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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. The vast majority of questions in this presentation are designed to be non- calculator. Further investigations on paper sizes and the reason for the root 2 ratio is to be found in the “Paper Sizes” presentation in the enrichment area. 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: Paper Please Content and skills covered Coverage and range: Level 2 At least 1 from each area

5. What mathematics might be involved with buying paper?

6. Paper Sizes 1189mm 841mm Did you know that all “A” paper sizes are derived from a single rectangular sheet of paper known as A0 paper? This has the dimensions shown. A0 Q1. How many lines of symmetry does a rectangle have? Q2. What is the order of rotational symmetry of a rectangle? 2 2

7. Paper Sizes A0 area = 1189 x 841 = 999 949 mm 2  1m 2 1189mm 841mm Did you know that all “A” paper sizes are derived from a single rectangular sheet of paper known as A0 paper? This has the dimensions shown. A0 Q3. Use a calculator to show that the area of this piece of paper  1m 2 Q4. Write down how far short of 1m 2 this is. 1 000 000 – 999 949 = 51 mm 2 Q5. Estimate how this area difference compares to the area of a standard postage stamp.  1/10 the area of a stamp.  2cm x 2½ cm

8. Paper Sizes A0 area = 1189 x 841 = 999 949 mm 2  1m 2 1189mm 841mm All the other “A” sizes are created by simply cutting each previous piece in half through its length, starting with the large AO piece. A0 Q6. Name one obvious advantage of using “A” sizes in a paper factory. A1 A2 A3 A4 A5 A6 A7 A8 little/no wastage

9. Paper Sizes A0 area = 1189 x 841 = 999 949 mm 2  1m 2 1189mm 841mm All the other “A” sizes are created by simply cutting each previous piece in half through its length, starting with the large AO piece. A0 A1 A2 A3 A4 A5 A6 A7 A8 Q7. How many A2 pieces of paper can be cut from the original AO piece? 4

10. Paper Sizes A0 area = 1189 x 841 = 999 949 mm 2  1m 2 1189mm 841mm All the other “A” sizes are created by simply cutting each previous piece in half through its length, starting with the large AO piece. A0 A1 A2 A3 A4 A5 A6 A7 A8 Q8. How many A3 pieces of paper can be cut from the original AO piece? Q9. Show that the formula 2 N can be used to find the number of AN’s in AO. (complete the table) AN2N2N A02 0 = 1 A12 1 = 2 A22 2 = 4 A3 A4 A5 A6 2 3 = 8 2 4 = 16 2 5 = 32 2 6 = 64 8 *

11. Paper Sizes A0 area = 1189 x 841 = 999 949 mm 2  1m 2 1189mm 841mm All the other “A” sizes are created by simply cutting each previous piece in half through its length, starting with the large AO piece. A0 A1 A2 A3 A4 A5 A6 A7 A8 Q10. The area of A1 is how many times that of A4? AN2N2N A02 0 = 1 A12 1 = 2 A22 2 = 4 A3 A4 A5 A6 2 3 = 8 2 4 = 16 2 5 = 32 2 6 = 64 8 Q11. Work out the perimeter of A0 paper giving your answer in metres. 4.06m *

12. Paper SizeA0A1A2A3A4 Length (mm)1188840594 Width (mm)840594 Q12. In the table below the length and width of the A0 paper has been rounded to make the calculations easier. Complete the table. *

13. Paper SizeA0A1A2A3A4 Length (mm)1188840594420297 Width (mm)840594420297210 Q12. In the table below the length and width of the A0 paper has been rounded to make the calculations easier. Complete the table. Q13. Measure the length and width of an A4 piece of paper to confirm your result. Paper SizeA0A1A2A3A4 Length (mm)1188840594420297 Width (mm)840594420297210 L:W Q14. If you fold your A4 in half along its length which paper size do you get. Q15. Write down the length and width of this size of paper without measuring. A5  210mm x 148mm Q16. Complete the table below for the length to width ratio of each size of paper. Give your answer to 3 d.p. and state what your results mean.

14. Paper SizeA0A1A2A3A4 Length (mm)1188840594420297 Width (mm)840594420297210 Q12. In the table below the length and width of the A0 paper has been rounded to make the calculations easier. Complete the table. Q13. Measure the length and width of an A4 piece of paper to confirm your result. Paper SizeA0A1A2A3A4 Length (mm)1188840594420297 Width (mm)840594420297210 L:W 1.414 Q14. If you fold your A4 in half along its length which paper size do you get. Q15. Write down the length and width of this size of paper without measuring. A5  210mm x 148mm Q16. Complete the table below for the length to width ratio of each size of paper. Give your answer to 3 d.p. and state what your results mean. All “A” paper sizes are the same shape!

15. A2 A3 A4 A5 A6 You may be familiar with this number if you have done some work on Pythagoras. If not key  2 into your calculator. The following diagram helps show that “A” paper sizes are the same shape. Q 17. By referring to the table below, show that each paper size is in fact an enlargement of the previous one by a scale factor of  2.

16. Paper Buying Q 18. Paper world have some special offers on their A4 paper as shown in the table below. Their economy A4 paper has a weight of 80g/m 2. Calculate the weight of a single sheet of this paper. 80  16 = 5g Q 19. Vicki decides to buy 1 ream of each type of paper. How much does this cost her? £18.80 Q 20. James buys 3 reams of economy, 1 ream of standard and 2 reams of premium. How much does this cost him and how many sheets does he have in total? £20.70, 3000 *

17. Q 21. What proportion of the cost of Deluxe Special is the cost of Economy? Write your answer as: (a) A fraction (b) A decimal (c) A percentage ¼ 0.25 25% Q 22. What is the ratio of the price of premium paper to the price of Economy paper. 3 : 1 Q 23. Jackie runs a small business that uses a lot of paper. Calculate the saving made if she bought a box of 5 reams of standard paper rather than buying individual reams? £2.70 *

18. Q 24. (a) Calculate the cost of purchasing “3 boxes of 5 reams” of premium quality paper. (b) Workout the price per ream. (c) What is the saving per ream compared to the price of purchasing a single ream? £48.45 £48.45/15 = £3.23 £2.47 *

19. Mean = £4.70, range = £5.70 Q 25. What is the mean and range of the prices for the individual reams? £4.65 Q 26. What is the median price for these individual reams? *

20. Paper World: Mean price = £4.70, range = £5.70 Q 27. “Planet Paper” are a local competitor of Paper World and they too have a sale on their A4 paper. Their prices are shown in the table below. Compare the prices from both places and decide which is cheaper. Planet Paper: Mean price = £4.85, range = £6.50 Paper World sell the cheaper paper and have less varied prices. *

21. 1000 000  500 = 2000 Q 28. A large company could easily use 1 million sheets of economy A4 paper in a year. How many reams is 1 million sheets of A4 paper? 5000 kg Q 29. Calculate the weight of this paper giving your answer in: (a) Kilograms (b) Tonnes 5 T 2.75 m Q 30. If the thickness of the economy paper is 0.11mm calculate the height of 50 reams. Give your answer in metres. *

22. Teacher Q & A (1) Q1. How many lines of symmetry does a rectangle have? Q2. What is the order of rotational symmetry of a rectangle? 2 2 Q3. Use a calculator to show that the area of this piece of paper  1m 2 Q4. Write down how far short of 1m 2 this is. 1 000 000 – 999 949 = 51 mm 2 Q6. Name one obvious advantage of using “A” sizes in a paper factory. little/no wastage Q7. How many A2 pieces of paper can be cut from the original AO piece? 4 Q8. How many A3 pieces of paper can be cut from the original AO piece? Q9. Show that the formula 2 N can be used to find the number of AN’s in AO. (complete the table) see table SL 9 8 Q10. The area of A1 is how many times that of A4? 8 Q11. Work out the perimeter of A0 paper giving your answer in metres. 4.06m A0 area = 1189 x 841 = 999 949 mm 2  1m 2 Q12. In the table below the length and width of the A0 paper have been rounded to make the calculations easier. Complete the table. See SL 11/12 Q13. Measure the length and width of an A4 piece of paper to confirm your result. Q14. If you fold your A4 in half along its length which paper size do you get. Q15. Write down the length and width of this size of paper without measuring. A5  210mm x 148mm Q16. Complete the table below for the length to width ratio of each size of paper. Give your answer to 3 d.p. and state what your results mean. All “A” paper sizes are the same shape! Teacher Q & A (1) Q5. Estimate how this area difference compares to the area of a standard postage stamp.  1/10 the area of a stamp.

23. Q 17. By referring to your answer to Q15, show that each paper size is in fact an enlargement of the previous one by a scale factor of  2. (see slide 16) Q 18. Paper world have some special offers on their A4 paper as shown in the table below. Their economy A4 paper has a weight of 80g/m 2. Calculate the weight of a single sheet of this paper. 80  16 = 5g Q 19. Vicki decides to buy 1 ream of each type of paper. How much does this cost her? £18.80 Q 20. James buys 3 reams of economy, 1 ream of standard and 2 reams of premium. How much does this cost him and how many sheets does he have in total? Q 21. What proportion of the cost of Deluxe Special is the cost of Economy? Write your answer as: (a) A fraction (b) A decimal (c) A percentage ¼ 0.25 25% Q 22. What is the ratio of the price of premium paper to the price of Economy paper. 3 : 1 Q 23. Jackie runs a small business that uses a lot of paper. Calculate the saving made if she bought a box of 5 reams of standard paper rather than buying individual reams? £2.70 £20.70, 3000 Q 24. (a) Calculate the cost of purchasing “3 boxes of 5 reams” of premium quality paper. (b) Workout the price per ream. (c) What is the saving per ream compared to the price of purchasing a single ream? £48.45 £48.45/15 = £3.23 £2.47 Mean = £4.70, range = £5.70 Q 25. What is the mean and range of the prices for the individual reams? £4.65 Q 26. What is the median price for these individual reams? Q 27. “Planet Paper” are a local competitor of Paper World and they too have a sale on their A4 paper. Their prices are shown in the table below. Compare the prices from both places and decide which is cheaper. Paper World sell the cheaper paper and have less varied prices. Paper World: Mean price = £4.70, range = £5.70 Planet Paper: Mean price = £4.85, range = £6.50 1000 000  500 = 2000 Q 28. A large company could easily use 1 million sheets of economy A4 paper in a year. How many reams is 1 million sheets of A4 paper? 5000 kg Q 29. Calculate the weight of this paper giving your answer in: (a) Kilograms (b) Tonnes 5 T 2.75 m Q 30. If the thickness of the economy paper is 0.11mm calculate the height of 50 reams. Give your answer in metres. Teacher Q & A (2)

24. Student Questions (1) Q1. How many lines of symmetry does a rectangle have? Q2. What is the order of rotational symmetry of a rectangle? Q3. Use a calculator to show that the area of this piece of paper  1m 2 Q4. Write down how far short of 1m 2 this is. Q6. Name one obvious advantage of using “A” sizes in a paper factory. Q7. How many A2 pieces of paper can be cut from the original AO piece? Q8. How many A3 pieces of paper can be cut from the original AO piece? Q9. Show that the formula 2 N can be used to find the number of AN’s in AO. (complete the table) see table SL 9 Q10. The area of A1 is how many times that of A4? Q11. Work out the perimeter of A0 paper giving your answer in metres. Q12. In the table below the length and width of the A0 paper have been rounded to make the calculations easier. Complete the table. See SL 11/12 Q13. Measure the length and width of an A4 piece of paper to confirm your result. Q14. If you fold your A4 in half along its length which paper size do you get. Q15. Write down the length and width of this size of paper without measuring. Q16. Complete the table below for the length to width ratio of each size of paper. Give your answer to 3 d.p. and state what your results mean. Q5. Estimate how this area difference compares to the area of a standard postage stamp.

25. Student Questions (2) Q 17. By referring to your answer to Q15, show that each paper size is in fact an enlargement of the previous one by a scale factor of  2. (see slide 16) Q 18. Paper world have some special offers on their A4 paper as shown in the table below. Their economy A4 paper has a weight of 80g/m 2. Calculate the weight of a single sheet of this paper. Q 19. Vicki decides to buy 1 ream of each type of paper. How much does this cost her? Q 20. James buys 3 reams of economy, 1 ream of standard and 2 reams of premium. How much does this cost him and how many sheets does he have in total? Q 21. What proportion of the cost of Deluxe Special is the cost of Economy? Write your answer as: (a) A fraction (b) A decimal (c) A percentage ¼ Q 22. What is the ratio of the price of premium paper to the price of Economy paper. Q 23. Jackie runs a small business that uses a lot of paper. Calculate the saving made if she bought a box of 5 reams of standard paper rather than buying individual reams? Q 24. (a) Calculate the cost of purchasing “3 boxes of 5 reams” of premium quality paper. (b) Workout the price per ream. (c) What is the saving per ream compared to the price of purchasing a single ream? Q 25. What is the mean and range of the prices for the individual reams? Q 26. What is the median price for these individual reams? Q 27. “Planet Paper” are a local competitor of Paper World and they too have a sale on their A4 paper. Their prices are shown in the table below. Compare the prices from both places and decide which is cheaper. Q 28. A large company could easily use 1 million sheets of economy A4 paper in a year. How many reams is 1 million sheets of A4 paper? Q 29. Calculate the weight of this paper giving your answer in: (a) Kilograms (b) Tonnes Q 30. If the thickness of the economy paper is 0.11mm calculate the height of 50 reams. Give your answer in metres.

26. Worksheet AN2N2N A02 0 = 1 A12 1 = 2 A22 2 = 4 A3 A4 A5 A6 Q8 Q11 and Q 15 Paper SizeA0A1A2A3A4 Length (mm)1188840594 Width (mm)840594 L:W Q17 and Q 29 Q26 Worksheet