Grow your brain N4 Numeracy Book 6 The wee Maths Book of Big Brain Growth 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. Numeracy 2.1, 2.2 and 2.3
O Extracting and interpreting data from at least two different straightforward graphical forms O1 I can extract data from a table 1. The table below shows the number of casualties on British roads in 2014 and the percentage change compared to 2013, 2009 and to the 2005-2009 average. (a) What was the number of people killed or seriously injured 2014? (b) What was the percentage increase in the numbers slightly injured between 2013 and 2014? (c) What was the percentage decrease in the killed between 2009 and 2014? (d) What was the percentage decrease in all casualties between the average during 2005-2009 and 2014? Page 2
2. The table below show the results of a national survey which asked the question Do you eat five a day?. Region Don t Know Enough More than enough Not enough London 4 96 10 82 Midlands of England 4 217 39 209 Scotland 1 61 9 89 South East England South West England North of England 3 153 17 78 1 83 18 67 6 244 35 197 Wales 0 39 5 44 (a) What number of respondents from Scotland replied enough? (b) What number of respondents from Wales replied don t know? (c) What percentage of respondents from the North of England replied More than enough? (d) What percentage of respondents from the London replied not enough? Page 3
3. The table below show the results of a national survey which asked the question How do you get to your work?. Region Bike Car On Foot Public Transport Other London 1 101 34 26 4 Scotland 3 116 27 13 8 Wales 1 71 14 3 4 (a) What number of respondents from Scotland replied car? (b) What number of respondents from Wales replied other? (c) What number of London from Wales replied bike? (d) What percentage of respondents from the London replied on foot? (e) What percentage of respondents from the Scotland replied public transport? (f) What percentage of respondents from the Wales replied car? (g) What number of respondents altogether replied public transport? (h) What percentage of respondents altogether replied on foot? Page 4
FATALITIES P2 I can extract data from a Bar Chart 4. The bar chart below illustrates the numbers of fatalities on British roads from 2000 to 2013. 4,000 Road Fatalities - Great Britain 3,500 3,000 2,500 2,000 1,500 1,000 500 0 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 YEAR Car Occupant All Road User Groups (a) What was the number of fatalities in 2006 who were car occupants? (b) What was the number of fatalities in 2004 from all road user groups? (c) What percentage of fatalities in 2003 who were car occupants? (d) What percentage of fatalities in 2010 who were car occupants? Page 5
FATALITIES 5. The bar chart below illustrates the numbers of fatalities on British roads from 2000 to 2011 which involve drivers who had been drinking compared to fatalities involving all road users. 3,500 Road Fatalities Involving Drink Drivers 3,000 2,500 2,000 1,500 1,000 500 0 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 YEAR Involving Drink Driving All Road User Groups (a) What number of fatalities in 2001 involved drink drivers? (b) What was the number of fatalities in 2009 from all road user groups? (c) What percentage of fatalities in 2005 involved drink drivers? (d) What percentage of fatalities in 2011 involved drink drivers? Page 6
6. The bar chart below illustrates the results of a survey from 1998 on the use of suncream by teenagers. The Numbers in the y-axis represent percent of respondents in that category. 90 Use of Suncream (1998) 80 70 60 50 40 30 Male Female 20 10 0 Sunbathing abroad Outdoors abroad, but not sunbathing Sunbathing in this country Outdoors in this country, doing something else Always use suncream in the sun Never use suncream but goes into the sun Never goes out in the sun (a) What percentage of males use suncream abroad? (b) What percentage of females use suncream while sunbathing in this country? (c) What percentage of males always use suncream in the sun? (d) What percentage of females use suncream never go out in the sun? Page 7
P3 I can extract data from a Line Graph 7. The bar chart below illustrates the numbers of fatalities on British roads from 2000 to 2013. ROAD FATALITIES - GREAT BRITAIN Pedestrian Pedal Cyclist 900 800 700 600 FATALITIES 500 400 300 200 100 0 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 YEAR (a) What was the number of pedestrian fatalities in 2003? (a) What was the number of cyclist fatalities in 2002? (a) What was the number of pedestrian fatalities in 2007? (a) What was the number of cyclist fatalities in 2010? Page 8
P4 I can extract data from a Stem and Leaf Diagram 8. The stem and leaf diagram below compares the test results of two S5 classes. 5AL 5BL 3 4 4 1 9 9 9 6 7 3 3 0 1 4 0 2 8 8 9 9 8 1 1 3 5 7 0 5 9 4/7 means 47 (a) List all the marks in 5AL between 30 and 40 inclusive. (b) List all the marks in 5BL between 20 and 30 inclusive. (c) List all the marks in 5AB greater than 30. (d) List all the marks in 5BL less than 30. Page 9
9. The stem and leaf diagram below compares the heights of the pupils in two S5 classes. 5AL 5BL 8 18 9 9 6 1 17 0 0 3 5 7 3 1 0 16 1 7 7 8 8 3 3 1 15 0 5 5 2 0 14 9 13/7 means 137cm (a) List all the heights in 5AL between 140cm and 150cm inclusive. (b) List all the heights in 5BL between 150cm and 160cm inclusive. (c) List all the heights in 5AB greater than 160cm. (d) List all the heights in 5BL less than 140cm. Page 10
P5 I can make and explain a decision using data from a Pie Chart 10. The pie chart below illustrates the results of a survey which asked Do you eat five portions of fresh fruit and vegetables each day. In total 2300 people were surveyed. Do you eat your five a day? Don't Know 1% Not Enough 42% Enough 49% More Than Enough 8% State the number of replies for each of the four categories? Page 11
P6 I can make and explain a decision using data from a variety of graphical forms 11. The area graph below illustrates information about fatalities on British roads during 2014. (a) Calculate the number of fatalities who were car occupants. (b) Calculate the number of fatalities who were pedestrians. (c) Calculate the number of fatalities who were pedal cyclists. Page 12
12. The area chart below shows information about injuries on British roads in 2014 by type of road and seriousness of injury. (a) Calculate the number of fatalities on built-up roads. (b) Calculate the number of serious injuries on non built-up roads. (c) Calculate the number of slight injuries on motorways. (d) Calculate the number injuries of all types on built-up roads. Page 13
P Making and explaining decisions based on the interpretation of data P1 I can make and explain a decision using data from a table 1. The table below shows the number of casualties on British roads in 2014 and the percentage change compared to 2013, 2009 and to the 2005-2009 average. (a) A newspaper headline read 1707 people killed on British road in 2013. Was this headline consistent with the table above? (b) In 2014 the Transport Minister said we ve managed to reduce the number of people killed or seriously injured on our roads by two and a half thousand people, compared to five years ago. Comment on the minister s claim. Page 14
2. The table below show the results of a national survey which asked the question Do you eat five a day?. Region Don t Know Enough More than enough Not enough London 4 96 10 82 Midlands of England 4 217 39 209 Scotland 1 61 9 89 South East England South West England North of England 3 153 17 78 1 83 18 67 6 244 35 197 Wales 0 39 5 44 (a) The Welsh Health Minister said Wales has the lowest number of respondents who are not eating five a day. Is her comment accurate? (b) Why might this comment be misleading? Justify your answer. Page 15
3. The table below show the results of a national survey which asked the question How do you get to your work?. Region Bike Car On Foot Public Transport Other London 1 101 34 26 4 Scotland 3 116 27 13 8 Wales 1 71 14 3 4 (a) The Mayor of London said The congestion charge in London is encouraging people to leave their car at home. We are now national leaders, in London, in using alternative modes of transport to get to work!. Is the Mayor of London s comment justified? Support your answer with calculations (b) The ratio of car users to public transport users, among people going to work in Scotland, is claimed to be 10:1. Does this survey confirm this ratio? Justify your answer Page 16
FATALITIES P2 I can make and explain a decision using data from a Bar Chart 4. The bar chart below illustrates the numbers of fatalities on British roads from 2000 to 2013. 4,000 Road Fatalities - Great Britain 3,500 3,000 2,500 2,000 1,500 1,000 500 0 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 YEAR Car Occupant All Road User Groups (a) Describe the trend in the number of fatalities of all road users between 2000 and 2013. (b) In 2013, the police released a statement which contained the phase about half of the fatalities on our roads are car occupants. Is this claim true? Justify your answer Page 17
FATALITIES 5. The bar chart below illustrates the numbers of fatalities on British roads from 2000 to 2011 which involve drivers who had been drinking compared to fatalities involving all road users. 3,500 Road Fatalities Involving Drink Drivers 3,000 2,500 2,000 1,500 1,000 500 0 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 YEAR Involving Drink Driving All Road User Groups Page 18 (a) Describe the trend in the number of fatalities involving Drink Drivers between 2000 and 2011. (b) In 2011, the police released a statement which contained the phase Although fatalities on our roads have decreased since 2000, the proportion involving drink drivers has stubbornly remain about the same. Is this claim true? Justify your answer
6. The bar chart below illustrates the results of a survey from 1998 on the use of suncream by teenagers. 90 Use of Suncream (1998) 80 70 60 50 40 30 Male Female 20 10 0 Sunbathing abroad Outdoors abroad, but not sunbathing Sunbathing in this country Outdoors in this country, doing something else Always use suncream in the sun Never use suncream but goes into the sun Never goes out in the sun (a) Who put themselves most at risk going into the sun, males or females? Justify your answer (b) More than double the number of males take the risk of going out in the sun without any protection when compared to females. Is this claim true? Justify your answer Page 19
P3 I can make and explain a decision using data from a Line Graph 7. The bar chart below illustrates the numbers of fatalities on British roads from 2000 to 2013. ROAD FATALITIES - GREAT BRITAIN Pedestrian Pedal Cyclist 900 800 700 600 FATALITIES 500 400 300 200 100 0 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 YEAR (a) Describe the trend in the number of fatalities of pedestrians, then describe the trend in the number of fatalities of cyclists, between 2000 and 2013. (b) In 2013 the federation for cyclists released a statement which contained the phase A much higher proportion of road fatalities in 2013 are cyclists compared to 2000. This is a problem which must be addressed!. Page 20 Is this claim true? Justify your answer.
P4 I can make and explain a decision using data from a Stem and Leaf Diagram 8. The stem and leaf diagram below compares the test results of two S5 classes. The test was out of 50 and the pass mark was 25. 5AL 5BL 3 4 4 1 9 9 9 6 7 3 3 0 1 4 0 2 8 8 9 9 8 1 1 3 5 7 0 5 9 4/7 means 47 (a) The teacher of 5AL told a parent that Half of the class passed the test Is this claim true? Justify your answer. (b) Cara is in 5BL and told her dad that Most of my class failed the test Is this claim true? Justify your answer. Page 21
9. The stem and leaf diagram below compares the heights of the pupils in two S5 classes. 5AL 5BL 8 18 9 9 6 1 17 0 0 3 5 7 3 1 0 16 1 7 7 8 8 3 3 1 15 0 5 5 2 0 14 9 13/7 means 137 cm (a) Half of the class have a height of 160cm or less Which class is the comment about. Justify your answer. (b) About 20% of students have a height of 175cm or above Is this claim true for both classes? Justify your answer. Page 22
P5 I can make and explain a decision using data from a Pie Chart 10. The pie chart below illustrates the results of a survey which asked Do you eat five portions of fresh fruit and vegetables each day. Do you eat your five a day? Don't Know 1% Not Enough 42% Enough 49% More Than Enough 8% (a) If 1260 people in the survey replied not enough, how many replied more than enough? (b) Half of all respondents meet that five a day target. Is this claim true? Justify your answer Page 23
P6 I can make and explain a decision using data from a variety of graphical forms 11. The area graph below illustrates information about fatalities on British roads during 2014. (a) A quarter of all fatalities were pedestrians. Is this claim true? Justify your answer (b) More than a fifth of all fatalities were motorcyclists. Is this claim true? Justify your answer Page 24
12. The area chart below shows information about injuries on British roads in 2014 by type of road and seriousness of injury. (a) The number of slight injuries on the motorway is less than the number of serious injuries on built-up roads. Comment on this statement. Justify your answer (b) The number of fatalities on motorways is a tenth of the number of fatalities on non-built-up roads. Comment on this statement. Justify your answer Page 25
Q Making and explaining decisions based on probability Q1 I can calculate the simple probability of an event occurring. 1. A ten sided spinner, numbered 1 to 10, is spun. Work out each of the following probabilities. 8 9 10 7 6 5 1 2 3 4 (a) The probability that the spinner will land on an odd number. (b) The probability that the spinner will land on a square number. 2. Sally recorded the musical instrument played by each of 30 students in the school orchestra. The table shows the results. Musical Instrument Frequency Clarinet 5 Guitar 12 Flute 7 Drums 6 One of the students in the school orchestra is chosen at random by a visiting inspector. Find the probability that this student plays the flute. Page 26
3. The residents in 3 regions of the UK were asked How do you get to the shops The results are show in the table below Region Bike Car On Foot Bus/Train Other London 1 101 34 26 4 Scotland 3 116 27 13 8 Wales 1 71 14 3 4 (a) In which region would you be most likely to go shopping by car? (b) In which region would you be most likely to go shopping on foot? (c) In which region would you be most likely to go shopping by public transport? Justify your answers with calculations 4. Two dice are thrown. What is: (a) the probability that the sum of the two dice is 7? (b) The probability that the difference is 2? (c) The probability of the product being a multiple of 5? Page 27
Q2 I have used probability to compare the likelihood of events occurring. 5. Two year groups are to send pupils to a concert. The pupils are chosen at random. S3 has 123 pupils and 15 tickets. S4 has 131 pupils and 18 tickets. In which year group does a pupil have the best chance of being selected? Justify your answer by calculation. 6. Tickets are being sold for two different prizes at a fayre. 80 tickets have been sold for prize A. 120 tickets have been sold for prize B. Corinne has 5 tickets for prize A and 8 tickets for prize B. Which prize has Corinne the better chance of winning? Justify your answer by calculation. 7. Which of the following is more likely to occur? Choosing a club from a pack of cards OR throwing a number less than 3 on an ordinary die. Justify your answer by calculation. Page 28
8. George has 2 bags filled with coloured counters. Bag A contains 3 red, 4 blue and 5 green counters. Bag B contains 5 red, 8 blue and 4 green counters. In which bag would you have a better chance of selecting a red counter? Justify your answer by calculation. 9. A teacher asks 2 different classes if they are right-handed or lefthanded. In class A, 6 out of 25 pupils are left handed. In class B, 11 out of 31 pupils are left handed. In which class does any one person have a better chance of being left handed? Justify your answer by calculation. 10. Mary bought tickets for the school raffle and the Church raffle. Out of 500 tickets for the school raffle, Mary had bought 15. Out of 200 tickets for the Church raffle, Mary had bought 5. In which raffle does Mary have a better chance of being a winner? Justify your answer by calculation. Page 29