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Circles: circumference and area – Grade 10 math lesson

Lesson 7 of 16 in the Grade 10 math course

US version. US grades, US spelling and dollars ($). · UK Maths Department

A complete 45-minute lesson for grade 10 (ages 15–16) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.

Time
45 minutes + 20 min homework
Grade
Grade 10 (ages 15–16)
You need
Paper, a pencil and this page
Graded
Instantly, with explanations

For parents: how to use this lesson

You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is graded straight away with a worked explanation, so you never have to grade anything.

  1. Read what your child will learn and the big ideas together.
  2. Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
  3. Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
  4. Finish with the exit ticket and the talk question: “Why is the circumference always about 3.14 times the diameter?”
  5. Later that day or the next day: the homework (20 minutes), then a practice test.

Watch out for

  • Using the diameter in the area formula. Area uses the radius: halve the diameter first.
  • Squaring π × r instead of just r. Only the radius is squared: π × r × r.

Tip for home: Measure round objects at home and check that circumference ÷ diameter is close to π.

What your child will learn

Learning goal: find the circumference and area of circles and the length of arcs and area of sectors.

Success looks like

  • I can find the circumference.
  • I can find the area.
  • I can find arc lengths and sector areas.

Key words

radius
from the center to the edge
diameter
across the circle through the center (2 × radius)
circumference
the distance around a circle
sector
a slice of a circle

What to have ready

  • Paper and a pencil
  • This page on a computer, tablet or phone
  • For the hands-on part: Wrap string around tins and plates, measure it and divide by the diameter: you get about 3.14 every time.

The big ideas (for the adult)

The circumference of a circle is π × diameter. The area is π × radius².

π (pi) is about 3.14. Give answers in terms of π when an exact answer is needed.

An arc or sector is a fraction of the whole circle: angle ÷ 360° of the circumference or area.

The lesson, step by step

45 minutes in 5 parts
PartTimeHow it is checked
Starter: quick recall5 minGraded by Classfern
Teaching input10 minNot assessed, self-checked
Worked examples and guided practice9 minNot assessed, graded by Classfern
Independent practice15 minGraded by Classfern
Closure and exit ticket6 minGraded by Classfern, self-checked

Starter, "your turn", practice and exit ticket are graded by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.

The lesson

It runs here on the page. No sign-up and no names – progress is kept only in this browser.

Homework and practice at home

20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all graded instantly.

More practice

All Grade 10 math lessons and tests · Math Department

More Grade 10 math lessons

Curriculum

Common Core State Standards HSG.C.B.5: “Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.”

Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.