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. The tiling worksheet is available in colour or black and white. The scale drawing at slide 9 is an accurate 1:30 scale drawing of the bathroom walls when printed. Check accuracy on your own printer and when photocopying. Calculator and non-calculator symbols are suggestions only and could be removed depending on the group. 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. 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: Creating a Bathroom: Content and skills covered Coverage and range: Level 2 At least 1 from each area

5. Open Question What maths could be involved in creating a bathroom? Creating a Bathroom © gaja_tz/bigstockphoto.com

6. Some Prices Some common bathroom items: Estimate the typical cost of each. 1.What is the ratio of (a) cost of bath : cost of sink (b) cost of toilet : cost of bath 3:1 1:2 £10 £300 £25 £12 £2.50 £150 £120 £90. £140 £100

7. Questions on Fittings 2. Ignoring the cost of flooring, tiles and labour, what will the total cost of the six remaining items be? Use these prices to get an initial rough estimate for the cost of the bathroom. Bath: £300 Toilet: £150 Sink: £100 Taps: £120 Shower: £140 Radiator: £90 Total: £900 3. What fraction of this cost is taken up by the toilet? 1 6 4. What percentage of the cost is taken up by the radiator? 10%

8. Use these prices to get an initial rough estimate for the cost of the bathroom. Bath: £300 Toilet: £150 Sink: £100 Taps: £120 Shower: £140 Radiator: £90 Total: £900 1 6 5. Ignoring the vinyl floor covering and estimating that you need 400 plain tiles, 60 decorative tiles and 10 hours labour from the plumber calculate the cost of this and find the final total cost. 20 boxes x £12 = £240 D.Tiles: 60 x £2.50 = £150 Labour: 10 x £25 = £250 Total: = £640 Final Total: = £1540 6. What percentage of this estimated final total is taken up by the tiles. (1 d.p) 390 1540 x 100 = 25.3%

9. Tiling 7. You experiment (on paper) with the idea of using 12 decorative tiles to make some symmetrical patterns on one of the walls. Use the remainder of the tiles to make patterns in each case with one line of symmetry (above) and two lines of symmetry (below), Decorative tiles 1 L o S 2 L o S a b c d

10. 8. Use the supplied worksheet to workout the scale of the drawing below. Tiling 9. Mark the following measurements on the diagram (all in cm). Door: h = 200, w = 65 Window: h = 68, w =124 Bath: l = 200, w = 60, h = 55 1:30 East Wall West Wall South Wall Bath Door Bath 210cm 240cm Window 216cm North Wall 124cm 55 cm 200cm 55 cm 60cm 200cm 65cm 68cm

11. Scale 1 : 30 Tiling East Wall West Wall South Wall Bath Door Bath 210cm 240cm Window 216cm North Wall 124cm 55 cm 200cm 55 cm 60cm 200cm 65cm 68cm East Wall: 2.4 x 2.16 = 5.184 m 2 West Wall: 2.4 x 2.16 - (2 x 0.55) = 4.084m 2 North Wall: 2.1 x 2.16 - (1.24 x 0.68) = 3.6928 m 2 South Wall: 2.1 x 2.16 - (2 x 0.65 + 0.6 x 0.55) = 2.906 m 2 10. Work out the area of each wall to be tiled (un-shaded) and find the total area in m 2. Give the total area to 2 d.p. Total Wall Area: = 5.184 + 4.084 + 3.6928 + 2.906 = 15.87 m 2 (2 d.p )

12. Tiling East Wall West Wall South Wall Bath Door Bath 210cm 240cm Window 216cm North Wall 124cm 55 cm 200cm 55 cm 60cm 200cm 65cm 68cm Scale 1 : 30 11. A tile is 25cm tall and 20cm wide. Use your answer to question10 (or any other method) to make an estimate of the number of tiles needed. Add an extra 10% on to this total for trimming and breakages. (2 sig fig) 15.87  0.05 = 317 tiles Area of one tile = 0.25 x 0.2 = 0.05 m 2 10% of 317 = 32 tiles Total = 350 (2 sig fig)

13. Tiling East Wall West Wall South Wall Bath Door Bath 210cm 240cm Window 216cm North Wall 124cm 55 cm 200cm 55 cm 60cm 200cm 65cm 68cm Scale 1 : 30 12. Each box contains 20 tiles and costs £12. How many boxes of tiles should you buy and what is the cost? 350  20 = 17.5  18 boxes needed 18 x £12 = £216

14. Flooring Scale 1 : 30 Flooring 13. Draw a plan view of the bathroom using a scale of 1: 30. 14. What area of floor needs to be covered? (don't include the area under the bath)‏ 210cm Bath 240cm 60cm 200cm Area to be covered: = 2.4 x 2.1 - (2 x 0.6) = 3.84m 2

15. Scale 1 : 30 Flooring 210cm Bath 240cm 60cm 200cm 15. The vinyl flooring (or lino) comes in 2m wide or 3m wide strips and costs £11 per square metre. You want to make the most economical choice and are not bothered about using two pieces and joining them together. (a) Which width will you choose and what length do you require? (b) What is the cost? (a) 2m x 2.4 m seems a sensible choice although there are other options. This will cover the area shown and leave only a small hidden join. 200 cm (b) 2 x 2.4 = 4.8 m 2 11 x 4.8 = £52.80

16. Pricing 16. Here is part of the electricians invoice. (a) Calculate the total amount charged. (b) What percentage of the final total was for the fittings? (c) What fraction of the total cost was the light? (simplest form) Pricing P. Lumber & Sons Plumbing services Excludes VAT Item Price Qty Bath £299.00 1 Shower £128.50 1 Sink £95.75 1 Toilet £145.00 1 Taps £115.25 1 Radiator £85.50 1 Sundries £42.36 1 Labour £288.64 1 Total £1410.00 Sparky's Electrical services Includes VAT Item Price Qty Light £35.00 1 Extractor- Fan £89.00 1 Switch £4.00 1 Labour £72.00 1 Total (b) 128/200 = 64% 35.00 89.00 4.00 72.00 £200.00 (a) (c) 35/200 = 7/40

17. Pricing P. Lumber & Sons Plumbing services Excludes VAT Item Price Qty Bath £299.00 1 Shower £128.50 1 Sink £95.75 1 Toilet £145.00 1 Taps £115.25 1 Radiator £85.50 1 Sundries £42.36 1 Labour £288.64 1 Total £1410.00 17. Here is part of the plumbers invoice. (a) Calculate the total amount charged by the plumber excluding VAT. (b) Calculate the VAT. (c) Calculate the final total. Sparky's Electrical services Includes VAT Item Price Qty Light £35.00 1 Extractor- Fan £89.00 1 Switch £4.00 1 Labour £72.00 1 Total £200.00 299.00 128.50 95.75 145.00 115.25 85.50 42.36 288.64 £1200.00 (a) 10% = £120 5% = £60 2½% = £30 VAT = £210 (b) VAT = 17 ½ % £1200 + £210 = £1410.00 (c)

18. Worksheet 1 Sym colour Worksheet

19. 2. B/W

20. 3. Scale Drawing 1 East Wall West Wall South Wall Bath Door Bath 210cm 240cm Window 216cm North Wall Worksheet Scale Drawing of Bathroom Walls

21. 4. Scale Drawing 2 210cm Bath 240cm 60cm 200cm Worksheet Scale Drawing of Bathroom Floor

22. 5. Invoices Pricing P. Lumber & Sons Plumbing services Excludes VAT Item Price Qty Bath £299.00 1 Shower £128.50 1 Sink £95.75 1 Toilet £145.00 1 Taps £115.25 1 Radiator £85.50 1 Sundries £42.36 1 Labour £288.64 1 Total £1410.00 Sparky's Electrical services Includes VAT Item Price Qty Light £35.00 1 Extractor- Fan £89.00 1 Switch £4.00 1 Labour £72.00 1 Total Worksheet

23. Students Q Sheet 1.What is the ratio of (a) cost of bath : cost of sink (b) cost of toilet : cost of bath 2. Ignoring the cost of flooring, tiles and labour, what will the total cost of the six remaining items be? 3. What fraction of this cost is taken up by the toilet? 4.What percentage of the cost is taken up by the radiator? 5. Ignoring the vinyl floor covering and estimating that you need 400 plain tiles, 60 decorative tiles and 10 hours labour from the plumber calculate the cost of this and find the final total cost. 6. What percentage of this estimated final total is taken up by the tiles. 7. You experiment (on paper) with the idea of using 12 decorative tiles to make some symmetrical patterns on one of the walls. (worksheet + coloured pens) 8. Use the supplied worksheet to workout the scale of the drawing below. 9. Mark the following measurements on the worksheet (all in cm). Door: h = 200, w = 65, Window: h = 68, w =124, Bath: l = 200, w = 60, h = 55 Question Sheet 1 Refer to Whiteboard

24. 10. Work out the area of each wall to be tiled (un-shaded) and find the total area in m2. Give the total area to 2 d.p. 11. A tile is 25cm tall and 20cm wide. Use your answer to question10 (or any other method) to make an estimate of the number of tiles needed. Add an extra 10% on to this total for trimming and breakages. (2 sig fig) 12. Each box contains 20 tiles and costs £12. How many boxes of tiles should you buy and what is the cost? 13. Draw a plan view of the bathroom using a scale of 1: 30. 14. What area of floor needs to be covered? (don't include the area under the bath) (worksheet or own drawing ‏ ) 15. The vinyl flooring (or lino) comes in 2m wide or 3m wide strips and costs £11 per square metre. You want to make the most economical choice and are not bothered about using two pieces and joining them together. (a) Which width will you choose and what length do you require? (b) What is the cost? 16. Here is part of the electricians invoice. (Worksheet needed) (a) Calculate the total amount charged. (b) What percentage of the final total was for the fittings? (c) What fraction of the total cost was the light? (simplest form) 17. Here is part of the plumbers invoice. (worksheet needed) (a) Calculate the total amount charged by the plumber excluding VAT. (b) Calculate the VAT. (c) Calculate the final total. Question Sheet 2

25. Teacher Q + A 1.What is the ratio of (a) cost of bath : cost of sink 3: 1 (b) cost of toilet : cost of bath 1: 2 2. Ignoring the cost of flooring, tiles and labour, what will the total cost of the six remaining items be? £900 3. What fraction of this cost is taken up by the toilet? 1/6 4.What percentage of the cost is taken up by the radiator? 10% 5. Ignoring the vinyl floor covering and estimating that you need 400 plain tiles, 60 decorative tiles and 10 hours labour from the plumber calculate the cost of this and find the final total cost. £640/£1540 6. What percentage of this estimated final total is taken up by the tiles (1 d.p) 25.3% 7. You experiment (on paper) with the idea of using 12 decorative tiles to make some symmetrical patterns on one of the walls. (worksheet + coloured pens) Presentation 8. Use the supplied worksheet to workout the scale of the drawing below. Students work 9. Mark the following measurements on the worksheet (all in cm). Students work Door: h = 200, w = 65, Window: h = 68, w =124, Bath: l = 200, w = 60, h = 55 Question Sheet 1 Refer to Whiteboard Teacher

26. 10.Work out the area of each wall to be tiled (un-shaded) and find the total area in m 2. Give the total area to 2 d.p. E. 5.184, W. 4.084, N. 3.6928, S. 2.906, Total 15.87 11. A tile is 25cm tall and 20cm wide. Use your answer to question10 (or any other method) to make an estimate of the number of tiles needed. Add an extra 10% on to this total for trimming and breakages. (2 sig fig) 350 12. Each box contains 20 tiles and costs £12. How many boxes of tiles should you buy and what is the cost? 18 Boxes/£216 13. Draw a plan view of the bathroom using a scale of 1: 30. students work 14. What area of floor needs to be covered? (don't include the area under the bath) (worksheet or own drawing ‏ ) 3.84 m 2 15. The vinyl flooring (or lino) comes in 2m wide or 3m wide strips and costs £11 per square metre. You want to make the most economical choice and are not bothered about using two pieces and joining them together. (a) Which width will you choose and what length do you require? 2m x 2.4 m (b) What is the cost? £52.80 16. Here is part of the electricians invoice. (Worksheet needed) (a) Calculate the total amount charged. £200 (b) What percentage of the final total was for the fittings? 64% (c) What fraction of the total cost was the light? (simplest form) 7/40 17. Here is part of the plumbers invoice. (worksheet needed) (a) Calculate the total amount charged by the plumber excluding VAT. £1200 (b) Calculate the VAT. £210 (c) Calculate the final total. £1410 Question Sheet 2