Converting Square Units
Alignments to Content Standards:
6.RP.A.3
Task
Jada has a rectangular board that is 60 inches long and 48 inches wide.
- How long is the board measured in feet? How wide is the board measured in feet?
- Find the area of the board in square feet.
- Jada said,
To convert inches to feet, I should divide by 12.
What went wrong with Jada's reasoning? Explain.
The board has an area of 48 in $ \times $ 60 in = 2,880 in^{ 2 }.
If I divide the area by 12, I can find out the area in square feet.
So the area of the board is 2,880 $ \div $ 12 = 240 ft^{ 2 }.
IM Commentary
Since this task asks students to critique Jada's reasoning, it provides an opportunity to work on Standard for Mathematical Practice 3 Construct Viable Arguments and Critique the Reasoning of Others.
Solution
- The board is 5 feet long and 4 feet wide.
- The area of the board is 20 ft^{ 2 }.
- While it is true that you convert inches to feet by dividing by 12, that doesnâ€™t work for converting square inches to square feet. Because a square foot is 12 inches on each side, there are 12^{ 2 } = 144 square inches per square foot (see the picture). Thus, $$2,880 \text{ in}^2 \times \frac{1 \text{ ft}^2}{144 \text{ in}^2} = 2,880 \div 144 \text{ ft}^2 = 20 \text{ ft}^2.$$
Converting Square Units
Jada has a rectangular board that is 60 inches long and 48 inches wide.
- How long is the board measured in feet? How wide is the board measured in feet?
- Find the area of the board in square feet.
- Jada said,
To convert inches to feet, I should divide by 12.
What went wrong with Jada's reasoning? Explain.
The board has an area of 48 in $ \times $ 60 in = 2,880 in^{ 2 }.
If I divide the area by 12, I can find out the area in square feet.
So the area of the board is 2,880 $ \div $ 12 = 240 ft^{ 2 }.