Fishtank Learning

3rd Grade Math
Unit 4: Area
Lesson 11

Objective

Apply the distributive property as a strategy to find the total area of a large rectangle.

Anchor Tasks - Problem 1

Andre is finding the area of this rectangle.

Grid divided into 42 equal squares, representing a 6x7 rectangle.

Andre writes 6 × 7.	He marks the rectangle like this:	He then writes:
		6 × (5 + 2) (6 × 5) + (6 × 2) 30 + 12 42

a. How are the numbers in Andre’s expressions related to his diagram?

b. How are 6 × 7 and 6 × (5 + 2) related to each other? What about 6 × 7 and (6 × 5) + (6 × 2)?

Guiding Questions

What strategy did Andre use to find the area of the rectangle?
How does the expression 6 × 7 relate to the diagram? What about 6 × (5 + 2)? (6 × 5) + (6 × 2)?
What’s another way the original rectangle could have been split? What expressions can you write to represent that decomposition?

Notes

Watch a video analysis of this Anchor Task in the Unit Launch, Big Idea 2, Step 2 starting at 0:33.

Anchor Tasks - Problem 2

Write three expressions that represent the area of the rectangle below.

Rectangle with dimensions 8 units by 10 units, shaded area 4 units by 1 unit.

Guiding Questions

How is this similar to the partioned rectangle in Anchor Task 1? How is it different?
What is the relationship between all three of these expressions?

Notes

The last question helps students see the equivalence of these various ways of representing the area of the rectangle. Writing a compound equation (e.g., $$14 \times 8 = (10 + 4) \times 8 = (10 \times 8) + (4 \times 8))$$ isn’t necessary but may help students understand the notation a bit better.

Anchor Tasks - Problem 3

Draw a rectangle on the grid below that matches the given expression.

Grid with 7 rows and 9 columns; text above reads

Problem Set

View Problem Set

Discussion of Problem Set

What three expressions did you write to represent the area model in #4a? How are each of those expressions represented in the area model?
What rectangle did you draw for #5? What other expressions could you write to represent its area?
Why are both Tori and Leo’s expressions correct in #6? What other expression could they have written to represent the area?
How did you find the total area for Mr. Nuccio’s sandwich shop after the new section was added? What made this problem different from the previous ones?

Target Task - Problem 1

Use the rectangle below to answer Parts (a) and (b).

Rectangle divided into 25 equal squares, each representing 1 square foot.

a. Which equation represents the total number of square feet represented by the rectangle above?

A. 4 × (3 + 2) = 4 + 3 + 2

B. 4 × (3 + 2) = 4 × 3 × 2

C. 4 × (3 + 2) = (4 × 3) × (4 × 2)

D. 4 × (3 + 2) = (4 × 3) + (4 × 2)

b. What is the area of the rectangle above? Show your work.

Target Task - Problem 2

Draw a rectangle that matches the expression in the grid underneath. Then, explain how the diagram represents the expression.

Grid with 7 rows and 4 columns, representing the expression (7×4)+(7×1).

Word Problem

The town needs to know the area of the playground so they can find how much mulch they need to cover it. The layout of the playground is shown below. What is the area of the playground?

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