3B · Chapter 12 · Lesson 1
Circles
Identify center, radius, diameter; compare radii and diameters.
Today's mathematical question
A circle has radius 29 cm. What is its diameter?
Learning target
Identify center, radius, diameter; compare radii and diameters.
Before starting: Earlier shape vocabulary and equal-length segments. Try the warm-up independently.
Prerequisite · 3 questions
Check earlier skills first
These are earlier ideas you need for today; revisit them if they are difficult.
- P1
How many corners does a triangle have?
Reveal explanation
Answer: 3
The triangle is a closed, three-sided polygon.
- P2
How many straight sides does a rectangle have?
Reveal explanation
Answer: 4
A rectangle is a closed quadrilateral with four straight sides and four right angles. Trace the boundary once and count the straight segments.
- P3
Is a square still a square when rotated?
Reveal explanation
Answer: Yes
Its side and angle relationships remain the same.
Learn and understand
Every point on a circle is the same distance from its center. That fixed distance is the radius. A diameter goes straight through the center and joins two points on the circle; it contains two radii. If the radius is 4 cm, the diameter is 8 cm. Mark a center and draw two segments from it to the circle. Both are radii. A diameter passes through the center from one side to the other, so it is two radii long.
Represent it three ways
- Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
- Pictorial: Sketch the center, one radius, and one diameter. Mark two equal halves along the diameter and label both.
- Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.
Important vocabulary
- center
- fixed point equally distant from every point on circle
- radius
- center-to-edge segment
- diameter
- through-center edge-to-edge segment
Fully worked examples and checks
Try each new understanding check before revealing the explanation.
Worked example 1
Explore, calculate, verify
A circle has radius 29 cm. What is its diameter?
- Identify the whole, the units, and what the question asks.
- A diameter joins two radii end to end through the center: 29 + 29 = 58 cm.
- Check that the answer uses the right units and makes sense.
Answer: 58 cm
Check your understanding 1
A circle has radius 20 cm. What is its diameter?
Reveal answer and explanation
40 cm — A diameter joins two radii end to end through the center: 20 + 20 = 40 cm.
Worked example 2
Explore, calculate, verify
A circle has diameter 54 cm. What is its radius?
- Identify the whole, the units, and what the question asks.
- The radius is half the diameter. 54 ÷ 2 = 27 cm.
- Check that the answer uses the right units and makes sense.
Answer: 27 cm
Check your understanding 2
A circle has diameter 44 cm. What is its radius?
Reveal answer and explanation
22 cm — The radius is half the diameter. 44 ÷ 2 = 22 cm.
Worked example 3
Explore, calculate, verify
A circle has radius 22 cm. What is its diameter?
- Identify the whole, the units, and what the question asks.
- A diameter joins two radii end to end through the center: 22 + 22 = 44 cm.
- Check that the answer uses the right units and makes sense.
Answer: 44 cm
Check your understanding 3
A circle has radius 25 cm. What is its diameter?
Reveal answer and explanation
50 cm — A diameter joins two radii end to end through the center: 25 + 25 = 50 cm.
Guided · 5 questions
Guided practice
Keep the model and earlier examples visible while practising.
- G1
A circle has radius 7 cm. What is its diameter?
Reveal explanation
Answer: 14 cm
A diameter joins two radii end to end through the center: 7 + 7 = 14 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - G2
A circle has diameter 52 cm. What is its radius?
Reveal explanation
Answer: 26 cm
The radius is half the diameter. 52 ÷ 2 = 26 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - G3
A circle has radius 18 cm. What is its diameter?
Reveal explanation
Answer: 36 cm
A diameter joins two radii end to end through the center: 18 + 18 = 36 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - G4
A circle has diameter 40 cm. What is its radius?
Reveal explanation
Answer: 20 cm
The radius is half the diameter. 40 ÷ 2 = 20 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - G5
A circle has diameter 26 cm. What is its radius?
Reveal explanation
Answer: 13 cm
The radius is half the diameter. 26 ÷ 2 = 13 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge.
Independent · 8 questions
Independent practice
Work these without hints and explain the method used. Write answers on paper.
- I1
A circle has radius 27 cm. What is its diameter?
Reveal explanation
Answer: 54 cm
A diameter joins two radii end to end through the center: 27 + 27 = 54 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - I2
A circle has diameter 50 cm. What is its radius?
Reveal explanation
Answer: 25 cm
The radius is half the diameter. 50 ÷ 2 = 25 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - I3
A circle has radius 9 cm. What is its diameter?
Reveal explanation
Answer: 18 cm
A diameter joins two radii end to end through the center: 9 + 9 = 18 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - I4
A circle has diameter 10 cm. What is its radius?
Reveal explanation
Answer: 5 cm
The radius is half the diameter. 10 ÷ 2 = 5 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - I5
A circle has diameter 36 cm. What is its radius?
Reveal explanation
Answer: 18 cm
The radius is half the diameter. 36 ÷ 2 = 18 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - I6
A circle has radius 16 cm. What is its diameter?
Reveal explanation
Answer: 32 cm
A diameter joins two radii end to end through the center: 16 + 16 = 32 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - I7
A circle has diameter 20 cm. What is its radius?
Reveal explanation
Answer: 10 cm
The radius is half the diameter. 20 ÷ 2 = 10 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - I8
A circle has radius 12 cm. What is its diameter?
Reveal explanation
Answer: 24 cm
A diameter joins two radii end to end through the center: 12 + 12 = 24 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge.
Challenge · 2 questions
Challenge and error analysis
Go beyond arithmetic: justify a claim, correct reasoning, or connect two representations.
- C1
Two circles have diameters 8 cm and 10 cm. Which has the larger radius and by how much?
Reveal explanation
Answer: Second circle, by 1 cm
Their radii are 4 cm and 5 cm; changing diameter by 2 cm changes radius by 1 cm.
- C2
If a compass is set to 4 cm and rotated around a fixed needle point, explain why every point on the drawn circle is 4 cm from the center.
Reveal explanation
Answer: 4 cm
The compass opening remains fixed while the pencil moves around the center.
Exit · 3 questions
Exit check
Solve independently, then return on another day to check retention.
- E1
A circle has diameter 6 cm. What is its radius?
Reveal explanation
Answer: 3 cm
The radius is half the diameter. 6 ÷ 2 = 3 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - E2
A circle has radius 4 cm. What is its diameter?
Reveal explanation
Answer: 8 cm
A diameter joins two radii end to end through the center: 4 + 4 = 8 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - E3
A circle has radius 24 cm. What is its diameter?
Reveal explanation
Answer: 48 cm
A diameter joins two radii end to end through the center: 24 + 24 = 48 cm.
The radius runs from center to edge. The diameter crosses the center from edge to edge.