 # Rectangles with given Perimeters

Videos, examples, and solutions to help Grade 3 students learn how to construct rectangles with a given perimeter using unit squares and determine their areas.

Common Core Standards: 3.MD.4, 3.MD.8, 3.G.1

Related Topics:
Lesson Plans and Worksheets for Grade 3,
Lesson Plans and Worksheets for all Grades,

New York State Common Core Math Grade 3, Module 7, Lesson 20, Lesson 21

Concept Development

How to find rectangles that have a perimeter of 16 units?
P = 2 × (L + W)

Lesson 20 Homework

1. Cut out the unit squares above. Then, use them to make as many rectangles as you can with a perimeter of 10 centimeters.
a. Estimate to draw your rectangles below. Label the side lengths of each rectangle.
b. Find the areas of the rectangles in Part (a) above.

2. Gino uses unit square tiles to make rectangles with a perimeter of 14 units. He draws his rectangles as shown below. Using square unit tiles, can Gino make another rectangle that has a perimeter of 14 units? Explain your answer.

3. Katie draws a square that has a perimeter of 20 centimeters.
a. Estimate to draw Katie’s square below. Label the length and width of the square.
b. Find the area of Katie’s square.
c. Estimate to draw a different rectangle that has the same perimeter as Katie’s square.
d. Which shape has a greater area, Katie’s square or your rectangle? Lesson 21 Homework

1. Margo finds as many rectangles as she can with a perimeter of 14 centimeters.
a. Shade Margo’s rectangles on the grid below. Label the length and width of each rectangle.
b. Find the areas of the rectangles in Part (a) above.
c. The perimeters of the rectangles are the same. What do you notice about the areas?

2. Tanner uses unit squares to build rectangles that have a perimeter of 18 units. He creates the chart below to record his findings.
a. Complete Tanner’s chart. You might not use all the spaces in the chart.
b. Explain how you found the widths and lengths in the chart above.

3. Jason and Dina both draw rectangles with perimeters of 12 centimeters, but their rectangles have different areas. Explain with words, pictures, and numbers how this is possible.

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