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.

  1. Set A

    Rule 1: Start at 0. Keep adding 3.

    rectangle partitioned vertically into 5 equal size rectangles

    Rule 2: Start at 0. Keep adding 6.

    rectangle partitioned vertically into 5 equal size rectangles

  2. Set B

    Rule 1: Start at 4. Keep adding 3.

    rectangle partitioned vertically into 5 equal size rectangles

    Rule 2: Start at 9. Keep adding 6.

    rectangle partitioned vertically into 5 equal size rectangles

  3. Set C

    Rule 1: Start at 0. Keep adding 5.

    rectangle partitioned vertically into 5 equal size rectangles

    Rule 2: Start at 0. Keep adding 3.

    rectangle partitioned vertically into 5 equal size rectangles

  4. 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

  1. Generate patterns for the two rules.

    Rule 1: Start with 0. Keep adding 4.

    Rule 2: Start with 0. Keep adding 6.

  2. Compare your patterns. What relationships do you notice?

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

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

Problem 2

Partner B

  1. Generate patterns for the two rules.

    Rule 1: Start with 0. Keep adding 2.

    Rule 2: Start with 0. Keep adding 3.

  2. Compare your patterns. What relationships do you notice?

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

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

Practice Problem

Problem 1

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

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

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