Lesson 9 Generate Patterns

    • Let’s explore rules and patterns.

Warm-up Choral Count: Two Patterns

Count by 6, starting at 0.

Now count by 12s, starting at 0.

What patterns do you see?

Activity 1 What’s the Pattern?

Problem 1

Jada and Priya create patterns using rules. Use each rule to complete their patterns.

  1. Jada’s rule: start with 0 and keep adding 4.

    rectangle partitioned vertically into 10 equal size rectangles

  2. Priya’s rule: start with 0 and keep adding 8.

    rectangle partitioned vertically into 10 equal size rectangles

Problem 2

If Jada and Priya continue their patterns, what number will be in Priya’s pattern when Jada’s pattern has:

  1. 40

  2. 60

Problem 3

  1. If Jada and Priya continue their patterns, what number will be in Jada’s pattern when Priya’s pattern has 192?

  2. What relationships do you notice between the numbers in Priya’s pattern and the numbers in Jada’s pattern?

Activity 2 More Patterns

Problem 1

Partner A:

Use each rule to create a pattern.

  1. Jada’s rule: Start at 0. Keep adding 2.

    rectangle partitioned vertically into 10 equal sized rectangle

  2. Priya’s rule: Start at 0. Keep adding 6.

    rectangle partitioned vertically into 10 equal sized rectangle

Problem 2

If the patterns continue:

  1. What number will be in Priya’s pattern when Jada’s pattern has 34? Explain or show your reasoning.

  2. What number will be in Jada’s pattern when Priya’s pattern has 120? Explain or show your reasoning.

Problem 3

What relationships do you notice between the numbers in Priya’s pattern and the numbers in Jada’s pattern?

Problem 4

Partner B:

Use each rule to create a pattern.

  1. Jada’s rule: Start at 0. Keep adding 3.

    rectangle partitioned vertically into 10 equal sized rectangle

  2. Priya’s rule: Start at 0. Keep adding 9.

    rectangle partitioned vertically into 10 equal sized rectangle

Problem 5

If the patterns continue:

  1. What number will be in Priya’s pattern when Jada’s pattern has 54? Explain or show your reasoning.

  2. What number will be in Jada’s pattern when Priya’s pattern has 198? Explain or show your reasoning.

Problem 6

What relationships do you notice between the numbers in Priya’s pattern and the numbers in Jada’s pattern?

Practice Problem

Problem 1

  1. List the first ten numbers starting at 0 and counting by 5s.

  2. List the first ten numbers starting at 0 and counting by 10s.

  3. What patterns do you observe between your two lists of numbers?