Singapore Math Drills Team · 22 September 2026
Free, distraction-free math drills aligned to the MOE syllabus. No sign-up needed to try.
By Primary 6, a question can look unfamiliar even when the key idea is one your child has practised before. A circle may ask for area or circumference, a trapezium may require the right pair of angles, and a tank question may hide a simple volume relationship inside a word problem. The calmest approach is to name the quantity being found before calculating.
This guide focuses on three skills: finding the area of a circle, finding an angle in a trapezium with parallel sides, and finding the height of water in a tank. On the free sample worksheet, your child meets these skills through visual examples and worked steps. The questions below are parallel practice, not a list to memorise. The goal is to build a reliable way to read, choose and check.
A circle has a radius of 14 cm. Find its area. (Take π = 22/7)
The area of a circle measures the space inside it. The formula is π × r × r, where r is the radius. Radius means the distance from the centre to the edge. It is half the diameter, so check the label before substituting a number. Here the radius is already given as 14 cm.
The cancellation step is not a shortcut that changes the value. It uses the factor 7 in the denominator with a factor 14 in the numerator before multiplying. This keeps the numbers manageable and makes it less likely that a child will make a long multiplication error. If they prefer, they can calculate 22 × 14 × 14 ÷ 7 and still reach 616 cm².
It is important to distinguish area from circumference. They describe different things even though both use the radius:
| Quantity | Formula | Result here | What it measures |
|---|---|---|---|
| Area | 22/7 × 14 × 14 | 616 cm² | Space inside the circle |
| Circumference | 2 × 22/7 × 14 | 88 cm | Length around the circle |
The units are a useful final check: cm² tells us we found space inside, while cm tells us we found a length around the edge.
Common mistake: Using the diameter as r. If a diagram gives the full distance across the circle, divide it by 2 before using the area formula.
Try this at home: Draw a circle, mark its centre and one radius, then ask your child to explain why the radius is not the full distance across.
In trapezium PQRS, PQ is parallel to SR and ∠P = 125°. Find ∠S.
This question is about choosing the correct pair of angles. Since PQ is parallel to SR, the angles at P and S lie between the parallel lines on the same side of the leg PS. These interior angles add to 180°. The shape in a question may be tilted, so follow the named vertices and the parallel marks rather than relying only on how it looks.
The note “diagram not drawn to scale” is important. A printed trapezium may make one angle look larger or smaller than it really is. Geometry questions are solved from the information given: the parallel lines, the named angles and the shared leg. If you are coaching, point to P and S and trace the side PS with your finger. That makes the relevant pair easier to see.
There are other angle pairs in a trapezium, but not every pair forms the same relationship. Before writing 180°, ask which two angles are connected by one leg between the parallel sides. That check prevents a child from choosing a pair simply because the labels are close together on the page.
Common mistake: Choosing an angle pair that does not share a leg between the parallel sides. ∠P and ∠S are the useful pair because both sit along PS.
Try this at home: Draw two parallel lines and connect them with a slanted leg, then label one interior angle and ask your child to mark the angle that pairs with it.
A rectangular tank has a base of 15 cm by 8 cm. It contains 960 cm³ of water. Find the height of the water.
This is a volume question where the height is unknown. A rectangular tank can be treated as a cuboid filled only to the water level. The base tells us the area of one layer of water, and the volume tells us how many cubic centimetres are in the tank. Once those two facts are connected, the missing height is found by division.
The “layers” picture helps here too. Each 1 cm layer across the base contains 120 cm³ of water. The tank contains 960 cm³, so 960 ÷ 120 tells us how many 1 cm layers fit: eight layers, or a water height of 8 cm. This interpretation is often clearer than treating the formula as a rule to rearrange blindly.
Be careful when the question uses litres. The relationship 1 ℓ = 1000 cm³ lets you convert a litre measurement into cubic centimetres before using the volume formula. Keep the base dimensions in the same unit as the requested height, and write the unit after every important line.
Common mistake: Dividing 960 by only one base side. The base is a rectangle, so both 15 cm and 8 cm are needed to find its area before finding the height.
Try this at home: Use a rectangular food container, estimate the base area, and discuss why doubling the water height would double the volume if the base stayed the same.
The free sample mini-drill gives your child a focused way to practise upper-primary ideas before a longer revision session. Heuristics and PSLE-style word problems build the habit of identifying the relationship first, while progressive hints and worked solutions make each next step visible. Adaptive practice can respond to recent performance, and spaced review brings circle, angle and volume skills back at useful intervals. The built-in scratch pad is there for drawing a radius, tracing a parallel-line pair or sketching tank layers. The result is a calm practice loop that keeps the working visible.
A circle has a radius of 7 cm. Find its circumference. (Take π = 22/7)
Hint: Circumference = 2 × π × r. Cancel the 7 first.
Try the free Primary 6 sample worksheet
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