State Standards
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 “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects. | Skip Counting by 2s Mat Hopscotch for Threes Mat |
| K.CC Counting and 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 11–19 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 “more of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. | |
| K.MD Measurement and Data | Classify objects and count the number of objects in each category. | |
| CC.K.MD.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, “flat”) or three-dimensional (“solid”). | 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/“corners”) 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?” | 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 – 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 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13). | Skip Counting by 2s Mat |
| 1.OA Operations and Algebraic 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 – 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 = ＿ – 3, 6 + 6 = ＿. | 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 — called a “ten.” | 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 “right rectangular prism.”) | |
| 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 — called a “hundred.” | 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, … , 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 Hop |
| CC.2.MD.8 | Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ (dollars) and ¢ (cents) symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? | Dollar Hop Money Hop |
| Represent and interpret data. | ||
| CC.2.MD.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 × 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 × 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 ÷ 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 ÷ 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 × ? = 48, 5 = __÷ 3, 6 × 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 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15 then 15 × 2 = 30, or by 5 × 2 = 10 then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) (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 ÷ 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 × 5 = 40, one knows 40 ÷ 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 × 80, 5 × 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 “times as much.”) | |
| 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 “how many more” and “how many less” 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 units—whole 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 “a unit square,” is said to have “one square unit” 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 × b and a × 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 “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. | Add/Subtract 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 ÷ 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 × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. (Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.) | Fraction Walk (Halves/Quarters) Fraction Walk (Thirds/Sixths) Equivalent Fraction Hop Floor Mat |
| CC.4.NF.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 × (1/4), recording the conclusion by the equation 5/4 = 5 × (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 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.) | Fraction Walk (Halves/Quarters) Fraction Walk (Thirds/Sixths) |
| CC.4.NF.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. K |