The purpose of this activity is for students to practice interpreting relationships between patterns generated from two different rules. Students may need to generate patterns beyond the boxes provided. Encourage them to continue the pattern as needed. Students may describe the patterns and relationships in different, but accurate ways. Encourage them to notice as many relationships as they can and describe the relationships in whatever way makes sense to them. This is the first time students see two patterns where the numbers in one pattern are not multiples of the numbers in the other pattern.

This activity uses MLR7 Compare and Connect. Advances: Representing, Conversing.

• “What is the same and what is different in the way we represented the relationships between the patterns?” (Some of us used numbers and symbols. Some of us wrote sentences.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• “What is the same and what is different about Set A and Set B?” (They both add the same amount, but one set starts at 0. Set B has a lot more odd numbers in it. In Set A, each number in Rule 2 is double the number in Rule 1, but in Set B, each number in Rule 2 is 1 more than double the number in Rule 1.)
• “For which pair of rules was it most challenging to notice and describe relationships?” (Set B because there was no multiple that worked to get from one pattern to the other. Set C because there weren’t doubles or halves.)

The purpose of this activity is for students to interpret more complex relationships in corresponding terms from patterns generated from two different rules. Both sets of rules generate patterns that have the same relationships between corresponding terms. Each of the terms in Rule 2 is  times greater than each of the corresponding terms in Rule 1 and each of the terms in Rule 1 is  the corresponding term in Rule 2. Some students may state these relationships in different ways. The relationships between these patterns build directly on the third pair of rules from the previous activity where the terms for Rule 1 were the corresponding terms in Rule 2.

• Ask previously selected students to share their thinking.
• Display or write the numbers in the patterns for Partner A.
• “How can we represent the relationship between the numbers in the patterns with multiplication equations?” (Each number in Rule 2 is the corresponding number in Rule 1. Each number in Rule 1 is the corresponding number in Rule 2:  , .)
• Display or write the numbers in the patterns for Partner B.
• “How can we represent the relationships between the numbers in the patterns with multiplication equations?” ( , .)