MathSpherecoombbriggsprimary.co.uk/classes/class5/07 Statistics... · 2020. 4. 15. · © MathSphere . Liquid X was heated in the science lab until it reached boiling point. It was

Mathematics

Y5 Interpreting graphs, tables and charts. 5730

(Also available in KS2 Booster.)

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© MathSphere www.mathsphere.co.uk

Booster: KS2: Interpreting graphs, tables and charts 4/5 Page 2 © MathSphere www.mathsphere.co.uk

Notes

Tables of prices or distances are popular questions and can prove to be quite tricky to answer, even with a calculator. At level 4/5 the questions usually involve multiple operations to reach the answer (eg two of one thing plus one of another). Encourage very careful reading of the table to ensure that the correct numbers are chosen. Pupils need to be acquainted with Venn diagrams and be able to interpret what they show. Not only are pupils expected to know the terms mean and mode but they are also expected to be able to explain the use of them on graphs. Line graphs are introduced on the 4/5 questions. It is important for children to realise that a line graph shows continuous data ie every point on the line has a value. Block graphs or bar charts can not be converted into line graphs as the values between the bars have no value. Scales also differ at this level. Encourage children to look carefully to see exactly how the numbers are going up or down on an axis and what each square or interval represents.

Reading information from pie charts is also introduced. Again these questions can be harder than they first appear as similar pie charts can have different total values – see page 17 as an example of this.


You may use a calculator for these questions. 1. What is the total cost for a return journey to Brighton for 2 adults and one child? 2. How much more does it cost for a single adult ticket to Brighton than for a child? 3. How much more does it cost 2 adults to go on a single journey to Portsmouth than to London?

4. How much less does it cost two children to make a return journey to London than for two adults?

From Cambridge to… London Brighton Portsmouth

Adult

single

£12.50

£15.25

£18.60

return

£18.50

£22.50

£26.75

Child

single

£6.25

£7.75

£9.30

return

£9.25

£11.45

£14.45

The table shows the cost of bus tickets from Cambridge to different cities.

£

£

£

£


You may use a calculator for these questions. 1. What is the total cost for a single journey to Corfe for 2 adults and 2 children? 2. How much more is a single adult ticket to go to Herston than for a child? 3. How much more does it cost 3 adults to go on a return journey to Harman than to Herston?

4. How much less does it cost two children to make a return journey to herston than for two adults?

From Swanage to Herston Harman Corfe

Adult

single

£1.90

£3.70

£4.85

return

£3.60

£5.65

£7.75

Child

single

£0.85

£1.65

£2.35

return

£1.35

£3.25

£3.95

The table shows the cost of train tickets from Swanage on the steam railway.

£

£

£

£


This chart shows the distance in miles between five cities. Bristol Cardiff Exeter Glasgow Inverness Bristol 170 82 379 540 Cardiff 170 109 397 558 Exeter 82 109 451 612 Glasgow 379 397 451 174 Inverness 540 558 612 174 Use the table to answer these questions. 1. How far is it from Bristol to Glasgow? 2. Jill goes from Exeter to Bristol and then on to Inverness. How many miles does she travel?

3. Buffy goes from Cardiff to Glasgow and then back to Cardiff. How many miles does she travel?

miles

Show your method. You may get a mark.

miles


miles


This chart shows the distance in miles between five cities. Aberdeen Brighton Lincoln Newcastle Sheffield Aberdeen 605 387 234 393 Brighton 605 216 349 233 Lincoln 387 216 154 47 Newcastle 234 349 154 131 Sheffield 393 233 47 131 Use the table to answer these questions. 1. How far is it from Lincoln to Brighton? 2. Alan goes from Aberdeen to Newcastle and then on to Sheffield. How many miles does he travel? 3. Mary travels from Brighton to Lincoln. Paul travels from Brighton to Newcastle. How much further does Paul travel? 4. Gary travels from Aberdeen to Newcastle and back. How far did he travel? 5. Gill goes from Brighton to Sheffield and then on to Aberdeen. How many miles does she travel?

miles

miles

miles

miles

miles


Dragon races

Some dragons had two races to see who was the fastest. Here are their times. Running race Flying race Reddy 17.6 seconds 3 minutes 04 seconds Puffy 14.2 seconds 3 minutes 24 seconds Smokey 19.8 seconds 2 minutes 56 seconds Steamy 15.3 seconds 3 minutes 10 seconds Firey 16.6 seconds 2 minutes 53 seconds 1. Who was the fastest in the Flying race? 2. Who finished the Running race in third place? 3. In the Flying race how many seconds was Smokey ahead of Steamy? 4. In the Running race how much quicker was Steamy than Reddy? 5. What was the difference in time between the fastest and slowest times in the Flying race?


Below is a chart of facilities for games in a village.

ROUND BALL

NOT ROUND BALL

OUTDOOR

Football Cricket

Rugby

NOT OUTDOOR

Basketball Squash

Badminton

Jane wanted to reorganise the information in the form of a Venn diagram. Write the games in the correct places on the Venn diagram below.

Round ball Outdoor


Below is information about football teams.

Premier League

Not Premier league

Red shirts

Arsenal

Man. United

Crewe

Not red shirts

Chelsea

Lincoln

Brighton

Alex wanted to reorganise the information in the form of a Venn diagram. Write the teams in the correct places on the Venn diagram below.

Premier

Red shirts


Children in a class collected money for Comic Relief by having some cake sales. This is a chart of the money they collected. Money collected = £10 John Fazim Shakira Estimate how much each child collected. John Fazim Shakira Together John and Fazim collected over £60. Explain how the chart shows this.

£10

£ £ £

……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………

£10 £10

£10 £10 £10 £10

£10 £10 £10 £10

£10


Graph showing number of children using the Internet

20

18

16

14

12

10

8

6

4

2

0

20 18

14 10 8 Mon Tue Wed Thu Fri

Day of the week Kath draws a dotted line on the graph. She says, “The dotted line shows the mean number of children using the internet for the 5 days.” 1. Use the chart to explain why Kath cannot be correct. 2. What is the mean number of children for the 5 days?

……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………


Number of children


Below is a table showing the number of birds spotted by children in their gardens.

Name Robin Thrush Sparrow Starling Jan 4 1 2 2 Phil 0 1 3 0 Ann 0 1 3 2 Carl 0 3 0 1

Linda 3 1 2 2

10

5

0

Number of birds in children’s gardens.

Robin Thrush Sparrow Starling BIRDS

The birds spotted by one child are not on the graph. Which child’s results are not on the graph? Explain how you know.

Num

ber of birds

……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………


Liquid X was heated in the science lab until it reached boiling point.

It was then left to cool.

The graph below shows how the temperature of liquid x changes as it cools.

1. Read from the graph how many minutes the liquid took to reach a temperature of 500C. 2. How many minutes was the temperature above 400C ? 3. How long did it take to cool from 800C to 200C ?

110

100

90

80

70

60

50

40

30

20

10

0

Liquid x cooling

0 10 20 30 40 50 Time in minutes

Temperature in oC

.

minutes

minutes

minutes


Jim entered a 10 kilometre running race. This is a graph to show how far he had gone at different times.

1. How far did Jim run in the first 10 minutes of the race? 2. How far had he run after 40 minutes? 3. What time did he finish the race in? 4. Jim says, “I ran further in the first 20 minutes than the last 20 minutes.” Explain how the graph shows this.

10

9

8

7

6

5

4

3

2

1

0

10 km road race.

0 10 20 30 40 50 Time in minutes

Distance travelled in

km.

x

x

x

x

x

x

60

……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………


Chris was ill during May. This is the chart showing his temperature. 1. For how many days was his temperature marked as more than 370C ? 2. Use the graph to estimate Chris’s temperature on 6th May. 3. Which date showed the first drop in temperature from the day before? 4. Which date showed the greatest rise in temperature from the day before? 5. Approximately what is the difference between the lowest and highest temperatures shown?

Temperature 0C

40 -

39 -

38 -

37 -

36 -

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Dates in May

x x x x

x

x x

x

x

x

x x x x x

days

0C

0C


This graph shows the cost of phoning abroad from a mobile or from a land line.

Cost of phoning

£4

£3

£2

£1

£0 0 1 2 3 4 5 6 7 8 Length of phone call in hours

Mobile Land line

1. How much does it cost to phone for 3 hours on a mobile phone? 2. How much does it cost to phone for 8 hours on a land line? 3. How much more does it cost to phone for 4 hours on a mobile than on a land line? 4. Approximately how much is it to phone for 6 hours on a land line?

£

£

£

£


Some children work out how much their families spend on vegetables in a month.

1. Which vegetable did the Smith family spend most money on? 2. The Jones family spent £20 on beans. Estimate how much they spent on carrots. The Jones family spent a total of £60 altogether and the Smith family spent £90. 3. Estimate how much more the Smith family spent on potatoes than the Jones family.

Jones family Smith family

peas

carrots

potatoes

beans

peas

carrots

potatoes

beans


Tim and Jo shared the running of the school shop. They each made a pie chart of the products they had sold.

Total 100 Total 45 1. Estimate the number of rulers that Tim sold. 2. Who sold more pencils. Circle Tim or Jo. 3. Explain how you know.

pencils pens

rulers erasers

Tim’s pie chart Jo’s pie chart

Tim / Jo

……………………………………………………………………………………………………………………… ……………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………………

pencils

pens

rulers

erasers


Answers

Page 3 1. £56.45 2. £7.50 3. £12.20 4. £18.50 Page 4 1. £14.40 2. £1.05 3. £6.15 4. £4.50 Page 5 1. 379 miles 2. 622 miles + mark for showing process 3. 794 miles + mark for correct process Page 6 1. 216 miles 2. 365 miles 3. 133 miles 4. 468 miles 5. 626 miles Page 7 1. Firey 2. Firey 3. 14 secs 4. 2.3 secs 5. 31 secs Page 8

Round ball Outdoor football

cricket basketball

squash

rugby

badminton


Answers cont.

Page 9 Page 10 John in the range of £27 to £28 Fazim in the range of £34 to £36 Shakira in the range of £32 to £34 Explanation which implies that John has a greater amount than £25 and Fazim has at least £35 so the total must be over £60. Page 11 1. Explanation that refers to the fact that the dotted line is on the 5 children bar and all the bars are bigger than this. 2. 14 Page 12 Ann Any answer referring to the combination of results missing including 2 starlings and 3 sparrows.

Premier Red shirts

Man United

Brighton

Chelsea

Arsenal Crewe

Lincoln


Answers cont.

Page 13 1. 15 minutes 2. 20 minutes 3. 30 minutes Page 14 1. 2 km 2. 8 km 3. about 55 minutes 4. Explanation which implies that in the first 20 minutes Jim ran more than 3 ½ km but he started the last 20 minutes past the 7 km mark so had less then 3 km to go. Page 15 1. 7 days 2. between 39.50C and 39.70C 3. May 7 4. May 6 5. approx 2.70C allow 0.1 either side Page 16 1. £1.50 2. £3.00 3. £0.50 or 50p 4. approx £2.25 allow 10p either side. Page 17 1. peas 2. about £10 3. approx £7.50 Page 18 1. about 34 – allow 5 either side 2. Tim 3. explanations which suggest that Tim sold ¼ of 100 pencils which is 25 and Jo only sold ½ of 45 pencils

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MathSpherecoombbriggsprimary.co.uk/classes/class5/07 Statistics... · 2020. 4. 15. · © MathSphere . Liquid X was heated in the science lab until it reached boiling point. It was