Grow your. Yellow 6. The wee Maths Book. Growth. of Big Brain. Guaranteed to make your brain grow, just add some effort and hard work

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1 Grow your Yellow 6 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! The wee Maths Book of Big Brain Growth Directions, Bearings and some Tables and Graphs 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.

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) (b) (c) (d) (e) (f) (g) (h) (i) Page 2

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 3

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) 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) 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 4

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 before the increase? 4. An extension on a house increases the floor area by 9%. If the floor area was 200m 2, 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 5

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 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 6

7 Section C When the percentage can be converted to a simple percentage 11. In a sale a shop reduces all its prices by %. 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? people go to a football match and 66 2 % stay until the final 3 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 7

8 N27t I can calculate percentage increase and decrease. Calculator allowed 1. A new luxury villa in Florida is valued at $ 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 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 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 8

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 Casas da Biquinha Ibis Quinta do Covanco NH Hotel 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 9

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 10

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 11

12 Life expectance from birth (years) 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 Life expectancy (Kenya) Year of birth Female Male (a) Describe the trend in life expectancy from birth between 1960 and (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 12

13 Number of Births 2. Aberloch is a small Scottish town. The number of births each year in Aberloch has been recorded since The graph below illustrates this information for 4 selected years. 600 Birth in Aberloch Year Male Female (a) Describe the trend in the total number of births from 1850 to (b) What was the total number of birth for each of the four years given? Page 13

14 3. The line below illustrates the numbers of fatalities on British roads from 2000 to ROAD FATALITIES - GREAT BRITAIN Pedestrian Pedal Cyclist FATALITIES YEAR (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 Page 14

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 15

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 16

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 Copy this Tally Chart into your jotter and use the list above to complete it. Shoe Size TALLY TOTAL Size 1 Size 2 Size 3 Size 4 Size 5 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? Page 17

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 18

19 Walk Cycle Car Bus Other 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? Walk Cycle Car Bus Other Number of people Use the information to copy and complete the graph below Page 19

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 20

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 21

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 (a) Copy and complete the frequency table for these results. Score Tally Frequency Total = (b) Draw a bar graph to illustrate these results. Page 22

23 2. Mr Odger measures the lengths of 20 throws of the javelin. The lengths (in metres) are shown below (a) Copy and complete the table to display this information. Score Tally Frequency Over 50 Total = (b) Draw a bar graph to illustrate these results. Page 23

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 24

25 World Population = 1 billion people Page 25

26 Fatal accidents in the United Kingdom involving drink driving = 25 fatalities 2013 Page 26