Unit 4, Lesson 13
Rectangles with Fractional Side Lengths
Grade 6
13.1
Warm-up
Notice and Wonder: Areas of Squares
What do you notice? What do you wonder?
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What do you notice? What do you wonder?
Here is a square with side lengths of 1 inch.
How many squares with side lengths of
Here is a rectangle that is
Show that a rectangle that is
Each of these multiplication expressions represents the area of a rectangle.
All regions shaded in light blue have the same area. Match each diagram to the expression that you think represents its area. Be prepared to explain your reasoning.
A rectangle with a horizontal dotted line about three quarters of the way down its width. The top portion is shaded blue.
A rectangle with a horizontal dotted line about three quarters of the way down its width and a vertical dotted line about three quarters of the way to the right of its length. The top left portion of the rectangle is shaded blue.
A vertically oriented rectangle shaded blue.
A rectangle with a vertical dotted line about three quarters of the way to the right of its length. The left portion of the rectangle is shaded blue.
If a rectangle has side lengths
A large square evenly divided into 4 smaller squares. The large square has bottom horizontal side length of 1 inch. Of the four smaller squares, the top left square is shaded blue. It has side lengths labeled one half inch.
This means that if we know the area and one side length of a rectangle, we can divide to find the other side length.
If one side length of a rectangle is
Then, we can find the other side length, in inches, using division: