### Lesson plan

# Arrays for Fraction Products

#### Learning Objectives

Students will be able to illustrate fraction factor products with arrays.

#### Introduction

*(5 minutes)*

- Show your students the following equation:
**2/3 x ?/? = 6/12**and have them think, pair, and share their thoughts on the missing factor fraction. - Call on students to share out their ideas. Note relevant academic terms for future reference and confirm the missing factor to be 3/4.
- Draw a rectangle where:
- The vertical side is labeled 3/4
- The horizontal side is labeled 2/3
- The center of the rectangle is labeled 6/12

- Tell your class that today’s lesson will be on how to draft an array for fraction products when both factors are also fractions. An
**array**is an illustration strategy, great for displaying products and sums of repeat addition.

#### Explicit Instruction/Teacher modeling

*(10 minutes)*

- On grid paper show your class a rectangle where:
- The vertical side is labeled 1/2
- The horizontal side is labeled 1/4
- Below the rectangle is the equation: 1/2 x 1/4 = 1/8

- Show your students how to divide the rectangle into two horizontal halves and shade one (1/2 total).
- Next, divide the rectangle vertically into four sections and shade in one part (1/4, you will notice some overlap).
- Explain that the overlap, 1/8, is an illustration of the product of 1/2 x 1/4 in the form of an array.

#### Guided Practice

*(10 minutes)*

- Guide your class through the same procedure for the following expressions:
- 3/4 x 1/5
- 1/6 x 2/7

#### Independent working time

*(10 minutes)*

- Answer any clarifying questions and hand out grid paper to your students.
- Have your class solve the following exercises with arrays:
- 3/4 x 2/9
- 5/6 x 4/5
- 6/7 x 2/5

#### Differentiation

**Support**

- Using unit fractions (i.e. 1/3, 1/4, 1/2, 1/5,) for factors makes easier arrays.

**Enrichment**

- Challenge students to draft arrays with mixed number factors by adding whole numbers to their fraction factors.

#### Technology Integration

- It’s convenient to snap pictures of student work at different stages, upload photos and import them into word processing documents like word or Google Sheets for online reference.
- Drafting student responses during reflection discussions via computer and projector for your class to see makes for an interactive lesson closure setup.

#### Assessment

*(5 minutes)*

- Show your students an array (i.e. for 2/3 x 3/5) and have them explain the equation it represents.

#### Review and closing

*(15 minutes)*

- Have your students share out exercise answers with the whole class. If they need help, they can "phone a friend" for assistance or "hand off" to a peer.
- Discuss: What can we learn from arrays for fraction products? Note student responses for future reference.