such as the quotient of 40 ÷ 8 can be found by determining what factor makes 40 when multiplied by 8Factor Fun Hop Mat
Skip Counting Mats Set
Multiplication Hop
111.xx.Grade3(b)(4)(K)solve one-step and multistep problems involving multiplication and division within 100 using strategies based on objects and pictorial models including:
arrays
area models
and equal groups properties of operations or recall of facts
Factor Fun Hop Mat
Skip Counting Mats Set
Multiplication Hop
111.xx.Grade3(b)(5)Algebraic Reasoning. The student applies mathematical process standards to analyze and create patterns and relationships. The student is expected to:
111.xx.Grade3(b)(5)(A)represent and solve one- and two-step problems involving addition and subtraction of whole numbers to 1000 using pictorial models such as strip diagrams and number lines and equationsAdd/Subtract Floor Mat
Place Value Hop - Millions (P2)
111.xx.Grade3(b)(5)(B)represent and solve one- and two-step multiplication and division problems within 100 using arrays and strip diagrams and equationsSkip Counting Mats Set
Multiplication Hop
111.xx.Grade3(b)(5)(C)describe a multiplication expression as a comparison such as 3 x 24 represents 3 times as much as 24Skip Counting Mats Set
Multiplication Hop
111.xx.Grade3(b)(5)(D)determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is either a missing factor or product such as the value 4 for [ ] makes 3 x [ ] = 12 a true equationSkip Counting Mats Set
Multiplication Hop
111.xx.Grade3(b)(5)(E)represent real-world relationships using number pairs in a table and verbal descriptions such as 1 insect has 6 legs and 2 insects have 12 legs and so forthSkip Counting Mats Set
Multiplication Hop
111.xx.Grade3(b)(6)Geometry and Measurement. The student applies mathematical process standards to analyze attributes of two-dimensional geometric figures to develop generalizations about their properties. The student is expected to
111.xx.Grade3(b)(6)(A)classify and sort two- and three-dimensional solids including:
cones
cylinders
spheres
triangular and rectangular prisms
and cubes
based on attributes using formal geometric language such as faces and edges and vertices
Geometric Shapes Hop
111.xx.Grade3(b)(6)(B)determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each rowGeometric Shapes Hop
Skip Counting Mats Set
111.xx.Grade3(b)(6)(C)decompose composite figures formed by rectangles into non-overlapping rectangles to determine the area of the original figure using the additive property of areaGeometric Shapes Hop
111.xx.Grade3(b)(6)(D)decompose two congruent two-dimensional figures into parts with equal areas and express the area of each part as a unit fraction of the whole and recognize that equal shares of identical wholes need not have the same shapeGeometric Shapes Hop
Fraction Walk Floor Mats
111.xx.Grade3(b)(7)Geometry and Measurement. The student applies mathematical process standards to select appropriate units and strategies and tools to solve problems involving customary measurement. The student is expected to:
111.xx.Grade3(b)(7)(A)represent fractions of halves and fourths and eighths as distances from zero on a number lineFraction Walk Floor Mats
Cartesian Coordinate Hop
111.xx.Grade3(b)(7)(B)determine the perimeter of a polygon or a missing length when given perimeter and remaining side lengths in problems;Geometric Shapes Hop
111.xx.Grade3(b)(7)(C)determine the solutions to problems involving addition and subtraction of time intervals in minutes using pictorial models or tools such as a 15- minute event plus a 30-minute event equals 45 minutesClock Hop Floor Mat
111.xx.Grade3(b)(7)(D)determine when it is appropriate to use measurements of liquid volume (capacity) or weight
111.xx.Grade3(b)(7)(E)determine liquid volume (capacity) or weight using appropriate units and tools
111.xx.Grade3(b)(8)Data Analysis. The student applies mathematical process standards to solve problems by collecting and organizing and displaying and interpreting data. The student is expected to:
111.xx.Grade3(b)(8)(A)summarize a data set with multiple categories using a frequency table or dot plot or pictograph or bar graph with scaled intervalsCartesian Coordinate Hop
111.xx.Grade3(b)(8)(B)solve one- and two-step problems using categorical data represented with a frequency table or dot plot or pictograph or bar graph with scaled intervalsCartesian Coordinate Hop

StandardDescription of StandardCorresponding Floor Mat
111.xx.Grade4(b)(1)Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
111.xx.Grade4(b)(1)(A)apply mathematics to problems arising in everyday life and society and the workplaceUS Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade4(b)(1)(B)use a problem-solving model that incorporates:
analyzing given information
formulating a plan or strategy
determining a solution
justifying the solution
and evaluating the problem-solving process and the reasonableness of the solution
US Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
manipulatives
paper/pencil
and technology as appropriate and techniques including:
mental math
estimation
and number sense as appropriate to solve problems
US Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade4(b)(1)(D)communicate mathematical ideas and reasoning and their implications using multiple representations including:
symbols
diagrams
graphs
and language as appropriate
US Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade4(b)(1)(E)create and use representations to organize and record and communicate mathematical ideasUS Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade4(b)(1)(F)analyze mathematical relationships to connect and communicate mathematical ideasUS Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade4(b)(1)(G)display and explain and justify mathematical ideas and arguments using precise mathematical language in written or oral communicationUS Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade4(b)(2)Number and Operations. The student applies mathematical process standards to represent and compare and order whole numbers and decimals and understand relationships related to place value. The student is expected to:
111.xx.Grade4(b)(2)(A)interpret the value of each place-value position as ten times the position to the right and as one-tenth of the value of the place to its leftPlace Value Hop - Decimals (P3)
111.xx.Grade4(b)(2)(B)represent the value of the digit in whole numbers through 1000000000 and decimals to the hundredths using expanded notation and numerals such as in the number 3.94 the 3 in the ones place is 3; the 9 in the tenths place is 0.9; and 4 in the hundredths place is 0.04; and 3.94 is sum of 3 ones 9 tenths and 4 hundredthsPlace Value Hop - Decimals (P3)
111.xx.Grade4(b)(2)(C)compare and order whole numbers to 1000000000 and represent comparisons using the symbols > < or =Place Value Hop - Decimals (P3)
111.xx.Grade4(b)(2)(D)round whole numbers to a given place value through the 100000’s placePlace Value Hop - Decimals (P3)
111.xx.Grade4(b)(2)(E)represent decimals including tenths and hundredths using concrete and visual models and moneyPlace Value Hop - Decimals (P3)
111.xx.Grade4(b)(2)(F)compare and order decimals using concrete and visual models to the hundredthsPlace Value Hop - Decimals (P3)
111.xx.Grade4(b)(2)(G)relate decimals to fractions that name tenths and hundredthsPlace Value Hop - Decimals (P3)
111.xx.Grade4(b)(2)(H)determine the corresponding decimal to the tenths or hundredths place of a specified point on a number linePlace Value Hop - Decimals (P3)
111.xx.Grade4(b)(3)Number and Operations. The student applies mathematical process standards to represent and generate fractions to solve problems. The student is expected to:
111.xx.Grade4(b)(3)(A)represent a fraction a/b as a sum of fractions 1/b where a and b are whole numbers and b > 0 including when a > bFraction Walk Floor Mats
111.xx.Grade4(b)(3)(B)decompose a fraction in more than one way into a sum of fractions with the same denominator using concrete and pictorial models and recording results with symbolic representations such as 7/8 = 5/8 + 2/8; 7/8 = 3/8 + 4/8; 2 7/8 = 1+ 1 + 7/8; 2 7/8 = 8/8 + 8/8 + 7/8Fraction Walk Floor Mats
111.xx.Grade4(b)(3)(C)determine if two given fractions are equivalent using a variety of methods including multiplying by a fraction equivalent to one or simplifying a fraction to lowest termsFraction Walk Floor Mats
Equivalent Fraction Hop Floor Mat
111.xx.Grade4(b)(3)(D)generate equivalent fractions to create equal numerators or equal denominators to compare two fractions with unequal numerators and unequal denominators and represent the comparison of two fractions using the symbols > < or =Fraction Walk Floor Mats
Equivalent Fraction Hop Floor Mat
111.xx.Grade4(b)(3)(E)represent and solve addition and subtraction of fractions with equal denominators and referring to the same whole using objects and pictorial models that build to the number line such as strip diagrams and properties of operationsFraction Walk Floor Mats
Equivalent Fraction Hop Floor Mat
111.xx.Grade4(b)(3)(F)estimate the reasonableness of sums and differences using benchmark fractions 0 and 1/4 and 1/2 and 3/4 and 1 referring to the same wholeFraction Walk Floor Mats
Equivalent Fraction Hop Floor Mat
111.xx.Grade4(b)(3)(G)represent fractions and decimals to the tenths or hundredths as distances from zero on a number lineFraction Walk Floor Mats
Equivalent Fraction Hop Floor Mat
Fractions Decimals and Percents Hop Mats
111.xx.Grade4(b)(3)(H)determine fractional and decimal quantities as being close to 0 and 1/2 and 1Fraction Walk Floor Mats
Equivalent Fraction Hop Floor Mat
Fractions Decimals and Percents Hop Mats
111.xx.Grade4(b)(4)Number and Operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations and decimal sums and differences in order to solve problems with efficiency and accuracy. The student is expected to:
111.xx.Grade4(b)(4)(A)add and subtract whole numbers and decimals to the hundredths place using a variety of methods including:
pictorial models
the inverse relationship between operations
concepts of place value
and efficient algorithms
Place Value Hop - Decimals (P3)
111.xx.Grade4(b)(4)(B)determine products of a number and 10 or 100 using properties of operations and place value understandingsMultiplication Hop
Skip Counting Mats Set
111.xx.Grade4(b)(4)(C)represent the product of 2 two-digit numbers using arrays or area models or equations including perfect squares through 15 x 15Multiplication Hop
Skip Counting Mats Set
111.xx.Grade4(b)(4)(D)use strategies and algorithms including the standard algorithm to multiply up to a four-digit number by a one-digit number and to multiply a two-digit number by a two-digit number. Strategies may include mental math and partial products and the commutative and associative and distributive propertiesMultiplication Hop
Skip Counting Mats Set
111.xx.Grade4(b)(4)(E)represent the quotient of up to a four-digit whole number divided by a one-digit whole number using arrays or area models or equationsMultiplication Hop
Skip Counting Mats Set
111.xx.Grade4(b)(4)(F)use strategies and algorithms including the standard algorithm to divide up to a four-digit dividend by a one-digit divisorMultiplication Hop
Skip Counting Mats Set
111.xx.Grade4(b)(4)(G)use strategies including rounding to the nearest 10 or 100 or 1000 and compatible numbers to estimate solutionsMultiplication Hop
Skip Counting Mats Set
111.xx.Grade4(b)(4)(H)solve one- and two-step problems involving multiplication and division including interpreting remainders with fluencyMultiplication Hop
Skip Counting Mats Set
111.xx.Grade4(b)(5)Algebraic Reasoning. The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to:
111.xx.Grade4(b)(5)(A)represent multistep problems involving the four operations with whole numbers using strip diagrams and equations with a letter standing for the unknown quantityOperations Hop
111.xx.Grade4(b)(5)(B)represent problems using an input-output table and numerical expressions to generate a number pattern that follows a given rule such as given the rule “Add 3” and the starting number 1 use the expressions 1 + 3 and 2 + 3 and 3 + 3 and so forth to generate a table to represent the relationship of the values in the resulting sequence and their position in the sequenceAdd/Subtract Floor Mat
Skip Counting Mats Set
111.xx.Grade4(b)(5)(C)use models to determine the formulas for the perimeter of a rectangle (l + w + l + w or 2l + 2w) including the special form for perimeter of a square(4s) and the area of a rectangle (l x w);Add/Subtract Floor Mat
Skip Counting Mats Set
111.xx.Grade4(b)(5)(D)solve problems related to perimeter and area of rectangles where dimensions are whole numbersAdd/Subtract Floor Mat
Skip Counting Mats Set
111.xx.Grade4(b)(6)Geometry and Measurement. The student applies mathematical process standards to analyze geometric attributes in order to develop generalizations about their properties. The student is expected to:
111.xx.Grade4(b)(6)(A)identify points and lines and line segments and rays and angles and perpendicular and parallel linesAngle Hop Mat
111.xx.Grade4(b)(6)(B)identify and draw one or more lines of symmetry if they exist for a two- dimensional figure
111.xx.Grade4(b)(6)(C)apply knowledge of right angles to identify acute right and obtuse trianglesAngle Hop Mat
111.xx.Grade4(b)(6)(D)use attributes to recognize rhombuses and parallelograms and trapezoids and rectangles and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategoriesAngle Hop Mat
Geometric Shapes Hop
111.xx.Grade4(b)(6)(E)classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified sizeAngle Hop Mat
Geometric Shapes Hop
111.xx.Grade4(b)(7)Geometry and Measurement. The student applies mathematical process standards to solve problems involving angles less than or equal to 180 degrees. The student is expected to:
111.xx.Grade4(b)(7)(A)illustrate the measure of an angle as the part of a circle whose center is at the vertex of the angle that is “cut out” by the rays of the angle. Angle measures are limited to whole numbersAngle Hop Mat
111.xx.Grade4(b)(7)(B)illustrate degrees as the units used to measure an angle where 1/360 of any circle is 1 degree and an angle that “cuts” n/360 out of any circle whose center is at the angle’s vertex has a measure of n degrees. Angle measures are limited to whole numbersAngle Hop Mat
111.xx.Grade4(b)(7)(C)determine the approximate measures of angles in degrees to the nearest whole number using a protractorAngle Hop Mat
111.xx.Grade4(b)(7)(D)draw an angle with a given measureAngle Hop Mat
111.xx.Grade4(b)(7)(E)decompose angles such as complementary and supplementary angles into two non-overlapping angles to determine the measure of an unknown angleAngle Hop Mat
111.xx.Grade4(b)(8)Geometry and Measurement. The student applies mathematical process standards to select appropriate customary and metric units as well as strategies and tools to solve problems involving measurement. The student is expected to:
111.xx.Grade4(b)(8)(A)identify relative sizes of measurement units within the customary and metric systems
111.xx.Grade4(b)(8)(B)convert measurements within the same measurement system - customary or metric - from a smaller unit into a larger unit or a larger unit into a smaller unit when given other equivalent measures represented in a table
111.xx.Grade4(b)(8)(C)solve problems that deal with measurements of length and intervals of time and liquid volumes and masses and money using addition or subtraction or multiplication or division as appropriateClock Hop Floor Mat
US Money Mats
Skip Counting Mats Set
111.xx.Grade4(b)(9)Data Analysis. The student applies mathematical process standards to solve problems by collecting and organizing and displaying and interpreting data. The student is expected to:
111.xx.Grade4(b)(9)(A)represent data on a frequency table or dot plot or stem and leaf plot marked with whole numbers and fractionsCartesian Coordinate Hop
111.xx.Grade4(b)(9)(B)solve one- and two-step problems using data in whole number and decimal and fraction form in a frequency table or dot plot or stem and leaf plotCartesian Coordinate Hop

StandardDescription of StandardCorresponding Floor Mat
111.xx.Grade5(b)(1)Mathematical Process Standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
111.xx.Grade5(b)(1)(A)apply mathematics to problems arising in everyday life and society and the workplaceUS Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade5(b)(1)(B)use a problem-solving model that incorporates analyzing given information and formulating a plan or strategy and determining a solution and justifying the solution and evaluating the problem-solving process and the reasonableness of the solutionUS Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
real objects
manipulatives
paper/pencil
and technology as appropriate and techniques including:
mental math
estimation
and number sense as appropriate to solve problems
US Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade5(b)(1)(D)communicate mathematical ideas and reasoning and their implications using multiple representations including symbols and diagrams and graphs and language as appropriateUS Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade5(b)(1)(E)create and use representations to organize and record and communicate mathematical ideasUS Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade5(b)(1)(F)analyze mathematical relationships to connect and communicate mathematical ideasUS Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade5(b)(1)(G)display and explain and justify mathematical ideas and arguments using precise mathematical language in written or oral communicationsUS Money Mats
Clock Hop Floor Mat
Operations Hop
Cartesian Coordinate Hop
Fraction Walk Floor Mats
111.xx.Grade5(b)(2)Number and Operations. The student applies mathematical process standards to represent and compare and order positive rational numbers and understand relationships as related to place value. The student is expected to:
111.xx.Grade5(b)(2)(A)interpret the value of each place-value position as one-tenth of the value of the place to its left or as ten times the value of the place to its rightPlace Value Hop - Decimals (P3)
111.xx.Grade5(b)(2)(B)represent the value of the digit in decimals through the thousandths using expanded notation and numeralsPlace Value Hop - Decimals (P3)
111.xx.Grade5(b)(2)(C)compare and order two decimals to thousandths and represent comparisons using the symbols > < or =Place Value Hop - Decimals (P3)
Operations Hop
111.xx.Grade5(b)(2)(D)round decimals to tenths or hundredthsPlace Value Hop - Decimals (P3)
111.xx.Grade5(b)(3)Number and Operations. The student applies mathematical process standards to develop and use strategies and methods for positive rational number computations in order to solve problems with efficiency and accuracy. The student is expected to:
111.xx.Grade5(b)(3)(A)estimate to determine solutions to mathematical and real-world problems involving addition or subtraction or multiplication or divisionAdd/Subtract Floor Mat
Skip Counting Mats Set
111.xx.Grade5(b)(3)(B)use strategies and algorithms including the standard algorithm to multiply a three-digit number by a two-digit number with fluencyMultiplication Hop
Skip Counting Mats Set
111.xx.Grade5(b)(3)(C)use strategies and algorithms including the standard algorithm to solve for quotients of up to a four-digit dividend and a two-digit divisor with fluencyMultiplication Hop
Skip Counting Mats Set
111.xx.Grade5(b)(3)(D)represent multiplication of decimals with products to the hundredths using objects and pictorial models including area modelsMultiplication Hop
Skip Counting Mats Set
111.xx.Grade5(b)(3)(E)solve for products of decimals to hundredths - including situations involving money - using strategies based on place-value understandings and properties of operations and the relationship to the multiplication of whole numbersMultiplication Hop
Skip Counting Mats Set
111.xx.Grade5(b)(3)(F)represent quotients to hundredths up to four-digit dividends and two-digit whole number divisors using objects and pictorial models including area modelsMultiplication Hop
Skip Counting Mats Set
111.xx.Grade5(b)(3)(G)solve for quotients to hundredths up to four-digit dividends and two-digit whole number divisors using strategies and algorithms including the standard algorithmMultiplication Hop
Skip Counting Mats Set
Place Value Hop - Decimals (P3)
111.xx.Grade5(b)(3)(H)represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models such as strip diagrams and properties of operationsMultiplication Hop
Skip Counting Mats Set
Fraction Walk Floor Mats
111.xx.Grade5(b)(3)(I)represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models including area modelsMultiplication Hop
Skip Counting Mats Set
Fraction Walk Floor Mats
111.xx.Grade5(b)(3)(J)represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 ÷ 7 and 7 ÷ (1/3) using objects and pictorial models including area modelsMultiplication Hop
Skip Counting Mats Set
Fraction Walk Floor Mats
111.xx.Grade5(b)(4)Algebraic Reasoning. The student applies mathematical process standards to develop concepts of expressions and equations. The student is expected to:
111.xx.Grade5(b)(4)(A)identify prime and composite numbers using patterns in factor pairsPrime Number Hop
111.xx.Grade5(b)(4)(B)represent and solve multistep problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantityOperations Hop
111.xx.Grade5(b)(4)(C)recognize the difference between additive and multiplicative numerical patterns given in a table or graphMultiplication Hop
Skip Counting Mats Set
111.xx.Grade5(b)(4)(D)describe the meaning of parentheses and brackets in a numeric expression such as 4 (14 + 5) is 4 times as large as (14 + 5)PEMDAS Hop
111.xx.Grade5(b)(4)(E)simplify numerical expressions including up to two levels of grouping excluding exponents such as (3 + 7) / (5 - 3)
111.xx.Grade5(b)(4)(F)use concrete objects and pictorial models to develop the formulas for the volume of a rectangular prism including the special form for a cube (V = l x w x h and V = s x s x s and V = Bh)
111.xx.Grade5(b)(4)(G)represent and solve problems related to perimeter and/or area such as for rectangles and composite figures formed by rectangles and related to volume such as for rectangular prismsMultiplication Hop
Skip Counting Mats Set
111.xx.Grade5(b)(5)Geometry and Measurement. The student applies mathematical process standards to classify two-dimensional figures by attributes and properties. The student is expected to classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties such as all rectangles have the property that opposite sides are parallel; therefore every rectangle is a parallelogram.Geometric Shapes Hop
111.xx.Grade5(b)(6)Geometry and Measurement. The student applies mathematical process standards to understand recognize and quantify volume. The student is expected to:
111.xx.Grade5(b)(6)(A)recognize a cube with side length of 1 unit as a “unit cube” having “one cubic unit of volume” and the volume of a three-dimensional figure as the number of unit cubes “n cubic units” needed to fill it with no gaps or overlaps if possible
111.xx.Grade5(b)(6)(B)determine the volume of a rectangular prism with whole number side lengths in problems related to the number of layers times the number of unit cubes in the area of the base
111.xx.Grade5(b)(7)Geometry and Measurement. The student applies mathematical process standards to select appropriate units and strategies and tools to solve problems involving measurement. The student is expected to solve problems by calculating conversions within a measurement system - customary or metric.
111.xx.Grade5(b)(8)Geometry and Measurement. The student applies mathematical process standards to identify locations on a coordinate plane. The student is expected to:
111.xx.Grade5(b)(8)(A)describe the key attributes of the coordinate plane and the process for graphing ordered pairs of numbers in the first quadrantCartesian Coordinate Hop
111.xx.Grade5(b)(8)(B)graph ordered pairs of numbers arising from mathematical and real-world problems in the first quadrant of the coordinate plane including those generated by number patterns or found in an input-output tableCartesian Coordinate Hop
111.xx.Grade5(b)(9)Data Analysis. The student applies mathematical process standards to solve problems by collecting and organizing and displaying and interpreting data. The student is expected to:
111.xx.Grade5(b)(9)(A)represent categorical data with bar graphs or frequency tables and numerical data including data sets of measurements in fractions or decimals with dot plots or stem and leaf plotsCartesian Coordinate Hop
111.xx.Grade5(b)(9)(B)represent discrete paired data on a scatter plotCartesian Coordinate Hop
111.xx.Grade5(b)(9)(C)solve one- and two-step problems using data from a frequency table or dot plot or bar graph or stem and leaf plot or scatter plotCartesian Coordinate Hop

StandardDescription of StandardCorresponding Floor Mat
111.xx.Kindergarten(b)(1)Reading/Beginning Reading Skills/Print Awareness. Students understand how English is written and printed. Students are expected to:
11.xx.Kindergarten(b)(1)(A)recognize that spoken words can be represented by print for communicationWord Hop Floor Mats
111.xx.Kindergarten(b)(1)(B)identify upper- and lower-case lettersAlphabet Hop
111.xx.Kindergarten(b)(1)(C)demonstrate the one-to-one correspondence between a spoken word and a printed word in textWord Hop Floor Mats
111.xx.Kindergarten(b)(1)(D)recognize the difference between a letter and a printed wordAlphabet Hop
Word Hop Floor Mats
Word Blending Mats
111.xx.Kindergarten(b)(1)(E)recognize that sentences are comprised of words separated by spaces and demonstrate the awareness of word boundaries (e.g. through kinesthetic or tactile actions such as clapping and jumping);Sentence Hops
111.xx.Kindergarten(b)(1)(F)hold a book right side up and turn its pages correctly and know that reading moves from top to bottom and left to right
111.xx.Kindergarten(b)(1)(G)identify different parts of a book (e.g. front and back covers; title page)
111.xx.Kindergarten(b)(2)(2) Reading/Beginning Reading Skills/Phonological Awareness. Students display phonological awareness. Students are expected to:
111.xx.Kindergarten(b)(2)(A)identify a sentence made up of a group of wordsSentence Hops
111.xx.Kindergarten(b)(2)(B)identify syllables in spoken wordsWord Hop Floor Mats
111.xx.Kindergarten(b)(2)(C)orally generate rhymes in response to spoken words (e.g. "What rhymes with hat?")Word Hop Floor Mats
111.xx.Kindergarten(b)(2)(D)distinguish orally presented rhyming pairs of words from non-rhyming pairs
111.xx.Kindergarten(b)(2)(E)recognize spoken alliteration or groups of words that begin with the same spoken onset or initial sound (e.g. "baby boy bounces the ball")
111.xx.Kindergarten(b)(2)(F)blend spoken onsets and rimes to form simple words (e.g. onset/c/ and rime/at/ make cat)Word Blending Mats
111.xx.Kindergarten(b)(2)(G)blend spoken phonemes to form one-syllable words (e.g./m/ …/a/ …/n/ says man)Word Blending Mats
111.xx.Kindergarten(b)(2)(H)isolate the initial sound in one-syllable spoken wordsWord Hop Floor Mats
111.xx.Kindergarten(b)(2)(I)segment spoken one-syllable words into two to three phonemes (e.g. dog:/d/ …/o/ …/g/)Word Hop Floor Mats
111.xx.Kindergarten(b)(3)Reading/Beginning Reading Skills/Phonics. Students use the relationships between letters and sounds; spelling patterns; and morphological analysis to decode written English. Students are expected to:
111.xx.Kindergarten(b)(3)(A)identify the common sounds that letters representMake-a-Word Hop
Word Blending Mats
111.xx.Kindergarten(b)(3)(B)use knowledge of letter-sound relationships to decode regular words in text and independent of content (e.g. VC; CVC; CCVC; and CVCC words)Make-a-Word Hop
Word Blending Mats
Word Hop Floor Mats
111.xx.Kindergarten(b)(3)(C)recognize that new words are created when letters are changed; added; or deletedWord Blending Mats
Make-a-Word Hop
111.xx.Kindergarten(b)(3)(D)identify and read at least 25 high-frequency words from a commonly used listWord Hop Floor Mats
111.xx.Kindergarten(b)(4)Reading/Beginning Reading/Strategies. Students comprehend a variety of texts drawing on useful strategies as needed. Students are expected to:
111.xx.Kindergarten(b)(4)(A)predict what might happen next in text based on the cover; title; and illustrationsQuestion Word Hop
111.xx.Kindergarten(b)(5)Reading/Vocabulary Development. Students understand new vocabulary and use it correctly when reading and writing. Students are expected to:
111.xx.Kindergarten(b)(5)(A)identify and use words that name actions; directions; positions; sequences; and locationsMake-a-Word Hop
111.xx.Kindergarten(b)(5)(B)recognize that compound words are made up of shorter words
111.xx.Kindergarten(b)(5)(C)identify and sort pictures of objects into conceptual categories (e.g. colors; shapes; textures)Color Hop
My First Shapes Hop
Attribute Hop
111.xx.Kindergarten(b)(5)(D)use a picture dictionary to find wordsAlphabet Hop
111.xx.Kindergarten(b)(6)Reading/Comprehension of Literary Text/Theme and Genre. Students analyze; make inferences; and draw conclusions about theme and genre in different cultural; historical; and contemporary contexts and provide evidence from the text to support their understanding. Students are expected to:
111.xx.Kindergarten(b)(6)(A)identify elements of a story including setting; character; and key eventsQuestion Word Hop
111.xx.Kindergarten(b)(6)(B)discuss the big idea (theme) of a well-known folktale or fable and connect it to personal experience
111.xx.Kindergarten(b)(6)(C)recognize sensory details
111.xx.Kindergarten(b)(6)(D)recognize recurring phrases and characters in traditional fairy tales; lullabies; and folktales from various cultures
111.xx.Kindergarten(b)(7)Reading/Comprehension of Literary Text/Poetry. Students understand; make inferences and draw conclusions about the structure and elements of poetry and provide evidence from text to support their understanding. Students are expected to respond to rhythm and rhyme in poetry through identifying a regular beat and similarities in word sounds.
111.xx.Kindergarten(b)(8)Reading/Comprehension of Literary Text/Fiction. Students understand; make inferences and draw conclusions about the structure and elements of fiction and provide evidence from text to support their understanding. Students are expected to:
111.xx.Kindergarten(b)(8)(A)retell a main event from a story read aloudQuestion Word Hop
111.xx.Kindergarten(b)(8)(B)describe characters in a story and the reasons for their actionsAlphabet Hop
111.xx.Kindergarten(b)(9)Reading/Comprehension of Informational Text/Culture and History. Students analyze; make inferences and draw conclusions about the author's purpose in cultural; historical; and contemporary contexts and provide evidence from the text to support their understanding. Students are expected to identify the topic of an informational text heard.
111.xx.Kindergarten(b)(10)Reading/Comprehension of Informational Text/Expository Text. Students analyze; make inferences and draw conclusions about expository text; and provide evidence from text to support their understanding. Students are expected to:
111.xx.Kindergarten(b)(10)(A)identify the topic and details in expository text heard or read; referring to the words and/or illustrations
111.xx.Kindergarten(b)(10)(B)retell important facts in a text; heard; or read
111.xx.Kindergarten(b)(10)(C)retell important facts in a text; heard; or readQuestion Word Hop
111.xx.Kindergarten(b)(10)(D)use titles and illustrations to make predictions about text
111.xx.Kindergarten(b)(11)Reading/Comprehension of Informational Text/Procedural Texts. Students understand how to glean and use information in procedural texts and documents. Students are expected to:
111.xx.Kindergarten(b)(11)(A)follow pictorial directions (e.g. recipes; science experiments); and
111.xx.Kindergarten(b)(11)(B)identify the meaning of specific signs (e.g. traffic signs; warning signs)
111.xx.Kindergarten(b)(12)Reading/Media Literacy. Students use comprehension skills to analyze how words; images; graphics; and sounds work together in various forms to impact meaning. Students continue to apply earlier standards with greater depth in increasingly more complex texts. Students (with adult assistance) are expected to:
111.xx.Kindergarten(b)(12)(B)identify techniques used in media (e.g. sound; movement)
111.xx.Kindergarten(b)(13)Writing/Writing Process. Students use elements of the writing process (planning; drafting; revising; editing; and publishing) to compose text. Students (with adult assistance) are expected to:
111.xx.Kindergarten(b)(13)(A)plan a first draft by generating ideas for writing through class discussion
111.xx.Kindergarten(b)(13)(B)develop drafts by sequencing the action or details in the story.
111.xx.Kindergarten(b)(13)(C)revise drafts by adding details or sentences
111.xx.Kindergarten(b)(13)(D)edit drafts by leaving spaces between letters and words; and
111.xx.Kindergarten(b)(13)(E)share writing with others
111.xx.Kindergarten(b)(14)Writing/Literary Texts. Students write literary texts to express their ideas and feelings about real or imagined people; events; and ideas. Students are expected to:
111.xx.Kindergarten(b)(14)(A)dictate or write sentences to tell a story and put the sentences in chronological sequenceSentence Hops
111.xx.Kindergarten(b)(14)(B)write short poems
111.xx.Kindergarten(b)(15)Writing/Expository and Procedural Texts. Students write expository and procedural or work-related texts to communicate ideas and information to specific audiences for specific purposes. Students are expected to dictate or write information for lists; captions; or invitations.
111.xx.Kindergarten(b)(16)Oral and Written Conventions/Conventions. Students understand the function of and use the conventions of academic language when speaking and writing. Students continue to apply earlier standards with greater complexity. Students are expected to:
111.xx.Kindergarten(b)(16)(A)understand and use the following parts of speech in the context of reading; writing; and speaking (with adult assistance):
(i) past and future tenses when speaking;
(ii) nouns (singular/plural);
(iii) descriptive words;
(iv) prepositions and simple prepositional phrases appropriately when speaking or writing (e.g. in; on; under; over); and
(v) pronouns (e.g. I; me)
Parts of Speech of Hop
111.xx.Kindergarten(b)(16)(B)speak in complete sentences to communicateSentence Hops
111.xx.Kindergarten(b)(16)(C)use complete simple sentencesSentence Hops
111.xx.Kindergarten(b)(17)Oral and Written Conventions/Handwriting; Capitalization; and Punctuation. Students write legibly and use appropriate capitalization and punctuation conventions in their compositions. Students are expected to:
111.xx.Kindergarten(b)(17)(A)form upper- and lower-case letters legibly using the basic conventions of print (left-to-right and top-to-bottom progression)Alphabet Hop
111.xx.Kindergarten(b)(17)(B)capitalize the first letter in a sentenceSentence Hops
Alphabet Hop
111.xx.Kindergarten(b)(17)(C)use punctuation at the end of a sentenceSentence Hops
111.xx.Kindergarten(b)(18)Oral and Written Conventions/Spelling. Students spell correctly. Students are expected to:
111.xx.Kindergarten(b)(18)(A)use phonological knowledge to match sounds to lettersWord Blending Mats
111.xx.Kindergarten(b)(18)(B)use letter-sound correspondences to spell consonant-vowel-consonant (CVC) words (e.g. "cut")Make-a-Word Hop
111.xx.Kindergarten(b)(18)(C)write one's own nameMake-a-Word Hop
111.xx.Kindergarten(b)(19)Research/Research Plan. Students ask open-ended research questions and develop a plan for answering them. Students (with adult assistance) are expected to:
111.xx.Kindergarten(b)(19)(B)decide what sources or people in the classroom; school; library; or home can answer these questions
111.xx.Kindergarten(b)(20)Research/Gathering Sources. Students determine; locate; and explore the full range of relevant sources addressing a research question and systematically record the information they gather. Students (with adult assistance) are expected to:
111.xx.Kindergarten(b)(20)(A)gather evidence from provided text sources; and
111.xx.Kindergarten(b)(20)(B)use pictures in conjunction with writing when documenting research
111.xx.Kindergarten(b)(21)Research/Gathering Sources. Students determine; locate; and explore the full range of relevant sources addressing a research question and systematically record the information they gather. Students (with adult assistance) are expected to:
111.xx.Kindergarten(b)(21)(A)listen attentively by facing speakers and asking questions to clarify information; and
111.xx.Kindergarten(b)(21)(B)follow oral directions that involve a short related sequence of actions.
111.xx.Kindergarten(b)(22)Listening and Speaking/Speaking. Students speak clearly and to the point; using the conventions of language. Students continue to apply earlier standards with greater complexity. Students are expected to share information and ideas by speaking audibly and clearly using the conventions of language.
111.xx.Kindergarten(b)(23)Listening and Speaking/Teamwork. Students work productively with others in teams. Students continue to apply earlier standards with greater complexity. Students are expected to follow agreed-upon rules for discussion; including taking turns and speaking one at a time.

## Virginia Standards of Learning

StandardDescription of StandardCorresponding Floor Mat
Number and Number SenseFocus: Whole Number Concepts
K.1The student, given two sets, each containing 10 or fewer concrete objects, will identify and describe one set as having more, fewer, or the same number of members as the other set, using the concept of one-to-one correspondence.Number Line 1-10 Floor Mat
K.2The student, given a set containing 15 or fewer concrete objects, will
a) tell how many are in the set by counting the number of objects orally;
b) write the numeral to tell how many are in the set; and
c) select the corresponding numeral from a given set of numerals.
Number Line 1-10 Floor Mat

Skip Counting by 2s

K.3 The student, given an ordered set of ten objects and/or pictures, will indicate the ordinal position of each object, first through tenth, and the ordered position of each object.Ordinal Numbers Hop
K.4The student will
a) count forward to 100 and backward from 10;
b) identify one more than a number and one less than a number; and
c) count by fives and tens to 100.

Skip Counting by 2s

Hop by Tens

Clock Hop
K.5The student will identify the parts of a set and/or region that represent fractions for halves and fourths.Fraction Walk for Halves/Fourths and Thirds/Sixths

Equivalent Fraction Hop
Computation and EstimationFocus: Whole Number Operations
K.6The student will model adding and subtracting whole numbers, using up to 10 concrete objects.Skip Counting by 2s
Measurement
MeasurementFocus: Instruments and Attributes
K.7The student will recognize a penny, nickel, dime, and quarter and will determine the value of a collection of pennies and/or nickels whose total value is 10 cents or less.Dollar Hop Mat
K.8The student will identify the instruments used to measure length (ruler), weight (scale), time (clock: digital and analog; calendar: day, month, and season), and temperature (thermometer).Clock Hop
K.9The student will tell time to the hour, using analog and digital clocks.Clock Hop
K.10The student will compare two objects or events, using direct comparisons or nonstandard units of measure, according to one or more of the following attributes: length (shorter, longer), height (taller, shorter), weight (heavier, lighter), temperature (hotter, colder). Examples of nonstandard units include foot length, hand span, new pencil, paper clip, and block.Measurement Hop Mat
GeometryFocus: Plane Figures
K.11The student will
a) identify, describe, and trace plane geometric figures (circle, triangle, square, and rectangle); and
b) compare the size (larger, smaller) and shape of plane geometric figures (circle, triangle, square, and rectangle).
My First Shapes Hop

Geometric Shapes Hop
Probability and StatisticsFocus: Data Collection and Display
K.12The student will describe the location of one object relative to another (above, below, next to) and identify representations of plane geometric figures (circle, triangle, square, and rectangle) regardless of their positions and orientations in space.My First Shapes Hop

Geometric Shapes Hop
K.13The student will gather data by counting and tallying.Add/Subtract Mat
K.14The student will display gathered data in object graphs, picture graphs, and tables, and will answer questions related to the data.Cartesian Coordinate
Patterns, Functions, and AlgebraFocus: Attributes and Patterning
K.15The student will sort and classify objects according to attributes.Attribute Word Hop
K.16The student will identify, describe, and extend repeating patterns.Attribute Word Hop

StandardDescription of StandardCorresponding Floor Mat
Number and Number SenseFocus: Place Value and Fraction Concepts
1.1The student will
a) count from 0 to 100 and write the corresponding numerals; and
b) group a collection of up to 100 objects into tens and ones and write the corresponding numeral to develop an understanding of place value.

Place Value Mat (P1)
1.2The student count forward by ones, twos, fives, and tens to 100 and backward by ones from 30.Skip Counting by 2s

Clock Hop

Hop Mat by Tens

Skip Counting by 3s
1.3The student will identify the parts of a set and/or region that represent fractions for halves, thirds, and fourths and write the fractions.Unit Circle Hop

Fraction Walk for Halves/Fourths and Thirds/Sixths

Equivalent Fraction Hop
Computation and EstimationFocus: Whole Number Operations
1.4The student, given a familiar problem situation involving magnitude, will
a) select a reasonable order of magnitude from three given quantities: a one-digit numeral, a two-digit numeral, and a three-digit numeral (e.g., 5, 50, 500); and
b) explain the reasonableness of the choice.
1.5The student will recall basic addition facts with sums to 18 or less and the corresponding subtraction facts.Skip Counting by 2s Mat
1.6The student will create and solve one-step story and picture problems using basic addition facts with sums to 18 or less and the corresponding subtraction facts.
MeasurementFocus: Time and Nonstandard Measurement
1.7The student will
a) identify the number of pennies equivalent to a nickel, a dime, and a quarter; and
b) determine the value of a collection of pennies, nickels, and dimes whose total value is 100 cents or less.
Dollar Hop Mat
1.8The student will tell time to the half-hour, using analog and digital clocks.Clock Hop
1.9The student will use nonstandard units to measure length, weight/mass, and volume.Measurement Hop
1.10The student will compare, using the concepts of more, less, and equivalent,
a) the volumes of two given containers; and
b) the weight/mass of two objects, using a balance scale.
1.11The student will use calendar language appropriately (e.g., names of the months, today, yesterday, next week, last week).Months of the Year Hop Mat

Days of the Week Hop Mat
GeometryFocus: Characteristics of Plane Figures
1.12The student will identify and trace, describe, and sort plane geometric figures (triangle, square, rectangle, and circle) according to number of sides, vertices, and right angles.Geometric Shapes Hop
1.13The student will construct, model, and describe objects in the environment as geometric shapes (triangle, rectangle, square, and circle) and explain the reasonableness of each choice.Geometric Shapes Hop
Probability and StatisticsFocus: Data Collection and Interpretation
1.14The student will investigate, identify, and describe various forms of data collection (e.g., recording daily temperature, lunch count, attendance, favorite ice cream), using tables, picture graphs, and object graphs.Cartesian Coordinate Hop
1.15The student will interpret information displayed in a picture or object graph, using the vocabulary more, less, fewer, greater than, less than, and equal to.Cartesian Coordinate Hop
Patterns, Functions, and AlgebraFocus: Patterning and Equivalence
1.16The student will sort and classify concrete objects according to one or more attributes, including color, size, shape, and thickness.
1.17The student will recognize, describe, extend, and create a wide variety of growing and repeating patterns.
1.18The student will demonstrate an understanding of equality through the use of the equal sign.Operations Floor Mat

StandardDescription of StandardCorresponding Floor Mat
Number and Number SenseFocus: Place Value, Number Patterns, and Fraction Concepts
2.1The student will
a) read, write, and identify the place value of each digit in a three-digit numeral, using numeration models;
b) round two-digit numbers to the nearest ten; and
c) compare two whole numbers between 0 and 999, using symbols (>, <, or =) and words (greater than, less than, or equal to).
Place Value Mat (P1)

Operations Floor Mat
2.2The student will
a) identify the ordinal positions first through twentieth, using an ordered set of objects; and
b) write the ordinal numbers.
Ordinal Numbers Hop
2.3The student will
a) identify the parts of a set and/or region that represent fractions for halves, thirds, fourths, sixths, eighths, and tenths;
b) write the fractions; and
c) compare the unit fractions for halves, thirds, fourths, sixths, eighths, and tenths.
Fraction Walk for Halves/Fourths and Thirds/Sixths

Equivalent Fractions Hop Floor Mat
2.4The student will
a) count forward by twos, fives, and tens to 100, starting at various multiples of 2, 5, or 10;
b) count backward by tens from 100; and
c) recognize even and odd numbers.
Skip Counting by 2s

Hop Mat by Tens

Computation and EstimationFocus: Number Relationships and Operations
2.5The student will recall addition facts with sums to 20 or less and the corresponding subtraction facts.Skip Counting by 2s
2.6The student, given two whole numbers whose sum is 99 or less, will
a) estimate the sum; and
b) find the sum, using various methods of calculation.
2.7The student, given two whole numbers, each of which is 99 or less, will
a) estimate the difference; and
b) find the difference, using various methods of calculation.
2.8The student will create and solve one- and two-step addition and subtraction problems, using data from simple tables, picture graphs, and bar graphs.Cartesian Coordinate Hop
2.9The student will recognize and describe the related facts that represent and describe the inverse relationship between addition and subtraction.Add/Subtract Mat
MeasurementFocus: Money, Linear Measurement, Weight/Mass, and Volume
2.10The student will
a) count and compare a collection of pennies, nickels, dimes, and quarters whose total value is \$2.00 or less; and
b) correctly use the cent symbol (¢), dollar symbol (\$), and decimal point (.).
Dollar Hop Mat

US Money Mat
2.11The student will estimate and measure
a) length to the nearest centimeter and inch;
b) weight/mass of objects in pounds/ounces and kilograms/grams, using a scale; and
c) liquid volume in cups, pints, quarts, gallons, and liters.
Measurement Hop
2.12The student will tell and write time to the nearest five minutes, using analog and digital clocks.Clock Hop
2.13The student will
a) determine past and future days of the week; and
b) identify specific days and dates on a given calendar.
Days of the Week Hop
2.14The student will read the temperature on a Celsius and/or Fahrenheit thermometer to the nearest 10 degrees.
GeometryFocus: Symmetry and Plane and Solid Figures
2.15The student will
a) draw a line of symmetry in a figure; and
b) identify and create figures with at least one line of symmetry.
Cartesian Coordinate Hop
2.16The student will identify, describe, compare, and contrast plane and solid geometric figures (circle/sphere, square/cube, and rectangle/rectangular prism).
Probability and StatisticsFocus: Applications of Data
2.17The student will use data from experiments to construct picture graphs, pictographs, and bar graphs.Cartesian Coordinate Hop
2.18The student will use data from experiments to predict outcomes when the experiment is repeated.Cartesian Coordinate Hop
2.19The student will analyze data displayed in picture graphs, pictographs, and bar graphs.Cartesian Coordinate Hop
Patterns, Functions, and AlgebraFocus: Patterning and Numerical Sentences
2.20The student will identify, create, and extend a wide variety of patterns.

StandardDescription of StandardCorresponding Floor Mat
Number and Number SenseFocus: Place Value and Fractions
3.1The student will
read and write six-digit numerals and identify the place value and value of each digit;

round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand; and

compare two whole numbers between 0 and 9,999, using symbols (>, <, or = ) and words (greater than, less than, or equal to).
Place Value Mat Mat P2
Place Value Mat P1
3.2The student will recognize and use the inverse relationships between addition/subtraction and multiplication/division to complete basic fact sentences. The student will use these relationships to solve problems.Skip Counting Mats by 2's 3's 4's 6's 7's 8's 9's
Factor Fun Hop Mat
Multiplication Hop
Hopscotch For Threes Mat
Skip Counting Stencils
3.3The student will
name and write fractions (including mixed numbers) represented by a model;

model fractions (including mixed numbers) and write the fractions’ names; and

compare fractions having like and unlike denominators, using words and symbols
(>, <, or =).
Fraction Walk for Halves/Quarters and Thirds/Sixths

Equivalent Fraction Hop Floor Mat

Operations Floor Mat
Computation and EstimationFocus: Computation and Fraction Operations
3.4The student will estimate solutions to and solve single-step and multistep problems involving the sum or difference of two whole numbers, each 9,999 or less, with or without regrouping.Add/ Subtract Floor Mat
3.5The student will recall multiplication facts through the twelves table, and the corresponding division facts.Skip Counting Mats by 2's 3's 4's 6's 7's 8's 9's

Factor Fun Hop Mat

Multiplication Hop

Hopscotch For Threes Mat

Skip Counting Hopping Stencil Full Set
3.6The student will represent multiplication and division, using area, set, and number line models, and create and solve problems that involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less.Cartesian Coordinate Hop Mat
3.7The student will add and subtract proper fractions having like denominators of 12 or less.Fraction Walk for Halves/Quarters and Thirds/Sixths

Equivalent Fraction Hop Floor Mat
MeasurementFocus: U.S. Customary and Metric Units, Area and Perimeter, and Time
3.8The student will determine, by counting, the value of a collection of bills and coins whose total value is \$5.00 or less, compare the value of the bills and coins, and make change.Dollar Hop Mat

US Money Mats
3.9The student will estimate and use U.S. Customary and metric units to measure
length to the nearest -inch, inch, foot, yard, centimeter, and meter;

liquid volume in cups, pints, quarts, gallons, and liters;

weight/mass in ounces, pounds, grams, and kilograms; and

area and perimeter.
Measurement Hop Mat (0-12 feet) Measurement Hop Mat (0-60 feet)
3.1The student will
measure the distance around a polygon in order to determine perimeter; and

count the number of square units needed to cover a given surface in order to determine area.
Cartesian Coordinate Hop Mat
3.11The student will
tell time to the nearest minute, using analog and digital clocks; and

determine elapsed time in one-hour increments over a 12-hour period.
Clock Hop Floor Mat
3.12The student will identify equivalent periods of time, including relationships among days, months, and years, as well as minutes and hours.Clock Hop Floor Mat
3.13The student will read temperature to the nearest degree from a Celsius thermometer and a Fahrenheit thermometer. Real thermometers and physical models of thermometers will be used.
GeometryFocus: Properties and Congruence Characteristics of Plane and Solid Figures
3.14The student will identify, describe, compare, and contrast characteristics of plane and solid geometric figures (circle, square, rectangle, triangle, cube, rectangular prism, square pyramid, sphere, cone, and cylinder) by identifying relevant characteristics, including the number of angles, vertices, and edges, and the number and shape of faces, using concrete models.Geometric Shapes Hop
3.15The student will identify and draw representations of points, line segments, rays, angles, and lines.Unit Circle Hop

Cartesian Coordinate Hop Mat

Angle Hop Floor Mat
3.16The student will identify and describe congruent and noncongruent plane figures.
Probability and StatisticsFocus: Applications of Data and Chance
3.17The student will
collect and organize data, using observations, measurements, surveys, or experiments;

construct a line plot, a picture graph, or a bar graph to represent the data; and

read and interpret the data represented in line plots, bar graphs, and picture graphs and write a sentence analyzing the data.
Cartesian Coordinate Hop Mat
3.18The student will investigate and describe the concept of probability as chance and list possible results of a given situation.
Patterns, Functions, and AlgebraFocus: Patterns and Property Concepts
3.19The student will recognize and describe a variety of patterns formed using numbers, tables, and pictures, and extend the patterns, using the same or different forms.Cartesian Coordinate Hop Mat
3.2The student will
investigate the identity and the commutative properties for addition and multiplication; and

identify examples of the identity and commutative properties for addition and multiplication.
Skip Counting Mats by 2's 3's 4's 6's 7's 8's 9's

Factor Fun Hop Mat

Multiplication Hop

Hopscotch For Threes Mat

Skip Counting Hopping Stencil Full Set

StandardDescription of StandardCorresponding Floor Mat
Number and Number SenseFocus: Place Value, Fractions, and Decimals
4.1The student will
identify orally and in writing the place value for each digit in a whole number expressed through millions;

compare two whole numbers expressed through millions, using symbols (>, <, or = ); and

round whole numbers expressed through millions to the nearest thousand, ten thousand, and hundred thousand.
Place Value Mat P2
4.2The student will
compare and order fractions and mixed numbers;

represent equivalent fractions; and

identify the division statement that represents a fraction.
Fraction Walk for Halves/Fourths and Thirds/Sixths

Equivalent Fractios Floor Mat
4.2The student will
read, write, represent, and identify decimals expressed through thousandths;

round decimals to the nearest whole number, tenth, and hundredth;

compare and order decimals; and

given a model, write the decimal and fraction equivalents.
Place Value Mat P3

Fraction, Decimal, and Percent Hop 1/2 and 1/4

Fraction, Decimal, and Percent Hop 1/3 and 1/4
Computation and EstimationFocus: Factors and Multiples, and Fraction and Decimal Operations
4.4The student will
estimate sums, differences, products, and quotients of whole numbers;

add, subtract, and multiply whole numbers;

divide whole numbers, finding quotients with and without remainders; and

solve single-step and multistep addition, subtraction, and multiplication problems with whole numbers.
Skip Counting Mats by 2's 3's 4's 6's 7's 8's 9's

Factor Fun Hop Mat

Multiplication Hop

Hopscotch For Threes Mat

Skip Counting Stencils

4.5The student will
determine common multiples and factors, including least common multiple and greatest common factor;

add and subtract fractions having like and unlike denominators that are limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fractions, using common multiples and factors;

add and subtract with decimals; and

solve single-step and multistep practical problems involving addition and subtraction with fractions and with decimals.
Equivalent Fraction Hop Floor Mat

Fraction Walk for Halves/Fourths and Thirds/Sixths

Fraction, Decimal, and Percent Hop 1/2 and 1/4

Fraction, Decimal, and Percent Hop 1/3 and 1/4
MeasurementFocus: Equivalence within U.S. Customary and Metric Systems
4.6The student will
estimate and measure weight/mass and describe the results in U.S. Customary and metric units as appropriate; and

identify equivalent measurements between units within the U.S. Customary system (ounces, pounds, and tons) and between units within the metric system (grams and kilograms).
4.7The student will
estimate and measure length, and describe the result in both metric and U.S. Customary units; and

identify equivalent measurements between units within the U.S. Customary system (inches and feet; feet and yards; inches and yards; yards and miles) and between units within the metric system (millimeters and centimeters; centimeters and meters; and millimeters and meters).
Measurement Hop Mat
4.8The student will
estimate and measure liquid volume and describe the results in U.S. Customary units; and

identify equivalent measurements between units within the U.S. Customary system (cups, pints, quarts, and gallons).
4.9The student will determine elapsed time in hours and minutes within a 12-hour period.Clock Hop Floor Mat
GeometryFocus: Representations and Polygons
4.1The student will
identify and describe representations of points, lines, line segments, rays, and angles, including endpoints and vertices; and

identify representations of lines that illustrate intersection, parallelism, and perpendicularity.
Unit Circle Hop

Cartesian Coordinate Hop Mat

Angle Hop Floor Mat
4.11The student will
investigate congruence of plane figures after geometric transformations, such as reflection, translation, and rotation, using mirrors, paper folding, and tracing; and

recognize the images of figures resulting from geometric transformations, such as translation, reflection, and rotation.
4.12The student will
define polygon; and

identify polygons with 10 or fewer sides.
Geometric Shapes Hop
Probability and StatisticsFocus: Outcomes and Data
4.13The student will
predict the likelihood of an outcome of a simple event; and

represent probability as a number between 0 and 1, inclusive.
4.14The student will collect, organize, display, and interpret data from a variety of graphsCartesian Coordinate Hop Mat
Patterns, Functions, and AlgebraFocus: Geometric Patterns, Equality, and Properties
4.15The student will recognize, create, and extend numerical and geometric patterns.
4.16The student will
recognize and demonstrate the meaning of equality in an equation; and

investigate and describe the associative property for addition and multiplication.

StandardDescription of StandardCorresponding Floor Mat
Number and Number SenseFocus: Prime and Composite Numbers and Rounding Decimals
5.1The student, given a decimal through thousandths, will round to the nearest whole number, tenth, or hundredth.Place Value Mat P3
5.2The student will
recognize and name fractions in their equivalent decimal form and vice versa; and

compare and order fractions and decimals in a given set from least to greatest and greatest to least.
Equivalent Fraction Hop Floor Mat

Fraction Walk for Halves/Fourths and Thirds/Sixths

Fraction, Decimal, and Percent Hop 1/2 and 1/4

Fraction, Decimal, and Percent Hop 1/3 and 1/4
5.3The student will
identify and describe the characteristics of prime and composite numbers; and

identify and describe the characteristics of even and odd numbers.
Prime Number Hop

Skip Counting Mat by 2's

Skip Counting Stencil 2s
Computation and EstimationFocus: Multistep Applications and Order of Operations
5.4The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers.Add / Subtract Floor Mat
5.5The student will
find the sum, difference, product, and quotient of two numbers expressed as decimals through thousandths (divisors with only one nonzero digit); and

create and solve single-step and multistep practical problems involving decimals.
5.6The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers and express answers in simplest form.Equivalent Fraction Hop Floor Mat

Fraction Walk for Halves/Quarters and Thirds/Sixths

Fraction, Decimal, and Percent Hop 1/2 and 1/4

Fraction, Decimal, and Percent Hop 1/3 and 1/4
5.7The student will evaluate whole number numerical expressions, using the order of operations limited to parentheses, addition, subtraction, multiplication, and division.PEMDAS Hop
MeasurementFocus: Perimeter, Area, Volume, and Equivalent Measures
5.8The student will
find perimeter, area, and volume in standard units of measure;

differentiate among perimeter, area, and volume and identify whether the application of the concept of perimeter, area, or volume is appropriate for a given situation;

identify equivalent measurements within the metric system;

estimate and then measure to solve problems, using U.S. Customary and metric units; and

choose an appropriate unit of measure for a given situation involving measurement using U.S. Customary and metric units.
Cartesian Coordinate Hop Mat

Measurement Hop Mat
5.9The student will identify and describe the diameter, radius, chord, and circumference of a circle.Unit Circle Hop (trig) Mat
5.1The student will determine an amount of elapsed time in hours and minutes within a 24-hour period.Clock Hop Floor Mat
5.11The student will measure right, acute, obtuse, and straight angles.Unit Circle Hop

Angle Hop Floor Mat
GeometryFocus: Classification and Subdividing
5.12The student will classify
angles as right, acute, obtuse, or straight; and

triangles as right, acute, obtuse, equilateral, scalene, or isosceles.
Unit Circle Hop

Angle Hop Floor Mat
5.13The student, using plane figures (square, rectangle, triangle, parallelogram, rhombus, and trapezoid), will
develop definitions of these plane figures; and

investigate and describe the results of combining and subdividing plane figures.
Probability and StatisticsFocus: Outcomes and Measures of Center
5.14The student will make predictions and determine the probability of an outcome by constructing a sample space.
5.15The student, given a problem situation, will collect, organize, and interpret data in a variety of forms, using stem-and-leaf plots and line graphs.Cartesian Coordinate Hop Mat
5.16The student will
describe mean, median, and mode as measures of center;

describe mean as fair share;

find the mean, median, mode, and range of a set of data; and

describe the range of a set of data as a measure of variation.
Patterns, Functions, and AlgebraFocus: Equations and Properties
5.17The student will describe the relationship found in a number pattern and express the relationship.

## Georgia Standards of Excellence

Georgia Standard of ExcellenceDescription of StandardCorresponding Floor Mat
K.CC. Counting and CardinalityKnow number names and the count sequence.
MGSEK.CC.1Count to 100 by ones and by tens.Add/Subtract Mat
Hop by 10's Mat
Hopscotch For Threes Mat
MGSEK.CC.2Count forward beginning from a given number within the known sequence (instead of having to begin at 1).Add/Subtract Mat
Hopscotch For Threes Mat
MGSEK.CC.3Write numbers 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).Skip Counting by 2's Mat
Hopscotch For Threes Mat
Skip Counting by 2s Stencil
Count to tell the number of objects.
MGSEK.CC.4Understand the relationship between numbers and quantities; connect counting to cardinality.Add/Subtract Mat
Hopscotch For Threes Mat
MGSEK.CC.4aWhen counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. (one-to-one correspondence).Skip Counting Mat by 2's
Hopscotch For Threes Mat
Skip Counting by 2s Stencil
MGSEK.CC.4bUnderstand that the last number name said tells the number of objects counted (cardinality). The number of objects is the same regardless of their arrangement or the order in which they were counted.Skip Counting Mat by 2's
Hopscotch For Threes Mat
Skip Counting by 2s Stencil
MGSEK.CC.4cUnderstand that each successive number name refers to a quantity that is one larger.Skip Counting Mat by 2's
Hopscotch For Threes Mat
Skip Counting by 2s Stencil
MGSEK.CC.5Count to answer "how many?" questions.Skip Counting Mat by 2's
Hopscotch For Threes Mat
Skip Counting by 2s Stencil
MGSEK.CC.5aCount to answer "how many?" questions about as many as 20 things arranged in a variety of ways (a line, a rectangular array, or a circle), or as many as 10 things in a scattered configuration.
MGSEK.CC.5bGiven a number from 1-20 count out that many objects.
MGSEK.CC.5cIdentify and be able to count pennies within 20. (Use pennies as manipulatives in multiple mathematical contexts.)
Compare Numbers
MGSEK.CC.6Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g. by using matching and counting strategies.Skip Counting by 2's Mat
Skip Counting by 2's Stencil
MGSEK.CC.7Compare two numbers between 1 and 10 presented as written numerals.Number Line 1-10 Mat
K.OA. Operations and Algebraic ThinkingUnderstand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
MGSEK.OA.1Represent addition and subtraction with objects, fingers, mental images, drawing, sounds (e.g. claps,) acting out situations, verbal explanations, expressions, or equations.Skip Counting by 2's Mat
Skip Counting by 2's Stencil
MGSEK.OA.2Solve addition and subtraction word problems, and add and subtract within 10 e.g. by using objects or drawings to represent the problem.Skip Counting by 2's Mat
Skip Counting by 2's Stencil
MGSEK.OA.3Decompose numbers less than or equal to 10 into pairs in more than one way, e.g. by using objects or drawings, and record each decomposition by a drawing or equation. (drawings need not include an equation).Number Line 1-10 Floor Mat
MGSEK.OA.4For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g. by using objects or drawings, and record the answer with a drawing or equation.Number Line 1-10 Floor Mat
MGSEK.OA.5Fluently add and subtract within 5.Number Line 1-10 Floor Mat
K.NBT. Number and Operations in Base TenWork with numbers 11-19 to gain foundation for place value.
MGSEK.NBT.1Compose and decompose numbers from 11-19 into ten ones and some further ones to understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones, (e.g. by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g. 18 = 10 + 8).Place Value Hop Mat P1
Number Line 1-10 Floor Mat
K.MD. Measurement and DataDescribe and compare measurable attributes.
MGSEK.MD.1Describe several measurable attributes of an object, such as length or weight. For example, a student may describe a shoe as, “This shoe is heavy! It is also really long!”
MGSEK.MD.2Directly compare two objects with a measurable attribute in common to see which object has "more of" / "less of" the attribute and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.
Classify objects and count the number of objects in each category.
MGSEK.MD.3Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.Number Line 1-10 Floor Mat
K.G. GeometryIdentify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
MGSEK.G.1Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.My First Shapes Hop
MGSEK.G.2Correctly name shapes regardless of their orientations or overall size.My First Shapes Hop
Geometric Shapes Hop
MGSEK.G.3Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid").
Analyze compare create and compose shapes.
MGSEK.G.4Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g. number of sides and vertices/ "corners") and other attributes (e.g. having sides of equal length).My First Shapes Hop
MGSEK.G.5Model shapes in the world by building shapes from components (e.g. sticks and clay balls) and drawing shapes.My First Shapes Hop
MGSEK.G.6Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?”My First Shapes Hop

1.OAOperations and Algebraic ThinkingRepresent and solve problems involving addition and subtraction.
MGSE1.OA.1Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g. by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.Skip Counting by 2's Mat
Skip Counting by 2's Stencil
MGSE1.OA.2Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g. by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.Skip Counting by 2's Mat
Skip Counting by 2's Stencil
Understand and apply properties of operations and the relationship between addition and subtraction.
MGSE1.OA.3Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)Skip Counting by 2's Mat
Hopscotch for Threes Mat
Skip Counting by 2's Stencil
MGSE1.OA.4Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8.Skip Counting by 2's Mat
Skip Counting by 2's Stencil
MGSE1.OA.5Relate counting to addition and subtraction (e.g. by counting on 2 to add 2).Skip Counting by 2's Mat
Skip Counting by 2's Stencil
MGSE1.OA.6Add and subtract within 20.Skip Counting by 2's Mat
Skip Counting by 2's Stencil
MGSE1.OA.6aUse strategies such as counting on; making ten (e.g. 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g. 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g. knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g. adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
MGSE1.OA.6bFluently add and subtract within 10.
Work with addition and subtraction equations.
MGSE1.OA.7Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.Skip Counting by 2's Mat
Skip Counting by 2's Stencil
MGSE1.OA.8Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 +___ = 11, 5 = ___ – 3, 6 + 6 = ___Skip Counting by 2's Mat
Skip Counting by 2's Stencil
1.NBTNumber and Operations in Base TenExtend the counting sequence
MGSE1.NBT.1Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.Add/Subtract Floor Mat
Understand place value.
MGSE1.NBT.2Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
MGSE1.NBT.2a10 can be thought of as a bundle of ten ones — called a “ten.”Add/Subtract Floor Mat
MGSE1.NBT.2bThe numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones (and 0 ones).Add/Subtract Floor Mat
MGSE1.NBT.2cThe numbers 10 20 30 40 50 60 70 80 90 refer to one two three four five six seven eight or nine tens (and 0 ones).Add/Subtract Floor Mat
Hop by Tens Mat
MGSE1.NBT.3Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, = , and <.Add/Subtract Floor Mat
Use place value understanding and properties of operations to add and subtract.
MGSE1.NBT.4Add within 100, including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of 10 (e.g. 24 + 9, 13 + 10, 27 + 40), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.Add/Subtract Floor Mat
MGSE1.NBT.5Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.Add/Subtract Floor Mat
MGSE1.NBT.6Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. (70 – 30, 30 – 10, 60 – 60)Add/Subtract Floor Mat
MGSE1.NBT.7Identify dimes, and understand ten pennies can be thought of as a dime. (Use dimes as manipulatives in multiple mathematical contexts.)
1.MDMeasurement and DataMeasure lengths indirectly and by iterating length units.
MGSE1.MD.1Order three objects by length; compare the lengths of two objects indirectly by using a third object.
MGSE1.MD.2Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. (Iteration)
Tell and write time.
MGSE1.MD.3Tell and write time in hours and half-hours using analog and digital clocks.Clock Hop Floor Mat
Represent and interpret data.
MGSE1.MD.4Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.
1.GGeometryReason with shapes and their attributes.
MGSE1.G.1Distinguish between defining attributes (e.g. triangles are closed and three-sided) versus non-defining attributes (e.g. color, orientation, overall size); build and draw shapes to possess defining attributes.Geometric Shapes Hop
MGSE1.G.2Compose two-dimensional shapes (rectangles, square, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prism, right circular cones, and right circular cylinders) to create a composite shape and compose new shapes from the composite shape. This is important for the future development of spatial relations which later connects to developing understanding of area, volume, and fractions.
MGSE1.G.3Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.Fraction Walk Halves/Fourths
Fraction Walk Thirds/Sixths
Equivalent Fraction Hop Mat

2.OAOperations and Algebraic ThinkingRepresent and solve problems involving addition and subtraction.
MGSE2.OA.1Use addition and subtraction within 100 to solve one- and two-step word problems by using drawings and equations with a symbol for the unknown number to represent the problem. Problems include contexts that involve adding to, taking from, putting together/taking apart (part/part/whole) and comparing with unknowns in all positions.
MGSE2.OA.2Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.Skip Counting by 2's Mat
Hopscotch for Threes Mat
Skip Counting by 2's Stencil
Work with equal groups of objects to gain foundations for multiplication.
MGSE2.OA.3Determine whether a group of objects (up to 20) has an odd or even number of members, e.g. by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.Skip Counting by 2's Mat
Skip Counting by 2's Stencil
MGSE2.OA.4Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.
2.NBTNumber and Operations in Base TenUnderstand the place value system.
MGSE2.NBT.1Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g. 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
MGSE2.NBT.1a100 can be thought of as a bundle of ten tens — called a “hundred.”Place Value Mat P1
Hop By Hundreds
MGSE2.NBT.1bThe numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).Place Value Mat P1
Hop By Hundreds
MGSE2.NBT.2Count within 1000; skip-count by 5s, 10s, and 100s.Place Value Mat P1
Hop By Hundreds
MGSE2.NBT.3Read and write numbers to 1000 using base-ten numerals, number names and expanded form.Place Value Mat P1
MGSE2.NBT.4Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.Place Value Mat P1
Use place value understanding and properties of operation to add and subtract.
MGSE2.NBT.5Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.Add/Subtract Floor Mat
Place Value Mat P1
MGSE2.NBT.6Add up to four two-digit numbers using strategies based on place value and properties of operations.Add/Subtract Floor Mat
Place Value Mat P1
MGSE2.NBT.7Add and subtract within 1000 using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method.Add/Subtract Floor Mat
Place Value Mat P1
MGSE2.NBT.8Mentally add 10 or 100 to a given number 100–900 and mentally subtract 10 or 100 from a given number 100–900.Add/Subtract Floor Mat
Place Value Mat P1
MGSE2.NBT.9Explain why addition and subtraction strategies work, using place value and the properties of operations.Add/Subtract Floor Mat
Place Value Mat P1
2.MDMeasurement and DataMeasure and estimate lengths in standard units.
MGSE2.MD.1Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.Measurement Hop
MGSE2.MD.2Measure the length of an object twice, using length units of different measurements; describe how the two measurements relate to the size of the unit chosen. Understand the relative size of units in different systems of measurement. For example, an inch is longer than a centimeter. (Students are not expected to convert between systems of measurement.)Measurement Hop
MGSE2.MD.3Estimate lengths using units of inches, feet, centimeters, and meters.Measurement Hop
MGSE2.MD.4Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.Measurement Hop
Relate addition and subtraction to length.
MGSE2.MD.5Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units e.g. by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.Add/Subtract Floor Mat
MGSE2.MD.6Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2 …, and represent whole-number sums and differences within 100 on a number line diagram.Add/Subtract Floor Mat
Work with time and money.
MGSE2.MD.7Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.Clock Hop Floor Mat
MGSE2.MD.8Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using \$ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies how many cents do you have?Dollar Hop Mat
Represent and interpret data.
MGSE2.MD.9Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.Cartesian Coordinate Hop Mat
MGSE2.MD.10Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.Cartesian Coordinate Hop Mat
2.GGeometryReason with shapes and their attributes.
MGSE2.G.1Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.Geometric Shapes Hop
MGSE2.G.2Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.Equivalent Fraction Hop Floor Mat
MGSE2.G.3Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.Unit Circle Hop Mat
Fraction Walk Halves/Fourths
Fraction Walk Thirds/Sixths
Equivalent Fraction Hop Floor Mat

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