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# Parts of a circle

Area, volume, circles and Pythagoras · Circles

<!-- Speaker note: 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). About 35 minutes (Predict and Run 6 min · Investigate 10 min · Modify 8 min · Practise and Make 11 min). -->

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## Today

**We are learning to** every point of a circle is the same distance from its centre: the radius. The diameter goes right across through the centre, two radii long (d = 2r). A chord joins any two points; the circumference is the distance all the way round.

- I can name the parts of a circle.
- I can find the diameter from the radius, and the radius from the diameter.
- I can explain why the diameter is the longest chord.

<!-- Speaker note: Before class: 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. -->

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## Why it matters

> Wheels, plates, clocks and pizza: why does a wheel roll smoothly? Because every point on its edge is the same distance from the axle.

<!-- Speaker note: A **circle** is every point the same distance from one point, its **centre**. That distance is the **radius** ($r$). - The **diameter** ($d$) goes right across through the centre. It is two radii: $d = 2r$, so $r = d \div 2$. - A **chord** is a straight line joining any two points on the circle. The diameter is the longest chord. - The **circumference** ($C$) is the distance all the way round: the circle's perimeter. -->

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<span style="background:#dbeafe; color:#1a1a1a; border:1.5px solid #3b82f6; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">💬 Discussion</span>

## Predict

**A circle has radius 5 cm. What is its diameter?**

- 2.5 cm
- 5 cm
- 10 cm
- 25 cm

<!-- Speaker note: What happens: 10 cm: the diameter goes from the edge, through the centre, to the other edge: two radii. 2.5 halves the radius. Take two or three predictions before anyone runs it. -->

<!-- Speaker note: Teacher: students who chose 2.5 halved the radius. -->

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## Try it

{{embed: https://studio.learningwaypoints.com/tutorials/_playground-board/index.html?id=deck%2Fmaths%2Fmeasurement%2Fparts-of-a-circle%2Fstep-2&code=widget%3A+circle%0Aslider+r%3A+1%2C+6%2C+2%0Aunits%3A+cm%0A&fresh=1}}

[Open this step in the tutorial](https://studio.learningwaypoints.com/tutorials/maths/measurement/parts-of-a-circle/?full=step-2#step-2)

<!-- Speaker note: Watch the radius and the diameter as the circle grows. -->

<!-- Speaker note: Teacher: ask what stays true as the circle grows. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## What happened?

* 10 cm: the diameter goes from the edge, through the centre, to the other edge: two radii. 2.5 halves the radius.

<!-- Speaker note: Reveal after running. Ask who predicted it, and what made them think so. -->

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<span style="background:#dbeafe; color:#1a1a1a; border:1.5px solid #3b82f6; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">💬 Discussion</span>

## Two radii make a diameter

Here are the relationships.

Now match the parts.

$$d = 2r$$

1) $r = 5 \Rightarrow d = 2 \times 5 = 10$ — Radius to diameter: double.
2) $d = 120 \Rightarrow r = 120 \div 2 = 60$ — Diameter to radius: halve.
3) $C$ — The circumference is the distance round; the next lessons find it from d.

<!-- Speaker note: Model this live on the board before revealing anything: write each line and say why, pausing to ask the class what comes next. Then click to reveal the lines and compare. Script. Start: write d = 2r and say "The diameter is two radii, end to end through the centre." Line 1: write r = 5 d = 2 × 5 = 10 and say "Radius to diameter: double." Line 2: write d = 120 r = 120 ÷ 2 = 60 and say "Diameter to radius: halve." Line 3: write C and say "The circumference is the distance round; the next lessons find it from d." -->

<!-- Speaker note: Teacher: draw a chord near the edge and one through the centre; compare lengths. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Two radii make a diameter

**Match each part of a circle to what it is.**

| | |
|---|---|
| `radius` | A. right across, through the centre |
| `diameter` | B. the distance all the way round |
| `chord` | C. a straight line joining two points on the circle |
| `circumference` | D. from the centre to the edge |

* Answer: radius → D. from the centre to the edge; diameter → A. right across, through the centre; chord → C. a straight line joining two points on the circle; circumference → B. the distance all the way round

<!-- Speaker note: The radius is half the diameter; the diameter is the longest chord; the circumference is the perimeter. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Find the mistake

**Jay works out how far a chair at the edge of a round table is from its centre. Click the line where he goes wrong.**

```
 1  A round table is 120 cm across, measured through the centre.
 2  The distance across through the centre is the radius.
 3  So the radius is 120 cm.
 4  A chair at the edge is 120 cm from the centre.
```

* Answer: line 2

<!-- Speaker note: Line 2: across through the centre is the diameter. The radius is half of it: 120 ÷ 2 = 60 cm. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Chords

**Is every chord a diameter?**

- Yes: they both go across the circle
- No: only a chord that passes through the centre is a diameter
- No: a chord is always curved

* Answer: No: only a chord that passes through the centre is a diameter

<!-- Speaker note: Every diameter is a chord (the longest one), but most chords miss the centre. -->

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<span style="background:#fef3c7; color:#1a1a1a; border:1.5px solid #f59e0b; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✍️ Activity</span>

## One change at a time



- **Diameter 7:** Each task changes one thing.
- **Diameter to radius:** 
- **Radius to diameter:** 
- **Opposite radii:** 

[Open this step](https://studio.learningwaypoints.com/tutorials/maths/measurement/parts-of-a-circle/?full=step-4#step-4)

<!-- Speaker note: What this step is for: One change at a time: an odd diameter on the board (a half radius), diameter to radius, radius to diameter with a decimal, then the longest chord and two radii in a line. Hints, in order: The radius is half of 7. For students who need more support: Use a paper circle folded in half (the fold is a diameter) and in quarters (the centre). For early finishers: How many 3 cm radius coasters fit, in a grid, on a 30 cm by 24 cm tray? The hard part, on purpose: 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. When students get stuck: A student calls the diameter the radius (Jay's mistake). Ask: Does it stop at the centre or go right across? Fix: Centre to edge is the radius; edge to edge through the centre is the diameter. / A student doubles when they should halve. Ask: Is the diameter bigger or smaller than the radius? Fix: The diameter is bigger: double the radius; halve the diameter. / A student thinks the circumference is a chord. Ask: Is it straight or curved? Fix: The circumference is the curved distance round. -->

<!-- Speaker note: Teacher: for diameter 7, ask why the radius is not a whole number. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Double

**A clock face has radius 12 cm. What is its diameter, in cm?**

* Answer: 24

<!-- Speaker note: 2 × 12 = 24 cm. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Halve

**A coin has diameter 3 cm. What is its radius, in cm?**

* Answer: 1.5

<!-- Speaker note: 3 ÷ 2 = 1.5 cm. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Longest chord

**What is the longest chord of a circle?**

- A radius
- A diameter
- The circumference
- Any chord near the edge

* Answer: A diameter

<!-- Speaker note: A chord through the centre, the diameter, is the longest. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Review: volume

**Review: a box is 2 cm by 3 cm by 4 cm. What is its volume, in cm³?**

* Answer: 24

<!-- Speaker note: 2 × 3 × 4 = 24 cm³. -->

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<span style="background:#fef3c7; color:#1a1a1a; border:1.5px solid #f59e0b; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✍️ Activity</span>

## Make: the biggest circle in a box

Then: how many of those circles fit side by side in the lid?

<!-- Speaker note: What this step is for: Fitting the biggest circle in a rectangle means reasoning about the diameter against the shorter side, then halving for the radius. Hints, in order: The circle must fit across the narrow way. / Its diameter can be at most the shorter side. -->

<!-- Speaker note: Teacher: let students sketch the lid before answering. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Exit ticket

**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.

<!-- Speaker note: Students answer on paper or a mini whiteboard before the reveal. Anyone who cannot answer needs the main idea again next lesson. Where this leads: 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). -->