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SATs practice · Year 6Chapter 1 · Number reasoning
Year 6 Maths reasoning (SATs) · Number reasoning · Lesson 1.5

Year 6 Maths reasoning (SATs): Choosing the operation and checking the answer

Part of the Year 6 Maths reasoning (SATs) number reasoning chapter. Chapter overview · whole chapter on one page

1.5

Choosing the operation and checking the answer

Year 6
Solve multi-step problems and decide which operation to use (Year 5-6), Use estimation to check whether an answer is sensible, and explain a method (Year 5-6)
Story. The school library has 1,840 books in 8 equal shelves. Mr Blake wants to know how many books are on each shelf, then he checks his answer by estimating.

Rule

Read the question twice. Decide which operations are needed and in which order.

Check the answer with an estimate: round each number first, work out a rough answer, and see if your answer is close.

Key ideas

  • Two steps: work out the total first, then share or take away.
  • Round to 1 significant figure to estimate, for example 368 x 5 is about 400 x 5 = 2000.
  • Always ask: is the answer about the right size?
Worked example 1.5.1
A bakery makes 368 rolls each day for 5 days. It sells 1,600 rolls. How many are left?

Method. Find the total first, then take away the sales.

  1. Find the total rolls made. 368 x 5 = 1,840 rolls.
    1,840 rolls
  2. Take away the rolls sold. Subtract the number sold from the total.
    1,840 - 1,600 = 240
  3. Check the answer. Rounding 368 up to 400 gives 400 x 5 = 2,000, and 2,000 - 1,600 = 400. The exact answer is smaller, because 368 was rounded up.
    about 400, and 240 is the exact answer
  4. Write the answer.
    240

Check. 368 x 5 = 1,840 and 1,840 - 1,600 = 240. ✓

Worked example 1.5.2
Estimate 4,980 x 6 by rounding, and say if the answer 29,880 is sensible.

Method. Round the first number, then multiply.

  1. Round 4,980 to the nearest 1,000. 4,980 is close to 5,000.
    5,000
  2. Estimate. 5,000 x 6 = 30,000.
    about 30,000
  3. Compare with the answer. 29,880 is very close to 30,000, so it is sensible.
    yes, 29,880 is sensible
  4. Write the answer.
    yes

Check. 5,000 x 6 = 30,000 and 30,000 - 29,880 = 120. ✓

Worked example 1.5.3
47 pupils go on a trip. Each bus seats 12 pupils. How many buses are needed?

Method. Divide, then decide whether to round up or down.

  1. Divide the pupils by the seats. 47 / 12 = 3 remainder 11.
    3 buses and 11 pupils
  2. Decide what the leftover means. The 11 pupils still need a seat, so one more bus is needed.
    3 + 1 = 4
  3. Write the answer. Four buses carry all 47 pupils.
    4
  4. Write the answer.
    4

Check. 4 x 12 = 48, which is enough for 47. ✓

Watch out

Watch out. When the answer is a remainder, read the question to decide whether to round up, down or ignore it.

Exam tip

Practice guide. Write the operation in words first: "total, then take away", or "share equally".

Exercise 1E  Practice: choosing the operation and checking

Non-calculator
1
FA pack has 36 pencils. A school buys 12 packs. How many pencils is that altogether?
2
FA cinema has 485 seats. 136 seats are empty. How many people are sitting down?
3
FEstimate 61 x 39 by rounding each number to the nearest 10. Write the estimate.
4
PSA bag of 8 apples costs 3 pounds 20 pence. Sana buys 4 bags. How much does she pay, in pounds?
5
PSTickets cost 7 pounds 50 pence each. Lena buys 5 tickets and pays with a 40 pound note. How much change does she get?
6
PSA tank holds 2,000 litres. It already has 1,375 litres. How many more litres can it hold?
7
PSMr Blake shares 1,840 books equally onto 8 shelves. How many books on each shelf?
8
RBen says "3,000 / 6 = 500, so 3,000 / 60 = 50." Is he right? Explain.
9
RSam works out 4,980 x 7 = 34,860. He checks it by working out 5,000 x 7 = 35,000 and says his answer is sensible. Is his check sensible? Choose one: Yes, 35,000 is close to 34,860, No, 4,980 x 7 must be 3,486 or No, 35,000 is much bigger than 34,860.
10
PSWrite a two-step word problem whose answer is 60, using the numbers 8 and 5 and the operations x and +.
11
PSRavi has 3 bags of 24 marbles and 14 loose marbles. He gives away 25 marbles. How many marbles does he have now?
12
PSA cake recipe needs 250 g of flour for 8 people. How much flour is needed for 24 people? Write the answer in grams.
13
RA school says "We need 600 chairs for 75 rows of 8 chairs." Is the number of chairs right? Explain with a calculation.

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