Circles: Circumference & Area
Calculate the circumference and area of circles using the formulae C = πd (or 2πr) and A = πr², and solve problems involving perimeters and areas of composite shapes that include circular parts
Entire curriculum
1858 concepts · 9 subjects
Share and support
Compare teaching approaches
Teaching approaches
Gakuva’s recommended starting approach is selected. You can still compare every option.
1 approach
Circles: Circumference & Area means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: String or a compass and ruler; Paper and pencil. 1. Say the goal of Circles: Circumference & Area in plain words once. 2. Adult measures a circle diameter and estimates circumference ≈ 3×diameter. 3. Child measures three circles and records diameter with a circumference estimate. 4. Fresh check: one fresh circumference estimate from diameter. Record and stop. Done: three diameter–circumference records. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.
Family records and proof options
Keep a record of your learning
Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.
Practice this concept
Start practiceCircles: Circumference & Area practice
Practice key ideas from Circles: Circumference & Area.
Free · no login · no ads · Practice answers and completion are not saved. Parent observation remains the lesson record.
Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
PhET Interactive Simulations · Practice link — not the full lesson
Area Builder
Before you open · source notes
Area Builder supports hands-on exploration for Circles: Circumference & Area. Not every lab worksheet.
Free interactive page, no sign-in required for the tested path.
Before you openAsk the learner what they changed in the sim or page and what they observed.
Opening this link does not save learning or assess mastery.
Source, access and review notes
Public PhET Interactive Simulations page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.
PhET Interactive Simulations. “Area Builder.” External page; Gakuva does not copy, host, embed, or redistribute materials.
Unknown — link only
Check understanding
- Calculate the circumference and area of a circle given its radius or diameter
- Find the perimeter or area of a composite shape made from rectangles and semicircles
- Explain the relationship between π, diameter, and circumference informally
“If your child wants to know how far a bicycle wheel travels in one full rotation, can they use the diameter of the wheel and π (pi) to work out the circumference?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Geometry
- Age range
- Ages 12–14
Standards