1.OA.3: Properties of Operations

I can use the commutative and associative properties to add numbers.

What Your Child Needs to Know

This standard focuses on helping your child understand and use properties of operations as strategies for adding numbers. First graders learn that changing the order of numbers when adding doesn't change the sum (commutative property) and that regrouping numbers when adding doesn't change the sum (associative property).

For example, they learn that 8+3 equals 3+8 (commutative property) and that 2+6+4 can be solved as 2+(6+4) = 2+10 = 12 (associative property). These properties help children develop mental math strategies and number sense.

Real World Practice

Visual models and hands-on activities

Visual Models

1. Number Balance

Use a balance scale to show that 3+5 weighs the same as 5+3, demonstrating the commutative property.

2. Domino Pairs

Use dominoes to show that 4+2 and 2+4 give the same sum, reinforcing that order doesn't matter.

3. Number Bonds

Use number bonds to show how numbers can be regrouped. For example, 2+7+3 can be regrouped as 2+(7+3) = 2+10 = 12.

4. Counters in Groups

Use different colored counters to show that grouping doesn't change the total. For example, (3+4)+2 = 3+(4+2).

Everyday Activities

1. Snack Sorting

Use different snacks to demonstrate the commutative property. Show that 3 crackers + 4 grapes equals 4 grapes + 3 crackers.

2. Building Blocks

Use building blocks of different colors to show that the order of addition doesn't change the total number of blocks.

3. Card Game: Make 10

Play a game where your child finds combinations that make 10 using the associative property. For example, with cards showing 2, 8, and 5, they can regroup to (2+8)+5 or 2+(8+5).

4. Domino Addition

Use dominoes to practice the commutative property. Show that adding the dots on the left side first or the right side first gives the same total.

Quick Checks

Strategies and quick activities

Strategies When Your Child Struggles

1. Use Concrete Objects

If your child struggles with the abstract concept, use physical objects to show that 5 blocks + 3 blocks equals 3 blocks + 5 blocks.

2. Make It Visual

Draw pictures to show that order doesn't matter in addition. Draw 4 apples and 2 bananas, then 2 bananas and 4 apples.

3. Look for Friendly Numbers

Teach your child to look for combinations that make 10. For example, in 7+5+3, regroup to 7+3+5 = 10+5 = 15.

4. Practice Fact Families

Create fact family cards showing related addition facts (3+5=8 and 5+3=8) to reinforce the commutative property.

5. Use a Number Line

Show that jumping 2 spaces then 5 more gets to the same spot as jumping 5 spaces then 2 more.

5-Minute Practice Activities

Activity 1: Flip and Match

Create cards with addition problems (4+3, 3+4). Have your child match pairs that have the same sum to reinforce the commutative property.

Activity 2: Make 10 First

Practice problems like 9+6+1, encouraging your child to regroup and make 10 first: 9+1+6 = 10+6 = 16.

Activity 3: Order Switch

Write an addition problem like 5+8. Ask your child to write it in a different order and solve both ways to show they get the same answer.

Activity 4: Three Number Challenge

Give your child three numbers (e.g., 4, 2, 6) and ask them to find different ways to add them. Show that the total is always the same.

Check Progress

Track improvement

By the middle of the year, your child should:

  • Understand that changing the order of addends doesn't change the sum
  • Apply the commutative property with sums up to 10
  • Recognize that grouping numbers differently doesn't change the sum

By the end of the year, your child should:

  • Apply the commutative property of addition fluently
  • Apply the associative property of addition fluently
  • Use properties of operations to add more efficiently
  • Explain why these properties work using objects or drawings

Mastery Signs

Your child understands this concept when they can:

  • Automatically apply properties of operations when solving problems
  • Explain how changing the order or grouping of numbers helps with mental math
  • Use properties to find efficient strategies for adding
  • Identify when to use specific properties to make calculations easier
  • Apply properties of operations in various contexts

Differentiation

Support for all learning levels

Below Grade Level

Practice problems focusing on simple addition with small numbers to build understanding of the commutative property.

📥 Download Practice Worksheet

At Grade Level

Standard practice with the commutative and associative properties using numbers within 20.

📥 Download Grade Level Worksheet

Above Grade Level

Advanced problems applying properties of operations with larger numbers and in more complex situations.

📥 Download Challenge Worksheet