Reasoning: Number and Calculation - Worksheets, Questions and Revision

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

Download PDF Jump to mark scheme (page 5)Reasoning: Number and Calculation revision guide

This topic is chapter 7 of KS2 Maths: Number and place value Practice Book.

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1.11 Reasoning: Number and Calculation

Calculators not allowed · about 50 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A garden centre sells bags of soil in 25 kg sacks. A landscaper needs 7.5 tonnes of soil. How many full 25 kg sacks should they buy? Show full working.

(3)

A bus journey takes 2 hours 45 minutes. If a driver completes 5 such journeys in a week, how many minutes does the driver spend driving on those journeys?

(2)

Sofia reads 64 pages in 80 minutes. At that rate, how many pages will she read in 3 hours 20 minutes? Show working.

(2)

A shop reduces the price of a jacket by 15%. The original price is £84. What is the sale price? Show your working.

(3)

Complete the function machine. Input 24 gives output 6. Input 40 gives output 10. What is the rule of the function? Show the operation.

(2)

A charity collected 1,275 stamps. They pack them into envelopes with 15 stamps in each. They want to share the envelopes equally between 7 schools. How many envelopes will each school get and how many stamps are left over (not in envelopes)?

(2)

Multiply 3,206 by 4. Then subtract 1,078. Show your working and give the answer.

(2)

Explain your answer. Two different methods are given to calculate 7/10 of 350. Method A: 350 ÷ 10 = 35, then 35 x 7 = 245. Method B: 350 x 0.7 = 245. Are both methods correct and why? Give a clear explanation.

(3)

There are 4 shelves. Each shelf holds 18 boxes. Each box contains 9 tins. How many tins are there in total? Then find the total if one shelf is removed and replaced with two extra shelves of the same size (so number of shelves changes by +1).

(2)

A school orders 48 boxes of pencils. Each box holds 24 pencils. The pencils are packed into pencil cases that hold 12 pencils each. How many pencil cases are needed to hold all the pencils?

(2)

Callum buys 3 games that cost 7.95, 12.50 and £4.60. He pays with a £50 note. How much change does he get? Show working in pounds and pence.

(3)

A baker makes 72 cupcakes. She packs them into boxes with 6 cupcakes in each box. After packing, she sells 7 boxes. How many cupcakes are left unpacked or unsold?

(3)

Priya has eight 250 g bars of chocolate and three 120 g bars. She melts all the chocolate and pours it into 100 g moulds. How many full moulds can she fill?

(2)

A museum sells tickets at £6.80 for children and £9.50 for adults. On one day they sell 42 child tickets and some adult tickets. The total takings are £618.10. How many adult tickets were sold?

(3)

A recipe needs 2 3/4 cups of flour to make 12 scones. How much flour is needed to make 20 scones? Give your answer as a mixed number in cups.

(2)

Order these numbers from smallest to largest: 0.208, 208/1000, 0.28

(2)

Mark scheme · 1.11 Reasoning: Number and Calculation

Question 1

M1 Convert tonnes to kg: 7.5 t = 7,500 kg
B2 Sacks needed 7,500 / 25 = 300 cao
Answer: 300 sacks

Question 2

M1 Convert 2 hours 45 minutes to minutes: 2 x 60 + 45 = 165 minutes
B1 Total for 5 journeys 165 x 5 = 825 minutes cao
Answer: 825 minutes

Question 3

M1 Find pages per minute: 64/80 = 0.8 pages per minute or 4/5
B1 Convert 3 h 20 min to 200 minutes and multiply: 0.8 x 200 = 160 pages cao
Answer: 160 pages

Question 4

M1 Correct calculation of 15% of 84 = 0.15 x 84 = 12.6 or 12.60
B2 Sale price 84 - 12.60 = 71.40 cao
Answer: 71.40

Question 5

M1 Recognises operation needed: dividing both inputs by 4 gives outputs
B1 Rule is divide by 4 or 'divide by 4' cao
Answer: Divide by 4

Question 6

M1 Envelopes made: 1,275 / 15 = 85 envelopes
B1 Each school gets 85 / 7 = 12 envelopes each with 1 envelope left over; stamps left not in envelopes = 0 because all stamps put in envelopes, so answer: 12 each, 0 stamps left cao
Answer: 12 envelopes each, 0 stamps left

Question 7

M1 Correct multiplication 3,206 x 4 = 12,824
B1 Correct subtraction 12,824 - 1,078 = 11,746 cao
Answer: 11,746

Question 8

M1 Recognises both methods find same value and are equivalent
B2 Clear explanation linking fraction and decimal: 7/10 = 0.7 so both give 245, with correct reasoning cao
Answer: Both are correct. 7/10 = 0.7 so 350 x 7/10 = 350 x 0.7 = 245

Question 9

M1 Total initially 4 x 18 x 9 = 648 tins
B1 After change shelves = 4 - 1 + 2 = 5 so 5 x 18 x 9 = 810 tins cao
Answer: Initially 648, then 810

Question 10

M1 Correct total pencils: 48 x 24 = 1,152
B1 Number of cases 1,152 / 12 = 96 cao
Answer: 96 cases

Question 11

M1 Correct total cost found: 7.95 + 12.50 + 4.60 = 25.05
B2 Correct change 50.00 - 25.05 = 24.95 cao
Answer: 24.95

Question 12

M1 Correct number of boxes filled: 72 / 6 = 12 boxes
B2 After selling 7 boxes, remaining cupcakes = (12 - 7) x 6 = 30 cao
Answer: 30 cupcakes

Question 13

M1 Correct total mass: 8 x 250 + 3 x 120 = 2,000 + 360 = 2,360 g
B1 Number of 100 g moulds 2,360 / 100 = 23 full moulds cao
Answer: 23 moulds

Question 14

M1 Find child takings: 42 x 6.80 = 285.60
B2 Remaining 618.10 - 285.60 = 332.50, adult tickets = 332.50 / 9.50 = 35 cao
Answer: 35 adults

Question 15

M1 Find flour per scone: 2 3/4 = 11/4 cups; 11/4 ÷ 12 = 11/48 cups per scone
B1 Multiply by 20: 11/48 x 20 = 220/48 = 55/12 = 4 7/12 cups cao
Answer: 4 7/12

Question 16

M1 Convert or compare decimals/fractions correctly, noting 208/1000 = 0.208
B1 States that 0.208 and 208/1000 are equal, with 0.28 the largest cao
Answer: 0.208 = 208/1000 (equal, smallest), then 0.28 (largest)

Reasoning: Number and Calculation - Worksheets, Questions and Revision

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