SERIES Geometry - Geometry - ... The

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  • Student BookSERIES

    GN

    ame

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    Geometry

    Teacher BookSERIES

    G

    Geometry

  • Copyright

    Contents

    Topic 1 Lines and angles (pp. 16) lines ________________________________________________

    classifying angles ______________________________________

    measuring angles ______________________________________

    hand it over apply ____________________________________

    itsallinthetiminginvestigate __________________________

    Topic 2 2D shapes (pp. 715) polygons _____________________________________________

    quadrilaterals _________________________________________

    triangles _____________________________________________

    circles _______________________________________________

    the shapes within apply _______________________________

    rip it up investigate ___________________________________

    Topic3Transformation,tessellationandsymmetry(pp.1624) line symmetry ________________________________________

    rotationalsymmetry ___________________________________

    transformation ________________________________________

    tessellation ___________________________________________

    enlargementandreduction ______________________________

    picture perfect create _________________________________

    design diva create ____________________________________

    Topic43Dshapes(pp.2532) typesandproperties ___________________________________

    nets ________________________________________________

    drawing 3D shapes _____________________________________

    to cube or not to cube investigate _____________________

    form an orderly queue apply ___________________________

    Date completed

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    Series G Geometry

    Series Authors:

    Rachel Flenley

    Nicola Herringer

    Copyright

    Series G Geometry

    Series Authors:

    Rachel Flenley

    Nicola Herringer

    Contents

    Section1Answers(pp.132) lines and angles _____________________________________ 1

    2D shapes __________________________________________ 7

    transformation,tessellationandsymmetry _______________ 16

    3D shapes __________________________________________ 25

    Section2Assessmentwithanswers(pp.3350) lines and angles _____________________________________ 33

    2D shapes __________________________________________ 37

    transformation,tessellationandsymmetry _______________ 41

    3D shapes __________________________________________ 47

    Section3Outcomes(pp.5153)

  • SERIES TOPIC

    1G 1Copyright 3P Learning

    Geometry

    1 Begin with a circular piece of paper.

    4 FoldBuptoD,youvenowcreated point E.

    7 Cut along fold lines EF and DG,onlytotheintersection.

    2 Fold the circle in half.

    5 Draw a perpendicular line from line CD to point E. Fold to create FE.

    3 FoldAtomeetB.

    6 Draw a perpendicular line from line CE to point D. Fold to create DG.

    This paper folding activity relies on a thorough understanding of the terms in the box above. Try your hand at it! You will need a thin circular piece of paper with a radius of at least 8 cm.

    These terms are commonly used when we work with lines and angles:paralleltheselinesarealwaysthesamedistanceapartateverypoint,theynevermeet perpendicular these lines intersect at right angles diagonal these are lines within a shape that join a vertex (corner) to another vertexintersectiontheplacewhere2ormorelinescrossovereachother

    Lines and angles lines

    1

    A B

    A BC

    C

    D

    E

    C

    D

    E

    C

    D

    E

    F

    F

    A B

    C

    C

    B

    D

    D

    E

    G

    D

    EF

    C

    D

    E

    C

    D

    EG

    G

    F

    C

    D

    EF

    8 Opentheshape.Whathaveyoumade? A flower.

  • SERIES TOPIC

    G 12Copyright 3P Learning

    Geometry

    a

    angle

    d

    angle

    b

    angle

    e

    angle

    c

    angle

    f

    angle

    Anangleistheamountofturnbetweentheintersectionoftwo rays (lines).

    Anglesareconventionallymeasuredindegreeson aprotractor.360isafullturn,180isahalfturn, and90isaquarterturn.

    Haveyouheardsomeonesay,Hedidacomplete180onthat.?Whatdoyouthinktheymeant?Whatdoes,Shedidafull360mean?

    Complete the table and use the information to help you to classify the angles below. Use a maths dictionary to help you work out any unknown terms.

    Lines and angles classifying angles

    vertexangle

    90

    270

    180360 0

    1

    2

    right angles are _____

    acute angles are _____________ than90

    obtuse angles are __________ than90andless than _____

    straight angles are exactly _____

    reflexanglesare greater than 180andlessthan _____

    revolutionangles are exactly _____

    Make sure you check which angle youre meant to be measuring! The little arc tells you here.

    Look at the interior angles in this shape. Mark any acute angles with a red arc; obtuse angles with a blue arc; reflex angles with a green arc; and right angles with an orange :

    acute

    90

    180180

    360360

    moreless

    right

    obtusereflex

    obtuse

    reflex

    G R

    R

    RB

    O G

  • SERIES TOPIC

    3G 1Copyright 3P Learning

    Geometry

    a b c

    Weuseprotractorstomeasureangles.

    1 Alignthebaselineontheprotractorwithoneofthe lines.

    2 Line up the vertex of the angle with the centre point of the protractor.

    3 Measurethedistancebetweenthetwolines,startingatthe0andcountinground.

    Lines and angles measuring angles

    List 5 sports or jobs where you think it would be important to consider angles. David Beckham can probably think of at least one.

    a ______________________ b ______________________ c ______________________

    d ______________________ e ______________________

    Measure the interior angles of this shape. Write the measurements next to each angle. The first one has been done for you.

    Use your protractor to measure these angles. Write the measurements next to the angles.

    baseline centre point

    This is an angle of50

    50

    0

    1

    3

    2

    _____

    __________

    25

    55

    150

    315

    60

    90

    70

    160

    90

    soccer player diver cricket

    builder architect

    Answers will vary and may include:

  • SERIES TOPIC

    G 14Copyright 3P Learning

    Geometry

    Make a time that shows an angle between the two hands of:

    Look at the clock.

    a Whatdoeseach5minutemarkerrepresentindegrees?____________

    b Whatabouteachminute?____________

    Lines and angles measuring angles

    Work with a partner on this activity. Take turns predicting where you think the missing ray of the angle should go. Starting at the dot, rule your predictions then measure with a protractor. Mark in the actual angle. Who was closer? Do you get more accurate with practice? Invent more of these on another piece of paper if you have time.

    a 45 b 60 c 270 d 135

    a b

    d

    c

    e

    4

    5

    6

    30 90

    24

    150

    120

    Decide where your first hand will go, then count round to create the angle.

    30

    6

    Answers will vary.

  • SERIES TOPIC

    5G 1Copyright 3P Learning

    Geometry

    What to do Spread your hand out in the box below and trace around

    it.Estimatethenmeasuretheanglesformedbetweeneachfinger.Themeasurementswillbeapproximateonly.

    Compareyourmeasurementswiththoseofapartner.Aretheysimilar?

    Hand it over apply

    Lookatthepictureofthehand.Whatwellknownanglewould you say is approximately formed by the thumb andforefinger?

    Getting ready

    Answers will vary.

  • SERIES TOPIC

    G 16Copyright 3P Learning

    Geometry

    Its all in the timing investigate

    What to do Howmanytimesdothehandsonaclockformarightanglewithina12-hourperiod?

    Showthetimesontheclocksasyoufindthem.

    Ifyoufind10ormore,youvemadeagreatstart.15ormore,youredoingverywell.Morethan20,youreindeedaTimeLordandpeopleshouldbowasyoupassby.

    Wehavegivenyouthefirstonetogetyoustarted.

    Youcanworkwithapartneronthisactivity.Youmayliketouseaclockwithmovablehands or to use copies of the clock faces below.

    12:16

    Getting ready

    2:27

    4:39

    6:49

    3:00

    12:49

    5:11

    7:22

    3:33

    1:22

    5:44

    7:54

    4:05

    1:54

    6:16

    8:27

    There are 22 times. Answers will vary and may include:

  • SERIES TOPIC

    7GCopyright 3P Learning

    Geometry 2

    2D shapes polygons

    Its time for a polygon pop quiz. Read through the questions and answer any you know. Now for