## Want to know how our mats align with your current state standards? Check out these lists to help you easily integrate our math mats into your curriculum.

*We are currently working to add more state standards. Please contact us if you are looking for a particular state standard!*

### Common Core State Standards

Kindergarten Math

Standard | Description of Standard | Corresponding Floor Mat |
---|---|---|

K.CC Counting and Cardinality | Know number names and the count sequence | |

CC.K.CC.1 | Count to 100 by ones and by tens. | Add/Subtract Mat Hop by Tens Mat Hopscotch for Threes Mat |

CC.K.CC.2 | Count 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.3 | Write 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 Cardinality | Count to tell the number of objects. | |

CC.K.CC.4 | Understand the relationship between numbers and quantities; connect counting to cardinality. | Add/Subtract Mat Hopscotch for Threes Mat |

CC.K.CC.4a | When 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 Add/Subtract Mat Hopscotch for Threes Mat |

CC.K.CC.4b | Understand 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 Add/Subtract Mat Hopscotch for Threes Mat |

CC.K.CC.4c | Understand that each successive number name refers to a quantity that is one larger. | Skip Counting by 2s Mat Add/Subtract Mat Hopscotch for Threes Mat |

CC.K.CC.5 | Count to answer βhow many?β 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 Cardinality | Compare numbers. | |

CC.K.CC.6 | Identify 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.7 | Compare two numbers between 1 and 10 presented as written numerals. | Number Line 1-10 Floor Mat |

K.OA Operations and Algebraic Thinking | Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. | |

CC.K.OA.1 | Represent 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.2 | Solve 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.3 | Decompose 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.4 | For 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.5 | Fluently add and subtract within 5. | Number Line 1-10 Floor Mat |

K.NBT Number and Operations in Base Ten | Work with numbers 11β19 to gain foundations for place value. | |

CC.K.NBT.1 | Compose 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.1 | Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. | Attribute Word Mat |

CC.K.MD.2 | Directly compare two objects with a measurable attribute in common, to see which object has βmore ofβ/βless ofβ 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.3 | Classify 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.1 | Describe 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.2 | Correctly name shapes regardless of their orientations or overall size. | My First Shapes Hop Geometric Shapes Hop |

CC.K.G.3 | Identify shapes as two-dimensional (lying in a plane, βflatβ) or three-dimensional (βsolidβ). | My First Shapes Hop |

K.G Geometry | Analyze, compare, create, and compose shapes. | |

CC.K.G.4 | Analyze 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/βcornersβ) and other attributes (e.g., having sides of equal length). | My First Shapes Hop |

CC.K.G.5 | Model 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.6 | Compose simple shapes to form larger shapes. For example, “can you join these two triangles with full sides touching to make a rectangle?β | My First Shapes Hop |

First Grade Math

Standard | Description of Standard | Corresponding Floor Mat |
---|---|---|

1.OA Operations and Algebraic Thinking | Represent and solve problems involving addition and subtraction. | |

CC.1.OA.1 | Use 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.2 | Solve 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 Thinking | Understand and apply properties of operations and the relationship between addition and subtraction. | |

CC.1.OA.3 | Apply 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.4 | Understand subtraction as an unknown-addend problem. For example, subtract 10 β 8 by finding the number that makes 10 when added to 8. | Skip Counting by 2s Mat |

1.OA Operations and Algebraic Thinking | Add and subtract within 20. | |

CC.1.OA.5 | Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). | Skip Counting by 2s Mat |

CC.1.OA.6 | Add 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 β 4 = 13 β 3 β 1 = 10 β 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 β 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 Thinking | Work with addition and subtraction equations. | |

CC.1.OA.7 | Understand 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 β 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. | Skip Counting by 2s Mat |

CC.1.OA.8 | Determine 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 = οΌΏ β 3, 6 + 6 = οΌΏ. | Skip Counting by 2s Mat |

1.NBT Number and Operations in Base Ten | Extend the counting sequence. | |

CC.1.NBT.1 | Count 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 Ten | Understand place value. | |

CC.1.NBT.2 | Understand 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.2a | 10 can be thought of as a bundle of ten ones β called a βten.β | Place Value Mat (P1) |

CC.1.NBT.2b | 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 Mat (P1) |

CC.1.NBT.2c | 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). | Place Value Mat (P1) |

CC.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 Mat (P1) |

1.NBT Number and Operations in Base Ten | Use place value understanding and properties of operations to add and subtract. | |

CC.1.NBT.4 | Add 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.5 | Given 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.6 | Subtract 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 Data | Measure lengths indirectly and by iterating length units. | |

CC.1.MD.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | |

CC.1.MD.2 | Measure 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 Data | Tell and write time. | |

CC.1.MD.3 | Tell and write time in hours and half-hours using analog and digital clocks. | Clock Hop |

1.MD Measurement and Data | Represent and interpret data. | |

CC.1.MD.4 | Organize, 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 Geometry | Reason with shapes and their attributes. | |

CC.1.G.1 | Distinguish 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.2 | Compose 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 βright rectangular prism.β) | |

CC.1.G.3 | Partition 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 |

Second Grade Math

Standard | Description of Standard | Corresponding Floor Mat |
---|---|---|

2.OA Operations and Algebraic Thinking | Represent and solve problems involving addition and subtraction. | |

CC.2.OA.1 | Use 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 Thinking | Add and subtract within 20. | |

CC.2.OA.2 | Fluently 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 Thinking | Work with equal groups of objects to gain foundations for multiplication. | |

CC.2.OA.3 | 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 2s; write an equation to express an even number as a sum of two equal addends. | Skip Counting by 2s Mat Add/Subtract Floor Mat |

CC.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. | |

2. NBT Number and Operations in Base Ten | Understand place value. | |

CC.2.NBT.1 | Understand 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.1a | 100 can be thought of as a bundle of ten tens β called a βhundred.β | Place Value Mat (P1) Hopping by 100s Mat |

CC.2.NBT.1b | 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). | Place Value Mat (P1) Hopping by 100s Mat |

CC.2.NBT.2 | CC.2.NBT.2 Understand place value. Count within 1000; skip-count by 5s, 10s, and 100s. | Place Value Mat (P1) Hopping by 100s Mat Add/Subtract Mat |

CC.2.NBT.3 | CC.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.4 | CC.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 Ten | Use place value understanding and properties of operations to add and subtract. | |

CC.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. | Place Value Mat (P1) Add/Subtract Mat |

CC.2.NBT.6 | Add up to four two-digit numbers using strategies based on place value and properties of operations. | Place Value Mat (P1) Add/Subtract Mat |

CC.2.NBT.7 | Add 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) Add/Subtract Mat |

CC.2.NBT.8 | Mentally 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) Add/Subtract Mat |

CC.2.NBT.9 | Explain 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) Add/Subtract Mat |

2.MD Measurement and Data | Measure and estimate lengths in standard units. | |

CC.2.MD.1 | Measure 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.2 | Measure 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.3 | Estimate lengths using units of inches, feet, centimeters, and meters. | Measurement Hop |

CC.2.MD.4 | Measure 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 Data | Relate addition and subtraction to length. | |

CC.2.MD.5 | Use 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.6 | Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, β¦ , and represent whole-number sums and differences within 100 on a number line diagram. | Add/Subtract Mat |

2.MD Measurement and Data | Work with time and money. | |

CC.2.MD.7 | Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. | Clock Hopa |

CC.2.MD.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ (dollars) and Β’ (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.9 | Generate 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.10 | Draw 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 Geometry | Reason with shapes and their attributes. | |

CC.2.G.1 | Recognize 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.2 | Partition 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.3 | Partition 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 |

Third Grade Math

Standard | Description of Standard | Corresponding Floor Mat |
---|---|---|

3.OA Operations and Algebraic Thinking | Represent and solve problems involving multiplication and division. | |

CC.3.OA.1 | Interpret products of whole numbers, e.g., interpret 5 Γ 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 Γ 7. | Skip Counting Mats Set Factor Fun Hop Mat Multiplication Hop |

CC.3.OA.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 Γ· 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. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 Γ· 8. | Skip Counting Mats Set Multiplication Hop |

CC.3.OA.3 | Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. | Skip Counting Mats Set Multiplication Hop |

CC.3.OA.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 Γ ? = 48, 5 = __Γ· 3, 6 Γ 6 = ?. | Skip Counting Mats Set Multiplication Hop |

3.OA Operations and Algebraic Thinking | Understand properties of multiplication and the relationship between multiplication and division. | |

CC.3.OA.5 | Apply properties of operations as strategies to multiply and divide. Examples: If 6 Γ 4 = 24 is known, then 4 Γ 6 = 24 is also known. (Commutative property of multiplication.) 3 Γ 5 Γ 2 can be found by 3 Γ 5 = 15 then 15 Γ 2 = 30, or by 5 Γ 2 = 10 then 3 Γ 10 = 30. (Associative property of multiplication.) Knowing that 8 Γ 5 = 40 and 8 Γ 2 = 16, one can find 8 Γ 7 as 8 Γ (5 + 2) = (8 Γ 5) + (8 Γ 2) = 40 + 16 = 56. (Distributive property.) (Students need not use formal terms for these properties.) | Skip Counting Mats Set Multiplication Hop |

CC.3.OA.6 | Understand division as an unknown-factor problem. For example, divide 32 Γ· 8 by finding the number that makes 32 when multiplied by 8. | Skip Counting Mats Set Factor Fun Hop Mat Multiplication Hop |

3.OA Operations and Algebraic Thinking | Multiply and divide within 100. | |

CC.3.OA.7 | Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 Γ 5 = 40, one knows 40 Γ· 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of one-digit numbers. | Skip Counting Mats Set Factor Fun Hop Mat Multiplication Hop Hopscotch for Threes Mat |

3.OA Operations and Algebraic Thinking | Solve problems involving the four operations, and identify and explain patterns in arithmetic. | |

CC.3.OA.8 | Solve two-step word problems using the four operations. 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. (This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).) | Skip Counting Mats Set Add/Subtract Floor Mat Operations Floor Mat |

CC.3.OA.9 | Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. | Skip Counting Mats Set Add/Subtract Floor Mat Hopscotch for Threes Mat |

3.NBT Number and Operations in Base Ten | Use place value understanding and properties of operations to perform multi-digit arithmetic. | |

CC.3.NBT.1 | Use place value understanding to round whole numbers to the nearest 10 or 100. | Place Value Mat (P1) |

CC.3.NBT.2 | Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. (A range of algorithms may be used.) | Place Value Mat (P1) Add/Subtract Floor Mat |

CC.3.NBT.3 | Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 Γ 80, 5 Γ 60) using strategies based on place value and properties of operations. (A range of algorithms may be used.) | Skip Counting Mats Set |

3.NF Numbers and Operations – Fractions | Develop understanding of fractions as numbers. | |

CC.3.NF.1 | Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) | Fraction Walk (Halves/Quarters) Fraction Walk (Thirds/Sixths) Equivalent Fraction Hop Floor Mat |

CC.3.NF.2 | Understand a fraction as a number on the number line; represent fractions on a number line diagram. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) | Fraction Walk (Halves/Quarters) Fraction Walk (Thirds/Sixths) Equivalent Fraction Hop Floor Mat |

CC.3.NF.2a | Represent a fraction 1/b on a number line diagram 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 based at 0 locates the number 1/b on the number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) | Fraction Walk (Halves/Quarters) Fraction Walk (Thirds/Sixths) Equivalent Fraction Hop Floor Mat |

CC.3.NF.2b | Represent a fraction a/b on a number line diagram 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. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) | Fraction Walk (Halves/Quarters) Fraction Walk (Thirds/Sixths) Equivalent Fraction Hop Floor Mat |

CC.3.NF.3 | Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) | Fraction Walk (Halves/Quarters) Fraction Walk (Thirds/Sixths) Equivalent Fraction Hop Floor Mat |

CC.3.NF.3a | Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) | Fraction Walk (Halves/Quarters) Fraction Walk (Thirds/Sixths) Equivalent Fraction Hop Floor Mat |

CC.3.NF.3b | Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3), Explain why the fractions are equivalent, e.g., by using a visual fraction model. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) | Fraction Walk (Halves/Quarters) Fraction Walk (Thirds/Sixths) Equivalent Fraction Hop Floor Mat |

CC.3.NF.3c | Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) | Fraction Walk (Halves/Quarters) Fraction Walk (Thirds/Sixths) Equivalent Fraction Hop Floor Mat |

CC.3.NF.3d | Compare two fractions with the same numerator or the same denominator, by reasoning about their size, Recognize that valid 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., by using a visual fraction model. (Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.) | Fraction Walk (Halves/Quarters) Fraction Walk (Thirds/Sixths) Equivalent Fraction Hop Floor Mat Operations Floor Mat |

3.MD Measurement and Data | Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. | |

CC.3.MD.1 | Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. | Clock Hop |

CC.3.MD.2 | Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm^3 and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems (problems involving notions of βtimes as much.β) | |

3.MD Measurement and Data | Represent and interpret data. | |

CC.3.MD.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step βhow many moreβ and βhow many lessβ problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. | Cartesian Coordinate Hop |

CC.3.MD.4 | Generate 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 unitsβwhole numbers, halves, or quarters. | Cartesian Coordinate Hop Measurement Hop |

3.MD Measurement and Data | Geometric measurement: understand concepts of area and relate area to multiplication and to addition. | |

CC.3.MD.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | |

CC.3.MD.5a | A square with side length 1 unit, called βa unit square,β is said to have βone square unitβ of area, and can be used to measure area. | |

CC.3.MD.5b | 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. | |

CC.3.MD.6 | Geometric measurement: understand concepts of area and relate area to multiplication and to addition. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). | |

CC.3.MD.7 | Relate area to the operations of multiplication and addition. | Skip Counting Mat Set |

CC.3.MD.7a | Find 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. | Skip Counting Mat Set |

CC.3.MD.7b | Multiply 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. | Skip Counting Mat Set |

CC.3.MD.7c | Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a Γ b and a Γ c. Use area models to represent the distributive property in mathematical reasoning. | |

CC.3.MD.7d | Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems. | |

3.MD Measurement and Data | Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures. | |

CC.3.MD.8 | Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different area or with the same area and different perimeter. | |

3.G Geometry | Reason with shapes and their attributes. | |

CC.3.G.1 | Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. | Geometric Shapes Hop |

CC.3.G.2 | Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part is 1/4 of the area of the shape. | Fraction Walk (Halves/Quarters) Fraction Walk (Thirds/Sixths) Equivalent Fraction Hop Floor Mat |

Fourth Grade Math

Standard | Description of Standard | Corresponding Floor Mat |
---|---|---|

CC.4.OA.1 | Use 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.2 | Use 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.3 | Use 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.4 | Gain 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.5 | Generate 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 βAdd 3β 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.1 | Generalize 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 Γ· 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.2 | Generalize 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.3 | Generalize 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) Add/Subtract Floor Mat |

CC.4.NBT.4 | Use 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.5 | Use 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.6 | Use 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.1 | Extend understanding of fraction equivalence and ordering. Explain why a fraction a/b is equivalent to a fraction (n Γ a)/(n Γ 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.2 | Extend 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.3 | Build 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.3a | Understand 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.3b | Decompose 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.3c | Add 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.3d | Solve 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.4 | Build 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.4a | Understand 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 Γ (1/4), recording the conclusion by the equation 5/4 = 5 Γ (1/4). | Fraction Walk (Halves/Quarters) Fraction Walk (Thirds/Sixths) |

CC.4.NF.4b | Understand 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 Γ (2/5) as 6 Γ (1/5), recognizing this product as 6/5. (In general, n Γ (a/b) = (n Γ a)/b.) | Fraction Walk (Halves/Quarters) Fraction Walk (Thirds/Sixths) |

CC.4.NF.4c | Solve 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.5 | Understand 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.6 | Understand 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.7 | Understand 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.1 | Solve 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), β¦. | Measurement Hop Clock Hop |

CC.4.MD.2 | Solve 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.3 | Solve 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.4 | Represent 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.5 | Geometric 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.5a | 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 βone-degree angle,β and can be used to measure angles. | Unit Circle Hop Mat |

CC.4.MD.5b | An 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.6 | Geometric 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.7 | Geometric 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.1 | Draw 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.2 | Draw 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.3 | Draw 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 |

Fifth Grade Math

Standard | Description of Standard | Corresponding Floor Mat |
---|---|---|

CC.5.OA.1 | Write and interpret numerical expressions. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. | PEMDAS Hop |

CC.5.OA.2 | Write and interpret numerical expressions. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation βadd 8 and 7, then multiply by 2β as 2 Γ (8 + 7). Recognize that 3 Γ (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. | PEMDAS Hop |

CC.5.OA.3 | Analyze 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 βAdd 3β and the starting number 0, and given the rule βAdd 6β 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.1 | Understand 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.2 | Understand 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.3 | Understand the place value system. Read, write, and compare decimals to thousandths. | Place Value Hop – Decimals (P3) |

CC.5.NBT.3a | Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 Γ 100 + 4 Γ 10 + 7 Γ 1 + 3 Γ (1/10) + 9 Γ (1/100) + 2 Γ (1/1000). | Place Value Hop – Decimals (P3) PEMDAS Hop |

CC.5.NBT.3b | Compare 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.4 | Understand the place value system. Use place value understanding to round decimals to any place. | Place Value Hop – Decimals (P3) |

CC.5.NBT.5 | Perform 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.6 | Perform 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.7 | Perform 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.1 | Use 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.2 | Use 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.3 | Apply 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 Γ· 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.4 | Apply 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.4a | Interpret the product (a/b) Γ q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a Γ q Γ· b. For example, use a visual fraction model to show (2/3) Γ 4 = 8/3, and create a story context for this equation. Do the same with (2/3) Γ (4/5) = 8/15. (In general, (a/b) Γ (c/d) = ac/bd.) | Fraction Walk (Halves/Quarters) Fraction Walk (Thirds/Sixths) |

CC.5.NF.4b | Find 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.5 | Apply 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 = (nΓa) / (nΓb) to the effect of multiplying a/b by 1. | Fraction Walk (Halves/Quarters) Fraction Walk (Thirds/Sixths) Factor Fun Hop |

CC.5.NF.6 | Apply 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.7 | Apply 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.7a | Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) Γ· 4 and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) Γ· 4 = 1/12 because (1/12) Γ 4 = 1/3. | Fraction Walk (Halves/Quarters) Fraction Walk (Thirds/Sixths) |

CC.5.NF.7b | Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 Γ· (1/5) and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 Γ· (1/5) = 20 because 20 Γ (1/5) = 4. | Fraction Walk (Halves/Quarters) Fraction Walk (Thirds/Sixths) |

CC.5.NF.7c | Solve 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.1 | Convert 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.2 | Represent 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.3 | Geometric 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 βunit cube,β is said to have βone cubic unitβ 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.4 | Geometric 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.5 | Geometric 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.5A | Find 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.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. | |

CC.5.MD.5C | Recognize 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.1 | Graph 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.2 | Graph 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.3 | Classify 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.4 | Classify 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

Kindergarten Math

Standard | Description of Standard | Corresponding Floor Mat |
---|---|---|

Counting and Cardinality | ||

NY-K.CC.1 | Count to 100 by ones and by tens. | Add/Subtract, Hop by Tens, Hundred Number Grid |

NY-K.CC.2 | Count 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.3 | Write 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.4 | Understand 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.4a | When 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.4b | Understand 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.4c | Understand 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.4d | Understand 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.5a | Answer 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., βHow many_____ are there?β | 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.5b | Given a number from 1β20, count out that many objects. | Skip Counting by 2’s, Add/Subtract, Hundred Number Grid, Number Word Hop |

NY-K.CC.6 | Identify 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.7 | Compare 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.1 | Represent 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.2a | Add 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.2b | Solve 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.3 | Decompose 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.4 | Find 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.5 | Fluently 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.6 | Duplicate, extend, and create simple patterns using concrete objects. | Add/Subtract, Hundred Number Grid |

Number and Operations in Base Ten | ||

NY-K.NBT.1 | Compose 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.1 | Describe 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.2 | Directly compare two objects with a common measurable attribute and describe the difference. | Measurement Hop, My First Shapes Hop, Attribute Word Hop |

NY-K.MD.3 | Classify 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.4 | Explore coins (pennies, nickels, dimes, and quarters) and begin identifying pennies and dimes. | Money Hop Mat, Dollar Hop |

Geometry | ||

NY-K.G.1 | Describe 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.2 | Name shapes regardless of their orientation or overall size. | My First Shapes Hop, Connect the Dots |

NY-K.G.3 | Understand the difference between two-dimensional (lying in a plane, βflatβ) and three-dimensional (βsolidβ) shapes. | My First Shapes Hop, Connect the Dots |

NY-K.G.4 | Analyze, 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/βcornersβ, or having sides of equal length. | My First Shapes Hop, Connect the Dots |

NY-K.G.5 | Model 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.6 | Compose larger shapes from simple shapes. e.g., join two triangles to make a rectangle. | My First Shapes Hop, Connect the Dots |

First Grade Math

Standard | Description of Standard | Corresponding Floor Mat |
---|---|---|

Operations and Algebraic Thinking | ||

NY-1.OA.1 | Use 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.2 | Solve 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., β’ If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) β’ 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.) | 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.4 | Understand subtraction as an unknown- addend problem within 20. e.g., subtract 10 β 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.5 | Relate 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.6a | Add and subtract within 20. Use strategies such as: β’ counting on; β’ making ten; β’ decomposing a number leading to a ten; β’ using the relationship between addition and subtraction; and β’ 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.6b | Fluently 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.7 | Understand 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 β 1 5 + 2 = 2 + 5 4 + 1 = 5 + 2 | Add/Subtract, Hundred Number Grid |

NY-1.OA.8 | Determine 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 οΌΏ β 3 = 5 6 + 6 = | Add/Subtract, Whole Part Number Bond, Hundred Number Grid |

Number and Operations in Base Ten | ||

NY-1.NBT.1 | Count 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, Hundred Number Grid |

NY-1.NBT.2 | Understand that the two digits of a two-digit number represent amounts of tens and ones. | Place Value |

NY-1.NBT.2a | Understand 10 can be thought of as a bundle of ten ones, called a “ten”. | Place Value |

NY-1.NBT.2b | Understand 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.2c | Understand 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.3 | NY-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 |

NY-1.NBT.4 | Add within 100, including: β’ a two-digit number and a one-digit number; β’ 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.5 | Given 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.6 | Subtract multiples of 10 from multiples of 10 in the range 10-90 using β’ concrete models or drawings, and β’ 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.1 | Order three objects by length; compare the lengths of two objects indirectly by using a third object. | Measurement Hop, Open Number Line |

NY-1.MD.2 | Measure the length of an object using same- size βlength unitsβ placed end to end with no gaps or overlaps. Express the length of an object as a whole number of βlength units.β Note: βLength unitsβ could include cubes, paper clips, etc. | Measurement Hop |

NY-1.MD.3a | Tell 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, oβclock and half past. | Clock Hop |

NY-1.MD.3b | Recognize and identify coins (penny, nickel, dime, and quarter) and their value and use the cent symbol (Β’) appropriately. | Money Hop Mat, Dollar Hop |

NY-1.MD.3c | Count 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 Β’ ) | Money Hop Mat, Dollar Hop |

NY-1.MD.4 | Organize, 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.1 | Distinguish between defining attributes versus non-defining attributes for a wide variety of shapes. Build and/or draw shapes to possess defining attributes. e.g., β’ A defining attribute may include, but is not limited to: triangles are closed and three-sided. β’ Non-defining attributes include, but are not limited to: color, orientation, and overall size. NoteΒ onΒ 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.2 | Compose 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 βright rectangular prism.β | My First Shapes Hop, Connect the Dots |

NY-1. G.3 | Partition 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 |

Second Grade Math

Standard | Description of Standard | Corresponding Floor Mat |
---|---|---|

Operations and Algebraic Thinking | ||

NY-2.OA.1a | Use 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.2a | Fluently add and subtract within 20 using mental strategies. Strategies could include: β’ counting on; β’ making ten; β’ decomposing a number leading to a ten; β’ using the relationship between addition and subtraction; and β’ 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 2βs. | Skip Counting by 2’s, Make Sums Set, Place Value |

NY-2.OA.3b | Write an equation to express an even number as a sum of two equal addends. | Doubles Hop Scotch |

NY-2.OA.4 | NY-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.1 | Understand 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.1a | Understand 100 can be thought of as a bundle of ten tens, called a “hundred.” | Place Value, Hop by Ten |

NY-2.NBT.1b | Understand 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. 2 | Count within 1000; skip-count by 5βs, 10βs, and 100βs. | 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. 4 | NY-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. 6 | NY-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. 7a | Add and subtract within 1000, using β’ concrete models or drawings, and β’ 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. 7b | Understand 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. 8 | Mentally 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. 9 | Explain 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.1 | Measure 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.2 | Measure the length of an object twice, using different βlength unitsβ for the two measurements; describe how the two measurements relate to the size of the unit chosen. | Measurement Hop |

NY-2.MD.3 | Estimate lengths using units of inches, feet, centimeters, and meters. | Measurement Hop |

NY-2.MD.4 | Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard βlength unit.β | Measurement Hop |

NY-2.MD.6 | Use 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.6 | Represent whole numbers as lengths from 0 on a number line with equally spaced points corresponding to the numbers 0, 1, 2, β¦, 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.7 | Tell 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.8a | Count 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.8b | Solve real world and mathematical problems within one dollar involving quarters, dimes, nickels, and pennies, using the Β’ (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.9 | Generate 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.10 | Draw 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.1 | Classify two-dimensional figures as polygons or non-polygons. | My First Shapes, Geometric Shapes, Connect the Dots |

NY-2.G.2 | Partition 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.3 | Partition 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 |

Third Grade Math

Standard | Description of Standard | Corresponding Floor Mat |
---|---|---|

Operations and Algebraic Thinking | ||

NY-3.OA.1 | Interpret products of whole numbers. e.g., Interpret 5 Γ 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 Γ 7. | Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch, Hopscotch for Threes, Hopscotch for Twos |

NY-3.OA.2 | Interpret whole-number quotients of whole numbers. e.g., Interpret 56 Γ· 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 Γ· 8. | Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch, Hopscotch for Threes, Hopscotch for Twos, |

NY-3.OA.3 | Use 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.4 | Determine 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 Γ ? = 48, 5 = Γ· 3, 6 Γ 6 = ?. | Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch, Hopscotch for Threes, Hopscotch for Twos, |

NY-3.OA.5 | Apply properties of operations as strategies to multiply and divide. e.g., β’ If 6 Γ 4 = 24 is known, then 4 Γ 6 = 24 is also known. (Commutative property of multiplication) β’ 3 Γ 5 Γ 2 can be found by 3 Γ 5 = 15, then 15 Γ 2 = 30, or by 5 Γ 2 = 10, then 3 Γ 10 = 30. (Associative property of multiplication) β’ Knowing that 8 Γ 5 = 40 and 8 Γ 2 = 16, one can find 8 Γ 7 as 8 Γ (5 + 2) = (8 Γ 5) + (8 Γ 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. | |

NY-3.OA.6 | Understand division as an unknown-factor problem. e.g., Find 32 Γ· 8 by finding the number that makes 32 when multiplied by 8. | |

NY-3.OA.7a | Fluently 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 Γ 5 = 40, one knows 40 Γ· 5 = 8. | |

NY-3.OA.7b | Know from memory all products of two one-digit numbers. 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-3.OA.8 | Solve 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.8a | Represent these problems using equations or expressions with a letter standing for the unknown quantity. | |

NY-3.OA.8b | Assess 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.9 | Identify 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.1 | Use 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.2 | Fluently 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 Γ 80, 5 Γ 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.1 | Understand a unit fraction, 1, is the quantity formed by 1 part when a whole is partitioned into b equal parts. Understand a fraction π as the quantity formed by a parts of size 1/π. Note: Fractions are limited to those with denominators 2, 3, 4, 6, and 8.” | Equivalent Fraction Hop, Fraction Walk Set |

NY-3.NF.2 | Understand 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.2a | Represent a fraction 1/π 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/π and that the endpoint of the part starting at 0 locates the number 1/π on the number line. | Equivalent Fraction Hop, Fraction Walk Set, Open Number Line |

NY-3.NF.2b | Represent a fraction ππ on a number line by marking off a lengths 1/π from 0. Recognize that the resulting interval has size π/π and that its endpoint locates the number π/π on the number line. | Equivalent Fraction Hop, Fraction Walk Set, Open Number Line |

NY-3.NF.3 | Explain 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.3a | Understand 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.3b | Recognize 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.3c | Express 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.1 | Tell 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.2a | Measure 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.2b | Add, 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 βtimes as much.β | |

NY-3.MD.3 | Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step βhow many moreβ and βhow many lessβ 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.4 | Generate 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 unitsβwhole numbers, halves, or quarters. | Measurement Hop |

NY-3.MD.5 | Recognize area as an attribute of plane figures and understand concepts of area measurement. | Number Grid, Cartesian Coordinate, Connect the Dots |

NY-3.MD.5a | Recognize a square with side length 1 unit, called βa unit square,β is said to have βone square unitβ of area, and can be used to measure area. | Number Grid, Cartesian Coordinate, Connect the Dots |

NY-3.MD.5b | Recognize 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.6 | Measure 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.7 | Relate area to the operations of multiplication and addition. | Number Grid, Cartesian Coordinate, Multiplication Hop, Connect the Dots |

NY-3.MD.7a | Find 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.7b | Multiply 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.7c | Use 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 Γ b and a Γ c. Use area models to represent the distributive property in mathematical reasoning. | Number Grid, Cartesian Coordinate, Multiplication Hop, Connect the Dots |

NY-3.MD.7d | Recognize 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.8a | Solve 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.8b | Identify 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.1 | Recognize 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 βregularβ and βirregular,β e.g., students should be able to classify an irregular pentagon as βa pentagon,β but do not need to classify it as an βirregular pentagon.β | My First Shapes Hop, Geometric Shapes, Connect the Dots |

NY-3.G.2 | Partition 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 |

Fourth Grade Math

Standard | Description of Standard | Corresponding Floor Mat |
---|---|---|

Operations and Algebraic Thinking | ||

NY-4.OA.1 | Interpret a multiplication equation as a comparison. Represent verbal statements of multiplicative comparisons as multiplication equations. e.g., β’ Interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 or 7 times as many as 5. β’ Represent βFour times as many as eight is thirty-twoβ 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.2 | Multiply 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.3 | 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. | Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch, Hopscotch for Threes, Hopscotch for Twos, Operations Hop, PEMDAS Hop |

NY-4.OA.3a | Represent 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.3b | Assess the reasonableness of answers using mental computation and estimation strategies including rounding. | |

Note: Multistep problems need not be represented by a single expression or equation. | ||

NY-4.OA.4 | 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. | Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch, Hopscotch for Threes, Hopscotch for Twos, Factor Fun |

NY-4.OA.5 | Generate 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 βAdd 3β 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.1 | 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. e.g., Recognize that 70 Γ 10 = 700 (and, therefore, 700 Γ· 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.2a | Read 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.2b | Compare 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.3 | Use 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.4 | Fluently 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.5 | 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. | Place Value (P2), PEMDAS Hop, Number Grid |

NoteΒ onΒ 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.6 | 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. NotesΒ onΒ 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.1 | Explain why a fraction π/π is equivalent to a fraction π Γ π / π Γ π 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.2 | Compare 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.3 | Understand a fraction π / π with π > 1 as a sum of fractions 1 / π. Note: 1 / π refers to the unit fraction for π / π. | Equivalent Fraction Hop, Fraction Walk Set, Open Number Line |

NY-4.NF.3a | Understand 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.3b | Decompose 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.3c | Add 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.3d | Solve 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.4 | Apply 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.4a | Understand a fraction π / π as a multiple of 1 / π. 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.4b | Understand a multiple of π / π as a multiple of 1 / π, and use this understanding to multiply a whole number by a fraction. e.g., Use a visual fraction model to express 3 Γ 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.5 | 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. e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 341/00. Notes: β’ 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. β’ 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.6 | Use decimal notation for fractions with denominators 10 or 100. e.g., β’ Rewrite 0.62 as 62 / 100 or 62 / 100 as 0.62. β’ Describe a length as 0.62 meters. β’ 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.7 | Compare 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.1 | Know relative sizes of measurement units: ft., in.; km, m, cm e.g., An inch is about the distance from the tip of your thumb to your first knuckle. A foot is the length of two-dollar bills. A meter is about the height of a kitchen counter. A kilometer is 2 Β½ 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.2 | Use 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.2a | Solve 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.2b | Represent 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.3 | Apply 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.4 | 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. 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.5 | Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. | Angle Hop |

4.MD.5a | Recognize 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 βone-degree angle,β and can be used to measure angles. | Angle Hop, Unit Circle |

4.MD.5b | Recognize 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.6 | Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. | Angle Hop |

NY-4.MD.7 | 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., using an equation with a symbol for the unknown angle measure. | Angle Hop, Unit Circle |

Geometry | ||

NY-4.G.1 | Draw 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.2a | Identify and name triangles based on angle size (right, obtuse, acute). | Angle Hop, Unit Circle |

NY-4.G.2b | Identify and name all quadrilaterals with 2 pairs of parallel sides as parallelograms. | My First Shapes Hop, Geometric Shapes |

NY-4.G.2c | Identify and name all quadrilaterals with four right angles as rectangles. | My First Shapes Hop, Geometric Shapes |

NY-4.G.3 | 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. | My First Shapes Hop, Geometric Shapes |

Fifth Grade Math

Standard | Description of Standard | Corresponding Floor Mat |
---|---|---|

Operations and Algebraic Thinking | ||

NY-5.OA.1 | Apply the order of operations to evaluate numerical expressions. e.g., β’ 6 + 8 Γ· 2 β’ (6 + 8) Γ· 2 Note: Exponents and nested grouping symbols are not included. | Operations Hop |

NY-5.OA.2 | Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. e.g., Express the calculation βadd 8 and 7, then multiply by 2β as (8 + 7) Γ 2. Recognize that 3 Γ (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.3 | 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. e.g., Given the rule βAdd 3β and the starting number 0, and given the rule βAdd 6β 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. 1 | 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 (P1, P2, P3) |

NY-5.NBT.2 | Use 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.3 | Read, write, and compare decimals to thousandths. | Place Value (P3) |

NY-5.NBT.3a | Read and write decimals to thousandths using base-ten numerals, number names, and expanded form. e.g., β’ 47.392 = 4 Γ 10 + 7 Γ 1 + 3 Γ π/ππ + 9 Γ π/πππ + 2 Γ π/ππππ β’ 47.392 = (4 Γ 10) + (7 Γ 1) + (3 Γ π/ππ ) + (9 Γ π/πππ ) + (2 Γπ/ππππ) β’ 47.392 = (4 Γ 10) + (7 Γ 1) + (3 Γ 0.1) + (9 Γ 0.01) + (2 Γ 0.001) | Place Value (P3) |

NY-5.NBT.3b | Compare 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.4 | Use place value understanding to round decimals to any place. | Place Value (P3) |

NY-5.NBT.5 | Fluently multiply multi-digit whole numbers using a standard algorithm. | Skip Counting Mats, Skip Counting Wall Banners, Multiplication Hop, Multiplication Hopscotch |

NY-5.NBT.6 | 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. Notes on and/or: β’ 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. β’ 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.7 | Using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between operations: β’ add and subtract decimals to hundredths; β’ 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 Γ· 0.05). Problems should not be so complex as to require the use of an algorithm (e.g., 0.37 Γ· 0.05). | Place Value (P3) |

Number and Operations – Fractions | ||

NY-5.NF.1 | 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. e.g., β’ 1/3 + 2/9 = 3/9 + 2/9 = 5/9 β’ 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.2 | Solve 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.3 | Interpret a fraction as division of the numerator by the denominator ( π/π = a Γ· 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.4 | Apply 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.4a | Interpret the product π/π Γ q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a Γ q Γ· b. e.g., Use a visual fraction model to show 2/3 Γ 4 = 8/3, and create a story context for this equation. Do the same with 2/3 Γ 4/5 = 8/15 . | Equivalent Fraction Hop, Fraction Walk Set, Open Number Line, Fractions, Decimals, Percentage Hop |

NY-5.NF.4b | Find 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.5 | Interpret multiplication as scaling (resizing). | Cartesian Coordinate, Number Grid |

NY-5.NF.5a | Compare 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 π/π = 5, 5 is half of 10 and 5 is 10 times larger than π/π . | Fraction Walk Set |

NY-5.NF.5b | Explain 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 π/π = π/π Γ π/π to the effect of multiplying ππ by 1. e.g., Explain why 4 Γ π/π is greater than 4. Explain why 4 Γ π/π is less than 4. ππ is equivalent to π/π because π/π Γ π/π = π/π. | Fraction Walk Set |

NY-5.NF.6 | Solve 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.7 | Apply 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.7a | Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. e.g., Create a story context for 1/3 Γ· 4 and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 1/3 Γ· 4 = 1/12 because 1/12 Γ 4 = 1/3. | Open Number Line |

NY-5.NF.7b | Interpret division of a whole number by a unit fraction, and compute such quotients. e.g., Create a story context for 4 Γ· 15 and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 Γ· 15 = 20 because 20 Γ 15 = 4. | Open Number Line |

NY-5.NF.7c | Solve 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.1 | Convert 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: β’ 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. β’ Grade 5 expectations for decimal operations are limited to work with decimals to hundredths. | |

NY-5.MD.2 | 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. 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.3 | Recognize volume as an attribute of solid figures and understand concepts of volume measurement. | |

NY-5.MD.3a | Recognize that a cube with side length 1 unit, called a βunit cube,β is said to have βone cubic unitβ of volume, and can be used to measure volume. | |

NY-5.MD.3b | Recognize 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.4 | Measure volumes by counting unit cubes, using cubic cm, cubic in., cubic ft., and improvised units | |

NY-5.MD.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | Cubed Number |

NY-5.MD.5a | Find 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 Γ w Γ h and V = B Γ 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.5c | Recognize 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.5 | Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. | |

NY-5.MD.5a | Find 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 Γ w Γ h and V = B Γ 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.5c | Recognize 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

Kindergarten Math

Standard | Description of Standard | Corresponding 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 Add/Subtract 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 Add/Subtract 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 Add/Subtract Floor Mat 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 Add/Subtract Floor Mat 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 Add/Subtract Floor Mat 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 arrangements | Number Line 1-10 Fruits and Vegetables Add/Subtract Floor Mat 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 Add/Subtract Floor Mat 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 Add/Subtract Floor Mat 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 Add/Subtract Floor Mat 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 Add/Subtract Floor Mat 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 s |