• Count to 100 by ones and by tens. (K.CC.A.1) 

• Count forward beginning from a given number within the known sequence (instead of having to begin at 1). (K.CC.A.2)

• 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). (K.CC.A.3)

K.CC.A Tools for Instruction:

Count forward by 1s

Identify Numerals to 5

Identify Numbers to 5

Identify Numerals to 10

Read, Write, and Show Numbers 11 to 20

• Understand the relationship between numbers and quantities; connect counting to cardinality. (K.CC.B.4) 

  • a. 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.

  • b. 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.

  • c. Understand that each successive number name refers to a quantity that is one larger. 

• 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. (K.CC.B.5)

K.CC.B Tools for Instruction:

Count Out Up to 3

Count Up to 3

Count up to 5 Objects

Count Groups of 0-5 Objects

Rote Count to 10

Making a Set Up to 10 Objects

• 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.1 (K.CC.C.6)

• Compare two numbers between 1 and 10 presented as written numerals. (K.CC.C.7)

K.CC.C Tools for Instruction:

Identify More and Less

One More

One Less

Compare within 5

Compare within 10

Understand Teen Numbers

Composing Teen Numbers

• Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. (K.OA.A.1) 

• Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. (K.OA.A.2) 

• 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). (K.OA.A.3)

• 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. (K.OA.A.4)

• Fluently add and subtract within 5. (K.OA.A.5)

K.OA.A Tools for Instruction:

Understand Addition

Count on to Add

Subtraction

Add and Subtract 1 and 2

Make Numbers to 5

Make 6, 7, 8, and 9

Adding Numbers Within 5

Add within 5

Count on to Add

Subtracting Numbers Within 5

Subtract within 5

Adding and Subtracting Numbers Within 5

Totals of Ten

Sums of Ten

Ways to Make 10

Find Missing Partners for Totals of 10

Number Pairs for Sums to 10

Find Missing Addends for Sums of 10

Add within 10

Subtract within 10

Subtract Numbers Less Than 10

Facts Practice

• 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 (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. (K.NBT.A.1)

K.NBT.A Tools for Instruction:

Understand Teen Numbers

Add and Subtract 1 and 2

Make a Set of up to 20 Objects

Read Write and Show Numbers 11-20

Count Teen Numbers

Composing Teen Numbers

• Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. (K.OA.A.1) 

• Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. (K.OA.A.2) 

• 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). (K.OA.A.3)

• 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. (K.OA.A.4)

• Fluently add and subtract within 5. (K.OA.A.5)

K.OA.A Tools for Instruction:

Addition & Subtraction Word Problems

Add and Subtract 1 and 2

Sums of 10

Missing Numbers

Make Numbers to 5

Understand Addition

Subtraction

Add Within 10

Subtract Within 10

Make 6, 7, 8. 9

Add Within 5

Subtract Within 5

Facts Practice

Adding Numbers Within 5

Subtracting Numbers Within 5

Adding & Subtracting Numbers Within 5

Totals of 10

Find Missing Partners for Totals of 10

Use Counters to Write Equations

Sort Addition Facts

Subtract Numbers Less Than 10

Composing Teen Numbers

Number Pairs for Sums to 10

Find Missing Addends for Sums of 10

Count on to Add

Ways to Make 10

Teen Numbers

Making 10s

Count Teen Numbers

• 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.2 (1.OA.A.1)

• 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. (1.OA.A.2)

1.OA.A Tools for Instruction:

Find Missing Addends

Solve Word Problems With Totals to 10

True and False Equations

Find the Unknown Number

Solve Word Problems With Totals to 20

Add and Subtract Tens

Finding 10 More and 10 Less

Addition and Subtraction Facts

Totals Greater Than Ten

Find the Rule

• 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.) (1.OA.B.3) 

• Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8. (1.OA.B.4) 

1.OA.B Tools for Instruction:

Find Missing Numbers

Count on to Subtract

• Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). (1.OA.C.5)

• 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). (1.OA.C.6)

1.OA.C Tools for Instruction:

Ways to Make 10

Count to Add or Subtract

Make a Ten to Add Within 20

Subtraction Within 20

Doubles Addition Facts

Two-Digit Addition Without Regrouping

• 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. (1.OA.D.7) 

• Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. (1.OA.D.8)

1.OA.D Tools for Instruction:

True and False Addition and Subtraction Equations

Number Pairs for Sums to 10

• 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. (2.OA.A.1)

2.OA.A Tools for Instruction:

Solve One-Step Addition and Subtraction Word Problems

Solve Two-Step Addition and Subtraction Word Problems

Use Subtraction to Solve Word Problems

• Fluently add and subtract within 20 using mental strategies.6 By end of Grade 2, know from memory all sums of two one-digit numbers. (2.OA.B.2)

2.OA.B Tools for Instruction:

Addition Strategies

Addition/Subtraction Fact Families

Two-Digit Addition and Subtraction

• 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. (1.NBT.C.4) 

• Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. (1.NBT.C.5) 

• 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. (1.NBT.C.6)

1.NBT.C Tools for Instruction:

Two-digit addition without Regrouping

Two-digit Addition with Regrouping

Add and Subtract Tens

Find Ten More and Ten Less

Add Tens to Two-digit Numbers

Add Two- and One-Digit Numbers

Add and Subtract Multiples of Ten

Solve Comparison Word Problems

Find the Unknown Number

Also see Resources for Addition and Subtraction Word Problem Types from the IA Core

• 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. (2.OA.A.1) 

2.OA.A Tools for Instruction:

Use Subtraction to Solve Word Problems

Solve Subtraction Word Problems

Solve One-Step Addition and Subtraction Word Problems

• Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. (2.NBT.B.5) 

• Add up to four two-digit numbers using strategies based on place value and properties of operations. (2.NBT.B.6) 

• 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. (2.NBT.B.7) 

• Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. (2.NBT.B.8)

• Explain why addition and subtraction strategies work, using place value and the properties of operations. (2.NBT.B.9) 

2.NBT.B Tools for Instruction:

Add Two-Digit Numbers without Regrouping

Two-Digit Subtraction with Regrouping

Two-Digit Subtraction without Regrouping

Two-Digit Subtraction

Adding and Subtracting 10 or 100

Add Three-Digit Numbers

Subtract Three-Digit Numbers

• 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. (3.NBT.A.2)

(*single standard, not cluster)

3.NBT.A.2 Tools for Instruction:

Three-Digit Addition

Three-Digit Subtraction

• 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. (2.OA.C.3)

• 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.OA.C.4)

2.OA.C Tools for Instruction:

Multiplication Concepts and Equations

• Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. (3.OA.A.1)

• 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. (3.OA.A.2) 

• 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.10 (3.OA.A.3)

• Determine the unknown whole number in a multiplication or division equation relating three whole numbers. (3.OA.A.4)

3.OA.A Tools for Instruction:

Solving Problems Involving Partitioning Equal Groups

Solving Problems Involving Sharing Equal Groups

Solving Problems with Equal Shares

Using Place Value to Multiply

• Apply properties of operations as strategies to multiply and divide. (3.OA.B.5) 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) 

• Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. (3.OA.B.6)

3.OA.B Tools for Instruction:

Write Multiplication and Division Facts

Use Order and Grouping to Multiply

Relate Multiplication and Division

• 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 two one-digit numbers. (3.OA.C.7)

3.OA.C Tools for Instruction:

Multiplication Facts with 3, 4, and 6

Multiplication Facts with 0, 1, 2, 5 and 10

Multiplication Facts with 7, 8, and 9

Know Division Facts

• 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.12 (3.OA.D.8)

• 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. (3.OA.D.9)

3.OA.D Tools for Instruction:

Multiply and Divide to solve one step word problems

Solve Two Step Word Problems

• Recognize area as an attribute of plane figures and understand concepts of area measurement. (3.MD.C.5) 

  • • • • a. 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.

        • b. 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. 

• Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). (3.MD.C.6) 

• Relate area to the operations of multiplication and addition. (3.MD.C.7)

  • • • • • a. 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.

          • b. 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.

          • c. 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.

          • d. 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.C Tools for Instruction:

Patterns in Addition and Multiplication

Finding Area

Add Areas

Rectangles with the Same Area

Multiply to Find Area

• 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 (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. (K.NBT.A.1)

K.NBT.A Tools for Instruction:

Understand Teen Numbers

Add and Subtract 1 and 2

Make a Set of up to 20 Objects

Read Write and Show Numbers 11-20

Count Teen Numbers

Composing Teen Numbers

• 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. (1.NBT.A.1)

1.NBT.A Tools for Instruction:

Count Forwards By 1’s

Count Forward by 10’s 

Count by Tens

Count Backwards by 1’s

Finding Patterns within 120

• Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

a. 10 can be thought of as a bundle of ten ones — called a "ten."

b. The numbers from 11 to 19 are composed of a ten and one, two, three, four,

five, six, seven, eight, or nine ones.

c. 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). (1.NBT.B.2) 

•  Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. (1.NBT.B.3)

1.NBT.B Tools for Instruction:

Teen Numbers

Making 10’s

Compare Two-Digit Numbers

Tens and Ones

Working with Teen Numbers

Identifying Tens and Ones

• 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:

a. 100 can be thought of as a bundle of ten tens — called a "hundred."

b. 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). (2.NBT.A.1)

• Count within 1000; skip-count by 5s, 10s, and 100s. (2.NBT.A.2) 

• Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. (2.NBT.A.3) 

• Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. (2.NBT.A.4)

2.NBT.A Tools for Instruction:

Model Three Digit Numbers

Compare and Order Three Digit Numbers

Read and Write Three Digit Numbers

• Use place value understanding to round whole numbers to the nearest 10 or 100. (3.NBT.A.1)

(*single standard, not cluster)

3.NBT.A.1 Tools for Instruction:

Rounding to the Nearest Ten or Hundred

Round Multi Digit Numbers