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Circles: π, Circumference & Area

Students meet pi (π) — the special number connecting a circle’s distance around to its distance across — and use it to find any circle’s circumference (πd) and area (πr²).

Grade 7Geometry50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
Start the Lesson
Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Know π relates circumference to diameter.
  • ✓Find circumference with C = πd.
  • ✓Find area with A = πr².
  • ✓Tell radius from diameter.
Essential Question

Every circle in the universe shares one magic number: its distance around divided by its distance across is always about 3.14. Why — and how do we use it?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Model · Interactive Tool

The Circle Tool

Project this and change the radius. Watch the circumference and area update, and see how each is built from the radius using π.

⭕ Change the radius — find circumference & areaTry it
Radius: 4 units

The Lesson · Gradual Release (I Do · We Do · You Do)

50 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — The Magic Number

5 min

Distance around ÷ distance across — always the same?

👩‍🏫 Teacher Moves

  • Measure round objects’ around and across.
  • Divide; get about 3.14.
  • Set the goal: circles and π.

🎒 Student Actions

  • Measure objects.
  • Divide and compare.
  • Predict the constant.
2

I Do — πd and πr²

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Define π ≈ 3.14.
  • Find circumference: C = πd.
  • Find area: A = πr².

🎒 Student Actions

  • Learn π.
  • Find circumference.
  • Find area.
3

We Do — Explore Together

13 min

Class drives the Circle Tool.

👩‍🏫 Teacher Moves

  • Change the radius; read C and A.
  • Connect diameter = 2r.
  • Estimate before computing.

🎒 Student Actions

  • Set the radius.
  • Read C and A.
  • Estimate to check.
4

You Do — On Your Own

12 min

Students find C and A.

👩‍🏫 Teacher Moves

  • Assign circumference and area problems.
  • Watch radius vs. diameter.
  • Solve a real circle problem.

🎒 Student Actions

  • Find C.
  • Find A.
  • Solve a problem.
5

Close — Close

5 min

One circle.

👩‍🏫 Teacher Moves

  • Give a radius or diameter.
  • Find C and A.
  • Hand out the exit ticket.

🎒 Student Actions

  • Find C and A.
  • Show the formulas.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics, including the Standards for Mathematical Practice.

CCSS
7.G.4

Know and use the formulas for the area and circumference of a circle.

CCSS
7.G.6

Solve problems involving area, volume, and surface area.

CCSS
7.G.1

Solve problems involving scale drawings of geometric figures.

SMP
MP.7

Look for and make use of structure in circle formulas.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Label radius, diameter on a circle.
  • Sentence frame: “C = πd; A = πr².”
  • Measure real circles.

Support & Access

IEP / 504
  • Provide the formulas on a card.
  • Use π ≈ 3.14 with a calculator.
  • Focus on circumference first.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Find the radius from the area.
  • Find the area of a semicircle.
  • Solve a composite-figure problem.
Materials

What to gather

  • 📽️Projector / board
  • 📓Math notebooks
  • 💻The Circle Tool
  • 📏String + rulers
  • 🧮Calculators
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

circlea round shape, all points equal from the centerradiuscenter to edge distancediameteredge to edge through the center (2r)circumferencethe distance around a circlepi (π)≈ 3.14, circumference ÷ diameterareathe space insidecenterthe middle pointformulaa rule for calculating
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
What is the circumference of a circle with diameter 10? (π ≈ 3.14)
About 31.4 (C = πd = 3.14 × 10).
QUESTION 2
What is the area of a circle with radius 3? (π ≈ 3.14)
About 28.3 (A = πr² = 3.14 × 9).
QUESTION 3
If a circle’s diameter is 8, what is its radius?
4 (radius is half the diameter).

Going deeper? Measure real circles.

Have students wrap string around round objects to measure circumference, measure the diameter, and divide to discover π for themselves. A printable circle-lab sheet is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Circles: Circumference & AreaFlip
Card 1
Term
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Meaning
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Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Circles: Circumference & AreaQuiz
Score: 0
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Question 1
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Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Circles: Circumference & AreaPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: area, center, circle, circumference, diameter, formula, pi (π), radius
  1. a rule for calculating
  2. the distance around a circle
  3. the middle point
  4. the space inside
  5. edge to edge through the center (2r)
  6. ≈ 3.14, circumference ÷ diameter
  7. a round shape, all points equal from the center
  8. center to edge distance

Part B · Show what you learned

  1. What is the circumference of a circle with diameter 10? (π ≈ 3.14)
  2. What is the area of a circle with radius 3? (π ≈ 3.14)
  3. If a circle’s diameter is 8, what is its radius?
Answer key — Part A: 1) formula · 2) circumference · 3) center · 4) area · 5) diameter · 6) pi (π) · 7) circle · 8) radius
Part B: 1) About 31.4 (C = πd = 3.14 × 10). 2) About 28.3 (A = πr² = 3.14 × 9). 3) 4 (radius is half the diameter).