Unit 7, Lesson 9
Perimeter Problems
Grade 3
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The purpose of an Estimation Exploration is to practice the skill of estimating a reasonable answer based on experience and known information.
The Statue of Liberty has 2 square bases—1 larger than the other. The larger base has side lengths of 132 feet each.
Estimate the perimeter of the smaller square base.
Record an estimate that is:
| too low | reasonable | too high |
|---|---|---|
None
The purpose of this activity is for students to find the length of a missing side of a shape when the perimeter is given, using any strategy that makes sense to them. The Activity Synthesis highlights the variety of methods students used to solve the problem.
This pentagon has a perimeter of 32 cm. What is the unknown side length? Explain or show your reasoning.
This rectangle has a perimeter of 56 feet. What are the lengths of the unlabeled sides? Explain or show your reasoning.
This pentagon has a perimeter of 65 inches. It has equal side lengths. What is the length of each side? Explain or show your reasoning.
None
The purpose of this activity is for students to solve problems in situations that involve perimeter (MP2). Students may draw diagrams with length labels or simply reason arithmetically. They also explain how each problem does or does not involve perimeter. The Activity Synthesis provides an opportunity to begin discussing the difference between area and perimeter, which will be fully explored in upcoming lessons.
Solve each problem. Explain or show your reasoning.
We learned that perimeter is the boundary of a flat shape.
We can find the length of a perimeter by adding the lengths of all the sides of the shape. We can also use multiplication when the shape has some equal side lengths.
We used our knowledge of shapes to find the perimeter even when some side lengths were missing, and to use the perimeter to find missing side lengths.
For example, if we know the perimeter of this rectangle is 32 feet, we can find the lengths of the three unlabeled sides.
A rectangle has 2 pairs of equal sides. So, we know 1 other side must be 12 feet.
Now we know the other 2 sides have a combined length of 8 feet.
The 3 unlabeled sides are 12 feet, 4 feet, and 4 feet.
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