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⭕ Primary Maths & Science Games · Grade 6 · Circles

Circle Circumference and Area: Roll It, Count It, Work It Out

Local Calculation · Private

The three classic circle slips are using the radius in C = πd, forgetting to square the radius, and writing a ring as 3.14 × (R − r)². Roll the circle once and count squares once, and the formulas make sense. (For cutting a circle into sectors to form a rectangle, see the area cut-and-paste visualizer.)

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How to play

  1. Explore has four views: parts of a circle (drag the orange dot), roll it (one full turn along a line, pause or scrub back), area (count 1 cm squares) and ring (set both radii).
  2. The readings on the right follow the radius, using π = 3.14.
  3. Levels: radius and diameter, circumference, working back from the circumference, area, and rings and semicircles. Parents shows the slips and prints worksheets.

Curriculum unit

Primary maths, grade 6: parts of a circle, circumference, area, rings and semicircles (PEP textbook, grade 6 volume 1, unit 5).

For parents and teachers

Mistakes are grouped as radius/diameter swaps, C with the radius and no × 2, doubling the diameter, circumference vs area, forgetting ÷ 2, not squaring, squaring the diameter, ring as (R − r)² and semicircles without the diameter. The worksheet targets the weakest level, with answers.

FAQ

Why is the circumference π times the diameter?
Roll a circle one full turn and the distance it covers is its circumference. For every circle that distance is 3.14159… times the diameter. That fixed number is π; in primary school we use 3.14.
Where does A = πr² come from?
Cut the circle into many equal sectors and fit them into a near-rectangle: its length is half the circumference, πr, and its width is r, so the area is πr × r = πr². Counting squares gives close to 3.14 × r² too.
How do I find the area of a ring?
Ring area = outer circle − inner circle = π(R² − r²). It is not π(R − r)².