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Scaled Drawings

National 4 REL 1.2b. Scaled Drawings. Enlarging and Reducing Drawing. Working with Scales. Making Simple Scale Drawings. Harder Scale Drawings. www.mathsrevision.com. Compass Points & Scale Drawings. Measuring & Scales. Similar Shapes & Scale Factor. National 4 REL 1.2b.

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Scaled Drawings

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  22. Drawing SAS Triangles SAS Triangles Side Side Angle Created by Mr. Lafferty

  23. Drawing SAS Triangles • Ruler 2. Protractor 3. Pencil & Paper Toolkit required Created by Mr. Lafferty

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

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

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

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

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

  29. If Gary walks to John then to Barry and then back to where he started. Write down all the directions he took. 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. Who is North of Daniel Who is East of John Who is South West of Barry Who is North East of Gary Compass Points National 4 REL 1.2b Frances John Barry N Daniel Julie Anne www.mathsrevision.com Amy Gary Paul Created by Mr. Lafferty Maths Dept.

  30. I leave the zoo to go back to my car which is in the town car park. Write down the directions I should take. After going to the park I want to go to the cinema. Tea Lane is closed. 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. I come out of the charity shop and need to catch a bus. Write down the directions to the bus station. I come out of school and go to the Park. Write down the directions I must take. Map Directions National 4 REL 1.2b N www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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