Sana buys 3 packs of pencils. Each pack costs 95p. She pays with a 5.00 pound note. How much change does she get? Show working.
(2)
6
Calculate 150 - (24 x 4) + 6.
(1)
7
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)
8
Work out 32 + 4 x 5. Note: 32 means 3 squared.
(1)
9
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)
10
Calculate 420 ÷ (7 x 3).
(1)
11
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)
12
Calculate 2 x (45 - 28) + 36 ÷ 6.
(1)
13
There are 3 boxes of biscuits. Each box contains (4 + 2) x 3 biscuits. How many biscuits are there altogether?
(2)
14
Explain why the answers to 6 + 2 x 5 and (6 + 2) x 5 are different. Give a clear reason.
(2)
15
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)
16
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)
17
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)
18
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)
Mark scheme · KS2.M-Y6N2 Order of Operations and Multi-Step Problems
Question 1
B1 23 cao
Answer: 23
Question 2
B1 6 cao
Answer: 6
Question 3
B1 51 cao
Answer: 51
Question 4
B1 14 cao
Answer: 14
Question 5
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 pounds 15 pence cao
Answer: 2.15
Question 6
B1 60 cao
Answer: 60
Question 7
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 8
B1 29 cao
Answer: 29
Question 9
M1 Divide 240 by 15 to find number of necklaces, e.g. 240 ÷ 15 = 16
B1 60 cao
Answer: 60
Question 10
B1 20 cao
Answer: 20
Question 11
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 12
B1 40 cao
Answer: 40
Question 13
M1 Evaluate (4 + 2) x 3 = 18 or show multiplication per box
B1 54 cao
Answer: 54
Question 14
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 15
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 pounds 50 pence cao
Answer: 87.50
Question 16
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 17
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 18
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