# Lesson 10 Interpret Relationships

Let’s find relationships between patterns.

## Warm-up True or False: Multiply and Divide

Decide if each statement is true or false. Be prepared to explain your reasoning.

## Activity 1 Mix and Match: 3 Patterns

Complete the patterns for each set of rules.

Set A

Rule 1: Start at 0. Keep adding 3.

Rule 2: Start at 0. Keep adding 6.

Set B

Rule 1: Start at 4. Keep adding 3.

Rule 2: Start at 9. Keep adding 6.

Set C

Rule 1: Start at 0. Keep adding 5.

Rule 2: Start at 0. Keep adding 3.

What are some relationships between the patterns for each set of rules? Be prepared to explain your thinking.

## Activity 2 Generate Patterns

## Problem 1

Partner A

Generate patterns for the two rules.

Rule 1: Start with 0. Keep adding 4.

Rule 2: Start with 0. Keep adding 6.

Compare your patterns. What relationships do you notice?

What number will be in pattern 2 when the number in the pattern 1 box is 40?

What number will be in pattern 1 when the number in the pattern 2 box is 120?

## Problem 2

Partner B

Generate patterns for the two rules.

Rule 1: Start with 0. Keep adding 2.

Rule 2: Start with 0. Keep adding 3.

Compare your patterns. What relationships do you notice?

What number will be in pattern 2 when the number in the pattern 1 box is 30?

What number will be in pattern 1 when the number in the pattern 2 box is 60?

## Practice Problem

## Problem 1

List the first ten numbers starting at 0 and counting by 6.

List the first ten numbers starting at 4 and counting by 6.

When the first list has the number 222, what number will be on the second list? Explain or show your reasoning.