3B · Chapter 12 · Lesson 7
Using a Compass
Construct circles with given centers and radii, checking consistent distance.
Today's mathematical question
Using a compass set to 18 mm, draw a circle. What must be the distance from the center to every point on the circle?
Learning target
Construct circles with given centers and radii, checking consistent distance.
Before starting: Prior lesson: Properties of Quadrilaterals. 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
Identify the most specific shape: a quadrilateral has four equal sides of 9 cm but no right angles.
Reveal explanation
Answer: rhombus
The shape is a rhombus. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.
- P2
Identify the most specific shape: a quadrilateral has two pairs of parallel sides, side lengths 8 and 10 cm, and no right angles.
Reveal explanation
Answer: parallelogram
The shape is a parallelogram. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.
- P3
Identify the most specific shape: a quadrilateral has four right angles and four equal sides of 5 cm.
Reveal explanation
Answer: square
The shape is a square. Check right angles, equal-length sides and parallel lines; the description distinguishes it from the other listed types.
Learn and understand
A compass makes circles by keeping the distance between its needle and pencil point fixed. Place the needle at the center, set the opening to the required radius, and rotate the pencil without changing the opening. Every resulting point must be the radius distance from the center. Place the needle at the chosen center and set the pencil exactly 3 cm away. Turn without changing the opening. A 3-cm radius produces a 6-cm diameter.
Represent it three ways
- Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
- Pictorial: Mark a center and measure the compass opening on a ruler. Construct the circle and check points around it using the same opening.
- Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.
Important vocabulary
- compass
- drawing instrument maintaining fixed radius
- radius
- fixed center-to-circle distance
- center
- the needle location
Fully worked examples and checks
Try each new understanding check before revealing the explanation.
Worked example 1
Explore, calculate, verify
Using a compass set to 18 mm, draw a circle. What must be the distance from the center to every point on the circle?
- Identify the whole, the units, and what the question asks.
- The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 18 mm from the center.
- Check that the answer uses the right units and makes sense.
Answer: 18 mm
Check your understanding 1
Using a compass set to 10 mm, draw a circle. What must be the distance from the center to every point on the circle?
Reveal answer and explanation
10 mm — The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 10 mm from the center.
Worked example 2
Explore, calculate, verify
Using a compass set to 1 cm, draw a circle. What must be the distance from the center to every point on the circle?
- Identify the whole, the units, and what the question asks.
- The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 1 cm from the center.
- Check that the answer uses the right units and makes sense.
Answer: 1 cm
Check your understanding 2
Using a compass set to 3 cm, draw a circle. What must be the distance from the center to every point on the circle?
Reveal answer and explanation
3 cm — The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 3 cm from the center.
Worked example 3
Explore, calculate, verify
Using a compass set to 21 mm, draw a circle. What must be the distance from the center to every point on the circle?
- Identify the whole, the units, and what the question asks.
- The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 21 mm from the center.
- Check that the answer uses the right units and makes sense.
Answer: 21 mm
Check your understanding 3
Using a compass set to 17 mm, draw a circle. What must be the distance from the center to every point on the circle?
Reveal answer and explanation
17 mm — The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 17 mm from the center.
Guided · 5 questions
Guided practice
Keep the model and earlier examples visible while practising.
- G1
Using a compass set to 23 mm, draw a circle. What must be the distance from the center to every point on the circle?
Reveal explanation
Answer: 23 mm
The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 23 mm from the center.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - G2
Using a compass set to 2 cm, draw a circle. What must be the distance from the center to every point on the circle?
Reveal explanation
Answer: 2 cm
The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 2 cm from the center.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - G3
Using a compass set to 12 mm, draw a circle. What must be the distance from the center to every point on the circle?
Reveal explanation
Answer: 12 mm
The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 12 mm from the center.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - G4
Using a compass set to 22 mm, draw a circle. What must be the distance from the center to every point on the circle?
Reveal explanation
Answer: 22 mm
The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 22 mm from the center.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - G5
Using a compass set to 19 mm, draw a circle. What must be the distance from the center to every point on the circle?
Reveal explanation
Answer: 19 mm
The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 19 mm from the center.
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
Using a compass set to 4 mm, draw a circle. What must be the distance from the center to every point on the circle?
Reveal explanation
Answer: 4 mm
The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 4 mm from the center.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - I2
Using a compass set to 5 mm, draw a circle. What must be the distance from the center to every point on the circle?
Reveal explanation
Answer: 5 mm
The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 5 mm from the center.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - I3
Using a compass set to 3 mm, draw a circle. What must be the distance from the center to every point on the circle?
Reveal explanation
Answer: 3 mm
The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 3 mm from the center.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - I4
Using a compass set to 16 mm, draw a circle. What must be the distance from the center to every point on the circle?
Reveal explanation
Answer: 16 mm
The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 16 mm from the center.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - I5
Using a compass set to 2 mm, draw a circle. What must be the distance from the center to every point on the circle?
Reveal explanation
Answer: 2 mm
The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 2 mm from the center.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - I6
Using a compass set to 20 mm, draw a circle. What must be the distance from the center to every point on the circle?
Reveal explanation
Answer: 20 mm
The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 20 mm from the center.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - I7
Using a compass set to 25 mm, draw a circle. What must be the distance from the center to every point on the circle?
Reveal explanation
Answer: 25 mm
The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 25 mm from the center.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - I8
Using a compass set to 9 mm, draw a circle. What must be the distance from the center to every point on the circle?
Reveal explanation
Answer: 9 mm
The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 9 mm from the center.
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 10 cm and 12 cm. Which has the larger radius and by how much?
Reveal explanation
Answer: Second circle, by 1 cm
Their radii are 5 cm and 6 cm; changing diameter by 2 cm changes radius by 1 cm.
- C2
If a compass is set to 5 cm and rotated around a fixed needle point, explain why every point on the drawn circle is 5 cm from the center.
Reveal explanation
Answer: 5 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
Using a compass set to 15 mm, draw a circle. What must be the distance from the center to every point on the circle?
Reveal explanation
Answer: 15 mm
The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 15 mm from the center.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - E2
Using a compass set to 14 mm, draw a circle. What must be the distance from the center to every point on the circle?
Reveal explanation
Answer: 14 mm
The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 14 mm from the center.
The radius runs from center to edge. The diameter crosses the center from edge to edge. - E3
Using a compass set to 7 mm, draw a circle. What must be the distance from the center to every point on the circle?
Reveal explanation
Answer: 7 mm
The fixed compass opening is the radius. Keep its needle fixed and rotate the pencil to keep every perimeter point 7 mm from the center.
The radius runs from center to edge. The diameter crosses the center from edge to edge.