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2 Whiteboardmaths.com © 2008 All rights reserved

3 Guidance Notes for Teachers Some indication of content and range at level 1 and 2 is shown on the next slide. Relevant slides show all the diagrams/questions/answers that are required. End slides have student question sheets and a teacher question/answer sheet. End slides have printable worksheets for students. Calculator symbols are suggestions only and could be removed depending on the group. * All of the questions appear one at a time in “type-writer” fashion so that you can take the students through each question/answer if you wish, without distraction from other questions on the screen at the same time. If you prefer to have all questions appear on a slide at the same time (or because its causing the show to run slow) then you will need to remove the animations. To do this choose: slide show/custom animation/ and click on the text boxes then choose “Remove” from the custom animation menu. Generic Advice: The preparation below is advisable in the majority of presentations. 1.Print off the teacher question and answer sheets/worksheets 2.Print off the student question sheets/worksheets 3.Run through the presentation yourself answering the questions 4.Decide how you are going to deliver the presentation. (a) Are you going to go through it from start to finish with the class, perhaps using it as an example/demonstration of functional maths and focusing on the development of the processing skills involved at each stage? (b) Are you going to use only part of the presentation? (c) Are you simply going to use the presentation to introduce the activity and let the class work on their own through the question sheets but refer to some of the elements/answers within the presentation when needed? 5.Remember the slides are editable so if you wish to introduce an open question/small investigation of your own then simply choose the relevant slide add/delete your own text (using a text box if needed).

4 Content and Skills Coverage and range: Level 1 Understand and use whole numbers and recognise negative numbers in practical contexts Add, subtract, multiply and divide using a range of mental methods Multiply and divide whole numbers by 10 and 100 using mental arithmetic Understand and use equivalences between common fractions, decimals and percentages Add and subtract decimal up to two decimal places Solve simple problems involving ratio, where one number is a multiple of the other Use simple formulae expressed in words for one- or two-step operations Solve problems requiring calculation with common measures including money, time, length, weight, capacity and temperature Convert units of measure in the same system Work out areas, perimeters and volumes in practical situations Construct models and draw shapes, measuring and drawing angles and identifying line symmetry Extract and interpret information from tables, diagrams, charts and graphs Collect and record discrete data and organise and represent information in different ways Find mean and range Use probability to show that some events are more likely to occur than others Understand outcomes, check calculations and explain results Understand and use positive and negative numbers of any size in practical contexts Carry out calculations with numbers of any size in practical contexts Understand, use and calculate ratio and proportion, including problems involving scale Understand and use equivalences between fractions, decimals and percentages Add and subtract fractions; add, subtract, multiply and divide decimals to a given number of decimal places Understand and use simple equations and simple formulae involving one- or two-step operations Recognise and use 2D representations of 3D objects. Find area, perimeter and volume of common shapes Use, convert and calculate using metric and, where appropriate, imperial measures Collect and represent discrete and continuous data, using ICT where appropriate Use and interpret statistical measures, tables and diagrams, for discrete and continuous data using ICT where appropriate Use statistical methods to investigate situations Use a numerical scale from 0 to 1 to express and compare probabilities Title: Going on Holiday Content and skills covered Coverage and range: Level 2 At least 1 from each area

5 Intro Mr and Mrs Robinson are going on holiday to stay with friends at a villa in Mallorca with their two children, Stephen and Gemma. They want to stay for exactly 10 nights and can travel both ways on any day of the week. Mr Robinson asked Gemma if she could use the internet to find the cheapest available flights from Stansted airport. What mathematics might be involved in going on a holiday overseas?

6 Flights Gemma came up with the following flight information. FlightMonTueWedThuFriSatSunDepArr LM Fare£40£60£57£32£75£40 FlightMonTueWedThuFriSatSunDepArr LM Fare£80£100£120 £150£120 Outbound Flights from Stansted to Palma Mallorca Return Flights from Palma Mallorca to Stansted All fares are inclusive of taxes and charges *Q2: What would be the total cost if they travelled on the Tuesday. £720 Q1: Why can’t they travel out to Mallorca on a Monday? Can’t return on Thursday *Q3: What was the cheapest total available cost of the fares? £448 *Q4: Determine the saving made over the Tuesday flight cost? £272 Q5: Calculate the percentage saving made by using this Friday flight (1d.p.) 37.8% *

7 Gemma asked Stephen to check her answers and he confirmed that they were correct. Gemma went off to show her dad the fare and wondered if she might get a few extra holiday Euros to spend when he found out about the saving. FlightMonTueWedThuFriSatSunDepArr LM Fare£40£60£57£32£75£40 FlightMonTueWedThuFriSatSunDepArr LM Fare£80£100£120 £150£120 Outbound Flights from Stansted to Palma Mallorca Return Flights from Palma Mallorca to Stansted All fares are inclusive of taxes and charges *

8 Stephen enjoyed his maths at school and he had recently been doing some work on data handling and he asked himself some questions from the table. He also thought about what other sorts of questions his maths teacher was likely to ask if she managed to get her hands on it. FlightMonTueWedThuFriSatSunDepArr LM Fare£40£60£57£32£75£40 FlightMonTueWedThuFriSatSunDepArr LM Fare£80£100£120 £150£120 Outbound Flights from Stansted to Palma Mallorca Return Flights from Palma Mallorca to Stansted All fares are inclusive of taxes and charges *

9 FlightMonTueWedThuFriSatSunDepArr LM Fare£40£60£57£32£75£40 FlightMonTueWedThuFriSatSunDepArr LM Fare£80£100£120 £150£120 Outbound Flights from Stansted to Palma Mallorca Return Flights from Palma Mallorca to Stansted All fares are inclusive of taxes and charges Q6: What is the modal fare for the return flights? £120 Q7: What is the median fare of the outbound flights? £48.50 *Q8: What is the range of the fares for all flights? £118 *Q9: On which day is the outbound fare 3/5 the price of the return fare? Tue *Q10: What is the ratio of Tue outbound to the Sat outbound fare? 4:5 *

10 FlightMonTueWedThuFriSatSunDepArr LM Fare£40£60£57£32£75£40 FlightMonTueWedThuFriSatSunDepArr LM Fare£80£100£120 £150£120 Outbound Flights from Stansted to Palma Mallorca Return Flights from Palma Mallorca to Stansted All fares are inclusive of taxes and charges *Q11: What percentage of the Sun outbound fare is the Fri outbound fare? 80% *Q12: What fraction of the Fri return fare is the Fri outbound fare? 4/15 Q13: State the arrival time in Mallorca in 12 Hour Clock pm Q14: How long does the flight to Mallorca take? 3 hours 25 minutes *Q15: How long is this in minutes? 205 minutes *

11 Getting There *Q16: The Robinson family will be travelling from their home in Bude, to the airport. Mr Smith reckons that the distance is 345 miles and he thinks that he can average 60 mph on the journey. How long should it take him to get to the airport? 5¾ hours *Q18: The family must be at the airport at least 2 hours before the flight departs at He intends to allow an extra hour for the journey in case of traffic congestion around London. What time do the Robinson family intend to set off from Bude? In: (a) 12 hour clock (b) 24 hour clock 2.15 am or 0215 Q19: Mr Robinson’s car should average 40 mpg on such a trip. How many gallons of fuel will he use on the trip? (1 d.p.). 8.6 gallons *Q20: 1 Gallon  4.5 litres. How many litres of fuel will he use? (nearest l ) 39 l *Q21: Fuel for his car costs £1.24 per litre. Calculate the total cost of using his car to get to the airport and back? (2 sig fig) £ 160 *Q17: His wife booked car parking for 10 days at Stansted at £5.88 a day. How much will this cost? £ *

12 Luggage Q22: The maximum weights for check-in luggage and hand luggage (1 piece each only per person) are shown below. As the family check-in they find that some of them have a problem. Discuss how it might be resolved. Max 20 kg Max 10 kg Suit Case Hand luggage DadMumGemmaStephen 17 kg22 kg15¾ kg16 kg 12 kg9½ kg8 kg5¼ kg © bigstockphoto.com

13 *Q23: Calculate the total weight of luggage that the family are taking. Max 20 kg Max 10 kg Suit Case Hand luggage DadMumGemmaStephen 17 kg22 kg15¾ kg16 kg 12 kg9½ kg8 kg5¼ kg 105½ kg *Q24: How far below the total allowed weight is this? 14½ kg *Q25: What is the weight of Mum’s hand luggage in pounds? 1 kg  2.2 lbs lbs *

14 CurrencyCurrency Exchange USA $2000 NorwayUKAustralia 5000 NOK£800$3000 (AUD) 1£= 1.26 € 1$ =0.68 € * 1 NOK = 0.12 € 1$ = 0.57 € ? € 1008 € 1360 € 600 € 1710 € Q26: Mr Robinson exchanged £800 at a machine at the airport into Euros. He also saw some international visitors exchanging money at the rates shown. Complete all the blanks in the table below.

15 Departure Board Q27: After a meal in the departure lounge Gemma checked the departure board again to see the details on their flight. How long is the flight delayed and which Gate do they need to go to board? Flight NumberDestinationGateTimeRemarks KLM 0015Berlin Departed OA 237Barcelona Go to Gate AI 4871Athens Go to Gate SP 724Madrid On time BA 3811Valletta New Time LM 321Palma New Time OA 5372Pathos On time NN 798Oslo On time CY5311Larnaca On Time 20 minutes, Gate 122

16 Temperatures Gemma rang her friend, Kate at the villa just before boarding to ask her what the weather was like. She said it had been hot and read out the temperatures for the last few days from a local newspaper. SunMonTueWedThu 17 o C 19 o C20 o C 22 o C25 o C28 o C30 o C Day Min Max * *Q28. The formula above is used for converting degrees Celsius ( o C) to degrees Fahrenheit ( o F). This formula can be approximated to F = 2C Use this less accurate but simpler formula to change all the temperatures in the table to degrees Fahrenheit. F = 9 5 C + 32 SunMonTueWedThu 66 o F 70 o F72 o F 76 o F82 o F88 o F92 o F Day Min Max *Q29. Use the exact formula to convert the maximum temperature on Sunday to degrees Fahrenheit. 68 o F *Q30. What was the mean Maximum daytime temperature in o C? 25 o C *Q31. What was the mean Minimum daytime temperature in o C? 18 o C

17 Gemma rang her friend, Kate at the villa just before boarding to ask her what the weather was like. She said it had been hot and read out the temperatures for the last few days from a local newspaper. SunMonTueWedThu 17 o C 19 o C20 o C 22 o C25 o C28 o C30 o C Day Min Max * *Q32. What proportion of the maximum Sunday temperature was the minimum temperature that day. Write your answer as: (a) A Fraction (b) A decimal (c) A percentage F = 9 5 C / /%

18 Runway Air Traffic Control gave LM 321 clearance to taxi to the holding point adjacent to the threshold of the runway. Aircraft almost always take off into wind so that they get help with lift and the runway-in-use is chosen mainly for this reason. On the runway threshold below, the large numbers indicate that on take-off the aircraft will be flying on a bearing of 320 o (i.e. almost North West). Q33: All numbers on runways consist of 2 digits. If an aircraft took off from the other end of this runway (i.e. in the opposite direction), what would the number on the threshold read and what would the bearing be? 14/140 o Q34: Air Traffic Control finally gave LM 321 clearance to take-off on runway 23 at Stansted. What bearing would this put the aircraft on during its take-off run. 230 Q35: A strong northerly wind would force the controllers to change the runway take-off direction. What would the 2-digit number read on the threshold at the other end of the runway? 05 Q36: What is the relationship between the two digit threshold numbers on opposite ends of any runway? Their difference is always 18 (180 o ) © bigstockphoto.com

19 Airborne Once the flight was airborne the captain announced to the passengers that they would be cruising at an altitude feet at a speed of 520 miles per hour. She later informed them that the outside temperature was -50 o C and that due to a strong tail wind they should arrive on time. The current weather in Palma was sunny with an outside air temperature of 35 o C. Q37. What was the cruising altitude to the nearest mile? (3 feet = 1 yard, 1760 yards = 1 mile. 7 miles Q38. What was the speed of the aircraft in km/hour? 1 km = 5/8 mile. 8/5 x 520 = 832 km/hr

20 Once the flight was airborne the captain announced to the passengers that they would be cruising at an altitude feet at a speed of 520 miles per hour. She later informed them that the outside temperature was -50 o C and that due to a strong tail wind they should arrive on time. The current weather in Palma was sunny with an outside air temperature of 35 o C. Q39. Use the conversion graph worksheet to determine the current outside temperature in Palma in o F. 95 o F Q40. Use the conversion graph worksheet to determine the temperature outside the aircraft. -58 o F Q41. There is only one instance where the temperature in o C has the same numerical value in o F. Use your conversion graph to find it. -40

21 Temperature ( o C) 0 Temperature ( o F) oCoC oFoF o C 95 o F -58 o F

22 Q42. And finally, Flight LM 321 was told by Air Traffic Control with 40 miles to run to Palma “descend report level 2000 feet, turn right onto a bearing of 240 o, report ILS established and call finals at 10 miles with undercarriage down and locked”. What runway was LM 321 given clearance to land on? 24 And a Happy Holiday to the Robinson family.

23 Teacher Q + A Sheets *Q2: What would be the total cost if they travelled on the Tuesday. £720 Q1: Why can’t they travel out to Mallorca on a Monday? Can’t return on Thursday *Q3: What was the cheapest total available cost of the fares? £448 Q6: What is the modal fare for the return flights? Q7: What is the median fare of the outbound flights? *Q8: What is the range of the fares for all flights? *Q9: On which day is the outbound fare 3/5 the price of the return fare? *Q10: What is the ratio of Tue outbound to the Sat outbound fare? *Q11: What percentage of the Sun outbound fare is the Fri outbound fare? *Q12: What fraction of the Fri return fare is the Fri outbound fare? 4/15 Q13: State the arrival time in Mallorca in 12 Hour Clock pm Q14: How long does the flight to Mallorca take? 3 hours 25 minutes *Q15: How long is this in minutes? 205 minutes *Q4: Determine the saving made over the Tuesday flight cost? £272 Q5: Calculate the percentage saving made by using this Friday flight (1d.p.) 37.8% £120 £48.50 £118 Tue 4:5 80% Teachers Q + A

24 5¾ hours *Q18: The family must be at the airport at least 2 hours before the flight departs at He intends to allow an extra hour for the journey in case of traffic congestion around London. What time do the Robinson family intend to set off from Bude? In: (a) 12 hour clock (b) 24 hour clock 2.15 am or 0215 Q19: Mr Robinson’s car should average 40 mpg on such a trip. How many gallons of fuel will he use on the trip? (1 d.p.). 8.6 gallons *Q20: 1 Gallon  4.5 litres. How many litres of fuel will he use? (nearest l ) 39 l *Q21: Fuel for his car costs £1.24 per litre. Calculate the total cost of using his car to get to the airport and back? (2 sig fig) £ 160 *Q17: His wife booked car parking for 10 days at Stansted at £5.88 a day. How much will this cost? £ *Q16: The Robinson family will be travelling from their home in Bude, to the airport. Mr Smith reckons that the distance is 345 miles and he thinks that he can average 60 mph on the journey. How long should it take him to get to the airport? Q22: The maximum weights for check-in luggage and hand luggage (1 piece each only per person) are shown below. As the family check-in they find that some of them have a problem. Discuss how it might be resolved. *Q23: Calculate the total weight of luggage that the family are taking. 105½ kg *Q24: How far below the total allowed weight is this? 14½ kg *Q25: What is the weight of Mum’s hand luggage in pounds? 1 kg  2.2 lbs lbs Q26: Mr Robinson exchanged £800 at a machine at the airport into Euros. He also saw some international visitors exchanging money at the rates shown. Complete all the blanks in the table below. (see slide 13) 1360/600/1008/1710 Q27: After a meal in the departure lounge Gemma checked the departure board again to see the details on their flight. How long is the flight delayed and which Gate do they need to go to board? (slide 14) 20 minutes, Gate 122 *Q28. The formula above is used for converting degrees Celsius ( o C) to degrees Fahrenheit ( o F). This formula can be approximated to F = 2C Use this less accurate but simpler formula to change all the temperatures in the table to degrees Fahrenheit. (See slide 15 + worksheet)

25 *Q29. Use the exact formula to convert the maximum temperature on Sunday to degrees Fahrenheit. 68 o F *Q30. What was the mean Maximum daytime temperature in o C? 25 o C *Q31. What was the mean Minimum daytime temperature in o C? 18 o C *Q32. What proportion of the maximum Sunday temperature was the minimum temperature that day. Write your answer as: (a) A Fraction (b) A decimal (c) A percentage 17/ /% Q33: All numbers on runways consist of 2 digits. If an aircraft took off from the other end of this runway (i.e. in the opposite direction), what would the number on the threshold read and what would the bearing be? 14/140 o Q34: Air Traffic Control finally gave LM 321 clearance to take-off on runway 23 at Stansted. What bearing would this put the aircraft on during its take-off run. 230 Q35: A strong northerly wind would force the controllers to change the runway take-off direction. What would the 2-digit number read on the threshold at the other end of the runway? 05 Q36: What is the relationship between the two digit threshold numbers on opposite ends of any runway? Their difference is always 18 (180 o ) Q37. What was the cruising altitude to the nearest mile? (3 feet = 1 yard, 1760 yards = 1 mile. 7 miles Q38. What was the speed of the aircraft in km/hour? 1 km = 5/8 mile. 8/5 x 520 = 832 km/hr Q39. Use the conversion graph worksheet to determine the current outside temperature in Palma in o F. 95 o F Q40. Use the conversion graph worksheet to determine the temperature outside the aircraft. -58 o F Q41. There is only one instance where the temperature in o C has the same numerical value in o F. Use your conversion graph to find it. -40 Q42. And finally, Flight LM 321 was told by Air Traffic Control with 40 miles to run to Palma “descend report level 2000 feet, turn right onto a bearing of 240o, report ILS established and call finals at 10 miles with undercarriage down and locked”. What runway was LM 321 given clearance to land on? 24

26 Student Question Sheet *Q2: What would be the total cost if they travelled on the Tuesday. Q1: Why can’t they travel out to Mallorca on a Monday? *Q3: What was the cheapest total available cost of the fares? Q6: What is the modal fare for the return flights? Q7: What is the median fare of the outbound flights? *Q8: What is the range of the fares for all flights? *Q9: On which day is the outbound fare 3/5 the price of the return fare? *Q10: What is the ratio of Tue outbound to the Sat outbound fare? *Q11: What percentage of the Sun outbound fare is the Fri outbound fare? *Q12: What fraction of the Fri return fare is the Fri outbound fare? Q13: State the arrival time in Mallorca in 12 Hour Clock. Q14: How long does the flight to Mallorca take? *Q15: How long is this in minutes? *Q4: Determine the saving made over the Tuesday flight cost? Q5: Calculate the percentage saving made by using this Friday flight (1d.p.) Student

27 *Q18: The family must be at the airport at least 2 hours before the flight departs at He intends to allow an extra hour for the journey in case of traffic congestion around London. What time do the Robinson family intend to set off from Bude? In: (a) 12 hour clock (b) 24 hour clock Q19: Mr Robinson’s car should average 40 mpg on such a trip. How many gallons of fuel will he use on the trip? (1 d.p.). *Q20: 1 Gallon  4.5 litres. How many litres of fuel will he use? (nearest l ) *Q21: Fuel for his car costs £1.24 per litre. Calculate the total cost of using his car to get to the airport and back? (2 sig fig) *Q17: His wife booked car parking for 10 days at Stansted at £5.88 a day. How much will this cost? *Q16: The Robinson family will be travelling from their home in Bude, to the airport. Mr Smith reckons that the distance is 345 miles and he thinks that he can average 60 mph on the journey. How long should it take him to get to the airport? Q22: The maximum weights for check-in luggage and hand luggage (1 piece each only per person) are shown below. As the family check-in they find that some of them have a problem. Discuss how it might be resolved. *Q23: Calculate the total weight of luggage that the family are taking. *Q24: How far below the total allowed weight is this? *Q25: What is the weight of Mum’s hand luggage in pounds? 1 kg  2.2 lbs. Q26: Mr Robinson exchanged £800 at a machine at the airport into Euros. He also saw some international visitors exchanging money at the rates shown. Complete all the blanks in the table below. (see slide 13) Q27: After a meal in the departure lounge Gemma checked the departure board again to see the details on their flight. How long is the flight delayed and which Gate do they need to go to board? (slide 14) *Q28. The formula above is used for converting degrees Celsius ( o C) to degrees Fahrenheit ( o F). This formula can be approximated to F = 2C Use this less accurate but simpler formula to change all the temperatures in the table to degrees Fahrenheit. (See slide 15 + worksheet)

28 *Q29. Use the exact formula to convert the maximum temperature on Sunday to degrees Fahrenheit. *Q30. What was the mean Maximum daytime temperature in o C? *Q31. What was the mean Minimum daytime temperature in o C? *Q32. What proportion of the maximum Sunday temperature was the minimum temperature that day. Write your answer as: (a) A Fraction (b) A decimal (c) A percentage Q33: All numbers on runways consist of 2 digits. If an aircraft took off from the other end of this runway (i.e. in the opposite direction), what would the number on the threshold read and what would the bearing be? Q34: Air Traffic Control finally gave LM 321 clearance to take-off on runway 23 at Stansted. What bearing would this put the aircraft on during its take-off run. Q35: A strong northerly wind would force the controllers to change the runway take-off direction. What would the 2-digit number read on the threshold at the other end of the runway? Q36: What is the relationship between the two digit threshold numbers on opposite ends of any runway? Q37. What was the cruising altitude to the nearest mile? (3 feet = 1 yard, 1760 yards = 1 mile. Q38. What was the speed of the aircraft in km/hour? 1 km = 5/8 mile. Q39. Use the conversion graph worksheet to determine the current outside temperature in Palma in o F. Q40. Use the conversion graph worksheet to determine the temperature outside the aircraft. Q41. There is only one instance where the temperature in o C has the same numerical value in o F. Use your conversion graph to find it. Q42. And finally, Flight LM 321 was told by Air Traffic Control with 40 miles to run to Palma “descend report level 2000 feet, turn right onto a bearing of 240o, report ILS established and call finals at 10 miles with undercarriage down and locked”. What runway was LM 321 given clearance to land on?

29 Worksheet 1 Suit Case Hand luggage DadMumGemmaStephen 17 kg22 kg15¾ kg16 kg 12 kg9½ kg8 kg5¼ kg Max 20 kg Max 10 kg SunMonTueWedThu 17 o C 19 o C20 o C 22 o C25 o C28 o C30 o C Day Min Max F = 9 5 C + 32 FlightMonTueWedThuFriSatSunDepArr LM Fare£40£60£57£32£75£40 FlightMonTueWedThuFriSatSunDepArr LM Fare£80£100£120 £150£120 Outbound Flights from Stansted to Palma Mallorca Return Flights from Palma Mallorca to Stansted Q1 – Q15 Q Q

30 Worksheet Temperature ( o C) 0 Temperature ( o F) oCoC oFoF Q


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