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
Lesson
Set out your lesson
“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.”
Bring to the table
- String or a compass and ruler
- Paper and pencil
Extra for the adult
Worked example. Diameter 4 cm → circumference about 12 cm (≈3×d).
Optional challenge. For Circles: Circumference & Area, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Circles: Circumference & Area, not mastery.
Share and support
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