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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

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

Example 2

Triangle with base 10 m and height 7 m

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.

Learn Through Video

Watch, pause, and explain

Use the chapter markers, key vocabulary, and reflection prompts to stay actively engaged while you watch.

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Now Playing

Perimeter, Area, and Volume Explained - Math with Mr. J

1 Perimeter, Area, and Volume Explained - Math with Mr. J 2 Circumference of a Circle - Math with Mr. J

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Warm-Up Guided Independent Challenge

Quick Start

Warm-Up

Warm-up 1

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

We Do

Guided Practice

Guided 1

Rectangle 8 by 5: P = 26 units.

Guided 2

Triangle sides 6, 9, and 11: P = 26 units.

Guided 3

Circle radius 7: C = 14 pi units.

Guided 4

Circle diameter 12: C = 12 pi units.

Guided 5

A square has perimeter 36: side = 9 units.

You Do

Independent Practice

Independent 1

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

Independent 2

Create and solve a second example with different values.

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.

IXL

Perimeter

Open resource

IXL

Circumference of Circles

Open resource

Khan Academy

Perimeter

Open resource

Khan Academy

Circumference of a Circle

Open resource

DeltaMath

DeltaMath: Perimeter of Polygons

Open resource

DeltaMath

DeltaMath: Circumference of Circles

Open resource

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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.

Question 1

What should happen before calculating?

Question 2

Which response gives the strongest evidence?

Question 3

What is an effective accuracy check?

Question 4

Why are units or labels important?

Question 5

What should a student do after finding an error?

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Lesson Complete

Great job on Perimeter and Circumference!

You reviewed the lesson, practiced the skill, and completed the mastery check.

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

At a Glance

Learning Targets

Interactive Vocabulary

Worked Examples

Rectangle 8 cm by 5 cm

Triangle with base 10 m and height 7 m

Common Questions

Common Misconceptions

Watch, pause, and explain

Perimeter, Area, and Volume Explained - Math with Mr. J

Ready to practice?

Practice until you can explain it

Warm-Up

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

Guided Practice

Rectangle 8 by 5: P = 26 units.

Triangle sides 6, 9, and 11: P = 26 units.

Circle radius 7: C = 14 pi units.

Circle diameter 12: C = 12 pi units.

A square has perimeter 36: side = 9 units.

Independent Practice

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

Create and solve a second example with different values.

Challenge & Real-World Practice

Nice work!

IXL

Perimeter

Circumference of Circles

Khan Academy

Perimeter

Circumference of a Circle

DeltaMath

DeltaMath: Perimeter of Polygons

DeltaMath: Circumference of Circles

Save today’s lesson and grow your MathBinder

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Complete the thought

What do you want to remember?

My Journal History

Ready to check your understanding?

Can you do this on your own?

Before you begin, I can…

What should happen before calculating?

Which response gives the strongest evidence?

What is an effective accuracy check?

Why are units or labels important?

What should a student do after finding an error?

How confident do you feel?

Your Results

Review and try again

Great job on Perimeter and Circumference!