Book A TITLE Series Name: Book Name: Book Code: ISBN 13: Published:
About Geometry Book A: Shape and Space 602A 9781869684815 2008
AUTHOR John Thompson
ACKNOWLEDGEMENTS The publishers wish to acknowledge the work of the following people in the various stages of publishing this resource. Design: Editor:
Glen Honeybone Murray Quartly
PUBLISHERS User Friendly Resources New Zealand PO Box 1820 Christchurch Tel: 0508500393 Fax: 0508500399
Australia PO Box 914 Mascot NSW 2020 Tel: 1800553890 Fax: 1800553891
United Kingdom Premier House 11 Marlborough Place Brighton, East Sussex BN1 1UB Tel: 08454507502 Fax: 08456880199
WEBSITE www.userfr.com
EMAIL info@userfr.com
COPYING NOTICE This is a photocopiable book and permission is given to schools or teachers who buy this resource to make photocopies or transparencies of all pages. The copies must be for internal school use only, and may not be given or sold to other educational institutions or teachers from other institutions.
COPYRIGHT User Friendly Resources, 2008
User Friendly Resources specialises in publishing educational resources for teachers and students across a wide range of curriculum areas, at both primary and secondary levels. If you wish to know more about our resources, or if you think your resource ideas have publishing potential, please contact us at the above address.
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Book A
Contents SHAPE AND SPACE
To the Teacher.............................................................................................................................. 5
Activity 1: Reviewing Basic Skills Activity Guidelines for Teachers ............................................................................................ 6 Activity 1A: Using the Equipment ........................................................................................ 7 Activity 1B: Following Instructions ...................................................................................... 8 Activity 1C: An Obstacle Course ..........................................................................................10 Activity 1D: Scale Diagrams ..................................................................................................12 Activity 1E: Review Questions..............................................................................................14 SelfAssessment ........................................................................................................................15 Answers........................................................................................................................................15
Activity 2: Constructions I Activity Guidelines for Teachers ..........................................................................................16 Activity 2A: The Parts of a Circle ..........................................................................................17 Activity 2B: Constructing Triangles ...................................................................................19 Activity 2C: Putting it into Practice ....................................................................................22 Activity 2D: Review Questions .............................................................................................23 SelfAssessment ........................................................................................................................24 Answers .......................................................................................................................................24
Activity 3: Constructions II Activity Guidelines for Teachers ..........................................................................................25 Activity 3A: Perpendiculars ...................................................................................................26 Activity 3B: Bisectors ...............................................................................................................29 Activity 3C: The Nine Point Circle........................................................................................31 Activity 3D: Review Questions .............................................................................................33
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Book A
Contents SHAPE AND SPACE
SelfAssessment ........................................................................................................................34
Activity 4: Building Containers Activity Guidelines for Teachers ..........................................................................................35 Activity 4A: Making Nets........................................................................................................36 Activity 4B: Pyramids...............................................................................................................38 Activity 4C: Eulerâ€™s Rule ..........................................................................................................39 Activity 4D: Review Questions .............................................................................................40 SelfAssessment ........................................................................................................................41 Answers........................................................................................................................................41
Activity 5: Angles and Lines Activity Guidelines for Teachers ..........................................................................................42 Activity 5A: All About Angles ...............................................................................................43 Activity 5B: Angles and Parallel Lines................................................................................45 Activity 5C: Applying Your Knowledge .............................................................................48 Activity 5D: Review Questions .............................................................................................50 SelfAssessment ........................................................................................................................51 Answers........................................................................................................................................51
Activity 6: Isometric Drawings Activity Guidelines for Teachers ..........................................................................................53 Activity 6A: 3D Shapes............................................................................................................54 Activity 6B: Some Other Shapes .........................................................................................56 Activity 6C: Being Creative ....................................................................................................57 Activity 6D: Review Questions .............................................................................................58 SelfAssessment ........................................................................................................................58
Isometric paper ..................................................................................................................59
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Book A
To the Teacher SHAPE AND SPACE
G
eometry is perhaps the oldest of mathematical disciplines and is certainly one that provides many applications to the ‘real world’. In About Geometry students are provided with a variety of activities which enable them to explore and apply geometric concepts. The activities encourage problemsolving and cooperative group work. Within most of the activities there is a range of difficulty. Often the final sections of an activity can be used for extension or enrichment work with more capable students. There is plenty of scope for the use of educational technology in these activities. A photocopier can be used to make copies of designs which need to be repeated. If a scanner is available then designs can be scanned and put into a publishing or word processing program. There is a large variety of specialised educational software commercially available as well as a wide range of geometric material on internet sites. A web search would locate this material.
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Book A
1
Reviewing Basic Skills
F O C U S Describe and interpret position using the language of distance and direction Draw and interpret scale maps
ACTIVITY GUIDELINES FOR TEACHERS
Introduction The purpose of this activity is to review some of the basic skills needed to explore geometry. These include using a ruler to accurately measure distance and measuring angles between 0o and 360o. Also required is the ability to do straightforward calculations involving ratios and scale factors. For teachers wanting to develop computermediated activities with their students, activities 1C and 1D could be done using suitable software.
Teaching Ideas •
Ensure that students can measure and draw angles (0° to 360°) and lines (in millimetres and centimetres). They should also be able to work with bearings.
•
Use the school grounds for a simple orienteering course. Distances could be measured in paces and angles restricted to multiples of 45°.
•
Have students describe how to get from one part of the room to another using the following rules: 
You can only move in units of one metre.

All movements must be parallel to one of the classroom walls.
•
Discuss reasons for using scale diagrams.
•
Make a list of places where scale diagrams are used and by whom. For example, architects and town planners.
•
Discuss ways of measuring angles outside of the classroom e.g. what angle does a car turn through when going round a curve in the road, angles of elevation. How steep is the road?
Reinforcement
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Orienteering
•
Map reading
•
Creating shapes using computer software
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Book A
1A
Using the Equipment
F O C U S Describe and interpret position using the language of distance and direction
SHAPE AND SPACE
What you need to do 1. Using a pencil, ruler, protractor and compass, find the length (in millimetres) of each of these lines. a)
b) Length =
mm
Length =
mm
Length =
mm
Draw and interpret scale maps c)
d) Length =
mm
2. Measure the angle between each pair of lines. a) Angle =
b)
Angle = c)
Angle =
Answer the following questions on your own paper. 3. a) Draw a horizontal line that is 120 millimetres long. b) Draw a vertical line that is 65 millimetres long. Get another student to measure your lines when you have finished drawing them. 4. Draw two lines that have an angle of 45o between them. 5. Draw a triangle and measure each of the angles between the sides. Accuracy check: Add your three answers together â€“ you should get 180o. This is because the interior angles of a triangle always add to 180o. ÂŠ Copyright User Friendly Resources.
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Book A
1B
Following Instructions
F O C U S Describe and interpret position using the language of distance and direction Draw and interpret scale maps
SHAPE AND SPACE
What you need to know In this activity you have to imagine that you are programming a robot to follow instructions. The robot can only understand the following words.
–
“Move forward
–
“Turn
centimetres.”
° clockwise.”
The ‘ ’ represents any number. Therefore the robot would understand instructions like:
–
“Move forward 12 centimetres.”
–
“Turn 125° clockwise.”
Before it starts moving the robot will always be facing north. Example Question: These instructions would move the robot from A to B and then to C. –
“Move forward 3 centimetres.”
–
“Turn 45° clockwise.”
–
“Move forward 10 centimetres.”
C
B
A What two instructions would get the robot straight back to A from C?
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Book A
1B
Following Instructions
F O C U S Describe and interpret position using the language of distance and direction Draw and interpret scale maps
SHAPE AND SPACE
What you need to do 1. In each of these two activities you need to follow the instructions and draw the movement. Now give the two instructions that would get the robot straight back to the starting point. Remember the robot always begins by facing north. Activity 1
a) Move forward 10 centimetres. b) Turn 120° clockwise. c)
Move forward 14 centimetres.
Activity 2
a) Move forward 5 centimetres. b) Turn 300° clockwise. c)
Move forward 5 centimetres.
d) Turn 120° clockwise. e) Move forward 5 centimetres.
2. Write down the instructions that the robot would need to follow this path, starting from A and moving clockwise until it is back at the starting point.
A
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Book A
1C
An Obstacle Course
F O C U S Describe and interpret position using the language of distance and direction Draw and interpret scale maps
SHAPE AND SPACE
What you need to know For this activity you have to design an obstacle course. The plan for the course should fit onto an A4 sheet of squared paper. The aim is to write instructions that the robot could follow to get around the obstacles in going from the start to the finish. There should be five obstacles and each should be between 10 cm2 and 20 cm2 in area. The start and finish points are at opposite ends of the paper.
What you need to do Designing the course 1. Mark in the start and finish positions on your paper. 2. Mark in the obstacles on your paper. They can be any shape but must be within the size limits given above. Writing the instructions 3. The only words that your robot understands are the sort of instructions used in activity 1B, e.g. “Move …”, “Turn …” 4. Write a set of instructions that will get your robot to go from the start to the finish, avoiding all the obstacles on the way. Testing the instructions 5. Give the map and instructions to someone else in your group. Get them to see if they can follow your instructions exactly and get from the start to the finish. Use the Obstacle Course grid. 6. How successful were your instructions? Describe any improvements that may be possible.
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