Arrays for Fraction Products
Students will be able to illustrate fraction factor products with arrays.
- 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
- Using unit fractions (i.e. 1/3, 1/4, 1/2, 1/5,) for factors makes easier arrays.
- Challenge students to draft arrays with mixed number factors by adding whole numbers to their fraction factors.
- 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.
- 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.