# Lesson 3

### Lesson Narrative

This lesson is optional. In this exploration in pure mathematics, students tackle a series of activities that explore the relationship between the greatest common factor of two numbers and related fractions using a geometric representation. The activities in this lesson build on each other, providing students an opportunity to express the relationship between the greatest common factor of two numbers and related fractions through repeated reasoning (MP8). Thus, the activities should be done in order. Doing all of the activities would take more than a single class period—possibly as many as four. It is up to the teacher how much time to spend on this topic. It is not necessary to do the entire set of problems to get some benefit from the activities in this lesson, although more connections are made the farther one gets. As with all lessons in this unit, all related standards have been addressed in prior units; this lesson provides an optional opportunity to go more deeply and make connections between domains.

### Learning Goals

Teacher Facing

• Coordinate diagrams and expressions involving equivalent fractions.
• Interpret and create diagrams involving a rectangle decomposed into squares.
• Recognize that decomposing rectangles into squares is a geometric way to determine the greatest common factor of two numbers.

### Student Facing

Let’s cut up rectangles.

Building On