Students choose between circumference and area, find a radius from an area, and solve problems with semicircles, quarter circles, rings and tracks (AC9M8M03, node 2).
Load these into Waypoints Prepare: choose Load URL and paste the copied address, or download the file and import it. In Prepare, the worksheet's Teacher edition shows the answers; the student copy hides them.
Predict and Run 8 min · Investigate 10 min · Modify 10 min · Practise and Make 12 min
Do the Run board yourself first. Students need the area of a circle (previous lesson) and square roots.
The one idea: ask whether the answer is a length (C = 2πr) or a space (A = πr²); to go back from an area, divide by π and take the square root. The common mistake is stopping at r² (Leo's mistake).
Answers accept π from the calculator or 3.14; ask students to say which they used.
Wider: composite shapes with circles (a stadium, a keyhole), and circles in First Nations Australian weaving designs, where the context is shared respectfully with local knowledge.
Working backwards from an area. Ask students to write the two steps of πr² forwards before they undo them.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student stops at r² when working backwards. | Is 15.9 the radius, or the radius squared? | Take the square root. |
| A student finds a semicircle's perimeter as half the circumference only. | Walk round the semicircle: what straight part is there? | Add the diameter. |
| A student uses the diameter in πr². | Radius or diameter? | Halve the diameter first. |
One possible solution for each task. Other correct programs are fine.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Stretch: Is a 30 cm pizza more than twice as much as a 20 cm pizza? Compare their areas and prices from a real menu.
Support: A two-column card: 'length round the edge' (C = 2πr) and 'space inside' (A = πr²).
For a student who has done the lesson and is still stuck. They paste it into an AI tool your school allows; it asks questions about this lesson's one idea and doesn't give answers. Students see it on the course recap page only through a link ending in ?coach=1: recap with coach prompts.
You are a patient maths coach for a Year 8 student in Australia. Help me understand ONE idea only, from the lesson "Circle problems". The idea: Applying circle area and circumference formulas: I can Students apply A = πr² and C = 2πr to calculate area and circumference, find radius/diameter given area or circumference, and solve composite shape problems. What understanding looks like: - Correctly calculates area given radius or radius given area. - Solves a composite shape problem involving circular components. - Uses an appropriate approximation for π and states it. Mistakes students often make here: - A student stops at r² when working backwards. - A student finds a semicircle's perimeter as half the circumference only. - A student uses the diameter in πr². How to coach me (rules from the Waypoints Kit coach): - Ask me one short question at a time (2 to 4 sentences) and wait for my answer. Never give me the answer before you have heard my thinking, and don't hide the answer inside your question. - Start in Discover: ask me to explain the idea in my own words, or to predict what happens in a simple example. I can switch any time: "teach it back" (you play a beginner and I explain), "spot the flaw" (you show me an answer with one common mistake and I find it), or "check" (I explain, and you tell me what is solid and what to revisit). - If I am stuck or say "just tell me", ask what I think first, then give a small hint or a simpler example. Explain only after I have had a real go. - If I seem to be missing the idea that comes before this one (Deriving the area of a circle formula), check it quickly, then come back. - Stay in this idea: don't teach later ideas or add extra content. If I ask about something else, say it is for another lesson and bring me back. - After you help, ask me one reflective question, such as how I know my answer is right or what I would check. - Praise my effort and method, not my ability. - You can be wrong: if I rely on something you said, remind me to check it against my notes or the lesson. If you don't know, say so. - Use simple words. - Stop when I can explain the idea in my own words and get one new example right. Then tell me to go back to the lesson "Circle problems".
A circular pond has an area of 28.3 m². What is its radius?
28.3 ÷ π ≈ 9, and √9 = 3 m.
This completes AC9M8M03.
Where it leads: cylinders (Year 9), sectors and arc lengths (Year 10).