Fractions and Problem Solving - Worksheets, Questions and Revision

18 original exam-style questions - 7 pages of questions with a full mark scheme - free printable PDF.

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KS1 · Number - Fractions

KS1.M10 Fractions and Problem Solving

STA NC-KS1-MATHS-STA · Calculators not allowed · about 45 minutes

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

The rectangle below is split into 2 equal parts.

Shade 1 half of the rectangle.

(1)

The square below is split into 4 equal parts.

Shade 1 quarter of the square.

(1)

Look at shapes A, B and C below. Each shape is split into equal parts, and some parts are shaded.

Tick the shape that shows exactly one third shaded.

The rectangle below is split into 4 equal parts, and 3 of the parts are shaded.

Circle the fraction that shows how much of the rectangle is shaded.

1/4 1/2 3/4 4/4

There are 14 apples in a basket.

Find half of the apples.

How many apples is that? ___

(1)

What is a quarter of 20?

Answer: ___

(1)

There are 12 sweets in a bag.

Circle one third of the sweets.

How many sweets did you circle? ___

(1)

Aaliyah picks 24 grapes. She eats three quarters of the grapes.

Work out how many grapes Aaliyah eats. Show your working.

Answer: ___

(2)

A baker makes 24 loaves of bread. She sells half of the loaves before lunch.

Work out how many loaves she sells before lunch. Show your working.

Answer: ___

(2)

A pizza is cut into 4 equal slices. Oliver eats one quarter of the pizza and his sister Isla eats one quarter of the pizza.

Work out what fraction of the pizza is left. Show your working.

Answer: ___

(2)

Mrs Okafor has 15 conkers. She shares them equally between herself, her son Kwame and her daughter Amara.

Work out how many conkers each person gets. Show your working.

Answer: ___

(2)

Put these fractions in order, starting with the smallest: 3/4, 1/4, 1/2

(2)

A quarter of a number is 5.

Work out the number. Show your working.

Answer: ___

(2)

A ribbon is 30 cm long. Deepak cuts it into 3 equal pieces.

Work out the length of each piece. Show your working.

Answer: ___

(2)

A square cake is cut into 2 pieces, but the pieces are not the same size.

Amelia says, 'One of the pieces is a half of the cake.'

Is Amelia correct? Explain your answer.

(2)

Farmer Singh collects 24 eggs. He sells half of the eggs at the market. Then he gives a quarter of the remaining eggs to his neighbour.

Work out how many eggs Farmer Singh has left. Show your working.

Answer: ___

(3)

Amara bakes 24 flapjacks. She shares them equally between herself and 3 friends. She then eats one third of her own share as a snack.

Work out how many flapjacks Amara eats as a snack. Show your working.

Answer: ___

(3)

A class has 28 pupils. One quarter of the pupils walk to school, one half of the pupils come by car, and the rest come by bus.

(a)Work out how many pupils walk to school and how many pupils come by car.(2)

(b)Work out how many pupils come by bus. Show a check that your answer is correct.(2)

Mark scheme · KS1.M10 Fractions and Problem Solving

Question 1

B1 exactly 1 of the 2 equal parts shaded cao
Answer: 1 of the 2 equal parts shaded

Question 2

B1 exactly 1 of the 4 equal parts shaded cao
Answer: 1 of the 4 equal parts shaded

Question 3

B1 A cao
Answer: A

Question 4

B1 3/4 cao
Answer: 3/4

Question 5

B1 7 cao
Answer: 7

Question 6

B1 5 cao
Answer: 5

Question 7

B1 4 cao
Answer: 4

Question 8

M1 finds one quarter of 24 (24 / 4 = 6) oe, or equivalent correct method
A1 18 cao
Answer: 18

Question 9

M1 finds half of 24 (24 / 2) oe, or equivalent correct method
A1 12 cao
Answer: 12

Question 10

M1 finds the fraction eaten, 1/4 + 1/4 = 2/4 oe
A1 1/2 (or 2/4) cao oe
Answer: 1/2 (2/4) of the pizza left

Question 11

M1 finds one third of 15 (15 / 3) oe, or equivalent correct method
A1 5 cao
Answer: 5 conkers each

Question 12

M1 fractions compared correctly using a common whole (e.g. quarters) oe
A1 1/4, 1/2, 3/4 cao
Answer: 1/4, 1/2, 3/4

Question 13

M1 uses the inverse operation, 5 x 4 oe
A1 20 cao
Answer: 20

Question 14

M1 finds one third of 30 (30 / 3) oe
A1 10 cm cao (units required)
Answer: 10 cm

Question 15

B1 No (Amelia is not correct)
B1 correct reason given oe, e.g. the two pieces must be equal in size for each to be one half, but here the pieces are unequal
Answer: No - the two pieces must be equal in size for each piece to be one half; here they are unequal, so neither piece is a half.

Question 16

M1 finds half of 24, 24 / 2 = 12 (eggs remaining after selling) oe
M1 finds one quarter of their 12, 12 / 4 = 3 (eggs given to neighbour), dep on first method, oe, ft
A1 9 cao (12 - 3), ft their values if the method is correct
Answer: 9 eggs

Question 17

M1 finds Amara's share, 24 / 4 = 6 (shared among Amara and 3 friends) oe
M1 finds one third of their 6, 6 / 3 = 2, dep on first method, oe, ft
A1 2 cao, ft their share if the method is correct
Answer: 2 flapjacks

Question 18

(a) B1 7 pupils walk to school (1/4 of 28 = 7)
(a) B1 14 pupils come by car (1/2 of 28 = 14)
(a) Answer: 7 pupils walk; 14 pupils come by car
(b) M1 28 - 7 - 14 oe (subtracting the walkers and car pupils from the total), ft their part (a)
(b) A1 7 cao, with a valid check shown, e.g. 7 + 14 + 7 = 28
(b) Answer: 7 pupils come by bus

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