# Lesson 18

Design With Fractions (optional)

### Lesson Purpose

The purpose of this lesson is for students to apply their understanding of fractions to create geometric designs.

### Lesson Narrative

This lesson is optional because it does not address any new mathematical content standards. It does provide students with an opportunity to apply precursor skills of mathematical modeling.

In this lesson, students apply their understanding of fractions to create geometric designs, starting with a given square. They are tasked with marking a fractional length ($$\frac{1}{2}$$ or $$\frac{1}{4}$$) of each side of the square with a point. They then connect the points, which creates a new shape within the square. Students iterate this process of marking a fractional length and connecting points to generate their designs.

To mark a given length, students apply their experience with partitioning a segment into equal parts. To mark a fractional length, they decide which endpoint of each side to use as a starting point, whether to always mark the points in the same direction (clockwise or counterclockwise), how many iterations are practical, and so on (MP4).

• Representation
• MLR2

### Learning Goals

Teacher Facing

• Apply fraction understanding to create geometric designs.

### Student Facing

• Let’s use fractions to create a design.

### Required Materials

Materials to Gather

Building On

### Lesson Timeline

 Warm-up 10 min Activity 1 15 min Activity 2 25 min Lesson Synthesis 10 min

### Teacher Reflection Questions

How did the student work that you selected impact the direction of the discussion? What student work might you pick next time if you taught the lesson again?

### Suggested Centers

• Rolling for Fractions (3–5), Stage 1: Equivalent Fractions (Addressing)
• Number Line Scoot (2–3), Stage 3: Halves, Thirds, Fourths, Sixths and Eighths (Addressing)
• Five in a Row: Multiplication (3–5), Stage 2: Factors 1–9 (Supporting)

### Print Formatted Materials

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