At Midtown school, one third of children travel by car

Megan asked children from two different schools,

‘How do you travel to school?’

Here are her results.

Foxwood school80 children

Midtown school240 children

Megan says,

‘The number of children walking to Foxwood school is more than the number walking to Midtown school.’

Is she correct?Circle Yes or No.

Yes / No

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Page 1 of 23Wootton+Community+Primary+School

Explain how you know.

1 mark

At Midtown school, one third of children travel by car.

The number of children who cycle is the same as the number who go on the bus.

How many children cycle to Midtown school?

2 marks


Seven children measured their heights.

Children Height (cm)

Stefan 144

Lara 136

Olivia 142

Chen 143

Maria 152

Dev 148

Sarah 150

What is the mean height of the children?

2 marks

2


Vicki puts 10 books on a shelf.

The 10 books take up 28 centimetres.

3

What is the mean (average) thickness of her books?

2 marks


The shelf is 120 centimetres long.

Vicki fills the shelf with a mixture of books like the first ten books.

Estimate how many books she can get on the 120 cm shelf.

2 marks

Carol counts the matches in 10 boxes.

She works out that the mean number of matches in a box is 51

4

Here are her results for 9 boxes.

1st January

48 49 50 51 52 53 54

✔

✔

✔

✔

✔

✔

✔

✔

✔


Calculate how many matches are in the 10th box.

2 mark

The arrow below points to the mean of the three numbers shown by crosses.

(a) Draw an arrow that points to the mean of the three numbers shown below.

1 mark

5

(b) The arrow below points to the mean of three numbers.

One of the numbers is missing.

Draw a cross to show the position of the missing number.

1 mark


Look at the information in these two pie charts.

Pupils in class 6K

Key:

Girls

Boys

6

Girls in class 6K

Key:

11 years old

Not 11 years old


Use the information in the two pie charts to complete the pie chart below.

Pupils in class 6K

Key:

11 years old girls

All other pupils inthe class

1 mark

This chart shows the number of different types of big cat in a zoo.

There are 20 big cats in the zoo altogether.

7


Here are some statements about the chart.

Tick the statements that are true.

There are more cheetahs than jaguars.

The total number of lions and tigers is 10

One-quarter of the big cats are cheetahs.

There are more than 5 jaguars.

2 marks

Alfie and his brother walked from home to their school.

Their school is 2 kilometres from home.

The graph shows information about Alfie’s journey.

8

(a) How does the graph show that Alfie walked at a constant speed for all of his journey?

______________________________________________________________1 mark


(b) Alfie’s brother left home 10 minutes before Alfie.

He arrived at school 20 minutes after Alfie.

He walked at a constant speed for all of his journey.

At what time did Alfie overtake his brother?

1 mark

This graph shows the distance Alfie and Chen walked in an afternoon. They started at 1:45pmand had two breaks.

9

How many kilometres did they walk between the first and second breaks?

1 mark


At what time did Alfie and Chen start their second break?

1 mark

Two companies sell toys online. They charge to deliver.

Describe the delivery cost of the second company.

The first company is done for you.

1 mark

10


This graph shows how the temperature changed in Liam’s room one afternoon.

Estimate the temperature at 3:15pm.

1 mark

11

Estimate the time when the temperature was highest.

1 mark

How much did the temperature change from 2pm to 2:30pm? Give your answer to the nearestdegree.

1 mark


100 girls and 50 boys were asked which kind of chocolate they like best.

These two pie charts show the results.

12

Dev says:

"The pie charts show that more girls than boys liked milk chocolate best."

Dev is correct.

Explain how you know.

1 mark


A shop sells drinks.

The pie chart compares the money a shop took last year for water, juice and soft drinks.

13

The shop took £8,264 for soft drinks.

Sales of water and juice were equal.

How much money did the shop take for juice last year?

2 marks


This graph shows the temperature in °C from 2 am to 3 pm on a cold day.

14

How many degrees warmer was it at 3 pm than at 3 am?

1 mark

At 6 pm the temperature was 4 degrees lower than at 3 pm.

What was the temperature at 6 pm?

1 mark


Mark schemes

(a) An explanation that shows that one quarterof 240 is more than one half of 80, eg:

• ‘Because only 40 are walking to Foxwoodand 60 are walking to Midtown’

• ‘Half of the people who walk is 40 anda quarter of the people who walk is 60’

No mark is awarded for circling ‘No’ alone.

Do not accept vague or incomplete explanations, eg:

• ‘Because at Foxwood it’s a half and atMidtown it’s a quarter’

• ‘Because there are 80 children at Foxwoodand 240 children at Midtown’

If ‘Yes’ is circled but a correct unambiguousexplanation is given then award the mark.

1U1

1

(b) Award TWO marks for the correct answer of 50

If the answer is incorrect, award ONE mark forevidence of an appropriate method, eg

240 ÷ 3 = 80

240 – 80 – 60 = 100

100 ÷ 2

Answer need not be obtained for the award of ONE mark.Up to 2

[3]

Award TWO marks for the correct answer of 145

If the answer is incorrect, award ONE mark for evidence of an appropriate method, e.g:

• 144136142143152148

+ 150 1015

1015 ÷ 7

Answer need not be obtained for the award of ONE mark.Up to 2

[2]

2


(a) Award TWO marks for correct answer of 2.8 cm.If answer is incorrect, award ONE mark for any appropriate calculationeven if the answer is incorrect, eg:

• 28 ÷ 10 = wrong answer.

A calculation MUST be performed for award of one mark.Up to 2

3

(b) Award TWO marks for WHOLE NUMBER ANSWER in therange 40 to 50 inclusive, eg:

• 42.8

If answer is outside range, award ONE mark for anappropriate calculation, eg:

• 120 ÷ 28 × 10 = wrong whole number answer.

• 120 ÷ 30 × 10 = wrong whole number answer.

• 30cm is 10 books.60cm is 20 books.120cm is ... wrong answer.

If answer is outside range, a calculation MUST be performed foraward of one mark. If calculation is based upon incorrect answer to16a, award TWO marks for correct calculation using an appropriatestrategy AND rounding of answer to whole number, even if outsiderange 40–50, eg:

• 120 ÷ answer to 16a = rounded whole number. OR ONE mark if there is either an error in calculation or failure to round to whole number.

Up to 2

[4]

Award TWO marks for the correct answer of 52

If the answer is incorrect award ONE mark for evidence of anappropriate method, eg

51 × 10 = 510

so number of matches =

510 – ((49 × 3) + (50 × 2) + (54 × 2) + 51 + 52)

The calculation need not be completed for the awardof the mark.

Up to 2

[2]

4


(a) Draws an arrow pointing to 12

Accept unambiguous indication of 12, eg:

• an arrow drawn within 2mm of the mark for 12

• 12 circled1

5

(b) Draws a cross on 7

Accept unambiguous indication of 7, eg:

• a cross drawn within 2mm of the mark for 7

• 7 circled1

[2]

Divides the pie chart into two correct sectors and shades/labels correctly, eg

•

Accept unambiguous indication of shading/labelling, eg

•

6

! Given key ignored

Condone incorrect shading provided their labelling is unambiguous

eg, accept

•


! Additional sectors shown

Ignore provided the sector(s) for 11 year-old girls are clearlyindicated

eg, accept

•

[1]

Award TWO marks for only two correct boxes ticked, as shown:

There are more cheetahs than jaguars.

The total number of lions and tigers is 10

One-quarter of the big cats are cheetahs.

There are more than 5 jaguars.

Award ONE mark for:

• only one correct box ticked and no incorrect boxes ticked

OR

• two correct boxes ticked and one incorrect box ticked.Accept alternative unambiguous positive indications, e.g. Y.

Up to 2 marks

[2]

7

Gives a correct interpretation of the graph, eg:

• It is a straight line

• It goes up steadily

• The angle of the line stays the same

8


• The gradient of the line is constant

Accept minimally acceptable explanation, eg:

• It is straight

• It doesn’ t bend

• It is a diagonal

Do not accept incomplete or ambiguous explanations that do notsufficiently imply a constant speed and /

or do not demonstrate the relationship holds for the

entire graph, eg:

• The line goes straight up

• It is not wobbly

• It is level

• Every 5 mins he walks the same distance

• He walks 1km in the first 15 mins and 1km in the second 15 mins

! Values read from graph

Accept, provided it is clear the relationship holds for the entiregraph.

Values should be accurate within +/− 0.1km and /or +/− 2 minutes, eg:

• 0.7km every 10 minutes

• Every 7.5 minutes he walks about half a km

! Calculation of kilometres per hour

Accept values in the range 3.7 to 4.3km per hour inclusive.1

(b) 08:10

! Accept values between 08:09 and 08:11 inclusive

! Time1

[2]

(a) 4 km1

(b) 4:15pm

The answer is a specific time1

[2]

9


Gives a correct description that indicates the delivery cost is constant, eg:

• The delivery cost is always £5

• The cost is always £5 no matter how much the toy costs

• Delivery stays the same as the cost of toy increases

Accept minimally acceptable explanation, eg:

• It is £5

Accept omission of the actual delivery cost, eg:

• It always costs the same

• The cost is the same

• The cost of the toy does not affect the delivery cost

! Condone correct response with the pound sign omitted, eg:

• It is always 5

! Condone explanations which refer to toys costing up to £20

Do not accept incomplete or ambiguous explanation, eg:

• They are equal amounts

[1]

10

(a) Accept answers in the range 22.2 to 22.8 exclusive.

Do not accept 22.2 or 22.81

(b) Accept answers in the range 2:48pm to 2:52pm inclusive.

The answer is a specific time.1

(c) 51

[3]

11

Award ONE mark for an explanation which recognises that thetwo pie charts represent different numbers of children, e.g:

• ‘25 boys like milk chocolate best and more than 25 girls do’

• ‘It’s almost half of 100 girls and that’s more than half of 50 boys’

• ‘The pie chart shows that half of the boys chose milk chocolate and that’s 25. About 45 girlschose milk chocolate because it’s nearly half of the girls’ pie chart’

• ‘25 boys chose milk chocolate, but (whole number in the range 40-49) girls chose milkchocolate’

12


• ‘There are twice as many girls as boys so a quarter of the girls’ pie chart is the samenumber as half of the boys’ pie chart, and it’s more than a quarter of the girls’

• of 50 boys chose milk = 25

of 100 girls chose plain = 25

and from the girls’ pie chart it is obvious that more chose milk than plain’

• ‘There are twice as many girls as boys and the sizes of the pie charts show this and thearea for boys who like milk chocolate is smaller than the area for girls who like it’.

Do not accept vague or incomplete explanations, e.g:

• ‘100 is more than 50’

• ‘More girls took part than boys so more girls like milkchocolate’

• ‘The section for boys who like milk chocolate is smaller thanthe section for girls who like it’.

Commentary: The pie charts are presented using the mathematical convention that their areasare proportional to the numbers they represent, i.e. in this example the chart for girls has twicethe area of the chart for boys.

[1]

Award TWO marks for the correct answer of £12396.

If the answer is incorrect, award ONE mark for evidence of an appropriate method, eg:

■ £8264 × 4

£33056

OR

£33056 − 8264

£24792

£24792 ÷ 2

OR

■ £8264 ÷ 2 = £4132£8264 + £4132

Answer need not be obtained for the award of ONE markUp to 2

[2]

13


(a) 7

1

Do not accept −7 or 7−

(b) −21

Do not accept 2−[2]

14


Documents

At Midtown school, one third of children travel by car