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Perimeter and Circumference

Students measure distance around polygons and circles and solve for missing dimensions.

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Beginner 15–20 minutes Volume & Area
Volume & Area Page 1 of 8
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At a Glance

Perimeter and Circumference
Binder SectionVolume & Area
DifficultyBeginner
Estimated Time15–20 minutes
PrerequisitesNone
Essential Question

How do dimensions determine a figure’s perimeter and area?

Build Understanding

Perimeter is the total distance around a polygon. Add every side length, using equal-side markings and algebra when a length is unknown.

Circumference is the distance around a circle. Use C = pi times d or C = 2 times pi times r. The diameter is twice the radius. Keep pi in exact answers or use the requested approximation.

Visual Model
4Thousands 3Hundreds 2Tens 7Ones

4,327 = 4,000 + 300 + 20 + 7

Goals

Learning Targets

  • Add all outside side lengths.
  • Use P = 2l + 2w for rectangles.
  • Use C = pi d or C = 2 pi r.
  • Label answers with linear units.
  • Work backward to find missing dimensions.
Click each word

Interactive Vocabulary

Reveal one step at a time

Worked Examples

Example 1

Rectangle 8 cm by 5 cm

1

P=2(8+5)=26 cm.

Example 2

Triangle with base 10 m and height 7 m

1

A=1/2(10)(7)=35 m².

Ask and explain

Common Questions

Is perimeter measured in square units? No, it uses linear units.
Can I use 3.14 for pi? Only when directions request an approximation.
Are radius and diameter interchangeable? No; d = 2r.
Notice and correct

Common Misconceptions

Using square units for perimeter

Perimeter uses linear units.

Adding dimensions for area

Area measures covering and uses multiplication or decomposition.

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Area and Perimeter lesson and examples

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Warm-Up Guided Independent Challenge
1
Quick Start

Warm-Up

Warm-up 1

Directions: Solve the problem. Show your thinking, then enter only your final answer.

Find the perimeter and area of a 9-by-4 rectangle.

Picture the area and perimeterUse the picture to organize what you know before you solve.
5 units3 units

Choose how you want to work or answer.

2
We Do

Guided Practice

3
You Do

Independent Practice

Independent 1

Directions: Solve independently. Show your work, check it, then enter only your final answer.

Find the perimeter and area of a 9-by-4 rectangle.

Picture the area and perimeterUse the picture to organize what you know before you solve.
5 units3 units

Choose how you want to work or answer.

Independent 2

Directions: Solve independently. Show your work, check it, then enter only your final answer.

Create and solve a second example with different values.

Picture the area and perimeterUse the picture to organize what you know before you solve.
5 units3 units

Choose how you want to work or answer.

4
Stretch Your Thinking

Challenge & Real-World Practice

🧩 Challenge

Design two rectangles with area 72 square units but different perimeters. Explain why equal area does not require equal perimeter.

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Success Criteria

Before you begin, I can…

  • I can identify the important information.
  • I can use accurate notation, labels, and units.
  • I can justify and verify my conclusion.
1
Question 1

What should happen before calculating?

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Question 2

Which response gives the strongest evidence?

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Question 3

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Question 4

Why are units or labels important?

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Question 5

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Next Lesson: Area of Triangles, Quadrilaterals, and Polygons → Back to Binder Topics

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