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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. Slide 28 is a printable exact scale drawing of the garden that students need to use/refer to throughout. Note that all dimensions are whole numbers except for the SW fence and the NE Hedge. Check that this is correct after printing and again after photocopying. You should print this now before you do anything else so as to become familiar with it. Slide 5 shows the plan of the garden in colour (without a background grid). Unfortunately background grids do not show up in PowerPoint once the presentation is running. The questions on Slides 6 to 10 show the same plan but reduced in size and superimposed with a grid. This is so that you can refer to the plan as the answers appear if you wish. This plan is degraded in quality since it is simply a snatched image of a slide but it should still be useful. Printable teacher Q + A sheets and student question sheets together with all worksheets can be found on slides towards the end. Calculator symbols are used throughout but these can easily be modified depending on the group if need be. 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: Garden Design: Content and skills covered Coverage and range: Level 2 At least 1 from each area

5. Intro Designing a Garden © Lisa Turay/bigstockphoto.com What mathematics might be involved in designing a garden? Stuart and Sarah are moving into their new house next month and they would like some help from you in designing their garden. They have made a simple initial design on their computer which they would like you to look over to see if it's OK and to check a few of the measurements and calculations for them. They have a scale drawing that you can use. Perhaps you could also help them with the placement of some additional features that they are considering adding (bird bath, footbath, ornamental statue and an extra flower bed). They are also a bit worried about the overall cost so maybe you can advise on this too!

6. Initial Design Scale 1cm = 1m WALL House Conservatory FENCEFENCE HEDGEHEDGE WALLWALL N Shed Pond Border Sand pit Patio Barbeque area Part of Drive Area Neighbour's Land FENCEFENCE Tree A Bench Tree with seat Tree B Sarah and Stuart’s Initial Design

7. Questions 1 - 21 *Q1: What is the length of the North wall? *Q2: What is the length of the East Hedge (behind bench) ? *Q3: What lies behind the SW Fence? 16 m 7 m Part of the drive area *Q4: Work out the following ratios: (a) Length of East wall : length of West fence (b) Length of patio : width of patio? 1 : 2 3 : 1 * 1 square = 2m

8. *Q5: Determine the perimeter of the garden (nearest metre). Accept 66 or 67 m *Q6: Approximately what fraction of the perimeter is taken up by the North wall? 1/4 *Q7: Find the distance between trees A and B (measure from the centre of trunk). *Q8: If fencing panels come in two metre lengths. How Many will be needed? 9 *Q9: In what direction is the conservatory from the tree with the seat? SE 4 m * 1 square = 2m

9. *Q10: The East hedge is 9 feet high. How high is it in yards? 3 *Q11: Given that 1 yard  0.9 m find the height in metres and centimetres. 2 m 70 cm *Q12: What area of the garden is taken up by the shed? 4½ m 2 *Q13: Find the diameter of the pond (not wall). 3 m *Q14: Calculate the area of garden taken up by the patio. 75 m 2 * 1 square = 2m

10. *Q15: Determine the area within the dotted lines behind the SW fence. 15 m 2 *Q16: Calculate the total area of the garden contained within the boundary. 297 m 2 *Q17: Calculate the perimeter of the inner wall around the pond. Take  = 3.142. 9.426 m *Q18: Give your answer to Q17 in: (a) m and cm to the nearest cm. (b) cm to 1 d.p. (c) mm 9 m 43 cm 942.69426 * 1 square = 2m

11. *Q19: Work out the surface area of water on the pond. Take  = 3.14 but give your answer to 1 significant figure. *Q20: The pond is 30 cm deep. Use your answer to Q19 to calculate the capacity of the pond in: (a) m 3 (b) cm 3 7 m 2 2.1 m 3 2 100 000 cm 3 *Q21: Use the facts above to find the following: (a) The capacity of the pond in litres (b) The mass of the water in (i) kg (ii) tonnes (iii) **The capacity of the pond in gallons (2 sig fig). 2 100 litres 2100 kg2.1 tonnes For Water 1 cm 3 = 1 ml = 1 g 1 litre = 1000 ml = 1 kg 1000 kg = 1 tonne 1 gallon  4 ½ litres 470 gallons * 1 square = 2m ** Calculator allowed

12. Q 22 Bird Bath WALL House Conservatory FENCEFENCE HEDGEHEDGE WALLWALL Scale 1cm = 1m N Shed Pond Border Sand pit Patio Barbeque area Part of Drive Area Neighbour's Land FENCEFENCE Tree A Bench Tree with seat Tree B Bird Bath Q22: The Bird Bath Q22: Stuart wants to add a bird bath. He intends to place is so that it is 6 metres from the house wall and 5 metres from the East hedge. Mark the position of the bird bath on your plan.

13. Q 23 Footpath WALL House Conservatory FENCEFENCE HEDGEHEDGE WALLWALL Scale 1cm = 1m N Shed Pond Border Sand pit Patio Barbeque area Part of Drive Area Neighbour's Land FENCEFENCE Tree A Bench Tree with seat Tree B Bird Bath Line of footpath Q 23: The Footpath Q23: Sarah would like to lay a stone path running from the patio area to the border. She wants the path to be equidistant from trees A and B. Mark the position of the path on the plan.

14. Q 24 Statue WALL House Conservatory FENCEFENCE HEDGEHEDGE WALLWALL Scale 1cm = 1m N Shed Pond Border Sand pit Patio Barbeque area Part of Drive Area Neighbour's Land FENCEFENCE Tree A Bench Tree with seat Tree B Line of footpath Bird Bath Q 24: The Ornamental Statue 5m Statue Q24: Sarah would also like an ornamental statue for the garden She decides to put this 5m from the point were both fences meet and equidistant from both. Mark the position of the statue on the plan.

15. Q 25 Flower Bed WALL House Conservatory FENCEFENCE HEDGEHEDGE WALLWALL Scale 1cm = 1m N Shed Pond Border Sand pit Patio Barbeque area Part of Drive Area Neighbour's Land FENCEFENCE Tree A Bench Tree with seat Tree B Statue Line of footpath Bird Bath Q 25: The Flower Bed Flower Bed Q25: Stuart thinks that some more flowers would be a good idea so he decides to add a flower bed of radius 2m against the west fence. It is to be centred at a point 4 metres south of the wall along the fence. Make an accurate drawing of the flower bed on the plan.

16. Final Design WALL House Conservatory FENCEFENCE HEDGEHEDGE WALLWALL Scale 1cm = 1m N Shed Pond Border Sand pit Patio Barbeque area Part of Drive Area Neighbour's Land FENCEFENCE Tree A Bench Tree with seat Tree B Statue Line of footpath Bird Bath Flower Bed The Final Design

17. Questions 26 - 40 c b a d *Q26:The triangular seat around the tree will be made of three identical pieces of wood as shown in the diagram. Each piece will be cut from a single strip of wood. Find the cutting angles indicated. Angle a = b = 150 0, Angle c = angle d = 30 0. *

18. Sand pit b a *Q27:. The boundary of the sand pit will consist of 12 large identical regular pentagons each of which will have to be cut from a stone slab as shown. Determine the cutting angles indicated. Angle a = 72 o, Angle b = 108 o. *Q28:. What is the name of the shape formed from the pentagons that contain the sand? Do-decagon

19. *Q29: Sarah is considering creating a paved area for underneath a garden swing that she hopes to buy. She wants some compressed rubber shapes and she would like them to tessellate. Which of the shapes below could she use. Regular Pentagon Regular Hexagon Regular Octagon Square Equilateral Triangle Rectangle

20. 1. Lawn 250 m 2 at £3.00 m 2 2. Replacement fencing: 10 x 1.8 m panels at £20 per panel 3 Paving stones for patio: 300 x £2.20 + £140 for edging 4 Six small trees at £30 each 6 Shed £285 7 Sand Pit £135 8 Pond £430 9 Bench £160 5 Patio table £260 + 4 chairs at £35 each 10 Wood for tree seating area £150 11 Barbeque £80 13 Stones for footpath £150 12 Bird Bath £60 14 Ornamental Statue £184 15 220 flower bulbs at £4 per pack of 25 £285 £135 £430 £160 £150 £80 £60 £150 £184 *Q 30: Sarah and Stuart made an initial rough estimate of the cost involved in the garden. Complete the blanks and work out the total. *

21. 1. Lawn 250 m 2 at £3.00 m 2 2. Replacement fencing: 10 x 1.8 m panels at £20 per panel 3 Paving stones for patio: 300 x £2.20 + £140 for edging 4 Six small trees at £30 each 6 Shed £285 7 Sand Pit £135 8 Pond £430 9 Bench £160 5 Patio table £260 + 4 chairs at £35 each 10 Wood for tree seating area £150 11 Barbeque £80 13 Stones for footpath £150 12 Bird Bath £60 14 Ornamental Statue £184 15 220 flower bulbs at £4 per pack of 25 £285 £135 £430 £160 £150 £80 £60 £150 £184 *Q 30: Sarah and Stuart made an initial rough estimate of the cost involved in the garden. Complete the blanks and work out the total. £750 £200 £800 £180 £400 £36 £4000 *

22. *Q31: Which item cost 10% of the total? *Q32: What fraction of the cost was taken up by the patio? *Q33: Express the proportion of the cost taken up by patio as (a) A percentage (b) A decimal *Q35: Work out the ratio of cost of footpath to cost of lawn. *Q36: Work out the ratio of cost of barbeque : cost of bird bath. *Q37: Stuart had seen the pond that he wanted to purchase and hoped to get a 15% reduction in the sale. What would the new price be? *Q38: The cost of items 2, 3, and 5 are 1/20, 1/5 an 1/10 of the total cost respectively. What fraction of the total cost did these items take up? Q39: What was the percentage cost of the lawn? Q40: Sarah wanted to reduce the cost by leaving out the purchase of the ornamental statue. What would the percentage saving be on this? Item 5 1/5 20%0.2 1 : 5 4 : 3 £365.50 7/20 18.75% 4.6% *Q34: Which item was approximately 1% of the total cost?. Item 15 Questions on Pricing *

23. Q+ A 1 *Q1: What is the length of the North wall? *Q2: What is the length of the East Hedge (behind bench) ? *Q3: What lies behind the SW Fence? 16 m 7 m Part of the drive area *Q4: Work out the following ratios: (a) Length of East wall : length of West fence (b) Length of patio : width of patio? 1 : 2 3 : 1 *Q5: Determine the perimeter of the garden (nearest metre). Accept 66 or 67 m *Q6: Approximately what fraction of the perimeter is taken up by the North wall? 1/4 *Q7: Find the distance between trees A and B (measure from the centre of trunk). *Q8: If fencing panels come in two metre lengths. How Many will be needed? 9 *Q9: In what direction is the conservatory from the tree with the seat? SE 4 m *Q10: The East hedge is 9 feet high. How high is it in yards? 3 *Q11: Given that 1 yard  0.9 m find the height in metres and centimetres. 2 m 70 cm *Q12: What area of the garden is taken up by the shed? 4½ m 2 *Q13: Find the diameter of the pond (not including the wall). 3 m *Q14: Calculate the area of garden taken up by the patio. 75 m 2 *Q15: Determine the area within the dotted lines behind the SW fence. 15 m 2 *Q16: Calculate the total area of the garden contained within the boundary. 297 m 2 *Q17: Calculate the perimeter of the inner wall around the pond. Take  = 3.142. 9.426 m *Q18: Give your answer to Q17 in: (a) m and cm to the nearest cm. (b) cm to 1 d.p. (c) mm 9 m 43 cm942.69426 *Q19: Work out the surface area of water on the pond. (  = 3.14) but give your answer to 1 sig fig. 7 m 2 *Q20: The pond is 30 cm deep. Use your answer to Q19 to calculate the capacity of the pond in: (a) m 3 (b) cm 3 2.1 m 3 2 100 000 cm 3 *Q21: Use the facts above to find the following: (a) The capacity of the pond in litres (b) The mass of the water in (i) kg (ii) tonnes (iii) **The capacity of the pond in gallons (2 sig fig). 2 100 litres 2100 kg 2.1 tonnes 470 gallons ** Calculator allowed Question + A Sheet (Teacher)

24. Q + A 2 You must show all your construction lines in questions 22 - 25 Q22: Stuart wants to add a birdbath. He intends to place is so that it is 6 metres from the house wall and 5 metres from the East hedge. Mark the position of the bird bath on the plan. Q23: Sarah would like to lay a stone path running from the patio area to the border. She wants the path to be equidistant from trees A and B. Mark the position of the path on the plan. Q24: She would also like an ornamental statue for the garden She decides to put this 5m from the point were both fences meet and equidistant from both. Mark the position of the statue on the plan. Q25: Stuart thinks that some more flowers would be a good idea so he decides to add a flower bed of radius 2m against the west fence. It is to be centred at a point 4 metres south of the wall along the fence. Make an accurate drawing of the flower bed on the plan. SL 11 SL 12 13 Slide 14 *Q26:The triangular seat around the tree will be made of three identical pieces of wood as shown in the diagram. Each piece will be cut from a single strip of wood. Find the cutting angles indicated. c b a d Angle a = b = 150 0, Angle c = angle d = 30 0. *Q27:. The boundary of the sand pit will consist of 12 large identical regular pentagons each of which will have to be cut from a stone slab as shown. Determine the cutting angles indicated. Sand pit b a Angle a = 72 o, Angle b = 108 o. *Q28:. What is the name of the shape formed from the pentagons that contain the sand? Do-decagon

25. Q + A 3 *Q29: Sarah is considering creating a paved area for underneath a garden swing that she hopes to buy. She wants some compressed rubber shapes and she would like them to tessellate. Which of the shapes below could she use. Regular Pentagon Regular Hexagon Regular Octagon Square Equilateral Triangle Rectangle *Q 30: Sarah and Stuart made an initial rough estimate of the cost involved in the garden. Complete the blanks and work out the total. (see worksheet) *Q31: Which item cost 10% of the total? *Q32: What fraction of the cost was taken up by the patio? Item 5 1/5 *Q33: Express the proportion of the cost taken up by patio as (a) A percentage (b) A decimal 20%0.2 *Q35: Work out the ratio of cost of footpath to cost of lawn. *Q36: Work out the ratio of cost of barbeque : cost of bird bath. *Q37: Stuart had seen the pond that he wanted to purchase and hoped to get a 15% reduction in the sale. What would the new price be? *Q38: The cost of items 2, 3, and 5 are 1/20, 1/5 an 1/10 of the total cost respectively. What fraction of the total cost did these items take up? Q39: What was the percentage cost of the lawn? Q40: Sarah wanted to reduce the cost by leaving out the purchase of the ornamental statue. What would the percentage saving be on this? 1 : 5 4 : 3 £365.50 7/20 18.75% 4.6% *Q34: Which item was approximately 1% of the total cost?. Item 15

26. Student Q 1 ** Calculator allowed *Q1: What is the length of the North wall? *Q2: What is the length of the East Hedge (behind bench) ? *Q3: What lies behind the SW Fence? *Q4: Work out the following ratios: (a) Length of East wall : length of West fence (b) Length of patio : width of patio? *Q5: Determine the perimeter of the garden (nearest metre). *Q6: Approximately what fraction of the perimeter is taken up by the North wall? *Q7: Find the distance between trees A and B (measure from the centre of trunk). *Q8: If fencing panels come in two metre lengths. How Many will be needed? *Q9: In what direction is the conservatory from the tree with the seat? *Q10: The East hedge is 9 feet high. How high is it in yards? *Q11: Given that 1 yard  0.9 m find the height in metres and centimetres. *Q12: What area of the garden is taken up by the shed? *Q13: Find the diameter of the pond (not including the wall). *Q14: Calculate the area of garden taken up by the patio. *Q15: Determine the area within the dotted lines behind the SW fence. *Q16: Calculate the total area of the garden contained within the boundary. *Q17: Calculate the perimeter of the inner wall around the pond. Take  = 3.142. *Q18: Give your answer to Q17 in: (a) m and cm to the nearest cm. (b) cm to 1 d.p. (c) mm *Q19: Work out the surface area of water on the pond. (  = 3.14) but give your answer to 1 sig fig. *Q20: The pond is 30 cm deep. Use your answer to Q19 to calculate the capacity of the pond in: (a) m 3 (b) cm 3 *Q21: Use the facts above to find the following: (a) The capacity of the pond in litres (b) The mass of the water in (i) kg (ii) tonnes (iii) **The capacity of the pond in gallons (2 sig fig). Question Sheet (Student)

27. Student Q 2 You must show all your construction lines in questions 22 - 25 Q22: Stuart wants to add a birdbath. He intends to place is so that it is 6 metres from the house wall and 5 metres from the East hedge. Mark the position of the bird bath on the plan. Q23: Sarah would like to lay a stone path running from the patio area to the border. She wants the path to be equidistant from trees A and B. Mark the position of the path on the plan. Q24: She would also like an ornamental statue for the garden She decides to put this 5m from the point were both fences meet and equidistant from both. Mark the position of the statue on the plan. Q25: Stuart thinks that some more flowers would be a good idea so he decides to add a flower bed of radius 2m against the west fence. It is to be centred at a point 4 metres south of the wall along the fence. Make an accurate drawing of the flower bed on the plan. SL 11 SL 12 13 Slide 14 *Q26:The triangular seat around the tree will be made of three identical pieces of wood as shown in the diagram. Each piece will be cut from a single strip of wood. Find the cutting angles indicated. c b a d *Q27:. The boundary of the sand pit will consist of 12 large identical regular pentagons each of which will have to be cut from a stone slab as shown. Determine the cutting angles indicated. Sand pit b a *Q28:. What is the name of the shape formed from the pentagons that contain the sand?

28. Student Q3 *Q29: Sarah is considering creating a paved area for underneath a garden swing that she hopes to buy. She wants some compressed rubber shapes and she would like them to tessellate. Which of the shapes below could she use. Regular Pentagon Regular Hexagon Regular Octagon Square Equilateral Triangle Rectangle *Q 30: Sarah and Stuart made an initial rough estimate of the cost involved in the garden. Complete the blanks and work out the total. (see worksheet) *Q31: Which item cost 10% of the total? *Q32: What fraction of the cost was taken up by the patio? *Q33: Express the proportion of the cost taken up by patio as (a) A percentage (b) A decimal *Q35: Work out the ratio of cost of footpath to cost of lawn. *Q36: Work out the ratio of cost of barbeque : cost of bird bath. *Q37: Stuart had seen the pond that he wanted to purchase and hoped to get a 15% reduction in the sale. What would the new price be? *Q38: The cost of items 2, 3, and 5 are 1/20, 1/5 an 1/10 of the total cost respectively. What fraction of the total cost did these items take up? Q39: What was the percentage cost of the lawn? Q40: Sarah wanted to reduce the cost by leaving out the purchase of the ornamental statue. What would the percentage saving be on this? *Q34: Which item was approximately 1% of the total cost?.

29. Garden Plan Scale 1cm = 1m WALL House Conservatory FENCEFENCE HEDGEHEDGE WALLWALL N Shed Pond Border Sand pit Patio Barbeque area Part of Drive Area Neighbour's Land FENCEFENCE Tree A Bench Tree with seat Tree B Sarah and Stuart’s Initial Design

30. Q30 Worksheet 1. Lawn 250 m 2 at £3.00 m 2 2. Replacement fencing: 10 x 1.8 m panels at £20 per panel 3 Paving stones for patio: 300 x £2.20 + £140 for edging 4 Six small trees at £30 each 6 Shed £285 7 Sand Pit £135 8 Pond £430 9 Bench £160 5 Patio table £260 + 4 chairs at £35 each 10 Wood for tree seating area £150 11 Barbeque £80 13 Stones for footpath £150 12 Bird Bath £60 14 Ornamental Statue £184 15 220 flower bulbs at £4 per pack of 25 £285 £135 £430 £160 £150 £80 £60 £150 £184 *Q 30: Sarah and Stuart made an initial rough estimate of the cost involved in the garden. Complete the blanks and work out the total. *