Primary 6 · Mathematics

P6 circles

For the area of a half circle you halve the whole circle, and it works. For the perimeter you cannot, and the reason costs a mark in almost every composite question. Here it is.

Level
P6
Usually taught
Term 2
Covers
3 concepts

What changes at P6

At Primary 6, a circle has two things to measure, and they use different formulas: the distance round the outside (the circumference, πd) and the space inside (the area, πr²). Learning the two formulas is the easy part.

The marks go on half and quarter circles. For the area, you take the whole circle and halve or quarter it, and that is correct. For the perimeter you cannot do the same, because cutting the circle makes a straight edge that a whole circle never had.

The sentence that costs the mark

A semicircle has a diameter of 14 cm. Find its perimeter. (Take π=227\pi = \frac{22}{7})

What the working usually does

perimeter =half the circle=22 cm

Half of the whole circle's distance round is 22 cm, and that is correct for the curved part. The working stops there.

What the question asked

perimeter =arc + diameter=36 cm

The perimeter is the whole boundary. The curved arc is 22 cm, and the straight edge the cut created is the 14 cm diameter.

Halving the whole circle is the right move for the AREA of a semicircle, so it feels right for the perimeter too. It is not, and that is the trap: a perimeter gains a straight edge the half circumference never counted. Both lines look like real working, and 22 cm looks sensible for a shape 14 cm across.

For the area, halve the whole circle. Correct.
14 cm
For the perimeter, the straight edge counts too.

The same question, worked properly

  1. Find the curved part

    arc = 12×227×14\frac{1}{2} \times \frac{22}{7} \times 14 = 22 cm

    The whole circumference is π × d. Half of it is the curved edge of the semicircle. Use the π the question gives, not a 3.14 from memory.

  2. Find the straight part

    straight edge = 14 cm

    This is the step that fails. Cutting the circle in half makes an edge the whole circle never had, and it is the diameter, already given as 14 cm. This is the line that goes missing.

  3. Add the two parts

    perimeter = 22 + 14 = 36 cm

    The perimeter is the distance all the way round the outside, so both edges count.

  4. See why halving fooled it

    area = 12×227×7×7\frac{1}{2} \times \frac{22}{7} \times 7 \times 7 = 77 cm²

    For the AREA, halving the whole circle IS correct, which is exactly why a child reaches for it on the perimeter. The perimeter is the one place the straight edge has to be added back.

How can you tell it has clicked?

You do not need to do the maths to check this. When a half or quarter circle asks for the perimeter, ask one thing before they start: "which edges do we add?"

A child who has understood names two: the curved arc and the straight edge. A child who says "half the circle" or reaches straight for a formula is the one who loses these marks, and they will lose them again on every composite figure.

One thing to try tonight

Cut something round in half at home. A roti prata, or a slice of bread. Point at the edge and ask how many kinds of edge a half has now. The answer is two: the curved one, and the flat cut.

Then have them run a finger all the way round the outside of one half, back to where they started. That finger has just traced the perimeter, and it does not lift off at the end of the curve.

What your child will meet in this topic

  • Circle Area
  • Circumference
  • Half and Quarter Circles

Most Singapore schools introduce this in Term 2, though schools do differ by a term either way. If your child’s school runs a different order, you can set it in the schedule on your dashboard.

What it leads to

Half and quarter circles spend the rest of P6 inside composite figures: a rectangle with a quadrant cut out, a semicircle on the end of a rectangle. Every one asks the same two questions separately, the perimeter and the area, and they behave differently.

A child who keeps perimeter and area apart handles those. A child who blurs them, halving for both, loses marks on the composite questions all the way to the PSLE.

More in Primary 6

Other topics in the same year, so you can see what sits either side of this one.

Struggling with the working rather than the topic itself? How to help your child with problem sums

See how your child is doing on this topic

StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.

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