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Whiteboardmaths.com © 2009 All rights reserved 5 7 2 1

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Guidance Notes for Teachers Some indication of content and range at level 1 and 2 is shown on the next slide. It could also be used as a single project given to students from start to finish. 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. The vast majority of questions in this presentation are designed to be non- calculator. 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).

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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: Comfort Carpets Content and skills covered Coverage and range: Level 2 At least 1 from each area

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© bigstockphoto.com What mathematics might be involved in fitting a carpet?

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Q1. How much does a 4m length of Berber cost, when cut from the 2m roll? ( before discount). Q2. How much would this be after discount? £64.80 Q3. Calculate the price per m 2. £8.10 £72.00 *

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Q4. How much does a 3m length of Royale cost, when cut from the 3m roll? ( after discount). Q5. Calculate the price per m 2. £13.50 £121.5 Q6. On the 4m roll width, what fraction of the Royale price is the Saxony price? (before discount). 6/7 *

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Q7. What is the ratio of the price of Saxony to the price of Berber from the 2m roll? (before discount). Q8. What percentage cost of the 3m roll Berber is the 2m roll Berber? (before discount). 72% 4:3 Q9. What is the mean and range of Berber carpet prices before discount? Mean = £25, range = £14 *

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Q10. Jenny wants to buy a 3m x 4m Royale carpet. Which carpet roll width would you advise her to use? (pre-discount). Use 4m roll as it saves her 4 x £45 - 3 x £56 = £12 Q11. How much is 10m 2 of Saxony carpet after discount? £108 Q12. What is the price of 15m 2 of Royale after discount? £202.50 *

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Sarah’s Bedroom 2.9m 4.85m 1.8m 3.2m Sarah’s Bedroom (Plan View) Q13. Which width of carpet should she choose? 3 m Sarah wants to fit a Berber carpet in her bedroom. She would like it fitted in one piece so that there are no joins. Q14. Assuming that she cannot have fractions of a metre cut from the roll, (a) What is the area of the purchased carpet? (b) How much wastage is there? 4.445 m 2 15 – (1.8 x 4.85 + 1.1 x 1.65) 15 m 2 75 cm Not to Scale © bigstockphoto.com

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2.9m 4.85m 1.8m 3.2m Sarah’s Bedroom (Plan View) Q15. How many metres of wooden gripper will she need? (Show your working). 15 metres Sarah decides to buy 15 m 2 of underlay for her carpet, together with carpet gripper and a single brass strip gripper (75 cm length) for the door area. “Comfort Carpets” will supply a fitter at a cost of £30. The discount offered applies to the carpet only. 75 p/metre £2.50 £3.50 m 2 75 cm 2.9 + 4.85 + 1.8 + 3.2 + 1.1 + 1.65 – 0.75 = 14.75 15 m needed Not to Scale * NB Wooden gripper is not used for the door space!

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2.9m 4.85m 1.8m 3.2m Sarah’s Bedroom (Plan View) Q16. Calculate the total cost of having the carpet fitted. £208.75 75 cm Carpet: £112.50 Underlay: £52.50 15m Gripper: £11.25 Brass strip: £2.50 Fitting: £30.00 Total: £208.75 Not to Scale * Sarah decides to buy 15 m 2 of underlay for her carpet, together with carpet gripper and a single brass strip gripper (75 cm length) for the door area. “Comfort Carpets” will supply a fitter at a cost of £30. The discount offered applies to the carpet only. 75 p/metre £2.50 £3.50 m 2 NB Wooden gripper is not used for the door space!

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Paul’s Living Room 75 p/metre £2.50 £3.50 m 2 3.9m 5.7m 2.85m 2.4m Paul’s living room Paul wants to fit a Royale carpet in his living room. He also wants it fitted in one piece so that there are no joins. Q17. Which width of carpet should he choose? 4 m Q18. Assuming that you cannot have fractions of a metre cut from the roll, (a) What is the area of the purchased carpet? (b) How much wastage is there? (2 d.p.) 24 – (5.7 x 2.85 + 2.4 x 1.05) 24 m 2 5.24 m 2 Not to Scale 75cm NB Wooden gripper is not used for the door space!

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75 p/metre £2.50 £3.50 m 2 3.9m 5.7m 2.85m 2.4m Paul’s living room Not to Scale Paul decides to buy 24 m 2 of underlay for his carpet, together with carpet gripper and a single brass strip (75 cm length) for the door area. “Comfort Carpets” will supply a fitter at a cost of £45. The discount offered applies to the carpet only. Q19. How many metres of wooden gripper will he need? (Show your working). 19 metres 2.4 + 3.9 + 5.7 + 2.85 + 3.3 + 1.05 – 0.75 = 18.45 19 m needed 75cm * NB Wooden gripper is not used for the door space!

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75 p/metre £2.50 £3.50 m 2 3.9m 5.7m 2.85m 2.4m Paul’s living room Not to Scale Paul decides to buy 24 m 2 of underlay for his carpet, together with carpet gripper and a single brass strip (75 cm length) for the door area. “Comfort Carpets” will supply a fitter at a cost of £45. The discount offered applies to the carpet only. Q20. Calculate the total cost of having the carpet fitted. Carpet: £302.40 Underlay: £84.00 19m Gripper: £14.25 Brass strip: £2.50 Fitting: £45.00 Total: £448.15 75cm £448.15 * NB Wooden gripper is not used for the door space!

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Q1. How much does a 4m length of Berber cost, when cut from the 2m roll? ( before discount). Q2. How much would this be after discount? £64.80 Q3. Calculate the price per m 2. £8.10 £72.00 Q4. How much does a 3m length of Royale cost, when cut from the 3m roll? ( after discount). Q5. Calculate the price per m 2. £13.50 £121.5 Q6. On the 4m roll width, what fraction of the Royale price is the Saxony price? (before discount). 6/7 Q7. What is the ratio of the price of Saxony to the price of Berber from the 2m roll? (before discount). Q8. What percentage cost of the 3m roll Berber is the 2m roll Berber? (before discount). 72% 4:3 Q9. What is the mean and range of Berber carpet prices before discount? Mean = £25, range = £14 Q10. Jenny wants to buy a 3m x 4m Royale carpet. Which carpet roll width would you advise her to use? (pre-discount). Use 4m roll as it saves her 4 x £45 - 3 x £56 = £12 Q11. How much is 10m 2 of Saxony carpet after discount? £108 Q12. What is the price 15m 2 of Royale after discount? £202.50 Teacher Q+A1 Teacher Q + A (1)

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Q13. Which width of carpet should she choose? 3 m Q14. Assuming that she cannot have fractions of a metre cut from the roll, (a) What is the area of the purchased carpet? (b) How much wastage is there? 4.445 m 2 15 – (1.8 x 4.85 + 1.1 x 1.65) 15 m 2 Q15. How many metres of wooden gripper will she need? (Show your working). 15 metres 2.9 + 4.85 + 1.8 + 3.2 + 1.1 + 1.65 – 0.75 = 14.75 Q16. Calculate the total cost of having the carpet fitted. (see slide 11) £208.75 Q17. Which width of carpet should he choose? 4 m Q18. Assuming that you cannot have fractions of a metre cut from the roll, (a) What is the area of the purchased carpet (b) How much wastage is there? (2 d.p.) 24 – (5.7 x 2.85 + 2.4 x 1.05) 24 m 2 5.24 m 2 Q19. How many metres of wooden gripper will he need? (Show your working). 19 metres 2.4 + 3.9 + 5.7 + 2.85 + 3.3 + 1.05 – 0.75 = 18.45 Q20. Calculate the total cost of having the carpet fitted. (see slide 14) £448.15 Teacher Q + A (2)

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Student Questions Q1. How much does a 4m length of Berber cost, when cut from the 2m roll? ( before discount). Q2. How much would this be after discount? Q3. Calculate the price per m 2. Q4. How much does a 3m length of Royale cost, when cut from the 3m roll? ( after discount). Q5. Calculate the price per m 2. Q6. On the 4m roll width, what fraction of the Royale price is the Saxony price? (before discount). Q7. What is the ratio of the price of Saxony to the price of Berber from the 2m roll? (before discount). Q8. What percentage cost of the 3m roll Berber is the 2m roll Berber? (before discount). Q9. What is the mean and range of Berber carpet prices before discount? Q10. Jenny wants to buy a 3m x 4m Royale carpet. Which carpet roll width would you advise her to use? (pre-discount). Q11. How much is 10m 2 of Saxony carpet after discount? Q12. What is the price 15m 2 of Royale after discount? Student Question Sheet (1)

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Q13. Which width of carpet should she choose? Q14. Assuming that she cannot have fractions of a metre cut from the roll, (a) What is the area of the purchased carpet? (b) How much wastage is there? Q15. How many metres of wooden gripper will she need? (Show your working). Q16. Calculate the total cost of having the carpet fitted. Q17. Which width of carpet should he choose? Q18. Assuming that you cannot have fractions of a metre cut from the roll, (a) What is the area of the purchased carpet (b) How much wastage is there? (2 d.p.) Q19. How many metres of wooden gripper will he need? (Show your working). Q20. Calculate the total cost of having the carpet fitted. Student Question Sheet (2)

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Worksheet 1 Worksheet (All Questions)

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Worksheet 2 3.9m 5.7m 2.85m 2.4m Paul’s living room Not to Scale 75cm 2.9m 4.85m 1.8m 3.2m Sarah’s Bedroom (Plan View) 75 cm Not to Scale Sarah wants to fit a Berber carpet in her bedroom. She would like it fitted in one piece so that there are no joins. Sarah decides to buy 15 m 2 of underlay for her carpet, together with carpet gripper and a single brass strip (75 cm length) for the door area. “Comfort Carpets” will supply a fitter at a cost of £30. The discount offered applies to the carpet only. For use with Q13 – Q16 For Use with Q17 – Q20 Paul wants to fit a Royale carpet in his living room. He also wants it fitted in one piece so that there are no joins. Paul decides to buy 24 m 2 of underlay for his carpet, together with carpet gripper and a single brass strip (75 cm length) for the door area. “Comfort Carpets” will supply a fitter at a cost of £45. The discount offered applies to the carpet only. 75 p/metre £2.50 £3.50 m 2 75 p/metre £2.50 £3.50 m 2

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