Circles: circumference and area – Grade 7 math lesson
Lesson 14 of 21 in the Grade 7 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 7 (ages 12–13) 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 7 (ages 12–13)
- 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.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- 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.
- Finish with the exit ticket and the talk question: “Why is the circumference always about 3.14 times the diameter?”
- 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
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Graded by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, graded by Classfern |
| Independent practice | 15 min | Graded by Classfern |
| Closure and exit ticket | 6 min | Graded 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
More Grade 7 math lessons
- Ratios
- Percent
- Proportional relationships
- Operations with integers
- Repeating decimals
- Evaluating expressions
- Simplifying expressions
- Expanding expressions
- Solving equations
- Inequalities
- Scale drawings and maps
- Angle relationships
- Area of triangles, parallelograms and trapezoids
- Volume and surface area
- Cross sections of 3-D figures
- Probability
- Experimental probability
- Compound events
- Box plots and interquartile range
- Sampling and making inferences
Curriculum
Common Core State Standards 7.G.B.4: “Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.”
Common Core State Standards 7.G.B.6: “Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.