P5 Maths — the teaching behind every question

Every Primary 5 topic: the method in one line, the picture to draw, and one question worked step by step before your child practises it.

← Kyly Tuition homePractise freePSLE topic guides

Pick a topic

16 topics. Each card ends with a button that takes your child straight into questions on that topic.

AnglesArea and perimeterArea of triangleAverageBar graphsDecimalsFractionsGeometryMeasurementPercentagePie chartRatioRateTimeVolumeWhole numbers

Angles: a straight edge holds 180°, a full turn holds 360°

Method: Decide which total applies first — 180° on a line, 360° round a point

65°48°67°
65° + 48° = 113°, so the angle left on the straight edge is 67°
  • A straight edge is half of a full turn, so the angles sitting on it add up to 180°.
  • A full turn all the way round one point adds up to 360°, which is twice a straight edge.
  • Add the angles you were given, then take that total away from 180° or from 360°.

One question, worked step by step

A book rest is folded so that its straight front edge is split into three angles. Two of the angles are 65° and 48°. What is the third angle?
Step 1: Put the two angles you were given together.65 + 48 = 113
Step 2: A straight edge holds 180°, so take that total away from 180°.180 − 113 = 67
Step 3: Check it: all three angles must come back to 180°.113 + 67 = 180
Where children go wrong: Using 360° for a straight edge and answering 247° — 360° belongs to angles all the way round one point, and a straight edge only has half of that.

Now try P5 questions on this topic →

Area and perimeter: half the perimeter is one length plus one width

Method: Halve the perimeter first, then take away the side you already know

13 cm10 cmarea = length × breadthperimeter = all four sides
perimeter 46 m and length 13 m, so the width is 23 − 13 = 10 m
  • The perimeter walks right round the shape: two lengths and two widths.
  • So half of the perimeter is one length plus one width — that is the step children skip.
  • The area is the space inside, found by multiplying the length by the width.

One question, worked step by step

A rectangular sandpit in a park has a perimeter of 46 m. Its longer side is 13 m. What is the area of the sandpit?
Step 1: Half the perimeter is one length plus one width.46 ÷ 2 = 23
Step 2: Take the 13 m side away to leave the width.23 − 13 = 10
Step 3: Area is length times width.13 × 10 = 130
Step 4: Check the perimeter: twice the half-perimeter must give back 46 m.23 × 2 = 46
Where children go wrong: Taking the 13 m away from the whole perimeter and calling 33 m the width — the perimeter holds two widths, so halve it before subtracting.

Now try P5 questions on this topic →

Area of triangle: a triangle is half of a rectangle

Method: Base × height, then halve it — and use the straight-up height, never a slanted side

base 18 cmheight 11 cm
base 18 cm and height 11 cm: half of 198 square cm is 99 square cm
  • Put two identical triangles together and you get a rectangle.
  • So one triangle is always half of base times height, whatever shape it is.
  • The height is the straight-up distance from the base to the top corner, not a slanted edge.

One question, worked step by step

A triangular bunting flag has a base of 18 cm and a straight-up height of 11 cm. One string carries 8 such flags. What area of cloth do the flags use altogether?
Step 1: Work out base times height first.18 × 11 = 198
Step 2: A triangle is half of that rectangle.198 ÷ 2 = 99
Step 3: Eight flags use eight times the cloth of one flag.99 × 8 = 792
Where children go wrong: Multiplying base by height and stopping at 198 — that is the rectangle around the triangle, and the triangle is exactly half of it.

Now try P5 questions on this topic →

Average: share the total out evenly, one for each reading

Method: Add every reading, then divide by how many readings there are

MonTueWedThuaverage 25
four days come to 100 cans, so every day levels out at 25 cans
  • The average is the number each day would get if every day were made equal.
  • So add all the readings first to find the total.
  • Then divide by how many readings you added — count them, never guess.

One question, worked step by step

A class collects drink cans for recycling. Monday 18 cans, Tuesday 24, Wednesday 30 and Thursday 28. What was the average number of cans collected each day?
Step 1: Add Monday and Tuesday.18 + 24 = 42
Step 2: Add Wednesday.42 + 30 = 72
Step 3: Add the last day, which gives the total.72 + 28 = 100
Step 4: Divide the total by the four days you added.100 ÷ 4 = 25
Where children go wrong: Dividing the total by the number of days that look busy instead of by all four — the average always divides by the number of readings.

Now try P5 questions on this topic →

Bar graphs: read one bar at a time against the scale

Method: Read each bar across to the numbered line, write it down, then choose add or subtract

35Mon48Tue42Wed55Thu40Fri
five days borrowed: 35, 48, 42, 55 and 40 books
  • A bar means nothing until you follow it across to the scale.
  • Write every value down in a list before you add anything.
  • The words how many more mean subtract; the word altogether means add.

One question, worked step by step

A school library records the books borrowed each day: Monday 35, Tuesday 48, Wednesday 42, Thursday 55 and Friday 40. (a) How many books were borrowed in those five days? (b) On average, how many books a day was that?
Step 1: Add Monday and Tuesday.35 + 48 = 83
Step 2: Add Wednesday.83 + 42 = 125
Step 3: Add Thursday.125 + 55 = 180
Step 4: Add Friday to finish the total.180 + 40 = 220
Step 5: Share the total among the five days.220 ÷ 5 = 44
Where children go wrong: Reading a bar one step off the scale and carrying that wrong number all the way through — run a finger across to the numbered line before writing the value.

Now try P5 questions on this topic →

Decimals: times 10, 100 and 1000 shifts the digits along

Method: Times 10 moves one place, times 100 moves two places, times 1000 moves three

× 101 place↓× 1002 places↓× 10003 places
4.25 × 10 = 42.5 and × 100 = 425: every step makes it bigger
  • Each place after the dot is ten times smaller than the place before it.
  • So multiplying by 10 pushes every digit one place to the left.
  • The answer must be bigger than the number you started with — check that first.

One question, worked step by step

A bowl of noodles at the school fun fair costs $4.25. (a) What do 10 bowls cost? (b) What do 100 bowls cost? (c) An order comes in for 300 bowls. How much money is that?
Step 1: Times 10 moves the digits one place.4.25 × 10 = 42.5
Step 2: Times 100 moves them two places.4.25 × 100 = 425
Step 3: 300 is 3 hundreds, so multiply by 3 first.4.25 × 3 = 12.75
Step 4: Then push that answer two places for the hundred.12.75 × 100 = 1275
Where children go wrong: Moving the digits two places for times 10 and answering $425 for ten bowls — times 10 is one place only, and ten bowls cannot cost a hundred times as much as one.

Now try P5 questions on this topic →

Fractions: same size parts first, then count them

Method: Rewrite both fractions in the same kind of part, then add the top numbers

one tray1/81/81/81/81/81/81/81/8
1/4 + 3/8 = 5/8 eaten, so 3/8 of the tray is left
  • You cannot add quarters to eighths until both are counted in the same size part.
  • Eighths are smaller parts, so one quarter becomes two eighths.
  • The whole tray is 8/8, so what is left is the whole take away what was eaten.

One question, worked step by step

A tray of kueh is shared out at a class party. The children eat 1/4 of the tray and the teachers eat 3/8 of it. What fraction of the tray is still there?
Step 1: A quarter is the same as two eighths.1/4 = 2/8
Step 2: Now both are counted in eighths.2/8 + 3/8 = 5/8
Step 3: The whole tray is eight eighths, so take the eaten part away from it.8/8 − 5/8 = 3/8
Where children go wrong: Adding the top numbers and the bottom numbers and calling it 4/12 — the parts must be the same size before they can be counted, so make both eighths first.

Now try P5 questions on this topic →

Geometry: the three angles inside a triangle add to 180°

Method: Add the angles you know, then take that total away from 180°

58°74°48°
58° + 74° = 132°, so the third angle is 48°
  • Every triangle, however stretched it looks, holds exactly 180° inside.
  • So two angles are always enough to find the third one.
  • A four-sided shape holds 360°, which is why a triangle is not 360°.

One question, worked step by step

A pennant is cut as a triangle. Two of its angles are 58° and 74°. What is the third angle?
Step 1: Add the two angles you know.58 + 74 = 132
Step 2: Take that total away from the 180° inside a triangle.180 − 132 = 48
Step 3: Check that all three come back to 180°.132 + 48 = 180
Where children go wrong: Using 360° because the shape looks wide and answering 228° — 360° is the total for a four-sided shape; a triangle is always 180°.

Now try P5 questions on this topic →

Measurement: change to one unit before you add or take away

Method: Convert both amounts to the same unit first, then calculate

1 m100 cm↓1 kg1000 g↓1 litre1000 ml
every step down the ladder is a multiplication by 100 or by 1000
  • 1 metre is 100 centimetres, so centimetres become metres by dividing by 100.
  • Two lengths in different units cannot be subtracted — one of them has to change first.
  • Say which unit the answer must be in before you start writing.

One question, worked step by step

Wei Ling is sewing a sash and the pattern asks for 2.5 m of ribbon. She already has a piece that is 180 cm long. How many more centimetres does she need?
Step 1: Change the 180 cm into metres so both lengths match.180 ÷ 100 = 1.8
Step 2: Both are metres now, so take away.2.5 − 1.8 = 0.7
Step 3: The question asks for centimetres, so change the answer back.0.7 × 100 = 70
Where children go wrong: Subtracting 1.8 from 2.5 and writing 0.7 cm — the 0.7 is in metres, because the two lengths had to be in metres before subtracting, so it is 70 cm.

Now try P5 questions on this topic →

Percentage: a discount is a part of the price, not a number of dollars

Method: Turn the percentage into a decimal, multiply the price, then take it off

$64 racket−$16$48
25% off $64: $16 comes off and $48 is paid
  • Per cent means out of a hundred, so 25% is 25 out of every 100.
  • Written as a decimal that is 0.25, and multiplying the price by it gives the money taken off.
  • A discount always makes the price smaller, so check the direction before writing the answer.

One question, worked step by step

A badminton racket usually costs $64. During the school sale everything is 25% off. (a) How much money is taken off the racket? (b) What does the racket cost in the sale?
Step 1: Change 25% into a decimal.25/100 = 0.25
Step 2: Multiply the price by it to get the money taken off.0.25 × 64 = 16
Step 3: Take the discount away from the usual price.64 − 16 = 48
Where children go wrong: Reading 25% as 25 dollars and taking $25 off a $64 racket — the percentage is a part of the price, so change it to 0.25 before multiplying.

Now try P5 questions on this topic →

Pie chart: every slice is a fraction of the whole survey

Method: Read the fraction on the slice, then take that fraction of the whole number

60°chess = 1/6of thewhole 360°
one sixth of the full turn is 60° of the 360° circle
  • A pie chart is one whole thing cut into slices.
  • The whole number in the question is what the fraction comes from — never one of the slices.
  • How many more means find both slices, then subtract the smaller from the bigger.

One question, worked step by step

A school asked 300 pupils to choose one club for the year. On the pie chart chess fills 1/6 of the circle, dance fills 1/4 and robotics fills 1/5. How many more pupils chose dance than chess?
Step 1: Share all 300 pupils into six equal parts for chess.300 ÷ 6 = 50
Step 2: Share all 300 pupils into four parts for dance.300 ÷ 4 = 75
Step 3: Find how many more chose dance than chess.75 − 50 = 25
Where children go wrong: Taking 1/6 of a slice of the survey instead of 1/6 of all 300 pupils — the fraction is always of the whole number the chart was drawn from.

Now try P5 questions on this topic →

Ratio: the two numbers are shares, so add them to get the parts

Method: Add the ratio numbers, share the total, then multiply to get each share

72 marbles in 9 parts4 parts5 parts
4 : 5 makes 9 equal parts, and 72 ÷ 9 = 8 marbles in each part
  • 4 : 5 means one share is 4 parts and the other is 5 parts of exactly the same size.
  • There are 4 + 5 = 9 parts altogether, and every part is worth the same amount.
  • Total divided by the parts gives one part; then multiply for each share.

One question, worked step by step

Two brothers share 72 marbles in the ratio 4 : 5. How many marbles does each brother get?
Step 1: Add the ratio numbers to find the total number of parts.4 + 5 = 9
Step 2: Share the 72 marbles among all those parts.72 ÷ 9 = 8
Step 3: The first brother takes 4 parts.8 × 4 = 32
Step 4: The second brother takes 5 parts.8 × 5 = 40
Step 5: Check the two shares come back to 72 marbles.32 + 40 = 72
Where children go wrong: Dividing 72 by 5 because 5 is the bigger number in the ratio — one part is 72 shared among all 9 parts, not among one of the ratio numbers.

Now try P5 questions on this topic →

Rate: what happens in one minute is the number you reuse

Method: Find the one-minute amount first, then use it to reach the target

180-litre tank8 min = 96 L? min
12 litres a minute, so the 84 litres still missing need 7 more minutes
  • A rate says what one unit does: 96 litres in 8 minutes is 12 litres every minute.
  • Find that one-unit amount first, because every later step uses it.
  • Then divide what is left by that amount to find how long it takes.

One question, worked step by step

A garden tap pours 96 litres of water into an empty tank in 8 minutes without stopping. The tank holds 180 litres. How many minutes does the tap take to fill it?
Step 1: Find how much water comes out in one minute.96 ÷ 8 = 12
Step 2: Find how much water is still missing.180 − 96 = 84
Step 3: Share the rest at 12 litres a minute.84 ÷ 12 = 7
Step 4: Add the minutes already spent to the minutes still needed.8 + 7 = 15
Where children go wrong: Dividing 8 by 96 and answering 0.08 litres a minute — the litres are being shared out among the minutes, so the litres go on top.

Now try P5 questions on this topic →

Time: cross the hour on the hour, then count what is left

Method: Count to the next o'clock first, then add the minutes left over

start16:5010 min17:0035 min17:35
10 minutes to reach 17:00, then 35 minutes more
  • Minutes past the hour start again at 60, never at 100.
  • Jumping to the next o'clock keeps the numbers small and safe.
  • Then add what is left over and write the ending time clearly.

One question, worked step by step

Swimming training starts at 16:50 and lasts 45 minutes. What time does training end?
Step 1: From 16:50 the next whole hour is 17:00; count how far that is.60 − 50 = 10
Step 2: Those 10 minutes come out of the 45, so find what is left.45 − 10 = 35
Step 3: Check the two jumps are the whole 45 minutes, so the end is 35 minutes past 17:00.10 + 35 = 45
Where children go wrong: Taking 50 away from 45, writing 5 minutes and ending at 17:05 — the minutes restart at 60 on the hour, so go through 17:00 instead of subtracting across it.

Now try P5 questions on this topic →

Volume: three measurements, and litres are thousands of cubic centimetres

Method: Length × breadth × height, then divide by 1000 for litres

60 cm30 cm40 cm
60 cm by 40 cm by 30 cm gives 72000 cubic cm, which is 72 litres
  • A volume fills a box, so all three measurements are needed — leave one out and you have a flat area.
  • Cubic centimetres become litres by dividing by 1000.
  • A tank that already holds water needs one more subtraction at the end.

One question, worked step by step

A classroom fish tank is a box 60 cm long, 40 cm wide and 30 cm high. It already holds 45 litres of water. How many more litres will fill it to the top?
Step 1: Length times breadth gives the base of the box.60 × 40 = 2400
Step 2: Then times the height to fill the box.2400 × 30 = 72000
Step 3: Change cubic centimetres into litres.72000 ÷ 1000 = 72
Step 4: Take away the water already in the tank.72 − 45 = 27
Where children go wrong: Multiplying only length by breadth and stopping at 2400 — that is the base of the tank, and a volume needs the height as well.

Now try P5 questions on this topic →

Whole numbers: total, take away, then share into groups

Method: Write the question as total, take away, share — one step at a time

216 packets244 bags
216 packets, 24 kept for the helpers, and the other 192 shared into 4 bags
  • A question with several parts is several steps, and each step uses the answer before it.
  • Underline the words that say what to do: altogether, kept aside, each bag.
  • Decide whether the last number is how many groups or how many go in one group.

One question, worked step by step

For Sports Day the committee brings 6 cartons with 36 packets of biscuits in each carton. They keep 24 packets for the helpers and pack the rest equally into 4 bags. How many packets go into each bag?
Step 1: How many packets are there altogether?6 × 36 = 216
Step 2: Take away the packets kept for the helpers.216 − 24 = 192
Step 3: Share the rest among the 4 bags.192 ÷ 4 = 48
Step 4: Check by multiplying back: 4 bags of 48 gives the 192 packed.48 × 4 = 192
Where children go wrong: Packing all 216 packets and forgetting the 24 kept aside — underline both the total and what is taken away before the first calculation.

Now try P5 questions on this topic →