Hello, it is Pip! Calculation is the toolkit for almost every maths question. Learn the methods, check your answers, and you will be quick and accurate.
Pip’s tip: Estimate first, keep place-value columns lined up, then check with an inverse operation.
Calculate 236 × 4.
200 × 4 = 800; 30 × 4 = 120; 6 × 4 = 24. Add 800 + 120 + 24 = 944.
Answer: 944.
Calculate 468 + 257.
725. 468 + 200 + 50 + 7 = 725.
Calculate 864 ÷ 6.
144. 600 ÷ 6 = 100; 240 ÷ 6 = 40; 24 ÷ 6 = 4. Add to get 144.
Calculate 7 + 6 × 4.
31. Multiply first: 6 × 4 = 24; then add 7.
CALC-01CALC-03CALC-13
Number bonds are pairs that make a target, like 64 and 36 making 100. For mental adding, split the second number into tens and ones and jump along a number line. A missing-number question is solved by using the inverse operation.
Animation: 47 + 38 in jumps
Start at 47. Add the tens first: 47 + 30 = 77. Then add the ones: 77 + 8 = 85. So 47 + 38 = 85. Split the second number into tens and ones and jump.
Worked example: Work out 47 + 38. Then find the missing number: □ + 27 = 63.
Answer: 85, and the missing number is 36
CALC-02CALC-05
Know your tables to 12 × 12. For harder facts, split one number into easy parts. Division is the inverse of multiplication, so 56 ÷ 8 asks "what times 8 makes 56?".
Worked example: Work out 14 × 5 and 56 ÷ 8.
Answer: 70 and 7
CALC-04
Line the digits up by place value and start at the units. In addition you carry when a column makes 10 or more. In subtraction you exchange: take 1 ten and turn it into 10 units.
Animation: column addition with carrying (487 + 356)
Start with the units (U) column. Units: 7 + 6 = 13. Write 3, carry the 1 ten. Tens (T): 8 + 5 + 1 = 14. Write 4, carry the 1 hundred. Hundreds (H): 4 + 3 + 1 = 8. So 487 + 356 = 843.
Worked example: Work out 503 − 276.
Answer: 227
CALC-06CALC-07
Short multiplication is for a one-digit multiplier. Long multiplication multiplies by the ones, then by the tens, then adds the two rows. The tens row needs a 0 placeholder because you are really multiplying by a multiple of 10.
Worked example: Work out 268 × 34.
Answer: 9,112
CALC-08CALC-09
Short division (the bus stop) shares one digit at a time. Long division does the same job with the working written out. When a division leaves a remainder, the story decides whether to round up, round down or give the remainder.
Worked example: Work out 972 ÷ 12. Then: 85 sweets are put in bags of 6. How many bags are needed?
Answer: 81, and 15 bags
CALC-10
When you multiply by 10, every digit moves one place to the left. By 100 it moves two places, by 1,000 three places. Dividing moves digits to the right. The decimal point stays still.
Animation: multiplying by 10 and 100
The columns are H (hundreds), T (tens), U (units), then tenths (t) and hundredths (h). Start with 9.5. × 10: every digit moves ONE column to the left. 9.5 becomes 95. × 100: every digit moves TWO columns left and a 0 fills the gap. 9.5 becomes 950. The decimal point never moves, only the digits. To divide, move them right.
Worked example: Work out 4.7 × 100 and 450 ÷ 1,000.
Answer: 470 and 0.45
CALC-11
A calculation is not always done from left to right. Do brackets first, then powers, then multiply and divide, then add and subtract. When the operations are on the same level, go left to right.
Worked example: Work out 6 + 4 × 5 − 2.
Answer: 24
CALC-12
Round the numbers to get a quick estimate. Then check the exact answer with the inverse operation: addition is checked by subtracting, and multiplication by dividing.
Worked example: Estimate 612 + 289, then work it out and check it.
Answer: 901 (estimate 900)
CALC-14
Read the question, underline what it asks, and draw a bar model. Do one step at a time and write what each answer means. The last step must answer the question.
Worked example: Pens cost £1.20 each. Mo buys 6 and pays with a £10 note. How much change does he get?
Answer: £2.80
Level 1 is Year 3, one step. Level 5 is a challenge with 3 to 5 steps. Try each one yourself before you read the steps.
What must be added to 64 to make 100?
Answer: 36
A box holds 12 eggs. Hana buys 7 boxes and 5 eggs break. How many eggs are not broken?
Answer: 79
A school buys 24 packs of 36 pencils and gives out 500 of them. How many pencils are left?
Answer: 364
Priya buys 4 comics at £1.85 each and a poster for £3.20. She pays with a £20 note. How much change does she get?
Answer: £9.40
A baker makes 8 trays of 24 rolls. She packs them in bags of 5 and sells all the full bags at £2.50 each. The ingredients cost £48. How much profit does she make?
Answer: £47
Lots of children make these slips. Spot them early and you will win marks.
ORDER_OPS_LEFT_TO_RIGHT
The mistake: Doing the sum strictly from left to right.
Why it is wrong: Multiplying and dividing come before adding and subtracting, so the order changes the answer.
How to avoid it: Look for × and ÷ first and do those. Put a ring around them before you start.
✗ Wrong: 92 − 36 ÷ 9: 92 − 36 = 56, 56 ÷ 9 = 6.2...
✓ Right: 36 ÷ 9 = 4 first, then 92 − 4 = 88.
PV_LONGMULT_NO_PLACEHOLDER
The mistake: Leaving out the 0 on the tens row.
Why it is wrong: The 3 in 34 means 30, so that row is ×30 and ends in 0. Without the 0 the row is ten times too small.
How to avoid it: Write the 0 in the units column before you start the second row.
✗ Wrong: 268 × 34: 1,072 + 804 = 1,876.
✓ Right: 1,072 + 8,040 = 9,112.
PV_SMALLER_FROM_LARGER
The mistake: In every column, subtracting the smaller digit from the larger.
Why it is wrong: The order of the numbers matters. You must take the bottom digit from the top digit, exchanging when needed.
How to avoid it: Estimate first, then exchange 1 ten for 10 units when the top digit is smaller.
✗ Wrong: 52 − 27: 7 − 2 = 5 and 5 − 2 = 3, so 35.
✓ Right: Exchange: 12 − 7 = 5, 4 − 2 = 2, so 25. Check: 25 + 27 = 52.
PV_ADD_A_ZERO
The mistake: Believing that multiplying by 10 means adding a zero to the end.
Why it is wrong: The digits move one place left. Adding a zero to a decimal does not change its value at all.
How to avoid it: Use a place value chart. The decimal point stays put and the digits move.
✗ Wrong: 9.5 × 10 = 9.50.
✓ Right: 9.5 × 10 = 95.
MULT_MAKES_BIGGER
The mistake: Expecting multiplication to give a bigger answer and division a smaller one.
Why it is wrong: Multiplying by a number less than 1 makes things smaller. Dividing by a number less than 1 makes things bigger.
How to avoid it: Think of "of": 6 × 0.5 is half of 6.
✗ Wrong: 6 × 0.5 = 12 (bigger than 6).
✓ Right: 6 × 0.5 = 3 (half of 6).
TECH_STOPPED_AT_STEP_1
The mistake: Giving an answer from the middle of a multi-step problem.
Why it is wrong: The middle answer is not what was asked.
How to avoid it: Before you answer, re-read the question and underline what it asks for.
✗ Wrong: Total spent is £10.60, so the change is £10.60.
✓ Right: Change = £20 − £10.60 = £9.40.
Five questions, easy to hard. Have a go on paper, then open the answer.
What must be added to 68 to make 100?
32
100 − 68 = 32. Check: 68 + 32 = 100.
Work out 12 × 6.
72
10 × 6 = 60 and 2 × 6 = 12, so 60 + 12 = 72.
Work out 508 − 279.
229
Exchange across the zero. Units: 18 − 9 = 9. Tens: 9 − 7 = 2. Hundreds: 4 − 2 = 2. Check: 229 + 279 = 508.
Work out 9 + 3 × 6 − 5.
22
3 × 6 = 18 first. Then 9 + 18 − 5 = 22.
A coach seats 48 children. How many coaches are needed for 250 children?
6 coaches
250 ÷ 48 = 5 remainder 10. The 10 left-over children still need a coach, so round up to 6.