Reasoning and Problem Solving (Year 4) - Worksheets, Questions and Revision

18 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 and Problem Solving (Year 4) revision guide

This topic is chapter 4 of KS2 Maths: Number and place value Practice Book.

1.8 Reasoning and Problem Solving (Year 4)

Calculators not allowed · about 55 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Liam has 245 stickers. He gives 38 stickers to Mia and 17 stickers to Noah. How many stickers does Liam have left?

(2)

A gardener plants bulbs in rows. Each row holds 9 bulbs. He plants 6 full rows and has 5 bulbs left. How many bulbs did he start with?

(2)

A bottle holds 1.5 litres of juice. How many millilitres is this? Then, if a glass holds 250 ml, how many full glasses can be filled from one bottle?

(a)Convert 1.5 litres to millilitres.(1)

(b)How many full 250 ml glasses can be filled from the bottle?(1)

A cinema has 8 rows with 12 seats in each row. Tickets for a showing sell for £6 each. If all seats are sold, what is the total money taken?

(2)

Nia ran 2.4 km on Monday and 3.6 km on Tuesday. How many metres did she run in total over the two days?

(2)

A school orders packs of pencils. Each pack has 10 pencils and costs 85p. They order 14 packs. What is the total cost in pounds and pence?

(2)

A class has 30 pupils. Two fifths of the class go on a trip. How many pupils go on the trip?

(2)

A farmer sorts 360 apples into boxes. He puts 9 apples in each small box and 30 apples in each crate. He uses only full boxes and crates and wants to use exactly 360 apples. Suggest one possible number of crates and small boxes he could use. Show how you know your answer is correct.

(3)

Explain why the number 48 can be made by adding three consecutive even numbers. Give an example and show the calculation.

(3)

A puzzle: Three friends share a bundle of carrots. Ali takes twice as many as Ben. Cara takes 5 fewer than Ali. Together they take 83 carrots. Explain whether this is possible and show why or why not.

(4)

A packet of 6 apples costs 78p. What is the cost of one apple in pence? Give your answer in pence.

(2)

Sofia reads 36 pages each day. How many days will it take her to read a book of 252 pages?

(2)

A rectangle has length 14 cm and width 6 cm. Sara draws the same rectangle 3 times to make a strip. What is the total area of the strip in square centimetres?

(2)

A baker uses 450 g of flour for 15 buns. How many grams of flour does he use for one bun?

(2)

Tom has three boxes. The first box has 24 marbles, the second has twice as many as the first, and the third has 6 fewer than the second. How many marbles are there altogether?

(2)

A shelf is 180 cm long. Emma places 5 identical books along the shelf with equal spaces between them and 10 cm at each end. What is the distance between each book (the equal space between books)?

(2)

There are 48 children in a class. They are split into groups of 6 for an activity. After making the groups, 2 children join from another class. How many groups of 6 can be made now?

(2)

A toy costs £4.75. Mary has £15. How many toys can she buy and how much change will she have left? Give the change in pounds and pence.

(2)

Mark scheme · 1.8 Reasoning and Problem Solving (Year 4)

Question 1

M1 Subtract 38 and 17 from 245 (correct subtraction seen)
B1 190 cao
Answer: 190

Question 2

M1 Multiply 6 x 9 = 54 and add 5 seen
B1 59 cao
Answer: 59

Question 3

(a) B1 1500 ml cao
(a) Answer: 1500
(b) B1 6 cao
(b) Answer: 6

Question 4

M1 Find total seats: 8 x 12 = 96 and multiply by 6 seen
B1 £576 cao
Answer: £576

Question 5

M1 Convert to metres or add decimals then convert: 2.4 + 3.6 = 6.0 km
B1 6000 m cao
Answer: 6000

Question 6

M1 Multiply 85p x 14 seen (85 x 14 = 1190)
B1 £11.90 cao
Answer: £11.90

Question 7

M1 Find 1/5 = 30 ÷ 5 = 6 or use fraction of 30: (2/5) x 30 seen
B1 12 cao
Answer: 12

Question 8

M1 Show a correct combination that sums to 360 using 9s and 30s (for example 6 crates x 30 = 180 and 20 small boxes x 9 = 180, or any other correct split)
B1 State a valid combination clearly (e.g. 6 crates and 20 small boxes)
B1 Calculation check shown to prove total 360 cao
Answer: One possibility: 6 crates and 20 small boxes

Question 9

M1 Show general reasoning or calculation using consecutive even numbers (e.g. let numbers be n, n+2, n+4 or find specific three even numbers)
B1 Give a correct example of three consecutive even numbers that add to 48 (e.g. 14, 16, 18)
B1 Show correct addition to make 48 (14 + 16 + 18 = 48) cao
Answer: For example 14, 16 and 18. 14 + 16 + 18 = 48

Question 10

M1 Set up relations: if Ben = b then Ali = 2b and Cara = 2b - 5, and write sum 2b + b + (2b - 5) = 83
M1 Solve equation: 5b - 5 = 83 => 5b = 88 => b = 17.6 seen or attempt to solve
B1 State that b is not a whole number so the split into whole carrots is not possible
B1 Conclude and justify: therefore they cannot share 83 carrots with given whole-number relations cao
Answer: Not possible because Ben would need 17.6 carrots, not a whole number

Question 11

M1 Division 78 ÷ 6 or equivalent grouping seen
B1 13 cao
Answer: 13

Question 12

M1 Division 252 ÷ 36 or grouping shown
B1 7 cao
Answer: 7

Question 13

M1 Area of one rectangle found: 14 x 6 = 84
B1 252 cao
Answer: 252

Question 14

M1 Division 450 ÷ 15 or grouping shown
B1 30 cao
Answer: 30

Question 15

M1 Find second box (24 x 2 = 48) and third box (48 - 6 = 42) or equivalent working
B1 114 cao
Answer: 114

Question 16

M1 Subtract end spaces (180 - 20 = 160) and divide by 4 gaps seen
B1 40 cm cao
Answer: 40 cm

Question 17

M1 Add 2 to 48 to get 50 then divide by 6 seen
B1 8 remainder 2 or 8 full groups, but question asks how many groups of 6 can be made now: 8 cao
Answer: 8

Question 18

M1 Division or repeated subtraction to find 3 toys (3 x 4.75 = 14.25) seen
B1 3 toys and 75p change (14.25 subtracted from 15 gives 0.75) cao
Answer: 3 toys, £0.75

Reasoning and Problem Solving (Year 4) - Worksheets, Questions and Revision

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