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Order of Operations and Multi-Step Problems - Worksheets, Questions and Revision

18 original exam-style questions - 4 pages of questions with a full mark scheme - free printable PDF.

Download PDFJump to mark scheme (page 5)Order of Operations and Multi-Step Problems revision guide

This topic is chapter 9 of KS2 Maths: Number and place value Practice Book.

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KS2 · Calculation

1.13 Order of Operations and Multi-Step Problems

Calculators not allowed · about 55 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Calculate 8 + 3 x 5.
(1)
2
Calculate 420 ÷ (7 x 3).
(1)
3
A recipe needs 2 1/2 cups of flour. Emma wants to make 3 batches. How many cups of flour does she need in total? Give your answer as a mixed number.
(2)
4
Calculate 2 x (45 - 28) + 36 ÷ 6.
(1)
5
There are 3 boxes of biscuits. Each box contains (4 + 2) x 3 biscuits. How many biscuits are there altogether?
(2)
6
Explain why the answers to 6 + 2 x 5 and (6 + 2) x 5 are different. Give a clear reason.
(2)
7
A charity sells homemade cakes. Each cake costs £2.50. On Monday they sell 8 cakes, on Tuesday they sell twice as many as Monday, and on Wednesday they sell 5 fewer than Tuesday. How much money do they make in total over the three days? Show your working.
(3)
8
A gardener plants flower beds. Each flower bed needs (12 - 3) x 5 bulbs. He plants 4 beds. How many bulbs does he plant altogether? Then, if bulbs are sold in packs of 10, how many full packs does he need? Show working.
(4)
9
Explain whether the following is always true, sometimes true or never true, and give a reason: "If you change the order that you add and multiply only numbers, the answer will stay the same." Use an example to support your explanation.
(6)
10
A school orders sports equipment. A set of cones costs £12.50 and a set of bibs costs £9.75. The school orders 6 sets of cones and (5 + 3) sets of bibs. They pay with a £200 school voucher. How much of the voucher is left? Show your working and give the answer to the nearest penny.
(6)
11
Work out (24 - 6) ÷ 3.
(1)
12
Calculate 7 x (10 - 4) + 9.
(1)
13
Work out 5 + 18 ÷ 6 x 3.
(1)
14
Sana buys 3 packs of pencils. Each pack costs 95p. She pays with a £5.00 note. How much change does she get? Show working.
(2)
15
Calculate 150 - (24 x 4) + 6.
(1)
16
A rectangle is 8 m long and 3 m shorter than the width. The width is divided into 2 equal parts. Find the area of one part. Show your working.
(3)
17
Work out 32 + 4 x 5. Note: 32 means 3 squared.
(1)
18
Liam has 240 beads. He makes necklaces that use 15 beads each. He then shares the necklaces equally between 4 friends. How many beads does each friend get? Show working.
(2)
Mark scheme · 1.13 Order of Operations and Multi-Step Problems

Question 1

  • B1 23 cao
  • Answer: 23

Question 2

  • B1 20 cao
  • Answer: 20

Question 3

  • M1 Multiply 2 1/2 by 3 or convert to improper fraction 5/2 x 3 = 15/2 seen
  • B1 7 1/2 cao
  • Answer: 7 1/2

Question 4

  • B1 40 cao
  • Answer: 40

Question 5

  • M1 Evaluate (4 + 2) x 3 = 18 or show multiplication per box
  • B1 54 cao
  • Answer: 54

Question 6

  • M1 Reference to order of operations, stating multiplication before addition or showing 2 x 5 done first for first expression
  • B1 Correct explanation that parentheses change the order so you add first in (6 + 2) x 5 leading to different results cao
  • Answer: Multiplication is done before addition unless brackets change the order; 6 + 2 x 5 = 6 + 10 = 16 but (6 + 2) x 5 = 8 x 5 = 40

Question 7

  • M1 Correctly find numbers sold each day, e.g. Monday 8, Tuesday 16, Wednesday 11
  • M1 Correctly find total cakes sold, e.g. 8 + 16 + 11 = 35
  • B1 87.50 or £87.50 cao
  • Answer: 87.50

Question 8

  • M1 Evaluate bulbs per bed correctly: (12 - 3) x 5 = 9 x 5 = 45
  • M1 Multiply by number of beds: 45 x 4 = 180
  • M1 Divide by 10 to find packs or show ceiling, e.g. 180 ÷ 10 = 18 seen
  • B1 180 bulbs and 18 packs cao
  • Answer: 180 and 18

Question 9

  • M1 Correct classification: answer states always true OR sometimes true OR never true
  • M1 If 'always true', gives a correct reason about commutative property for single operation examples; if 'sometimes true', explains that mixing operations changes order importance unless brackets are used
  • M1 Gives an example showing when order matters, e.g. 2 + 3 x 4 = 2 + 12 = 14 but (2 + 3) x 4 = 20
  • M1 Explains role of brackets or order of operations in the example
  • B1 Clear conclusion that it is sometimes true: changing order of only additions is fine, but mixing addition and multiplication can change the result unless brackets are used cao
  • B1 Example calculation given and conclusion linked to example cao
  • Answer: Sometimes true; adding only numbers can be done in any order, but when addition and multiplication are mixed the order matters unless brackets are used, for example 2 + 3 x 4 = 14 but (2 + 3) x 4 = 20

Question 10

  • M1 Correctly evaluate number of bib sets: (5 + 3) = 8 seen
  • M1 Correctly find cost of cones: 6 x 12.50 = 75.00 seen
  • M1 Correctly find cost of bibs: 8 x 9.75 = 78.00 seen
  • M1 Add costs correctly: 75.00 + 78.00 = 153.00 seen
  • B1 Correct subtraction from voucher: 200.00 - 153.00 = 47.00 cao
  • B1 Final answer given to nearest penny as 47.00 or 47.00 cao
  • Answer: 47.00

Question 11

  • B1 6 cao
  • Answer: 6

Question 12

  • B1 51 cao
  • Answer: 51

Question 13

  • B1 14 cao
  • Answer: 14

Question 14

  • M1 Correct subtraction of total cost from 5.00 or correct total cost seen, e.g. 3 x 0.95 = 2.85
  • B1 2.15 or £2.15 cao
  • Answer: 2.15

Question 15

  • B1 60 cao
  • Answer: 60

Question 16

  • M1 Correctly use width = length + 3 or substitute: width = 8 + 3 = 11 seen
  • M1 Divide width by 2 and multiply by length or area method shown, e.g. (11/2) x 8 seen
  • B1 44 m2 cao
  • Answer: 44

Question 17

  • B1 29 cao
  • Answer: 29

Question 18

  • M1 Divide 240 by 15 to find number of necklaces, e.g. 240 ÷ 15 = 16
  • B1 60 cao
  • Answer: 60

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