The purpose of this activity is for students to generate two different patterns, given two different rules, and recognize relationships between corresponding terms (MP7). Students may notice a variety of relationships between the two patterns and may describe them generally (all of the numbers in one pattern are contained in the other pattern) or more specifically (the numbers of the second pattern are every other number from the first pattern). To answer the questions about corresponding terms in the patterns, students may continue the patterns or use the relationship between the patterns. The number 192 is deliberately chosen to encourage using the relationship between the patterns.

When students find and explain patterns related to the rules and relationships, they look for and express regularity in repeated reasoning (MP8).

This activity uses MLR2 Collect and Display. Advances: Conversing, Reading, Writing. 

• “Are there any other words or phrases that are important to include on our display?”
• As students share responses, update the display, by adding (or replacing) language, diagrams, or annotations.
• Remind students to borrow language from the display as needed.
• “Are all of Priya’s numbers in Jada’s pattern? How do you know?” (Yes, there are 2 fours in 8 so each of Priya’s numbers appears twice as far out in Jada’s list.)
• “What relationships do you see between Jada's pattern and Priya’s pattern?” (Each number in Priya’s pattern is double the corresponding number in Jada’s pattern. Each number in Jada’s pattern is half the corresponding number in Priya’s pattern.)

The purpose of this activity is for students to practice generating two different patterns from two different rules and observe and quantify relationships between corresponding terms. Both sets of rules generate patterns that have the same relationships between corresponding terms. Each of Priya’s terms is 3 times greater than each of Jada’s corresponding terms and each of Jada’s terms is of Priya’s corresponding terms.

When students find and explain patterns related rules and relationships, they look for and express regularity in repeated reasoning (MP8).

• Ask previously identified students to share their thinking.
• Display completed patterns from both sets of rules.
• “How are the patterns from the pairs of rules the same? How are they different?” (Some of the numbers are in all four patterns. Some numbers aren’t in any pattern like 5 and 11. In both sets of rules, Priya’s numbers are 3 times greater than Jada’s numbers and Jada’s numbers are Priya’s numbers.)
• “How would you describe the relationship between Priya's pattern and Jada's pattern?” (Priya's numbers are all 3 times as much as Jada's corresponding numbers.)
• “What can I multiply the numbers in Priya’s pattern by to get the corresponding numbers in Jada’s pattern?” (, each number in Jada's pattern is the corresponding number in Priya's pattern.)