1. 25-May-15Created by Mr. Lafferty Maths Dept. Measuring & Scales Working with Scales Scaled Drawings Scaled Drawings www.mathsrevision.com Making Simple Scale Drawings Harder Scale Drawings Compass Points & Scale Drawings Enlarging and Reducing Drawing Similar Shapes & Scale Factor National 4 REL 1.2b

2. 25-May-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com National 4 REL 1.2b

3. 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1. To explain how to enlarge or reduce a given shape by a factor. 1. Be able to enlarge a shape by a factor. Enlarging & Reducing Enlarging & Reducing 2. Be able to reduce a shape by a factor. National 4 REL 1.2b

4. Enlarging & Reducing 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Double the size of the shape. Half the size of the shape. National 4 REL 1.2b

5. 25-May-15Created by Mr. Lafferty Maths Dept. Now try Ex 1 Q1 (e)(g)(i) (j) Q2 (c)(d)((g)(h) Ch5 (page 50) www.mathsrevision.com Enlarging & Reducing Enlarging & Reducing National 4 REL 1.2b

6. 25-May-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com National 4 REL 1.2b

7. 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.To understand the term scale. 1. To explain the term scale on a map. 2. Calculate the real life distances using a scaled. Scales Scales National 4 REL 1.2b

8. 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com In order to make sense of a map or scale diagram the scale must be known. Scales Scales National 4 REL 1.2b

9. 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com In order to make sense of a map or scale diagram the scale must be known. Scales Scales 4 cm For this scale model 1 cm represents 1m This means for every 1 metre of the actual car, 1cm is drawn on the map. National 4 REL 1.2b

10. 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com 6cm The scale of this drawing is 1cm = 5m What is the actual length of the tree ? Scales Scales 6 x 5 = 30m National 4 REL 1.2b

11. 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com 5cm The scale of this drawing is 1cm = 90cm What is the actual length of the bus in metres ? Scales Scales 5 x 90 = 450cm 4.5m National 4 REL 1.2b

12. 25-May-15Created by Mr. Lafferty Maths Dept. Now try Ex 2 Ch5 (page 52) www.mathsrevision.com Scales National 4 REL 1.2b

13. 25-May-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com National 4 REL 1.2b

14. 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1. To draw a scale drawing given suitable information. 1. From information given make a scaled drawing. Scaled Drawings Scaled Drawings National 4 REL 1.2b

15. 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Problem A garden is rectangular in shape and has length 12m and breadth 8m. Make rough sketch of the garden. 12m 8m Scaled Drawings Scaled Drawings Draw an accurate scaled drawing of the garden Use a scale of 1cm represents 2m National 4 REL 1.2b

16. 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com 12m 8m Scaled Drawings Scaled Drawings Use a scale of 1cm represents 2m 12m 8m National 4 REL 1.2b

17. 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Problem A road junction is triangular in shape. A rough sketch is given below. 20m Scaled Drawings Scaled Drawings Draw an accurate scaled drawing of the junction Use a scale of 1cm represents 2m 12m National 4 REL 1.2b

18. Scaled Drawings Scaled Drawings 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Use a scale of 1cm represents 2m 20m 12m 20m 12m Find the real life length of the 3 rd side 2 x 11.6 = 23.2m National 4 REL 1.2b

19. 25-May-15Created by Mr. Lafferty Maths Dept. Now try Ex3 Ch5 (page 55) www.mathsrevision.com Scaled Drawings Scaled Drawings National 4 REL 1.2b

20. 25-May-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com National 4 REL 1.2b

21. 25-May-15Created by Mr. Lafferty21 ‘To construct a triangle given the length of two sides and the included angle’ Aim of the Lesson Drawing SAS Triangles

22. 25-May-15Created by Mr. Lafferty22 Drawing SAS Triangles SAS Triangles Angle Side Side

23. 25-May-15Created by Mr. Lafferty23 Drawing SAS Triangles Toolkit required 1.Ruler 2.Protractor 3.Pencil & Paper

24. 25-May-15Created by Mr. Lafferty24 Drawing SAS Triangles Example : Draw to scale the triangle ABC with AB = 6cm and angle CAB = 30 o and AC = 5cm Step 1Draw line AB=6cm AB C Step 2Measure angle CAB from A Step 3Draw the line AC = 5cm through X. Label it C. Step 4Join C to B. Check angles add to 180 o A B C 30 o X

25. 25-May-15Created by Mr. Lafferty Maths Dept. Now try Ex 4 Ch5 (page 58) www.mathsrevision.com Scale Drawings National 4 REL 1.2b

26. 25-May-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com National 4 REL 1.2b

27. 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1.To show how to write down directions using a map. 2. To explain how to construct a scale drawing using bearings. 1. Be able to make sense of a map. Directions & Scale Drawings Directions & Scale Drawings 2.Write down accurate directions from a map. 3. Construct and interpret an accurate scale drawing. National 4 REL 1.2b

28. 25-May-15 Created by Mr. Lafferty Maths Dept. Compass Points N S E W 090 o 360/000 o 270 o 180 o SE Half way between South and East SW Half way between South and West Half way between North and West NW NE Half way between North and East

29. Compass Points Compass Points If Anne walks to Julie then to Amy and then back to where she started. Write down all the directions she took. If Daniel is facing North and turns clockwise to face Anne. How many degrees is this. If Daniel is facing Frances and turns clockwise to face Amy. How many degrees is this. If Amy is facing Paul and turns anti-clockwise to face Daniel. How many degrees is this. 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com John Julie Gary Frances Daniel Amy Barry Anne Paul N Who is North of Daniel Who is East of John Who is South West of Barry Who is North East of Gary National 4 REL 1.2b If Gary walks to John then to Barry and then back to where he started. Write down all the directions he took.

30. National 4 REL 1.2b Map Directions I leave the zoo to go back to my car which is in the town car park. Write down the directions I should take. There’s a fire at the library. Right down the directions the fire engine should take. I come out of the swimming pool and turn right then left. I go into the building second on my the right. Name the building. After going to the park I want to go to the cinema. Tea Lane is closed. Write down the directions I should take. I come out of school and go to the Park. Write down the directions I must take. I come out of the charity shop and need to catch a bus. Write down the directions to the bus station. 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com N

31. N 25-May-15 Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Make an accurate scale drawing of this sketch. 1cm represents 3km Scaled Drawings using Bearings N 50 o 15km 50 o 1cm represents 3km 15km

32. 12km N 120 o 1cm represents 2km N 25-May-15 Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Make an accurate drawing of the plane journey 1cm represents 2km Scaled Drawings using Bearings N 120 o 12km 45 o 8km N 45 o 8km

33. 25-May-15Created by Mr. Lafferty Maths Dept. Now try Ex 5 Ch5 (page 61) www.mathsrevision.com Compass points & Scale Drawings Compass points & Scale Drawings National 4 REL 1.2b

34. 25-May-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com National 4 REL 1.2b

35. 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1. To explain the connection between measuring and scale. 1. Understand the connection between measuring and scale. 2. Be able to do solve problems in context. Measuring & Scales National 4 REL 1.2b

36. 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Given that the scale of this drawing is 1cm = 35cm What is the actual length of the car in metres ? 10 x 35 = 350 cm Measuring & Scales ? m 3.5 m National 4 REL 1.2b

37. ? m 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Given that the scale of this drawing is 1cm = 700cm What is the actual height of the wind turbine in metres ? 9 x 700 = 6300 cm Measuring & Scales 63 m National 4 REL 1.2b

38. 25-May-15Created by Mr. Lafferty Maths Dept. Now try Extension Booklet Ex 6E Ch5 (page 19) www.mathsrevision.com Measuring & Scales National 4 REL 1.2b

39. 25-May-15Created by Mr. Lafferty Maths Dept. Starter Questions Starter Questions www.mathsrevision.com National 4 REL 1.2b

40. 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com Learning Intention Success Criteria 1. To explain the meaning of the word ‘similar’ and ‘factor’ in mathematics. Enlarge and reduce similar shapes by a given factor. 1. Understand the words similar and factor. Similar Shapes Similar Shapes 2. Be able to enlarge / reduce a shape by a given factor. National 4 REL 1.2b

41. Enlarging & Reducing 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com These two photos are of the same view 1.5cm 2cm 3cm 4cm The second is double the size of the first. The first could be ENLARGED to make the second. Enlarged by a Scale Factor of two (Double) National 4 REL 1.2b

42. Enlarging & Reducing 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com These two photos are of the same view 1.5cm 2cm 3cm 4cm The first is half the size of the second. The second could be REDUCED to make the first. Reduced by a Scale Factor of a half National 4 REL 1.2b

43. 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com These two rectangles are similar. 2cm 4cm 8cm The first has been ENLARGED by a factor (ESF) of 2 Similar Shapes Similar Shapes National 4 REL 1.2b

44. 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com These two rectangles are similar. 2cm 4cm ?cm 12cm The first has been ENLARGED by a factor (ESF) of 3 Similar Rectangles Similar Rectangles Find the enlargement factor Find the missing length ? cm ? = 2 x 3 = 6cm National 4 REL 1.2b

45. 25-May-15Created by Mr. Lafferty Maths Dept. www.mathsrevision.com These two rectangles are similar. 8cm 16cm ?cm 4cm The first has been ENLARGED by a factor (ESF) of 4 Similar Rectangles Similar Rectangles Find the reduction factor Find the missing length ? cm ? = 8 ÷ 4 = 2cm National 4 REL 1.2b

46. Given the shapes are similar, find the values y and z ? Scale Factor applies to ANY SHAPES that are mathematically similar. 15 cm 3 cm 7 cm 2cm y z 6 cm Scale factor = ESF = 3 15 = 5 is 2 x 5 = 10 1.4 cm Scale factor = RSF = 5 1 is 6 x 0.2 = 1.2 = 0.2 yz

47. Given the shapes are similar, find the values a and b ? Scale Factor applies to ANY SHAPES that are mathematically similar. 8 cm 7.5 cm b 10 cm Scale factor = RSF = 10 4 = 0.4 is 8 x 0.4 = 3.2 Scale factor = ESF = 4 is 2 x 2.5 = 5 = 2.5 ab 4 cm 2cm a 3 cm

48. Scale factors 8cm 12cm Enlargement Scale factor? Reduction Scale factor? 5cm 7.5cm ESF = RSF = Can you see the relationship between the two scale factors? www.mathsrevision.com 12 8 8 12 3 2 = 2 3 = National 4 REL 1.2b

49. 9cm a Find a given ESF = 3 b 15cm By finding the RSF Find the value of b. ESF = 3 a 9 = Scale factors www.mathsrevision.com 27cm 5cm 1 3 RSF = b 15 == 5 National 4 REL 1.2b

50. 25-May-15Created by Mr. Lafferty Maths Dept. Now try Extension Booklet Ex 7E Ch5 (page 21) www.mathsrevision.com Scale factors National 4 REL 1.2b