3.OA.9: Patterns in Arithmetic

Visual Models to Use

• Multiplication Tables - Color-code patterns in a multiplication table (e.g., highlight all multiples of 3 in blue, all multiples of 4 in red)
• Number Charts - Use 100-charts to identify patterns when counting by different numbers
• Pattern Blocks - Create repeating patterns with shapes, then translate these into number patterns
• Input/Output Tables - Create tables showing what happens when you apply the same rule to different numbers

Everyday Activities

1. Pattern Hunt

Look for patterns in everyday life: tile arrangements, brick patterns on buildings, or fabric designs. Discuss how these patterns repeat and how they could be described mathematically.

2. Skip Counting Challenges

Practice skip counting by different numbers (2s, 3s, 5s, 9s) and discuss the patterns you notice. For example, when counting by 5s, the numbers always end in 0 or 5.

3. Calendar Patterns

Use a monthly calendar to identify patterns. What happens when you count by 7s (days of the week)? What patterns do you notice when you highlight certain dates?

4. Pattern Prediction

Start a number pattern (like 3, 6, 9, 12...) and ask your child to predict the next several numbers. Then have them create their own patterns for you to continue.

Strategies When Your Child Struggles

1. Start Simple

Begin with easy-to-recognize patterns like counting by 2s or 5s before moving to more complex patterns. Use visual supports like number lines or charts.

2. Use Color-Coding

Have your child color-code patterns in a multiplication table or hundred chart to make them more visible. For example, color all multiples of 3 in blue.

3. Connect to Properties

Help your child understand why patterns work by connecting them to properties:

• Commutative property: 3 × 4 = 4 × 3
• Associative property: (2 × 3) × 5 = 2 × (3 × 5)
• Distributive property: 7 × 6 = 7 × (5 + 1) = 7 × 5 + 7 × 1

4. Look for Relationships

Help your child see relationships between numbers in a pattern. For example, in the pattern 5, 10, 15, 20..., each number is 5 more than the previous number, or each number is 5 times its position in the pattern.

5-Minute Practice Activities

1. What's My Rule?

Give your child a series of input-output pairs (e.g., 1→3, 2→6, 3→9) and ask them to figure out the rule (in this case, multiply by 3).

2. Even/Odd Patterns

Explore what happens when you add or multiply even and odd numbers. Create a chart to track the patterns:

• Even + Even = ?
• Even + Odd = ?
• Odd + Odd = ?
• Even × Even = ?
• Even × Odd = ?
• Odd × Odd = ?

3. Pattern Completion

Give your child a pattern with missing numbers (e.g., 2, 4, __, 8, __, 12) and ask them to fill in the blanks.

4. Multiplication Table Exploration

Have your child explore a row or column in the multiplication table and describe the patterns they notice.

Mid-Year Expectations

By the middle of third grade, your child should be able to:

• Identify simple patterns in addition and multiplication tables
• Recognize even and odd number patterns
• Continue a given arithmetic pattern
• Describe patterns using simple language
• Use patterns to help with basic computation

End-of-Year Expectations

By the end of third grade, your child should be able to:

• Identify various patterns in addition and multiplication tables
• Explain patterns using properties of operations
• Create their own arithmetic patterns
• Use patterns to check the reasonableness of calculations
• Apply pattern recognition to solve problems more efficiently

Mastery Signs

Your child has mastered this standard when they can:

• Independently identify multiple patterns in arithmetic operations
• Clearly explain why patterns work using mathematical properties
• Create and extend arithmetic patterns
• Use pattern recognition as a problem-solving strategy
• Connect patterns to real-world situations
• Apply pattern knowledge to check their work and find shortcuts

Below Grade Level

For students who need additional support with basic pattern recognition and understanding.

Download Practice Worksheet

At Grade Level

For students who are working at the expected level for this standard.

Download Grade Level Worksheet

Above Grade Level

For students who are ready for more challenging pattern analysis and creation.

Download Challenge Worksheet