In this activity, students generate a pattern that results in multiples of 15 and analyze and describe what they notice. The intent is to draw students’ attention to patterns in the digits in the tens and ones place, encourage them to consider why those patterns exist, and predict whether a given number could be a multiple of 15. The goal in this activity is not to elicit clear justifications, but rather to encourage students to use their understanding of place value and properties of operations to reason more generally about the features of numerical patterns that are not explicit in the rule.

This activity uses MLR5 Co-craft Questions. Advances: writing, reading, representing

• “What is your plan for figuring out whether 250 will be a number in Mai’s pattern?”
• “What are some of the things you noticed in the numbers in Mai’s pattern? How can you use one of the things you noticed to figure out if 250 will be a number in the pattern?”

• Invite students to share their observations and explanations for any features of the pattern they notice. Record them for all to see.
• Invite other students to share their explanation on whether 250 could be a number in Mai’s pattern. Highlight explanations that make use of the features students noticed (for example, that it must be a multiple of 30 if it has a 0 in the ones place).

In previous activities, students generated and analyzed numerical patterns that involve adding the same amount to each term. In this activity, students generate and analyze numerical patterns that involve multiplying each term by the same factor. They generate two patterns that follow a rule of doubling the term—one that starts with 1 and a second pattern that starts with 10. As students describe what they notice about each pattern, they may also use what they know about place value and properties of operations to compare the patterns. This reasoning will be helpful for future lessons that involve multiplying with multi-digit numbers.

As students make sense of what is happening to the numbers in these patterns, it may be helpful for some students to create a drawing or diagram. It may be helpful for students to revisit their work with Lin’s bottle cap pattern from a previous lesson. 

• Invite previously selected students to share how they generated the pattern that starts with 10 and what they noticed.
• “How were the numbers in Andre’s patterns the same? How were they different?” (They’re all even. The second pattern has all the same digits except it has a 0 in the ones place. The second pattern is different because they’re all multiples of 10.)