Students name the parts of a circle (centre, radius, diameter, chord, circumference), use d = 2r in both directions, and reason about the biggest circle that fits a rectangle (AC9M7M03, node 1).
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 6 min · Investigate 10 min · Modify 8 min · Practise and Make 11 min
Do the Run board yourself first. Students meet these words informally in primary school; this lesson makes them exact.
The one idea: the radius is centre to edge; the diameter is two radii right across; d = 2r. The common mistake is mixing them up in context (Jay's mistake). Circumference is named here and found in the next two lessons.
Keeping radius and diameter apart in word problems. Ask students to sketch the circle and mark the given length on it before they double or halve.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student calls the diameter the radius (Jay's mistake). | Does it stop at the centre or go right across? | Centre to edge is the radius; edge to edge through the centre is the diameter. |
| A student doubles when they should halve. | Is the diameter bigger or smaller than the radius? | The diameter is bigger: double the radius; halve the diameter. |
| A student thinks the circumference is a chord. | Is it straight or curved? | The circumference is the curved distance round. |
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.
Stretch: How many 3 cm radius coasters fit, in a grid, on a 30 cm by 24 cm tray?
Support: Use a paper circle folded in half (the fold is a diameter) and in quarters (the centre).
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 "Parts of a circle". The idea: Features of circles and their relationships: I can identify and name the features of a circle (radius, diameter, circumference, chord) and state that diameter = 2 × radius. What understanding looks like: - Correctly identifies and labels all key features of a circle. - States that diameter = 2 × radius and applies it correctly. - Does not confuse radius with diameter. Mistakes students often make here: - A student calls the diameter the radius (Jay's mistake). - A student doubles when they should halve. - A student thinks the circumference is a chord. 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. - 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 "Parts of a circle".
A circular pond has diameter 9 m. Find its radius. What is a chord?
4.5 m. A straight line joining two points on the circle.
Next: Discovering π (node 2): how the circumference compares to the diameter.
Where it leads: circle theorems (Year 10), and the area of a circle (Year 8).