students’ integrated maths module for angle 1 · activities: 4: types of angles 25 a: roofs and...

Students’

Integrated Maths

Module

for

Angle 1

Author: Steve Hadfield

Editor: Mark R O’Brien

OTRNet Publications

www.otrnet.com.au

Check our website for phone, fax and address details.

Copyright ©2000 by OTRNet Publications, PO Box 49, Glen Forrest, Western Australia,6071. All rights reserved. No part of this publication may be reproduced or transmittedin any form, or by any means, electronic or manual, including photocopying, scanning,recording, or by any information storage or retrieval system, without permission in writingfrom the publisher.

First published: November 2000First reprinted: October 2002Second reprint: November 2007Revised: January 2019

Design and Editing: Mark R. O’Brien Cover Design: Ali B Design

Ph: 0411 4301 09E-mail: [email protected]

National Library of AustraliaCataloguing-in-Publication data

For secondary studentsISBN-13: 978-1-876800-04-8ISBN-10: 1-876800-04-6

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Introduction for students:

At the end of this module you should have increased your ability to;

C Make estimates of angle size and distanceC Measure angle sizes and bearingsC Use distance and scales on maps and plansC Use direction and bearings on maps

Table of Contents:

Activities: 4: Types of Angles 25

A: Roofs and Fence Lines 4 5: Angle Relationships 26

B: Angle Measures 7 6: Bearings 30

C: Making A Compass Bearing Gauge 8

D: Angles of Elevation and Depression 9 Puzzles:

D+: Making An Inclinometer 11 A: Angle Riddle 32

E: 3D Situations 12 B: Australian Swimming Greats 34

F: Investigation: angles on Grids 14

Applications:

Student Recording 16 A: Clock Angles 35

B: Mapping 37

Notes 17 C: Newspaper Search: Housing Design 40

D: Project: World Bearings 42

Exercises:

1: Angles and Measurement 20 Student Reflection 43

2: Angles and Labels 22

3: Parallel and Perpendicular Lines 24 Answers to Exercises 44

© OTRNet Publications: www.otrnet.com.au

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Activity A:Materials required: Protractor and ruler

Roofs and Fence lines

Task 1: The diagram here shows the angle that a roof meets the ceiling of a house.

Use a protractor to measure the angle that these roofs are at:

Task 2: Which roof is the steepest?

Task 3: At what angle is the steepest roof?

Task 4: How was measuring roof 4 different to measuring the first three roofs?


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1. Roof at an angle of 20E 2. Roof at an angle of 40E

3. Roof at an angle of 30E 4. Roof the left end at 25E and right at 50E

Task 5: Draw the roof onto these houses at the angle given. The first roof hasbeen started for you.

Task 6: Draw a house here and put on a roof at an angleof your choice. Write down the angle of the roof.


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Task 7: The diagram below shows the fence lines of properties in a new housingdevelopment. Use your protractor to measure the 15 angles.

Task 8: List all of the angles on the housing development that measure less than90E.

Task 9: List all of the angles you measured that measure exactly 90E.

Task 10: List all of the angles you measured that measure more than 90E.

Task 11: Add together the sizes of these pairs of angles: 3 & 4: 10 & 11: 13 & 14:

Task 12: What do you notice about the sums in Task 11?

Task 13: Add together this set of angles; 5, 6, 7 & 8:

Task 14: Add together this set of angles; 4, 6, 14 & 15:


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Activity B:Materials required: Protractor

Angle Measures

Task 1: There are four angles formed by the intersection of these two lines.Measure each of these angles.

Task 2: What do you notice about angles 1 & 3 and angles 2 & 4?

Task 3: Add together these pairs of angles: 1 & 4: 2 & 3:

Task 4: What is the sum of all four measured angles?

Task 5: Draw three other different pairs of intersecting lines as in the first diagramand repeat your measurements and any observations. Summarise yourfindings.

Task 6: Complete this conclusion using the words that follow the paragraph:When _____ lines intersect, _____________ angles are always the same sizeas each other and ______ of the angles ______ up to _______.

opposite, all, 360E, two, add


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Activity C:

Materials needed: Card or plastic for gauge Pens to mark the card or plasticScissors180E Protractor

Making a Compass Bearings Gauge

Task 1: Cut out a base for your gauge. This should be circular and have a radiusbetween 3cm and 5cm.

Task 2: Mark the centre of your gauge.

Task 3: Mark a point on the edge of your gauge as the North point. Draw a linejoining this point to the centre of your gauge. It should look like thediagram on the right.

Task 4: Use you 180E protractor to accurately mark in East,

South and West on the edges of your gauge.

Task 5: Starting at the North point and going clockwise use theprotractor to mark points on your gauge every 10E.

Task 6: Starting at the North point and going clockwise label the followingbearings: 030E, 060E, 090E, 120E, 150E, 180E, 210E, 240E, 270E,300E, 330E.

Task 7: What bearings coincided with: East? , South? , West? .

Task 8: There are two bearings that can be used for North. What do you think they are?


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Activity D:

Angles of Elevation and Depression

Materials required: Inclinometer, protractor, measuring tape.

This sketch shows angles ofelevation and depression inrelation to a yacht and a man on acliff.

Task 1: Are the angles of elevation and depression always going to be equal insize? Investigate this in the sketch below by measuring the angles andthen draw in one other sketch to confirm what you found.

Task 2: Complete the following paragraph using some of these words:

elevation depression vertical horizontal smallerequal larger angle above below

Both the __________of elevation and the angle of __________ aremeasured from __________ . However, the angle of elevation ismeasured ________ the horizontal, while the angle of depression ismeasured __________ the horizontal. Both angles are __________ in size.


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An inclinometer is an instrument for measuring angles ofdepression or elevation. A diagram of what aninclinometer looks like is shown here.

You need to look at an inclinometer to complete these tasks:

Task 3: What measurement units does this instrument use?

Task 4: Find the highest and lowest readings on the instrument. What do thesesignify when you are measuring angles?

Task 5: If you and a friend each measured the angle of elevation of the top of abuilding you may get different results. Explain two things that could causethis difference?

Task 6: Find a tree (or other suitable object) and mark apoint on the ground about 20m from the tree. Measure the angle of elevation of the top of thetree. As you move towards the tree or away fromthe tree, what happens to the angle of elevationof the top of the tree?

Task 7: Using the same mark, measure the angle of depression of the base ofthe tree. As you move forward and backward, how does this anglechange?


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Task 8: Use an inclinometer to measure angles of elevation and depressionfor some objects around your school or home, noting also the distancefrom the object being measured.

Some suggestions:SCHOOL trees

flagpolebuildingbottom of the pooltop of the blackboard

HOME treestop of the housebottom of the stairschimneyTV antenna

Activity D+:

Making an Inclinometer

Materials required: Piece of card Piece of plastic Protractor

Straw Sticky tape Drawing pin

Task 1: On one side of the card draw up a scale asshown in this diagram:

Task 2: Also mark the scale at 5E intervals.

Task 3: Cut a pointer out of the piece of plastic that will reach from the top to thescale.

Task 4: Pin the pointer loosely to the card.

Task 5: Sticky tape the straw along the top ofthe card as a sight.

Your inclinometer is finished.


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Activity E:Materials required: Models of a cube, rectangular prism and a

triangular prism.

3D Situations

Here are sketches of three common 3D objects.

Task 1: Use these diagrams to shade pairs of parallel faces for each object.

Which of, and how many of these drawings, were not required?

Task 2: These diagrams show two of the many pairs of parallel edges of a cube .

How many pairs are there in total?

This number is the same for a rectangular prism. Why?

How many are there for a triangular prism?


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Task 3: These sketches show two of themany pairs of perpendicularedges of a cube. They form a 90E angle.(These don’t always look like 90Eangles due to a 2D drawing of a3D object.)

How many such pairs of perpendicular edges are there for a cube?

How many for a rectangular prism?

How many for a triangular prism?

Task 4: Lines in 3D which are not parallel, yet do not intersect, are called skewlines. A particular edge on a cube has four edges which are skew to it. The first diagram below shows one of these. Draw in the other three.

Task 5: Draw diagrams below to show four examples of skew lines on each of arectangular prism and a triangular prism.


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Activity F:

Materials required: Square dot paper

Investigation: Angles on Grids

Task 1: This first grid in this diagram shows an angle drawn on a nine point gridwith its vertex on a corner dot.

How many angles can be drawn using this corner dot as the vertex, andfinishing on the outside dots? Use the grids above to draw them all, not allgrids will be needed.

Will there be the same amount of angles from each corner?

How many angles could be drawn from the four corners?

How many different size angles are there? What is the size of the largest possible angle?

Task 2: We can also use a middle dot on a side as the vertex of the angle. Oneexample is shown here.

How many angles can be drawn using this middle dot as the vertex, andfinishing on the outside dots? Use the grids above to find out, not all willgrids be needed.


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Will there be the same amount of angles from each middle dot?

How many angles could be drawn from the four middle dots?

How many different size angles are there?

What is the size of the largest possible angle?

Task 3: We could also use the centre dot as a vertex as shown in this diagram.

How many angles could be drawn using the centre dot as the vertex. Usethe grids above to draw them all.

How many different size angles could be drawn?

Task 4: What is the total number of angles that can be drawn on a 9 point grid,using any point as the vertex?

How many different size angles are there?


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Student Recording:

Write at least two pieces of information about each of theseconcepts that you have explored in earlier lessons. Then try togive an example relating to each. Use diagrams where it helps.

angle:

degrees:

bearing:

parallel:

perpendicular:

angle of elevation:

angle of depression:


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Notes

Angle

When two lines meet an angle is formed. The size of the angle is defined as the spacebetween the two intersecting lines and is measured in degrees. The symbol for degreesis E. For example; 67E.

The intersecting lines meet at a vertex.

Angles are measured using an instrument called a protractor like the one shown here.

When measuring angles, the lengths ofthe sides is not important. Themeasurement of the space between theintersecting lines is the size of the angle.

Diagram 2 here is a larger sketch, but theangle in Diagram 1 is a lot larger. Thespace between the lines is more.

Angles are generally labelled using three letters or just the vertex if there is a singleangle present.

pTDR or pRDT or pD pWGB and pBGL and pWGL


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Types of Angles

There are five types of angles in relation to size.

Acute Angle: Less than 90E eg.

Right Angle: Exactly 90E eg.

Obtuse Angle: Between 90E and 180E eg.

Straight Angle: Exactly 180E eg.

Reflex Angle: Greater than 180E eg.

Angle Relationships

Adjacent Angles Vertically Opposite Angles

Angles which share a common line. Opposite angles are congruent (equal size).These are formed by intersecting lines.

Complementary Angles Supplementary AnglesAdd to 90E e.g. 35E and 55E Add to 180E e.g. 110E and 70E


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A bearing of 120 degrees is shown.

Parallel and Perpendicular Lines

Parallel lines in 2D are those that do not intersect. Some examples are shown here.

Perpendicular lines, like those shown below, intersect at right angles (90E).

Bearings

A bearing is a direction on the Earth’s surface. Bearings aremeasured in degrees, starting from North, in a clockwisedirection.

North is known as 000E or 360E.

East is 090E. South is 180E. West is 270E.

Notice how three digits are used as a convention for allbearings.

Angles of Elevation and Depression

An angle of depression is measured downfrom horizontal.

An angle of elevation is measured up fromhorizontal.


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Exercise 1: Angles and Measurement

Measure angles to the nearest degree in these exercises.

1. Measure the size of each of these angles.

(a) (b) (c) (d)

2. Measure the size of each of the following angles.

(a) (b) (c) (d)

3. Use your protractor to draw angles with the following sizes.

(a) 35E (b) 72E (c) 16E (d) 124E (e) 155E (f) 95E


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4. Estimate the size of each of these angles, to the nearest 10E.

A = _____, B = _____, C = _____, D = _____, E = _____, F = _____

5. Order these angles from smallest to largest.

____, ____, ____, ____, ____, ____, ____, ____

6. State which angle, P or Q, is larger in each case.

(a) _____ (b) _____ (c) _____ (d) _____ (e) _____ (f) _____


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7. One complete rotation is 360E.

Find the angle size of:(a) two rotations (b) three rotations

(c) half of a rotation (d) quarter of a rotation

(e) one and a half rotations (f) two and a half rotations

(g) a third of one rotation

EXERCISE 2: Angles and Labels

1. Consider this angle.(a) Name the vertex of the angle.

(b) Name the angle in three ways.

2. Name each of these angles in three ways.

3. Name three different angles inthis diagram.


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4. Draw diagrams to show:

(a) pRST

(b) pFPD

(c) pAKL and pLKR on the same diagram.

(d) p WTG and pGTX on the same diagram.

5. Measure each of these angles.

(a) pAFC

(b) pEFA

(c) p DFB

(d) p CFB

6. There are 6 acute angles in this diagram.Name each of them.


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Exercise 3: Parallel and Perpendicular Lines

1. State whether these sketches show parallel lines, perpendicular lines or neither.

2. True or False?(a) All horizontal lines are parallel to each other.

(b) All vertical lines are perpendicular to one another.

(c) All vertical lines are perpendicular to all horizontal lines.

(d) To any given line there are an infinite number of parallel lines.

3. This map shows a part of a city suburb. Use the map to answer the followingquestions.

(a) Name all the streets or roadsparallel to the MorseHighway.

(b) How many streets or roads areparallel to Carter St?

(c) Name all of the streets or roadsperpendicular to Saddle St.

(d) Name two pairs of parallelstreets or roads which are nextto Kell Park.

(e) Which streets or roads are parallel to no others?

(f) Name three pairs streets or roads that do not intersect but appear to beperpendicular.


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EXERCISE 4: Types of Angles

1. Match each angle type with its correct definition.

I Right angle A exactly 180EII Straight Angle B more than 180EIII Acute Angle C between 90E and 180EIV Obtuse Angle D less than 90EV Reflex Angle E exactly 90E

2. Label each of these angle sizes as either acute, right, obtuse, straight orreflex.

(a) 124E (b) 90E

(c) 32E (d) 190E

(e) 145E (f) 180E

(g) 56E (h) 230E

(i) 95E (j) 8E

3. What type are each of the angles marked with a dot below?

A = ____________, B = ____________, C = ____________, D = ____________,

E = ____________, F = ____________, G = ____________, H = ____________,

I = ____________, J = ____________, K = ____________.


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4. The following abbreviations are used in this question:

A: Acute angle R: Right angle O: Obtuse angleS: Straight angle RF: Reflex >: greater than <: less than

Write whether each of the following statements are Always True, Possibly True orNever True.

(a) A + A = R (b) O + A = RF

(c) R + R = S (d) R + A = S

(e) R + A = O (f) R + A < S

(g) A + A = S (h) A + A < R

(i) O + R = RF (j) R + O > S

EXERCISE 5: Angle Relationships

1. For each diagram state which relationship/s on this list is shown:

C: Complementary angles S: Supplementary anglesA: Adjacent angles O: Opposite anglesE: Equal size (congruent)

(a) _____, (b) _____, (c) _____, (d) _____, (e) _____, (f) _____, (g) _____, (h) _____


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2. Label these pairs of angles as either:

C: Complementary angles S: Supplementary angles or N: Neither

(a) 40E, 50E (b) 56E, 134E

(c) 35E, 65E (d) 125E, 55E

(e) 110E, 70 (f) 90E, 0E

(g) 38E, 52E (h) 7E, 173E

3. Find the supplement of:

(a) 70E (b) 123E

(c) 22E (d) 90E

4. Find the complement of:(a) 20E (b) 67E

(c) 8E (d) 45E

5. Name pairs of adjacent angles from these diagrams.

(a) one pair (b) two pairs

______ & ______ _____ & _____, _____ & _____

(c) four pairs

_____ & _____, _____ & _____

_____ & _____, _____ & _____


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6. Name the two pairs of vertically opposite angles in each of the following.

(a) (b)

_____ & _____, _____ & _____ _____ & _____, _____ & _____

7. Find the value of the variable/s in each diagram.

a = _____ b = _____ c = _____ d = _____ e = _____

f = _____ g = _____ h = _____ i = _____ j = _____

k = _____ l = _____ m = _____ n = _____


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8. Find the complement and supplement of

(a) 34.5E Complement = ___________ Supplement = __________

(b) 4.8E Complement = ___________ Supplement = __________

9. Which of these are possible?(a) Adjacent angles can be supplementary.

(b) Opposite angles can be complementary.

(c) Adjacent angles can be opposite.

(d) Supplementary angles can be opposite.

(e) complementary angles can be adjacent.

10. Use your knowledge of anglerelationships, and the fact thatangles in a triangle sum to 180E tofind the value of each of the variablesin this diagram.

a = _____ b = _____ c = _____ d = _____ e = _____

f = _____ g = _____ h = _____ i = _____ j = _____


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Exercise 6: Bearings

1. This diagram shows some of the eight majorcompass points and bearings.

Complete the diagram by writing the directionand bearing at each arrow head.

2. What bearings do these diagrams show?

(a) _____, (b) _____, (c) _____, (d) _____, (e) _____, (f) _____, (g) _____, (h) _____

3. Draw sketches like those above to illustrate the bearings below. There is no needto use a protractor here, just estimate and sketch.(a) 075E (b) 150E

(c) 260E (d) 325E

(e) 020E (f) 310E

(g) 115E (h) 195E


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4. Question 1 shows the eight major compass points and their bearings. Whichcompass direction are these bearings closest to?(a) 200E (b) 100E (c) 300E

(d) 140E (e) 040E (f) 320E

(g) 015E (h) 230E

5. Use a protractor to find the bearing of each of these directions. To do this youmust draw a north line on each.

(a) ______, (b) ______, (c) ______, (d) ______, (e) ______.

6. For each of the following, find the bearing from:(i) A to B (ii) B to A

(a)(i) ____, (ii) ____ (b)(i) ____, (ii) ____ (c)(i) ____, (ii) ____

Your pairs of answers for the three parts above should each have a difference of 180E. These are called opposite bearings.


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7. Find the opposite bearing for:

(a) 200E (b) 085E

(c) 340E (d) 157E

8. Complete this table for points X and Y.

Bearing X to Y 060E 195E 180E 276E 025.5E

Bearing Y to X 222E 350E 005E

Puzzle A:

Why did the acute angle not trust the

obtuse angle?

In the diagram on the next page, draw angles of thegiven size in the direction indicated from each of thelines. Make sure that the angle is at the end with themeasurement. The line you will draw will give you aletter to match with the angle measurement in thecode below. Where the line crosses more than oneletter, select the first it crosses.

30E 40E 90E 65E 115E 5E 130E 80E 70E 40E 22E 5E 50E

115E 80E 170E 65E 110E 50E 30E 80E 90E 110E 80E 30E 30E 22E 160E


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Puzzle B:

Australian swimming greats

Draw bearings in the diagram at the bottom of the page todecode these names of five famous Australian Swimmers.

1960's155E 295E 110E 110E 320E 140E 110E 080E 260E 230E

1970's260E 205E 320E 175E 230E 035E 080E 295E 250E 005E

1980's280E 110E 320E 055E 230E 140E 310E 125E 055E 095E 205E 320E 155E

1990's260E 295E 260E 125E 230E 080E 175E 230E 125E 250E 250E

2000's125E 320E 175E 280E 205E 080E 110E 025E 230E


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Application A:

Clock Angles

This clock shows a time of 3 pm. The smallest angle between thehands of the clock at this time is 90E (a quarter of a full circle).

Task 1: What is the smallest angle between the hands at 1 p.m. 2 p.m?

Check your answers before continuing.(At 1 p.m. = 30E, at 2 p.m. = 60E)

Task 2: Complete this table for the smallest angle between the hands of a clock.

Time 0.54 0.58 0.63 0.67 0.71 0.75 0.79 0.83 0.88 0.92 0.96 12midnight

Angle 30E 60E

Task 3: Will these angles be the same for a.m. times?

Task 4: Through what angle will the minute hand move over a period of:

(a) one hour? (b) half an hour?

(c) quarter of an hour? (d) 10 minutes?

(e) 20 minutes (f) 40 minutes?

(g) 45 minutes? (h) 25 minutes?

Task 5: Through what angle will the hour hand move over a period of:

(a) one hour? (b) half an hour?

(c) quarter of an hour? (d) 4 hours?

(e) 12 hours?


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What is the angle between the hands of a clock at 3:30 p.m?

This angle is less than 90E (between the 3 and the 6) but more than60E (between the 4 and the 6).

The angle we require is half way (because it is half past) betweenthese values, i.e. 75E.

Task 6: Find the size of the angle between the hands of a clock at:

(a) 1:30 pm (b) 2:30 am

(c) 5:30 pm (d) 8:30 am

(e) 9:30 pm (f) 11:30 am

For other times you will need to consider the angle the hour handis moving during different parts of an hour. (Refer back to Task 5.)

For example: At 1:15 pm the angle is 60E (between 1 and 3)subtract 7.5E (a quarter of the 30E between 1 and 2) which givesthe required angle of 52.5E.

Task 7: Find the smallest angle between the hands of aclock at:

(a) 12:15 pm (b) 3:15 am(c) 5:15 pm (d) 8:15 am(e) 10:15 pm (f) 11:15 am

Task 8: Use the same idea to work out the angle at:

(a) 2:45 am (b) 4:45 pm(c) 6:45 am (d) 8:45 pm(e) 9:45 am (f) 11:45 pm

Task 9: Find the angle between the hands of a clock at:

(a) 4:10 pm (b) 10:20 am(c) 8:50 pm (d) 12:40 am


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Application B: Materials required: Ruler, compass bearings gauge, blank A4 paper

Mapping

Task 1: Draw accurate diagrams to show each of these situations.

(a) A hiker walks north for 4 km and then 5 km on a bearing of 070E.(Use 1 cm = 1 km for your scale)

(b) A ship leaves port on a bearing of 165E, travels for 60 km, andthen travels 45 km on a bearing of 115E.(Use 1 cm = 10 km for your scale)

(c) A plane, searching for a lost ship, travels 80 km to the search zoneat a bearing of 045E and then begins its search with 20 km sweepson bearings of 090E, 280E, 080E, 290E and 070E.(Choose a scale of your own)

Task 2: Give a description, similar to those above, to match each of thesesituations.


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This map shows Lindeman Island off the coast of Queensland.

Task 3: Using the North point on the map as a reference, find the bearings from:(a) Boat Port to Gap Beach(b) Gap Beach to Boat Port(c) Picaninny Point to Mt Oldfield(d) Billy Goat Point to Coconut Beach(e) Gap Beach to East Point

Task 4: Using a scale of 1cm:400m find out the direct distance from:(a) Mt Oldfield to East Point(b) Tourist Resort to Thumb Point(c) Picaninny Point to Coconut Beach

Task 5: Estimate the length and width of Lindeman Island and Little LindemanIsland.


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Task 6: Use the three maps that follow to find approximate bearings (to thenearest 10E) between the cities of:

(a) Melbourne and Brisbane(b) Derby and Adelaide(c) Auckland and Christchurch(d) Gisborne and Invercargill(e) New York and Los Angeles(f) Miami and Chicago


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Application C:

Newspaper Search: Housing Design

Look at the house plan shown here. Theinternal walls usually meet at right anglesbut in some places there are obtuse anglesand acute angles.

Task 1:

1. Highlight ten right angles in thisplan.

2. Highlight in a different colour, fourobtuse angles.

3. Highlight in a different colour, twoacute angles.

Task 2:

4. What units would the measurements on this house plan be?

5. What is the length and width of the study?

6. What is the area of the games room?

Task 3: Collect a house plan from a newspaper. On the plan highlight rightangles, obtuse angles and acute angles in different colours using alegend to explain the colour system.


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Task 4: The pictures that follow show a series of real, three dimensional objectsrepresented in a two dimensional picture. When this happens rightangles often appear to be a different size. For each picture, highlight anintersection which would be a right angle on the real object.

Task 5: Collect five cuttings from newspapers or magazines of objects where rightangles appear to be a different size. Highlight a right angle on each.


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Application D:

Project: World Bearings

Task 1: Photocopy or accurately trace a map from an atlas showing at least tencities or towns on the map. (Try to use a map about A4 size.)

Task 2: Find a way to identify North on the map and draw a North point on themap to clearly show this direction.

Task 3: Mark one city as the base.

Task 4: Give the bearings from the base city of 5 other cities on the map.

Task 5: Starting from the base city write down in the table below a journey via 4other cities and back to the base city.

Task 6: For each stage of the journey in Task 5 give the bearing to get from city tocity.

City Bearing

Start: Base Base to 1.

1 1 to 2.

2 2 to 3.

3 3 to 4.

4 4 to Base.

End: Base


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Student Reflection

What have I learned in this module?

What new words did I learn during this module?

Look at the outcomes at the start of the module (page 3). Have I progressed on each ofthese outcomes?

What do I need to improve on?

Write about one thing in this module I found interesting.

What do I think was the most important concept in this module?

Where could the maths in this module be used in our society?

One area I would like to look more at is:

Write something about how the bits in this module connect to each other.

Write something about how the bits in this module connect to other modules.


44 [SIMM] Angle 1

ANSWERS TO EXERCISES:

Exercise 1:1. (a) 31E (b) 44E (c) 78E (d) 63E2. (a) 90E (b) 125E (c) 105E (d) 166E4. (a) 40E (b) 140E (c) 90E (d) 80E (e) 160E (f) 30E5. W, T, Y, S, U, X, V, Z6. (a) P (b) Q (c) Q (d) P (e) P (f) P7. (a) 720E (b) 1080E (c) 180E (d) 90E (e) 540E (f) 900E (g) 120EExercise 2: 1. (a) C (b) pGCR, pRCG, pC2. (a) pB, pTBL, pLBT (b) pM, pWMP, pPMW3. pVXW, pVXY, pWXY5. (a) 101E (b) 92E (c) 155E (d) 65E6. pLNM, pLNP, pLNQ, pMNP, pMNQ, pPNQExercise 3:1. (a) neither (b) perpendicular (c) parallel (d) perpendicular (e) neither (f) parallel (g) perpendicular2. (a) true (b) false (c) true (d) true3. (a) Saddle St, Hallam Rd, Troy Rd (b) 4 (c) Carter St, Law St, Yale Rd, West St, Short St (d) Yale Rd & West St, Troy Rd & Saddle St (e) Port Rd, Angel St (f) choose from: Hallam Rd & Yale Rd, Short St & Troy Rd, Short St & Hallam Rd, Morse Hwy & Law St, Morse Hwy & West StExercise 4:1. I: E, II: A, III: D, IV: C, V: B2. (a) obtuse (b) right (c) acute (d) reflex (e) obtuse (f) straight (g) acute (h) reflex (i) obtuse (j) acute3. A: right B: acute C: acute D: obtuse E: acute F: straight G: obtuse H: right I: acute J: obtuse K: reflex4. (a) possibly (b) possibly (c) always (d) never (e) always (f) always (g) never (h) possibly (i) always (j) alwaysExercise 5:1. (a) A (b) A, S (c) O, E (d) A, C (e) A, S, E (f) O, E, S (g) A (h) C2. (a) C (b) N (c) N (d) S (e) S (f) C (g) C (h) S3. (a) 110E (b) 57E (c) 158E (d) 90E4. (a) 70E (b) 23E (c) 82E (d) 45E5. (a) pTRS & pSRP (b) pEBD & pDBC, pDBC & pCBA (c) pWYU & pUYZ, pUYZ & pZYX, pZYX & pXYW, pXYW & pWYU6. (a) pMNP & pLNQ, pMNL & pPNQ (b) pHJK & pGJL, pHJG & pKJL7. a = 63E b = 26E c = 70E d = 104E e = 75E f = 32E g = 70E h = 135E i = 85E j = 95E k = 85E l = 122E m = 58E n = 122E8. (a) 55.5E, 145.5E (b) 85.2E, 175.2E9. (a) Yes (b) Yes (c) No (d) Yes (e) Yes10. a = 22E b = 158E c = 74E d = 74E e = 106E f = 84E g = 48E h = 132E i = 48E j = 132EExercise 6:1. The missing entries (from North): 000E, NE, 135E/SE, 180E/S, 270E/W, 315E/NW2. (a) 120E (b) 050E (c) 215E (d) 145E (e) 315E (f)250E (g) 080E (h) 330E4. (a) S (b) E (c) NW (d) SE (e) NE (f) NW (g) N (h) SW5. (a) 076E (b) 158E (c) 255E (d) 187E (e) 308E6. (a)(i) 090E (ii) 270E (b)(i) 065E (ii) 245E (c)(i) 135E (ii) 315E7. (a) 020E (b) 265E (c) 160E (d) 337E8. Missing entries from left to right: 240E, 015E, 042E, 170E, 000E, 096E, 185E, 205.5E


students’ integrated maths module for angle 1 · activities: 4: types of angles 25 a: roofs and...

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