Yellow

6

The wee

Maths Book of Big Brain

Growth

Directions, Bearings and some Tables

and Graphs

Grow your

brain Guaranteed to

make your brain

grow, just add

some effort and

hard work

Don’t be afraid if

you don’t know

how to do it, yet!

It’s not how fast

you finish, but that

you finish.

It’s always better

to try something

than to try nothing.

Don’t be worried

about getting it

wrong, getting it

wrong is just part

of the process

known better as

learning.

Page | 2

Percentages (MNU 2-07a)

N25f I can compare quantities given in different formats.

Revision

Write each of the following vulgar fractions in their simplest form.

(a) 𝟓

𝟏𝟎𝟎 (b)

𝟐𝟎

𝟏𝟎𝟎 (c)

𝟒𝟎

𝟏𝟎𝟎

(d) 𝟓𝟎

𝟏𝟎𝟎 (e)

𝟕𝟓

𝟏𝟎𝟎 (f)

𝟑𝟎

𝟏𝟎𝟎

(g) 𝟖𝟎

𝟏𝟎𝟎 (h)

𝟏𝟎

𝟏𝟎𝟎 (i)

𝟐𝟓

𝟏𝟎𝟎

Page | 3

1. Write each as a vulgar fraction (in its simplest form) and a decimal

fraction.

(a) 25% (b) 50% (c) 20%

(d) 70% (e) 1% (f) 10%

2. Write each as a vulgar fraction (in its simplest form) and a decimal

fraction.

(a) 75% (b) 5% (c) 35%

(d) 15% (e) 30% (f) 85%

3. Write each as a vulgar fraction (in its simplest form) and a decimal

fraction.

(a) 80% (b) 40% (c) 55%

(d) 50% (e) 95% (f) 65%

4. Complete Worksheet 1

Use your understanding of rounding to express your answers to an

appropriate degree of accuracy.

5. Use your worksheet to help you write down the percentages

equivalent to the following vulgar fractions

(a) 𝟏

𝟐 (b)

𝟏

𝟏𝟎 (c)

𝟏

𝟒

(d) 𝟏

𝟓 (e)

𝟏

𝟐𝟎 (f)

𝟑

𝟒

Page | 4

6. Use your worksheet to help you write down the decimal fraction

equivalent to the following vulgar fractions

(a) 𝟑

𝟏𝟎 (b)

𝟐

𝟓 (c)

𝟕

𝟐𝟎

(d) 𝟕

𝟏𝟎 (e)

𝟑

𝟐𝟎 (f)

𝟑

𝟓

7. Use your worksheet to help you write down each decimal as a

percentage and a vulgar fraction in its simplest form.

(a) 𝟎 ∙ 𝟓 (b) 𝟎 ∙ 𝟐𝟓 (c) 𝟎 ∙ 𝟐

(d) 𝟎 ∙ 𝟎𝟓 (e) 𝟎 ∙ 𝟏 (f) 𝟎 ∙ 𝟑

8. Use your worksheet to help you write down each decimal as a

percentage and a vulgar fraction in its simplest form.

(a) 𝟎 ∙ 𝟕 (b) 𝟎 ∙ 𝟏𝟓 (c) 𝟎 ∙ 𝟕𝟓

(d) 𝟎 ∙ 𝟗 (e) 𝟎 ∙ 𝟔𝟓 (f) 𝟎 ∙ 𝟔

Page | 5

N26s I can find a percentage of a quantity involving at most

4 digits (Non Calculator).

Section A – When the percentage is a single digit.

1. At a comedy show 4% of the audience buy a

programme.

If 1500 attend the show, how many buy a

programme?

2. A bottle of iodine solution contains 7% iodine by volume.

What volume of iodine is there in a 500ml bottle?

3. A restaurant increases its prices by 3%.

How much will the increase be on a steak which cost £22∙50 before

the increase?

4. An extension on a house increases the floor area by 9%.

If the floor area was 200m2, calculate the increase?

5. A brand of cereal is usually sold in 700g

packs.

During a special promotion and extra 5%

is added to each box.

How much extra is added to the pack?

Page | 6

Section B – When the percentage is a multiple of ten

6. A travel firm offers a discount of 40% off the full price of package

holiday.

The full price of the package holiday is £760.

How much is the discount?

7. A metal alloy contains 90% pure gold.

How much gold is there in 270g of the alloy?

8. A hotel in Glasgow offers 70% off the full price of a weekend break.

How much is this saving if the full price of a weekend break is £350.

9. A new TV costs £375.

You must pay 30% deposit.

How much is the deposit?

10. Joanne’s car insurance is reduced by 60% because she has not made a

claim.

The normal cost of her insurance is £420.

How much is Joanne’s reduction?

Page | 7

Section C – When the percentage can be converted to a simple

percentage

11. In a sale a shop reduces all its prices by 331

3%.

I want to buy a hat which, before the price rise, cost £15 and a pair of

shoes which cost £25.

How much will I save in the sale?

12. There are 130 people living on Albert Square and 50% are women.

How many are women live in Albert Square?

13. 1200 people go to a football match and 662

3% stay until the final

whistle.

How many fans are still at the game for the final whistle?

14. The original price of a coffee machine

was £700.

The shop reduced the price by 10%,

and then cut the reduced price by 20%.

What does the machine now cost?

15. Jim bought a cat for £60.

Later he sold the cat for a profit of 75%.

How much profit did he make?

Page | 8

N27t I can calculate percentage increase and decrease.

Calculator allowed

1. A new luxury villa in Florida

is valued at $375000. It is

expected to rise in value by

13% during its first year.

What will the value of the

villa be at the end of the

first year?

2. Mrs Dodds buys a new car for £25000.

It depreciates in value by 8% during its first year.

How much will Mrs Dodds car be worth at the end of the first year?

3. Jorge buys a new house for £80 000. The value of the house

depreciates by 11% in the first year.

How much would his house be worth at the end of the first year?

4. Company shares worth £1,200 drop in value over a month by 18%.

How much were the shares worth at the end of the month?

5. The Pollards bought a bungalow for £110,000.

It appreciated in value by 28% in three years.

How much was the bungalow worth at the end of three years?

Page | 9

Statistics and Graphs (MNU 2-20a, MNU 2-20b, 3-21a)

D4s I can extract and interpret data from a table including

listing a number of possibilities.

1. Ben and Eva are going on holiday to Lisbon for 4 nights.

They have £450 to spend on their hotel room.

List all the hotels, from the table below, which they can afford.

Hotel Cost for 4 days Cost for 7 days

Holiday Inn £410 £720

Casas da Biquinha £482 £840

Ibis £330 £570

Quinta do Covanco £489 £850

NH Hotel £432 £756

2. Callum is looking for a new mobile phone contract.

He streams a lot of music and wants at least 5Gb of data included.

List all the deals, from the table below, which he could pick.

Deal Included Calls Included Data

Starter plan 400 minutes 500MB

All Round Plan unlimited 6GB

Ultimate Plan unlimited 15GB

Loyalty Plan 1000minutes 2GB

Brand New Plan 100 minutes 8GB

Page | 10

D5s I can extract and interpret data from a pictograph

1. Look at the pictograph of world population below.

(a) How many people were living in the world in 1650?

(b) What was the population of the world in 1999?

(c) What is the projected population of the world in 2070?

Page | 11

2. Look at the pictograph below, which illuatrates the number of people

killed in the UK as a result of drink driving.

(a) How many people were killed in 2007?

(b) How many people were killed in 2013?

(c) Describe the trend in deaths involving drink driving?

What conclusion could you come to as a result of this trend?

Page | 12

0

10

20

30

40

50

60

70

1960 1970 1980 1990 2000 2010

Lif

e e

xpecta

nce f

rom

bir

th (

years

)

Year of birth

Life expectancy (Kenya)

Female Male

D6s I can extract and interpret data from bar charts and

line graphs

1. The graph below displays information on life expectancy from birth in

Kenya.

(a) Describe the trend in life expectancy from birth between 1960

and 2010.

(b) Kenya is in East Africa.

This area has been the subjected

to drought and famine.

In 1999/2000 famine affected

close to 4∙4 million Kenyans.

What effect did this have on life

expectancy?

Explain your answer

Page | 13

0

100

200

300

400

500

600

1850 1900 1950 2000

Num

ber

of

Bir

ths

Year

Birth in Aberloch

Male Female

2. Aberloch is a small Scottish town.

The number of births each year in Aberloch has been recorded since

1850.

The graph below illustrates this information for 4 selected years.

(a) Describe the trend in the total number of births from 1850 to

2000.

(b) What was the total number of birth for each of the four years

given?

Page | 14

0

100

200

300

400

500

600

700

800

900

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013

FATALITIES

YEAR

ROAD FATALITIES - GREAT BRITAIN

Pedestrian Pedal Cyclist

3. The line below illustrates the numbers of fatalities on British roads

from 2000 to 2013.

(a) What was the number of pedestrian fatalities in 2003?

(b) What was the number of cyclist fatalities in 2002?

(c) Describe the trend in pedestrian fatalities and compare it against

the trend in pedal cyclist fatalities between 2000 and 2013.

Page | 15

D7t I can construct a frequency/tally table from the results

of a survey

1. Shoppers in the supermarket were asked in a survey which was their

favourite fruit. Here is a list of their responses.

Banana Apple Banana Banana

Grape Orange Apple Apple

Strawberry Orange Apple Banana

Orange Orange Strawberry Banana

Banana Grape Apple Apple

Apple Orange Strawberry Strawberry

Copy this Tally Chart into your jotter and use the list above to

complete it.

FRUIT TALLY TOTAL

Apple

Banana

Grape

Orange

Strawberry

Use the information in the tally chart to answer the questions below

in your jotter.

(a) Which fruit was the most popular?

(b) Which fruit was the least popular?

(c) Which two fruits were preferred by the same number of people?

(d) How many more people preferred Apples to Grapes?

(e) How many fewer people preferred Strawberries to Bananas?

(f) How many people were surveyed all together?

(g) Order the fruits from most popular to least popular?

Page | 16

2. (a) Copy and fill in the number section in the woodland table.

Creature Tally Number

Wood ant |||| |||| |

Woodlice |||| |||| |||

Small fly |||

Caterpillar ||

Slug ||||

Snail |

(b) Copy and fill in the tally section in the heathland table

Creature Tally Number

Wood ant 2

Woodlice 4

Small fly 7

Caterpillar 8

Slug 5

Snail 4

(c) Which minibeasts are the most common in woodland?

(d) Which minibeasts are least common in heathland?

Page | 17

3. A children’s shoe shop took a survey of their customers shoe size over

one day. Here is a list of their responses.

4 2 2 2 1 3 1 2 2

3 4 1 2 3 2 2 1 1

3 1 3 5 1 2 3 4 2

Copy this Tally Chart into your jotter and use the list above to

complete it.

Use the information in the tally chart to answer the questions below

in your jotter.

(a) Which shoe size was most popular?

(b) Which shoe size was the least popular?

(c) What was the largest shoe size?

(d) What was the smallest shoe size?

(e) How many more children had size 2 shoes than had size 4 shoes?

(f) How many fewer children had size 5 shoes than size 1 shoes?

(g) How many customers did the shop have on the day of the survey?

(h) Order the shoe sizes from most popular to least popular?

Shoe Size TALLY TOTAL

Size 1

Size 2

Size 3

Size 4

Size 5

Page | 18

4. John wants to know what things he can do in France.

He asks his friends what they like to do on holiday.

This is what he found out:

Sun bathing Sight seeing Water sports Water sports Sight seeing

Water sports Sight seeing Sun bathing Sun bathing Sun bathing

Sun bathing Sun bathing Water sports Sight seeing Sight seeing

Sight seeing Sun bathing Sight seeing Sun bathing Water sports

(a) Put the data into a frequency table.

(b) How many more people liked sun bathing compared to water

sports?

Page | 19

D8t I can construct a bar graph from a frequency table

1. In a survey, the pupils in some first year classes were asked “How do you get to school?” The results are shown in the table.

How do you get to school?

Number of people

Walk Cycle Car Bus

Other

18 13 8 15 4

Use the information to copy and complete the graph below.

Walk

Cycle

Car

Bus

Oth

er 0

2

4

6

8

10

12

14

16

18

20

Page | 20

2. The table below shows the results of a survey.

Holidaymakers were asked “what is your favourite activity when on

holiday”

Activity Frequency

Sun bathing 13

Water sports 7

Sight seeing 10

Draw a bar chart to illustrate the information in the table.

3. The table below shows the results of a biology field trip.

Creature Tally Number

Wood ant |||| 5

Woodlice |||| |||| | 11

Small fly |||| || 7

Caterpillar |||| 4

Slug |||| |||| 9

Snail ||| 3

Use the table to construct a bar chart.

Page | 21

4. Ben observed the colour of cars that drove past his house in one hour.

Here are his results:

Red Red Pink Yellow Silver Blue Silver Red

Blue Silver Silver Black Blue White Red Black

Blue Blue Silver Red Blue Silver White Blue

Silver Black Blue Black Silver Red Blue Black

Blue Red Silver Blue Blue Blue Yellow Red

(a) Construct a frequency table using the above results.

(b) Display this data in a bar chart.

5. A shopping centre carried out a survey to see what people liked most

about the facilities.

The responses are displayed in the table below.

Parking Parking Food Court Water sports Cloths Shops

Food Court Location Cloths Shops Food Court Sun bathing

Cloths Shops Food Court Cloths Shops Cloths Shops Cloths Shops

Food Court Cloths Shops Food Court Cloths Shops Cloths Shops

(a) Summaries the results in a frequency table.

(b) Construct a bar graph to illustrate the results.

(c) An advertising company is trying to attract more shoppers to the

shopping centre.

Use the results from the survey to choose a main theme for the

company to use in their adverts.

Give a reason for your answer.

Page | 22

D9t I can construct a frequency table which includes class

intervals.

1. The number of visitors to the school library, at lunchtime, was

recorded each day for two weeks.

The results are shown below.

38 22 19 27 25 44 52

12 34 36 38 51 18 36

(a) Copy and complete the frequency table for these results.

(b) Draw a bar graph to illustrate these results.

Score Tally Frequency

10 – 19

Total =

Page | 23

2. Mr Odger measures the lengths of 20 throws of the javelin.

The lengths (in metres) are shown below.

33 21 42 12 27

36 46 28 21 13

39 52 34 43 30

10 32 57 12 39

(a) Copy and complete the table to display this information.

(b) Draw a bar graph to illustrate these results.

Score Tally Frequency

1 – 10

11 - 20

21 - 30

31 - 40

41 - 50

Over 50

Total =

Page | 24

A well nurtured and emotionally healthy pupil will know that

they can improve their brain power through regularly applying

themselves to his/her studies in class and by completing all of

the tasks in this booklet.

He/she will feel more included, respected and will develop greater levels of

responsibility if you regularly discuss with them their progress, both progress

in class and progress through this booklet.

You will encourage him/her to be a passive learner and intellectually lazy if

you show them how to attempt every question. Encourage them to think for

themselves. Your child will achieve more if they actively experiment with

the questions in this booklet, safe in the knowledge that they can learn from

any mistakes made.

Tips for Parents

1. Talk to your child on a regular basis about the work they are

attempting in Mathematics.

2. Give praise for appropriate effort and resilience, and avoid praise

which uses the words clever or smart.

3. Talk about your child's brain power improving through hard work

and not being something that is fixed.

4. Mistakes are part of the learning process. Your child should be able

to experiment with Maths safe in the knowledge that they can learn

from their mistakes.

5. Talk about your child’s progress in a way which emphasises their

own ability to influence a positive and successful future. This will

encourage them to become more resilient and equipped to meet

the challenges of the course.

Page | 25

= 1 billion people

World Population

1650

1850

1930

1975

1999

2012

2070

Page | 26

= 25 fatalities

Fatal accidents in the United Kingdom involving drink driving

2007

2008

2009

2010

2011

2012

2013