Students use C = πd and C = 2πr to find circumferences, check against circles rolled out on the board, go backwards with d = C ÷ π, and design a trundle wheel (AC9M7M03, node 3).
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 15 min · Modify 12 min · Practise and Make 10 min
Do the Run board yourself first. Students need π as C ÷ d (previous lesson), d = 2r, and dividing decimals (a calculator is fine).
The one idea: C = πd, because that is what π means. The common mistake is using the radius in place of the diameter (Mei's mistake, a spiral of Parts of a circle). Rearranging to d = C ÷ π uses the inverse-operations idea from Algebra.
Going backwards from a circumference to a radius takes two steps (divide by π, then halve). Ask students to write which length they have and which they want before they press any calculator keys.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student multiplies π by the radius (Mei's mistake). | Is the given length across the whole circle or half way? | Double the radius to get the diameter, or use C = 2πr. |
| A student multiplies by π when going backwards. | Should the diameter be bigger or smaller than the circumference? | Smaller: divide by π. |
| A student forgets units or mixes cm and m. | What unit is your answer in? What does the question want? | Convert at the end: 100 cm = 1 m. |
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: The Earth's equator is about 40 000 km. Estimate the Earth's diameter. If a rope round the equator were made 1 m longer, how high above the ground would it float?
Support: Keep C = πd and d = 2r on the board; use 3.14 on a calculator (the π key gives answers a little different from 3.14).
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 7 student in Australia. Help me understand ONE idea only, from the lesson "Circumference". The idea: Using π to calculate circumference and diameter: I can Students use C = πd (or C = 2πr) to calculate the circumference given the diameter or radius, and rearrange to find diameter given circumference. What understanding looks like: - Correctly calculates circumference given diameter or radius. - Correctly finds diameter given circumference. - Uses an appropriate approximation for π and specifies it. Mistakes students often make here: - A student multiplies π by the radius (Mei's mistake). - A student multiplies by π when going backwards. - A student forgets units or mixes cm and m. 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 (Discovering π as a constant ratio), 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 "Circumference".
Find the circumference of a circle with radius 4 cm. A circle has circumference 12.56 cm: find its diameter. (π ≈ 3.14)
2 × 3.14 × 4 = 25.12 cm. 12.56 ÷ 3.14 = 4 cm.
This completes AC9M7M03.
Where it leads: the area of a circle and composite shapes with circles (Year 8), arc length (Year 10), and Pythagoras (AC9M8M06, next in this pathway).