P4 Maths — the teaching behind every question

Every Primary 4 topic: the method in one line, the picture to draw, and one question worked step by step before your child practises it.

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

Whole numbers: which digit decides a rounding

Method: Underline the digit that decides, then look only at the digit on its right

46724000600702
4 thousands, 6 hundreds, 7 tens and 2 ones
  • Every digit in a number has a house: hundreds, tens, ones.
  • To round, find the digit of the house you are rounding to, and underline it.
  • The digit on its RIGHT is the only one that decides: 5 or more goes up, 4 or less stays.

One question, worked step by step

Round 4672 to the nearest hundred.
Step 1: The hundreds digit is 6, so the two hundreds it sits between are 4600 and 4700.4672 is between 4600 and 4700
Step 2: The digit on its right is 7, and 7 is 5 or more, so the hundred goes up.4700
Step 3: Check: 4672 is 72 away from 4600 but only 28 away from 4700.4672 - 4600 = 72, 4700 - 4672 = 28
Where children go wrong: Rounding down because the last digit 2 is small — the digit that decides is the TEN on the right of the hundreds, which is 7.

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Fractions: make the parts the same size before you compare

Method: Same denominator first, then compare the top numbers

one pizza1/81/81/81/81/81/81/81/8
3/8 shaded: three of eight equal slices
  • A fraction only tells you the size of a part when you know how many parts the whole was cut into.
  • One quarter and two eighths are the same amount of pizza, cut differently.
  • So before comparing or adding, rewrite both fractions with the same number of parts.

One question, worked step by step

Ali ate 3/8 of a pizza. Ben ate 1/4 of the same size pizza. Who ate more?
Step 1: One quarter is the same as two eighths, because 8 is four times 2.1/4 = 2/8
Step 2: Now both are counted in eighths: Ali 3 eighths, Ben 2 eighths.3/8 and 2/8
Step 3: 3 eighths is more than 2 eighths, so Ali ate more.3 - 2 = 1
Where children go wrong: Saying Ben ate more because 4 is smaller than 8 — a bigger bottom number means SMALLER parts, but you must still compare the same number of parts.

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Decimals: tenths and hundredths are houses too

Method: Read the decimal place by place, and fill empty places with zeros before comparing

1one whole↓0.1one tenth = 1/10↓0.01one hundredth = 1/100
3 tenths and 7 hundredths make 0.37
  • The first place after the dot counts tenths, the second counts hundredths.
  • 3 tenths and 7 hundredths is written 0.37, and it is thirty-seven hundredths.
  • To compare two decimals, give both the same number of places by writing zeros.

One question, worked step by step

Write 3 tenths and 7 hundredths as a decimal, then say whether it is more or less than 0.4.
Step 1: Tenths go in the first place, hundredths in the second.3/10 + 7/100 = 0.37
Step 2: Give 0.4 a second decimal place by writing a zero, so 0.40.0.4 = 0.40
Step 3: Compare hundredths: 37 hundredths is less than 40 hundredths.0.37 < 0.40
Where children go wrong: Writing 3 tenths 7 hundredths as 0.307 — the places are counted from the dot outwards, and no place is skipped.

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Money: total first, then change from what was handed over

Method: Two steps only — add what was spent, then subtract from the note

12.85book3.6pen16.45total20note
Book $12.85 and pen $3.60 — together $16.45, handed over $20
  • Change is what is left after the whole bill is paid, so the bill comes first.
  • Line the dollars under dollars and the cents under cents.
  • Check your change by adding it back to the bill; it must make the note again.

One question, worked step by step

A book costs $12.85 and a pen costs $3.60. Sam pays with a $20 note. How much change does he get?
Step 1: Add the two prices to find the bill.12.85 + 3.60 = 16.45
Step 2: Take the bill away from the note.20.00 - 16.45 = 3.55
Step 3: Check by adding the change back to the bill.16.45 + 3.55 = 20.00
Where children go wrong: Forgetting the cents and taking 13 away from 20 — $12.85 is not $13, and the cents must be carried properly.

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Time: jump in whole hours first, then the minutes

Method: Add the hours, then add the minutes, then tidy up past 60 minutes

film starts19:451 hour later20:4550 minutes more21:35
1 h 50 min after 19:45 lands at 21:35
  • Time does not work in tens — sixty minutes make one hour.
  • Jump the whole hours first, then the leftover minutes.
  • If the minutes pass 60, carry one hour across and take 60 away from the minutes.

One question, worked step by step

A film starts at 19:45 and lasts 1 hour 50 minutes. What time does it end?
Step 1: Add the whole hour: 19:45 becomes 20:45.19:45 + 1 hour = 20:45
Step 2: Add 50 minutes: 45 and 50 make 95 minutes, which is 1 hour 35 minutes.45 + 50 = 95 minutes = 1 h 35 min
Step 3: So one more hour and 35 minutes after 20:45 is 21:35.20:45 + 50 minutes = 21:35
Where children go wrong: Adding 1.50 to the time as if time were decimals — 19:45 plus 1 and a half hours is 21:15, not 21:35.

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Measurement: every step down the ladder is a multiplication

Method: Fix the ladder in your head: km → m → cm → mm, each step × 10 or × 1000

km3.4 km↓m× 1000 = 3400 m↓cm× 100 = 340 000 cm
3.4 km down to metres is one step of × 1000
  • A bigger unit needs fewer numbers: 1 km is only 1000 m.
  • Going from a big unit to a small one multiplies; going the other way divides.
  • Write the ladder first and you cannot use the wrong number by accident.

One question, worked step by step

A running route is 3.4 km long. How many metres is that?
Step 1: 1 km is 1000 m, so every kilometre becomes a thousand metres.1 km = 1000 m
Step 2: Multiply by 1000, which moves the digits three places.3.4 × 1000 = 3400
Step 3: Check backwards by dividing: 3400 m back to km is 3.4.3400 ÷ 1000 = 3.4
Where children go wrong: Multiplying by 100 because that is the step for centimetres — kilometres to metres is a thousand, not a hundred.

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Area and perimeter: the fence or the paint?

Method: Fence goes round the edge, paint covers the inside

12 cm7 cmarea = length × breadthperimeter = all four sides
A rectangle 12 cm by 7 cm
  • Perimeter is the distance all the way round, measured in cm or m.
  • Area is the flat space inside, measured in square cm or square m.
  • So one is a length you add, and the other is a multiplication of two lengths.

One question, worked step by step

A rectangle is 12 cm long and 7 cm wide. Find its area and its perimeter.
Step 1: Area is the space inside: length × width, in square centimetres.12 × 7 = 84
Step 2: Perimeter is the edge: twice the length plus twice the width, or twice the sum.2 × (12 + 7) = 38
Step 3: Check that the perimeter is bigger than one side but smaller than all four added wrongly — 38 cm is just over 3 sides of 12.12 + 12 + 7 + 7 = 38
Where children go wrong: Adding the four sides to get the area — 12 + 7 + 12 + 7 is the distance around the rectangle, not the space inside it.

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Angles: a straight line always holds 180°

Method: Find the line, add what you know, take it away from 180°

55°70°?
Three angles along one straight edge: 55°, 70° and the rest
  • The angles sitting along one straight edge together make a straight line's worth: 180 degrees.
  • A right angle is 90°, which is half of that line.
  • So the unknown angle is what is left when the known ones are taken away.

One question, worked step by step

Three angles lie on a straight line. Two of them are 55° and 70°. Find the third.
Step 1: Angles on a straight line add up to 180°.180°
Step 2: Add the two you know.55 + 70 = 125
Step 3: Take that away from 180 to find what is left.180 - 125 = 55
Where children go wrong: Using 90° or 360° as the total — a straight line is half a full turn, which is 180°.

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Geometry: cut a strange shape into rectangles you know

Method: Split the shape, find each area, then add them back

8 cm5 cmarea = length × breadthperimeter = all four sides
An L-shape split into 8 cm × 5 cm and 4 cm × 3 cm
  • Area formulas only work for shapes you already know.
  • So an L-shape is not a problem: cut it into two rectangles.
  • Careful with the missing side — work it out from the sides opposite it.

One question, worked step by step

An L-shape is cut into two rectangles: 8 cm by 5 cm, and 4 cm by 3 cm. Find the total area.
Step 1: Find the area of the big rectangle.8 × 5 = 40
Step 2: Find the area of the small one.4 × 3 = 12
Step 3: Add them, because the two rectangles together are the whole shape.40 + 12 = 52
Where children go wrong: Multiplying the outside sides of the L-shape as if it were one big rectangle — the corner is missing, so the shape must be split.

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Nets: six faces, and every face is a square

Method: Count the faces first, then multiply one face's area

666666
Six squares, each 6 cm by 6 cm
  • A net is the box opened out flat, so the net's area is the box's whole surface.
  • A cube has six faces, all the same square.
  • So find one face, then multiply by six — nothing more.

One question, worked step by step

A cube has edges of 6 cm. What is the total area of its net?
Step 1: One face is a square, so its area is the edge multiplied by itself.6 × 6 = 36
Step 2: A cube has six faces, so multiply that by six.6 × 36 = 216
Step 3: Check that the answer is more than one face and exactly six times it.216 ÷ 36 = 6
Where children go wrong: Multiplying 6 by 6 and stopping at 36 — that is only one face of the six the net carries.

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Graphs: read each bar, then decide add or subtract

Method: Name the question first — total, difference, or most — then use only the bars it needs

12Mon18Tue9Wed15Thu
Books borrowed Monday to Thursday
  • Every bar is one number; the height is read off the scale, not guessed.
  • A question that says altogether wants an addition; a question that says how many more wants a subtraction.
  • Read the scale carefully: one square on the paper may stand for two books.

One question, worked step by step

The bar graph shows books borrowed: Monday 12, Tuesday 18, Wednesday 9, Thursday 15. How many books were borrowed altogether, and how many more on Tuesday than Wednesday?
Step 1: Altogether means add every bar.12 + 18 + 9 + 15 = 54
Step 2: How many more on Tuesday than Wednesday means subtract the smaller bar.18 - 9 = 9
Step 3: Check the difference is smaller than the taller bar and larger than zero.9 < 18
Where children go wrong: Answering a 'how many more' question by adding the two bars, or missing the tallest bar when asked for the total.

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Patterns: find the step, then count the gaps

Method: The jump between terms is the pattern; the number of gaps is one fewer than the term number

3+7+11+15+...+?+4 each time
Each term is 4 more than the one before
  • Find how much the numbers grow by each time. That is the step.
  • Between the first term and the tenth there are nine steps, not ten.
  • So the tenth term is the first term plus nine steps.

One question, worked step by step

The pattern is 3, 7, 11, 15, ... What is the 10th term?
Step 1: The numbers go up by 4 each time.7 - 3 = 4
Step 2: From the 1st term to the 10th term there are 9 jumps.10 - 1 = 9
Step 3: Nine jumps of 4 is 36, so add that to the first term.9 × 4 = 36, 3 + 36 = 39
Where children go wrong: Using ten jumps instead of nine — the first term is already on the page, so only the gaps after it are added.

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Heuristics: draw the units before you calculate

Method: One unit for the smaller amount, then count how many units the total holds

Ali 3uBen 1u96 in all = 4u
Ali 3 units, Ben 1 unit — together 4 units make 96
  • 'Three times as many' means three units against one unit.
  • Together they make four units, and those four units are the total given.
  • So find one unit by dividing, and the answer follows.

One question, worked step by step

Ali has three times as many stamps as Ben. Together they have 96 stamps. How many does Ben have?
Step 1: Ali is 3 units and Ben is 1 unit, so together they are 4 units.3 + 1 = 4
Step 2: Those 4 units are worth 96, so one unit is 96 divided by 4.96 ÷ 4 = 24
Step 3: Check: Ben 24, Ali 72, and 24 + 72 makes 96 again.24 × 3 = 72, 24 + 72 = 96
Where children go wrong: Dividing 96 by 3 because Ali is three times Ben — the 96 is shared by FOUR units, not three.

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