2. Whiteboardmaths.com © 2008 All rights reserved 5 7 2 1

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. We would like to thank the Settle – Carlisle Partnership, in particular J.P. Buckley for their help in allowing use of the photographs/gradient diagram and other information from their Website at http://www.settle-carlisle.co.uk/index.cfm http://www.settle-carlisle.co.uk/index.cfm * 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: Settle-Carlisle Railway Content and skills covered Coverage and range: Level 2 At least 1 from each area

5. Brief History The Settle to Carlisle Railway What mathematics might be involved in going on a train on this mountain railway?

6. Brief History The 72 mile route from Settle to Carlisle takes you on a journey through the magnificent Yorkshire Dales, over the 24 arches of the Ribblehead Viaduct before plunging into the longest tunnel on the line at Blea Moor. Emerging onto the side of Dentdale, the line leaves the Dales at Garsdale and makes its way through the gentle, lush rolling hills of the Eden Valley, with rural villages and market towns before arriving at the great border city of Carlisle. The journey takes you through 14 tunnels and over 20 viaducts. The line is probably the most scenic railway journey in England. It has survived two attempts to close it - once in the early 1960s and later in the 1980s. Both attempts caused local and national outrage. However, fortunes have now changed as millions of pounds have been spent upgrading tracks and stations. Some 6000 men worked on building the Settle-Carlisle Line between 1869 and 1876 before it was open for use by the then Midland Railway Company. A couple of miles down the valley towards Ingleton is Chapel – le Dale where a memorial exists in the church yard for those who died building the line. Many died through outbreaks of smallpox, as well as those injured or killed during construction. The Settle to Carlisle Railway

7. Settle – Carlisle Railway (72 miles) Settle Station © bigstockphoto.com

8. Intro Ribblehead Viaduct with Pen-y-ghent in the Background SETTLE Horton Ribblehead Dent Gardsdale Kirkby Stephen Appleby Langwathby Lazonby Armathwaite CARLILSE The first five stations of the route lie in North Yorkshire, the remainder are in Cumbria. The three stations shown in the diagram straddle the famous Three Peaks of Ingleborough, Whernside and Pen-y-gent, all located in the Yorkshire Dales National Park. Many walkers/hikers use the line to help them organise their walking within the area. It is easy to hop on/off the train and do short walks close by the stations. The more ambitious walkers might use the line to walk some of the nearby peaks or perhaps take part in the Three Peaks Challenge. Ingleton Dent Pen-y-ghent (2277 ft) Ingleborough (2372 ft) Whernside (2415 ft) Horton in Ribblesdale Ribblehead Dent 3 Peaks Challenge (25 miles in 12 hours) Start/Finish Pen-y-ghent café in Horton 4 miles Chapel-le-Dale N

9. Time Table Q1: What time does the first train of the day leave Settle? 0950 Q2: Where is its 5 th stop? Kirkby Stephen Q3: How long does this train take to get to Dent? 26 minutes Q4: How long does it take to reach its destination? 1 hour 44 minutes Q5: One train departs from Garsdale station at 1616. What time is this in 12 hour clock? 4.16 pm © bigstockphoto.com

10. Q6: How many stops does the 1044 train have after leaving Settle? 3 Q7: Sarah missed the 1107 train from Lazonby. How long will she have to wait for the next one? 1 hour 56 minutes Q8: Which two stations have the least number of trains each day. Dent/Garsdale Q9: Give the time in 12 hour clock for the first train from Armathwaite. 8.08 am Q10: Phillipa spent the day at a friends’ house in Horton. She must be home in Appleby no later than 5.00 pm. What is the time of the latest train that she can leave on? 1553

11. -0950104411461348154519032022 -0958-11541357155319112031 -1006-12021405160119192041 -1016-1212141416111929- -1021-1217142016161934- 0728103411221230143216291947- 0740104711361243144516411959- 07541101-1257145916552013- 08001107-1303150417012019- 08081115-1311151217092027- 0824113412171329153217282047- Settle Horton in Rib’dale Ribblehead Dent Garsdale Kirkby Stephen Appleby Langwathby Lazonby & Kirk Armathwaite Carlisle 0620-085311511400150316181755 0634-090712051414-16321809 0641-091412121421-16391816 0647-092012181427-16451822 0703-093512331443154017011837 0717-094812451455155317141849 --100112591509-17281903 --100613041514-17331908 -0714101713131523-17421917 -0721102313201529-17491924 -0729103113281538163517581932 Carlisle Armathwaite Lazonby & Kirk Langwathby Appleby Kirkby Stephen Garsdale Dent Ribblehead Horton in Rib’dale Settle Settle – Carlisle: Mondays – Fridays. Carlisle – Settle: Mondays – Fridays. - - - - - - - - - - - - - - - - - - - 2100 2106 2114 SETTLE Horton Ribblehead Dent Gardsdale Kirkby Stephen Appleby Langwathby Lazonby Armathwaite Carlisle N Q11: John caught the 0853 train from Carlisle to Settle. He came back on the first train in the afternoon. What time did he get back to Carlisle at? 1532 Q12: How long did he spend in total on the train in: (a) Hours and minutes (b) Minutes 3 h 22m 202 min Q13: What time does the last train of the day depart Horton? (in 12 hour clock). 9.06 pm

12. -0950104411461348154519032022 -0958-11541357155319112031 -1006-12021405160119192041 -1016-1212141416111929- -1021-1217142016161934- 0728103411221230143216291947- 0740104711361243144516411959- 07541101-1257145916552013- 08001107-1303150417012019- 08081115-1311151217092027- 0824113412171329153217282047- Settle Horton in Rib’dale Ribblehead Dent Garsdale Kirkby Stephen Appleby Langwathby Lazonby & Kirk Armathwaite Carlisle 0620-085311511400150316181755 0634-090712051414-16321809 0641-091412121421-16391816 0647-092012181427-16451822 0703-093512331443154017011837 0717-094812451455155317141849 --100112591509-17281903 --100613041514-17331908 -0714101713131523-17421917 -0721102313201529-17491924 -0729103113281538163517581932 Carlisle Armathwaite Lazonby & Kirk Langwathby Appleby Kirkby Stephen Garsdale Dent Ribblehead Horton in Rib’dale Settle Settle – Carlisle: Mondays – Fridays. Carlisle – Settle: Mondays – Fridays. - - - - - - - - - - - - - - - - - - - 2100 2106 2114 SETTLE Horton Ribblehead Dent Gardsdale Kirkby Stephen Appleby Langwathby Lazonby Armathwaite Carlisle N Q14: What is the longest period of time that someone living in Settle can spend in Carlisle before returning on the last train? 5 6 h 21 m Q15: How many trains leave Lazonby for Settle during the afternoon? 4 Q16: What is the ratio of trains arriving at Settle to trains arriving at Langwathby each day? 2:3 Q17: What fraction of trains arriving in Settle came from Carlisle? ¾

13. -0950104411461348154519032022 -0958-11541357155319112031 -1006-12021405160119192041 -1016-1212141416111929- -1021-1217142016161934- 0728103411221230143216291947- 0740104711361243144516411959- 07541101-1257145916552013- 08001107-1303150417012019- 08081115-1311151217092027- 0824113412171329153217282047- Settle Horton in Rib’dale Ribblehead Dent Garsdale Kirkby Stephen Appleby Langwathby Lazonby & Kirk Armathwaite Carlisle 0620-085311511400150316181755 0634-090712051414-16321809 0641-091412121421-16391816 0647-092012181427-16451822 0703-093512331443154017011837 0717-094812451455155317141849 --100112591509-17281903 --100613041514-17331908 -0714101713131523-17421917 -0721102313201529-17491924 -0729103113281538163517581932 Carlisle Armathwaite Lazonby & Kirk Langwathby Appleby Kirkby Stephen Garsdale Dent Ribblehead Horton in Rib’dale Settle Settle – Carlisle: Mondays – Fridays. Carlisle – Settle: Mondays – Fridays. - - - - - - - - - - - - - - - - - - - 2100 2106 2114 SETTLE Horton Ribblehead Dent Gardsdale Kirkby Stephen Appleby Langwathby Lazonby Armathwaite Carlisle N Q18: What proportion of trains arriving at Settle stop at Dent? Give your answer as a: (a) Fraction (b) Decimal (c) Percentage 5/8 0.625 62.5% Q19: What is the probability that a train stopping at Garsdale will do so in the afternoon? t 4/5 Q20: What percentage of trains arriving at Settle each day did not come from Carlisle? 25%

14. Tickets Settle toSingle Appleby Langwathby Carlisle Day Return £9.30 £11.40 £15.80 £11.20 £14.70 £18.90 Day Ranger Prices correct with effect Jan 08 Child prices (5 to 15 years) are 50% of the adult fare and under fives travel free. Horton£2.70 £2.90 Dent£4.10 £4.60 £21.50 Sample Fares Ribblehead Station *Q21: Find the cost of two adult day return tickets from Settle to Appleby? £22.40 *Q22: Calculate the cost of ten single adult tickets from Settle to Dent? £41.00 *Q23: Peter, Jackie and their two children, Gemma aged 16 and Robert aged 12 are going to Horton from Settle for the day to climb Pen-y-ghent. They will catch an evening train back to Settle. Calculate the total cost of the fares. £10.15 *Q24: Another family of four with two children aged 4 and 10, are going to visit some scenic spots on the line including a short walk near the Ribblehead viaduct after first making a quick visit to friends in Carlisle. How much would a Day Ranger ticket cost for this family? £53.75 *

15. Gradient Gradient Profile * * * * *** ** * Station Now Closed Miles From Settle Junction Height in Feet A ruler and a sharp pencil are essential when using this worksheet. A small amount of error will be allowed in some answers due to thickness of lines etc.

16. Gradient Profile * * * * *** ** * Station Now Closed Miles From Settle Junction Height in Feet Q25: Dent is the highest railway station in England. What is its height?  1150 ft *Q26: How far does the train climb going from Settle to Dent.  620ft *

17. Gradient Profile * * * * *** ** * Station Now Closed Miles From Settle Junction Height in Feet *Q27: How far is Ais Gill summit from Settle station? 25 miles *Q28: What is the distance between Appleby and Langwathby?  10½ miles *

18. Gradient Profile * * * * *** ** * Station Now Closed Miles From Settle Junction Height in Feet Q29: Calculate the rate of descent from Ais Gill summit to Ormside.  45 ft/mile Q30: How does this compare to the rate of ascent from Settle to Ribblehead? Steeper (450/12  37.5 ft/mile) *

19. Gradient Profile * * * * *** ** * Station Now Closed Miles From Settle Junction Height in Feet *Q31: What fraction of the stations shown are now closed? 9/20 *Q32: What percentage of the stations shown remain open? 55% *

20. 3 Peaks Heights *Q33: The altitude (height above mean sea level) of Pen-y-ghent is shown on the diagram below. Give this altitude in yards. 759 yards Q34: Calculate an estimate for this altitude in metres given that 1 m  1.09 yards. Give your answer to the nearest metre. 696 m Q35: Calculate an estimate for the altitude in metres of Whernside. 739 m * Ingleton Dent Pen-y-ghent (2277 ft) Ingleborough (2372 ft) Whernside (2415 ft) Horton in Ribblesdale Ribblehead Dent 3 Peaks Challenge (25 miles in 12 hours) Start/Finish Pen-y-ghent café in Horton 4 miles Chapel-le-Dale N

21. *Q36: What is the distance of the 3 Peaks Challenge in kilometres? 40 km *Q37: Given that 1mile = 8/5 km, express the distance from Dent station to Dent village in km. 6 and 2/5 or 6.4 miles *Q38: Stuart completed the 3 Peak Challenge in 8 hours 20 minutes. What was his average speed in mph. 3 mph * Ingleton Dent Pen-y-ghent (2277 ft) Ingleborough (2372 ft) Whernside (2415 ft) Horton in Ribblesdale Ribblehead Dent 3 Peaks Challenge (25 miles in 12 hours) Start/Finish Pen-y-ghent café in Horton 4 miles Chapel-le-Dale N

22. *Q39: The distance from Horton station to Dent station is 12 miles and takes the train approximately 18 minutes. Calculate the average speed for the journey in mph. 40 mph *Q40: What is the range of the heights of the 3 peaks. 138 ft *Q41: Calculate the mean height of the 3 peaks. (3 sig fig) 2350 ft * Ingleton Dent Pen-y-ghent (2277 ft) Ingleborough (2372 ft) Whernside (2415 ft) Horton in Ribblesdale Ribblehead Dent 3 Peaks Challenge (25 miles in 12 hours) Start/Finish Pen-y-ghent café in Horton 4 miles Chapel-le-Dale N

23. 3 Peaks Bearings Ingleton Dent Pen-y-ghent (2277 ft) Ingleborough (2372 ft) Whernside (2415 ft) Horton in Ribblesdale Ribblehead Dent 3 Peaks Challenge (25 miles in 12 hours) Start/Finish Pen-y-ghent café in Horton 4 miles *Q42: Use your protractor to measure the bearing of Pen-y-ghent from Whernside. (measure from the centre of the triangulation point).  127 o Chapel-le-Dale Please note that because this in not a completely accurate scale drawing, the actual bearings in the answers that follow, although very close to true life, are not exact. N

24. Ingleton Dent Pen-y-ghent (2277 ft) Ingleborough (2372 ft) Whernside (2415 ft) Horton in Ribblesdale Ribblehead Dent 3 Peaks Challenge (25 miles in 12 hours) Start/Finish Pen-y-ghent café in Horton 4 miles *Q42: Use your protractor to measure the bearing of Pen-y-ghent from Whernside. (measure from the centre of the triangulation point).  127 o Chapel-le-Dale *Q43: Measure the bearing of Ingleborough from Pen-y-ghent.  276 o Please note that because this in not a completely accurate scale drawing, the actual bearings in the answers that follow, although very close to true life, are not exact. N

25. Ingleton Dent Pen-y-ghent (2277 ft) Ingleborough (2372 ft) Whernside (2415 ft) Horton in Ribblesdale Ribblehead Dent 3 Peaks Challenge (25 miles in 12 hours) Start/Finish Pen-y-ghent café in Horton 4 miles *Q42: Use your protractor to measure the bearing of Pen-y-ghent from Whernside. (measure from the centre of the triangulation point).  127 o Chapel-le-Dale *Q43: Measure the bearing of Ingleborough from Pen-y-ghent.  276 o *Q44: Without using a protractor state the bearing of Whernside from Pen-y-ghent.  307 o Please note that because this in not a completely accurate scale drawing, the actual bearings in the answers that follow, although very close to true life, are not exact. N

26. 3 Peaks Temperature *Q45: When climbing hills and mountains the temperature decreases on average by 3 degrees Celsius for each 1000 ft of ascent. Some walkers set off from Horton (approximate altitude 530 ft) where the temperature was 2 o C to climb up Whernside. Estimate the temperature on the summit of Whernside. -3/-4 o C. * Ingleton Dent Pen-y-ghent (2277 ft) Ingleborough (2372 ft) Whernside (2415 ft) Horton in Ribblesdale Ribblehead Dent 3 Peaks Challenge (25 miles in 12 hours) Start/Finish Pen-y-ghent café in Horton 4 miles Chapel-le-Dale N

27. Ingleton Dent Pen-y-ghent (2277 ft) Ingleborough (2372 ft) Whernside (2415 ft) Horton in Ribblesdale Ribblehead Dent 3 Peaks Challenge (25 miles in 12 hours) Start/Finish Pen-y-ghent café in Horton 4 miles MonTueWedThuFriSatSun 3oC3oC5oC5oC1oC1oC0oC0oC-1 o C-3 o C-10 o C 8oC8oC10 o C4oC4oC3oC3oC0oC0oC-2 o C-4 o C Day Min Max *Q46: The table below shows some data on minimum and maximum temperatures as recorded on the summit of Ingleborough over a seven day period in early January. What is the modal temperature over the period. 3oC3oC *Q47: What is the range of the temperatures? 20 degrees * Chapel-le-Dale N

28. Ingleton Dent Pen-y-ghent (2277 ft) Ingleborough (2372 ft) Whernside (2415 ft) Horton in Ribblesdale Ribblehead Dent 3 Peaks Challenge (25 miles in 12 hours) Start/Finish Pen-y-ghent café in Horton 4 miles *Q48: What is the median of the minimum temperatures over the period? 0oC0oC MonTueWedThuFriSatSun 3oC3oC5oC5oC1oC1oC0oC0oC-1 o C-3 o C-10 o C 8oC8oC10 o C4oC4oC3oC3oC0oC0oC-2 o C-4 o C Day Min Max *Q49: What is the median of the maximum temperatures over the period? 3oC3oC * Chapel-le-Dale N

29. Ingleton Dent Pen-y-ghent (2277 ft) Ingleborough (2372 ft) Whernside (2415 ft) Horton in Ribblesdale Ribblehead Dent 3 Peaks Challenge (25 miles in 12 hours) Start/Finish Pen-y-ghent café in Horton 4 miles *Q50. The formula below is used for converting degrees Celsius ( o C) to degrees Fahrenheit ( o F). This formula can be approximated to F = 2C + 32. Use this slightly less accurate but simpler formula to change all the temperatures in the table to degrees Fahrenheit. MonTueWedThuFriSatSun 3oC3oC5oC5oC1oC1oC0oC0oC-1 o C-3 o C-10 o C 8oC8oC10 o C4oC4oC3oC3oC0oC0oC-2 o C-4 o C Day Min Max * Chapel-le-Dale MonTueWedThuFriSatSun 38 o F42 o F34 o F32 o F30 o F26 o F12 o F 48 o F52 o F40 o F38 o F32 o F28 o F24 o F Day Min Max N F = 9 5 C + 32

30. Ingleton Dent Pen-y-ghent (2277 ft) Ingleborough (2372 ft) Whernside (2415 ft) Horton in Ribblesdale Ribblehead Dent 3 Peaks Challenge (25 miles in 12 hours) Start/Finish Pen-y-ghent café in Horton 4 miles *Q51: Use the accurate formula to convert the maximum temperature on Tuesday to o F. 50 o F MonTueWedThuFriSatSun 3oC3oC5oC5oC1oC1oC0oC0oC-1 o C-3 o C-10 o C 8oC8oC10 o C4oC4oC3oC3oC0oC0oC-2 o C-4 o C Day Min Max * Chapel-le-Dale MonTueWedThuFriSatSun 38 o F42 o F34 o F32 o F30 o F26 o F12 o F 48 o F52 o F40 o F38 o F32 o F28 o F24 o F Day Min Max N F = 9 5 C + 32

31. 3 Peaks Visibility Ingleton Dent Pen-y-ghent (2277 ft) Ingleborough (2372 ft) Whernside (2415 ft) Horton in Ribblesdale Ribblehead Dent 3 Peaks Challenge (25 miles in 12 hours) Start/Finish Pen-y-ghent café in Horton 4 miles Q52: The distance (D) to the horizon in miles for someone stood at a height (h) feet above mean sea level is given by the formula below: D =  1.5h On an exceptionally clear day, how far could you see if you were stood at the summit of Ingleborough? (nearest mile). 60 miles Chapel-le-Dale N

32. Ingleton Dent Pen-y-ghent (2277 ft) Ingleborough (2372 ft) Whernside (2415 ft) Horton in Ribblesdale Ribblehead Dent 3 Peaks Challenge (25 miles in 12 hours) Start/Finish Pen-y-ghent café in Horton 4 miles Q53: The distance (D) to the horizon in kilometres for someone stood at a height (h) metres above mean sea level is given by the formula below: D =  13h Ingleborough is 724m above sea level. Check that this formula agrees with your previous answer. 97 x 5/8  60 miles Chapel-le-Dale N

33. Teachers Q + A Teacher Q + A Q1: What time does the first train of the day leave Settle? 0950 Q2: Where is its 5 th stop? Kirkby Stephen Q3: How long does this train take to get to Dent? 26 minutes Q4: How long does it take to reach its destination? 1 hour 44 minutes Q5: One train departs from Garsdale station at 1616. What time is this in 12 hour clock? 4.16 pm Q6: How many stops does the 1044 train have after leaving Settle? 3 Q7: Sarah missed the 1107 train from Lazonby. How long will she have to wait for the next one? 1 hour 56 minutes Q8: Which two stations have the least number of trains each day. Dent/Garsdale Q9: Give the time in 12 hour clock for the first train from Armathwaite. 8.08 am Q10: Phillipa spent the day at a friends’ house in Horton. She must be home in in Appleby no later than 5.00 pm. What is the time of the latest train that she can leave on? 1553 Q11: John caught the 0853 train from Carlisle to Settle. He came back on the first train in the afternoon. What time did he get back to Carlisle at? 1532 Q12: How long did he spend on the train in: (a) Hours and minutes (b) Minutes 3 h 22m 202 min Q13: What time does the last train of the day depart Horton? (in 12 hour clock). 9.06 pm Q14: What is the longest period of time that someone living in Settle can spend in Carlisle before returning on the last train? 6 h 21 m Q15: How many trains leave Lazonby for Settle during the afternoon? 4 Q16: What is the ratio of trains arriving at Settle to trains arriving at Langwathby each day? 2:3 Q17: What fraction of trains arriving in Settle came from Carlisle? ¾ Q18: What proportion of trains arriving at Settle stop at Dent? Give your answer as a: (a) Fraction (b) Decimal (c) Percentage 5/8 0.62562.5% Q19: What is the probability that a train stopping at Garsdale will do so in the afternoon? 4/5 Q20: What percentage of trains arriving at Settle each day did not come from Carlisle? 25%

34. *Q21: Find the cost of two adult day return tickets from Settle to Appleby? £22.40 *Q22: Calculate the cost of ten single adult tickets from Settle to Dent? £41.00 *Q23: Peter, Jackie and their two children, Gemma aged 16 and Robert aged 12 are going to Horton from Settle for the day to climb Pen-y-ghent. They will catch an evening train back to Settle. Calculate the total cost of the fares. £10.15 *Q24: Another family of four with two children aged 4 and 10, are going to visit some scenic spots on the line including a short walk near the Ribblehead viaduct after first making a quick visit to friends in Carlisle. How much would a Day Ranger ticket cost for this family? £53.75 Q25: Dent is the highest railway station in England. What is its height?  1150 ft *Q26: How far does the train climb going from Settle to Dent.  620ft *Q27: How far is Ais Gill summit from Settle station? 25 miles *Q28: What is the distance between Appleby and Langwathby?  10½ miles Q29: Calculate the rate of descent from Ais Gill summit to Ormside.  45 ft/mile Q30: How does this compare to the rate of ascent from Settle to Ribblehead? *Q31: What fraction of the stations shown are now closed? 9/20 *Q32: What percentage of the stations shown remain open? 55% *Q33: The altitude (height above mean sea level) of Pen-y-ghent is shown on the diagram below. Give this altitude in yards. 759 yards Q34: Calculate an estimate for this altitude in metres given that1 m  1.09 yards. Give your answer to the nearest metre. 696 m Q35: Calculate an estimate for the altitude in metres of Whernside. 739 m *Q36: What is the distance of the 3 Peaks Challenge in kilometres? 40 km *Q37: Given that 1mile = 8/5 km, express the distance from Dent station to Dent village in km. 6 and 2/5 or 6.4 miles *Q38: Stuart completed the 3 Peak Challenge in 8 hours 20 minutes. What was his average speed in mph. 3 mph *Q39: The distance from Horton station to Dent station is 12 miles and takes the train approximately 18 minutes. Calculate the average speed for the journey in mph. 40 mph *Q40: What is the range of the heights of the 3 peaks. 138 ft Steeper (450/12  37.5 ft/mile)

35. *Q41: Calculate the mean height of the 3 peaks. (3 sig fig) 2350 ft *Q45: When climbing hills and mountains the temperature decreases on average by 3 degrees Celsius for each 1000 ft of ascent. Some walkers set off from Horton (approximate altitude 530 ft) where the temperature was 2 o C to climb up Whernside. Estimate the temperature on the summit of Whernside. -3/-4 o C. *Q46: The table below shows some data on minimum and maximum temperatures as recorded on the summit of Ingleborough over a seven day period in early January. What is the modal temperature over the period. (worksheet) 3oC3oC *Q47: What is the range of the temperatures? 20 degrees *Q48: What is the median of the minimum temperatures over the period? 0oC0oC *Q49: What is the median of the maximum temperatures over the period? 3oC3oC *Q50. The formula below is used for converting degrees Celsius ( o C) to degrees Fahrenheit ( o F). This formula can be approximated to F = 2C + 32. Use this slightly less accurate but simpler formula to change all the temperatures in the table to degrees Fahrenheit. (see slide 27 for solutions). *Q51: Use the accurate formula to convert the maximum temperature on Tuesday to o F. 50 o F Q52: The distance (D) to the horizon in miles for someone stood at a height (h) feet above mean sea level is given by the formula: D =  1.5h: On an exceptionally clear day, how far could you see if you were stood at the summit of Ingleborough? (nearest mile). 60 miles Q53: The distance (D) to the horizon in kilometres for someone stood at a height (h) metres above mean sea level is given by the formula: D =  13h: Ingleborough is 724m above sea level. Check that this formula agrees with your previous answer. 97 x 5/8  60 miles *Q42: Use your protractor to measure the bearing of Pen-y-ghent from Whernside. (measure from the centre of the triangulation point).  127 o *Q43: Measure the bearing of Ingleborough from Pen-y-ghent.  276 o *Q44: Without using a protractor state the bearing of Whernside from Pen-y-ghent.  307 o

36. Student Question Sheet Student Q1: What time does the first train of the day leave Settle? Q2: Where is its 5 th stop? Q3: How long does this train take to get to Dent? Q4: How long does it take to reach its destination? Q5: One train departs from Garsdale station at 1616. What time is this in 12 hour clock? Q6: How many stops does the 1044 train have after leaving Settle? Q7: Sarah missed the 1107 train from Lazonby. How long will she have to wait for the next one? Q8: Which two stations have the least number of trains each day. Q9: Give the time in 12 hour clock for the first train from Armathwaite. Q10: Phillipa spent the day at a friends’ house in Horton. She must be home in in Appleby no later than 5.00 pm. What is the time of the latest train that she can leave on? Q11: John caught the 0853 train from Carlisle to Settle. He came back on the first train in the afternoon. What time did he get back to Carlisle at? Q12: How long did he spend on the train in: (a) Hours and minutes (b) Minutes Q13: What time does the last train of the day depart Horton? (in 12 hour clock). Q14: What is the longest period of time that someone living in Settle can spend in Carlisle before returning on the last train? Q15: How many trains leave Lazonby for Settle during the afternoon? Q16: What is the ratio of trains arriving at Settle to trains arriving at Langwathby each day? Q17: What fraction of trains arriving in Settle came from Carlisle? Q18: What proportion of trains arriving at Settle stop at Dent? Give your answer as a: (a) Fraction (b) Decimal (c) Percentage Q19: What is the probability that a train stopping at Garsdale will do so in the afternoon? Q20: What percentage of trains arriving at Settle each day did not come from Carlisle?

37. *Q21: Find the cost of two adult day return tickets from Settle to Appleby? *Q22: Calculate the cost of ten single adult tickets from Settle to Dent? *Q23: Peter, Jackie and their two children, Gemma aged 16 and Robert aged 12 are going to Horton from Settle for the day to climb Pen-y-ghent. They will catch an evening train back to Settle. Calculate the total cost of the fares. *Q24: Another family of four with two children aged 4 and 10, are going to visit some scenic spots on the line including a short walk near the Ribblehead viaduct after first making a quick visit to friends in Carlisle. How much would a Day Ranger ticket cost for this family? Q25: Dent is the highest railway station in England. What is its height? *Q26: How far does the train climb going from Settle to Dent. *Q27: How far is Ais Gill summit from Settle station? *Q28: What is the distance between Appleby and Langwathby? Q29: Calculate the rate of descent from Ais Gill summit to Ormside. Q30: How does this compare to the rate of ascent from Settle to Ribblehead? *Q31: What fraction of the stations shown are now closed? *Q32: What percentage of the stations shown remain open? *Q33: The altitude (height above mean sea level) of Pen-y-ghent is shown on the diagram below. Give this altitude in yards. Q34: Calculate an estimate for this altitude in metres given that1 m  1.09 yards. Give your answer to the nearest metre. Q35: Calculate an estimate for the altitude in metres of Whernside. *Q36: What is the distance of the 3 Peaks Challenge in kilometres? *Q37: Given that 1mile = 8/5 km, express the distance from Dent station to Dent village in km. *Q38: Stuart completed the 3 Peak Challenge in 8 hours 20 minutes. What was his average speed in mph. *Q39: The distance from Horton station to Dent station is 12 miles and takes the train approximately 18 minutes. Calculate the average speed for the journey in mph. *Q40: What is the range of the heights of the 3 peaks.

38. *Q41: Calculate the mean height of the 3 peaks. (3 sig fig) *Q45: When climbing hills and mountains the temperature decreases on average by 3 degrees Celsius for each 1000 ft of ascent. Some walkers set off from Horton (approximate altitude 530 ft) where the temperature was 2 o C to climb up Whernside. Estimate the temperature on the summit of Whernside. *Q46: The table below shows some data on minimum and maximum temperatures as recorded on the summit of Ingleborough over a seven day period in early January. What is the modal temperature over the period. (worksheet) *Q47: What is the range of the temperatures? *Q48: What is the median of the minimum temperatures over the period? *Q49: What is the median of the maximum temperatures over the period? *Q50. The formula below is used for converting degrees Celsius ( o C) to degrees Fahrenheit ( o F). This formula can be approximated to F = 2C + 32. Use this slightly less accurate but simpler formula to change all the temperatures in the table to degrees Fahrenheit. (see slide 27 for solutions). *Q51: Use the accurate formula to convert the maximum temperature on Tuesday to o F. Q52: The distance (D) to the horizon in miles for someone stood at a height (h) feet above mean sea level is given by the formula: D =  1.5h: On an exceptionally clear day, how far could you see if you were stood at the summit of Ingleborough? (nearest mile). Q53: The distance (D) to the horizon in kilometres for someone stood at a height (h) metres above mean sea level is given by the formula: D =  13h: Ingleborough is 724m above sea level. Check that this formula agrees with your previous answer. *Q42: Use your protractor to measure the bearing of Pen-y-ghent from Whernside. (measure from the centre of the triangulation point). *Q43: Measure the bearing of Ingleborough from Pen-y-ghent. *Q44: Without using a protractor state the bearing of Whernside from Pen-y-ghent.

39. Worksheet1

40. Worksheet2 Child prices (5 to 15 years) are 50% of the adult fare and under fives travel free. Settle toSingle Appleby Langwathby Carlisle Day Return £9.30 £11.40 £15.80 £11.20 £14.70 £18.90 Day Ranger Prices correct with effect Jan 08 Horton£2.70 £2.90 Dent£4.10 £4.60 £21.50 Ticket Prices

41. Worksheet 3 Gradient Profile * * * * *** ** * Station Now Closed Miles From Settle Junction Height in Feet

42. Worksheet4 Ingleton Dent Pen-y-ghent (2277 ft) Ingleborough (2372 ft) Whernside (2415 ft) Horton in Ribblesdale Ribblehead Dent 3 Peaks Challenge (25 miles in 12 hours) Start/Finish Pen-y-ghent café in Horton 4 miles Chapel-le-Dale MonTueWedThuFriSatSun 3oC3oC5oC5oC1oC1oC0oC0oC-1 o C-3 o C-10 o C 8oC8oC10 o C4oC4oC3oC3oC0oC0oC-2 o C-4 o C Day Min Max