# Lesson 3

From Visual Patterns to Numerical Patterns

### Lesson Purpose

The purpose of this lesson is for students to analyze, describe, and extend numerical patterns that follow a rule.

### Lesson Narrative

Previously, students explored growing and repeating patterns and reasoned about the patterns using words, numbers, and operations. In this lesson, students investigate patterns in a geometric context and explore how the side lengths, area, perimeter, and other features of a rectangle change when the rectangle changes by a rule. In doing so, students practice looking for and making use of structure (MP7).

Students also practice reasoning quantitatively and abstractly (MP2) as they interpret the values in number sequences that represent geometric features of rectangles, and vice versa. (For example, 6, 8, 10, 12, . . . may represent the area, in square centimeters, of a series of rectangles whose width is 2 centimeters and whose length grows by 1 centimeter each time.)

The second activity in this lesson is optional as it allows students more time to work with the ideas from the first activity.

• Representation
• MLR2

### Learning Goals

Teacher Facing

• Analyze patterns represented visually and numerically.
• Use numbers, words, and the idea of factors and multiples to describe and extend patterns in the features of rectangles.

### Student Facing

• Let’s look at numerical patterns we can write to describe patterns in rectangles.

### Required Materials

Materials to Gather

Building On

Addressing

Building Towards

### Lesson Timeline

 Warm-up 10 min Activity 1 20 min Activity 2 20 min Activity 3 15 min Lesson Synthesis 10 min Cool-down 5 min

### Teacher Reflection Questions

Identify who has been sharing their ideas in class lately.  Make a note of students whose ideas have not been shared and look for an opportunity for them to share their thinking in tomorrow’s lesson.

### Suggested Centers

• Can You Draw It? (1–5), Stage 4: Area and Perimeter (Supporting)
• Five in a Row: Multiplication (3–5), Stage 2: Factors 1–9 (Supporting)

### Print Formatted Materials

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### Additional Resources

 Google Slides For access, consult one of our IM Certified Partners. PowerPoint Slides For access, consult one of our IM Certified Partners.