Lesson 13Rectangles with Fractional Side Lengths
Learning Goal
Let’s explore rectangles that have fractional measurements.
Learning Targets
I can use division and multiplication to solve problems involving areas of rectangles with fractional side lengths.
Warm Up: Areas of Squares
Problem 1
What do you notice about the areas of the squares? Write your observations.
Consider the statement: “A square with side lengths of
inch has an area of square inches.” Do you agree or disagree with the statement? Explain or show your reasoning.
Activity 1: Areas of Squares and Rectangles
Your teacher will give you graph paper and a ruler.
Problem 1
On the graph paper, draw a square with side lengths of 1 inch. Inside this square, draw another square with side lengths of
Use your drawing to answer the questions.
How many squares with side lengths of
inch can fit in a square with side lengths of 1 inch? What is the area of a square with side lengths of
inch? Explain or show your reasoning.
Problem 2
On the graph paper, draw a rectangle that is
For each question, write a division expression and then find the answer.
How many
-inch segments are in a length of inches? How many
-inch segments are in a length of inches?
Problem 3
Use your drawing to show that a rectangle that is
Activity 2: Areas of Rectangles
Problem 1
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.
Use the diagram that matches
to show that the value of is .
Are you ready for more?
Problem 1
The following rectangles are composed of squares, and each rectangle is constructed using the previous rectangle. The side length of the first square is 1 unit.
Draw the next four rectangles that are constructed in the same way. Then complete the table with the side lengths of the rectangle and the fraction of the longer side over the shorter side.
short side
long side
Describe the values of the fraction of the longer side over the shorter side. What happens to the fraction as the pattern continues?
Activity 3: How Many Would It Take? (Part 2)
Problem 1
Noah would like to cover a rectangular tray with rectangular tiles. The tray has a width of
Find the length of the tray in inches.
If the tiles are
inch by inch, how many would Noah need to cover the tray completely, without gaps or overlaps? Explain or show your reasoning. Draw a diagram to show how Noah could lay the tiles. Your diagram should show how many tiles would be needed to cover the length and width of the tray, but does not need to show every tile.
Lesson Summary
If a rectangle has side lengths
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