Standards:

4.OA.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, gian the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informal why the numbers will continue to alternate in this way.

Objectives:

Math Objective: I can use reasoning skills and division to examine and extend repeating patterns.

Language Objective: I can use mathematical language to discuss how they could determine a given term of a pattern.

Vertical Alignment:

3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.

4.OA.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, gian the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informal why the numbers will continue to alternate in this way.

5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisiting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane.

Notes:

1. In order to be successful with this lesson, students need to be able to use strategies to divide, including solving division equations with remainders. In Chapter 4 of this curriculum, students learned that remainders do have a powerful meaning and place in mathematics. This lesson will extend that understanding to using remainders as a key in extending repeating patterns

2. This lesson requires informal class discussion and investigation of patterns. Students should explore the patterns and ideas behind extending them.

Lesson Outline:there

There is a lot of modeling and explanation needed for students to grasp this concept, doing this lesson in person is recommended.

🚀Launch

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As you discuss possible answers, lead students to seeing the pattern with odds and evens. Show how you can tell what shape different numbers will be without extending the pattern.

🤔Explore

Students investigate the numbers associated with a AAB pattern. We want students to notice how they can use multiples and division to be able to know what shapes would come next.

See the Advantage Math outline for discussion points. You may need to help students see that multiples help them.

There is an activity done by writing a list of term numbers and corresponding shapes and finding the patterns in the numbers. This needs to be explained to students and modeled well. You can find the instructions for this on step 20-23 in Advantage Math.

💬Discuss

Students think about how a remainder could impact extending a pattern.

✅Exit Ticket

Students identify the core pattern and then are asked to find the 21 term of the pattern without extending it. They then reflect on their learning.

Additional Resources:

Differentiation:

Challenge: For students who need a challenge, ask them to find large numbered terms (up to four digits).

Struggling: For students who are struggling with finding a given term with division, investigate whether the problem is with understanding the pattern or with the division itself.