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# Operations and Algebraic Thinking Activities

## Kindergarten

K.OA.1

Use Pictures to Add and Subtract

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

K.OA.2

Let's Add and Subtract

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.3

Make Bigger Numbers

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.4

Friends of Ten

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.5.i

Add Within 5

Add within 5.

K.OA.5.ii

Subtract Within 5

Subtract within 5.

## 1st Grade

1.OA.1

Word Problems

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.

1.OA.3

Number Families

Count to 100 by ones and by tens.

Apply properties of operations as strategies to add and subtract.

1.OA.4

Number Families

Understand subtraction as an unknown-addend problem.

1.OA.5

Skip Counting

Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

1.OA.6.i

Add and Subtract Up to 20

Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.

1.OA.6.ii

Add and Subtract Up to 20

Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.

1.OA.7

What is Equal?

Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false.

1.OA.8

Find the Missing Number

Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.

## 2nd Grade

2.OA.1

Word Problems

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.2

Add and Subtract with Fluency

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

2.OA.2

Math Fact Practice

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

2.OA.3

Odds and Evens

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.4

Arrays

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.

## 3rd Grade

3.OA.1

Multiplying Whole Numbers

Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each.

3.OA.2

Dividing Whole Numbers

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.3

Multiply, Divide: Word Problems

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.

3.OA.4

Unknown Number Equations

Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

3.OA.5

Properties of Multiplication

Apply properties of operations as strategies to multiply and divide.

3.OA.6

Division as an Unknown Factor

Understand division as an unknown-factor problem.

3.OA.7

Multiply, Divide: 1-5

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.7

Multiply, Divide: 6-10

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.8

Two-Step Word Problems

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.

## 4th Grade

4.OA.1

Multiplicative Comparisons

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.

4.OA.2

Multiply with Word 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.

4.OA.3

Multistep Word 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.

4.OA.4

Prime and Composite Numbers

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.

4.OA.4

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.

4.OA.5

Number and Shape 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.

## 5th Grade

5.OA.1

Intro to Order of Operations

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

5.OA.1

Practice Order of Operations

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

5.OA.1

Order of Operations

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

5.OA.2

Words to Numbers

Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

5.OA.3

Patterns from Ordered Pairs

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.

5.OA.3

Understand Patterns

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.