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Teacher Book SERIES F Geometry

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Page 1: SERIES Geometry - Grade 5 ASW - UNIT 1 Decimalsgrade5asw.weebly.com/uploads/2/2/4/1/22418994/... · Lines and angles – measuring angles Use a protractor to complete these angles

Student BookSERIES

FN

ame

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____

____

____

____

____

____

____

____

_

Geometry

Teacher BookSERIES

F

Geometry

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Copyright ©

Contents

Topic 1 – Lines and angles (pp. 1–6)• lines ________________________________________________

• introducing angles _____________________________________

• measuring angles ______________________________________

• timepasses–investigate ________________________________

Topic 2 – 2D shapes (pp. 7–15)• polygons _____________________________________________

• quadrilaterals _________________________________________

• triangles _____________________________________________

• circles _______________________________________________

• circle sense – apply ____________________________________

• how many triangles? – investigate ________________________

Topic3–Transformation,tessellationandsymmetry(pp.16–24)• symmetry ____________________________________________

• transformation ________________________________________

• tessellation ___________________________________________

• tessellate and create – create ____________________________

• digit,DrJones–create _________________________________

Topic4–3Dshapes(pp.25–34)• introduction __________________________________________

• polyhedrons __________________________________________

• spheres,conesandcylinders _____________________________

• drawing 3D shapes _____________________________________

• nets ________________________________________________

• 2 halves make a whole … – apply _________________________

• tomb raider – investigate _______________________________

Date completed

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Series F – Geometry

Series Authors:

Rachel Flenley

Nicola Herringer

Copyright ©

Series F – Geometry

Series Authors:

Rachel Flenley

Nicola Herringer

Contents

Section1–Answers(pp.1–34)• lines and angles _____________________________________ 1

• 2D shapes __________________________________________ 7

• transformation,tessellationandsymmetry _______________ 16

• 3D shapes __________________________________________ 25

Section2–Assessmentwithanswers(pp.35–48)• lines and angles _____________________________________ 35

• 2D shapes __________________________________________ 37

• transformation,tessellationandsymmetry _______________ 41

• 3D shapes __________________________________________ 45

Section3–Objectives(p.49)

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SERIES TOPIC

1F 1Copyright © 3P Learning

Geometry

See if you understand these terms by completing this quick test. Draw:

Follow the instructions and fill in the missing information:

a Look at the horizontal line in the box below. Horizontal lines lie flatstandingup(tickonebox).WecallthelineABasitstartsatAandendsatB.

b Draw a 5 cm verticallineupfrompointA.WhatkindofangleisformedbythetwolinesatA? ______________

c Whentwolinesmeetinsuchanangle,wesaythatthey’reperpendicular to eachother.Drawanother5cmlineupfromB.IsthislineperpendiculartolineABaswell? ______________

d NowlookatlinesACandBD.Aretheyperpendicularorparalleltoeachother? ______________

e Ifyousaidparallel,you’dberight.Parallellinesarealwaysthesamedistanceawayfromeachotherat any point and can never meet.

f DrawalinethatisparalleltolineABbyjoiningCD.

g Curves can also be parallel. Draw 2 parallel curves in the shape.

Whenweclassifylinesweusetermssuchasparallel,perpendicular,verticalandhorizontal.Knowing these terms makes it easier for us to understand and work with shapes.

Lines and angles – lines

1

2

A B

C D

a 2 parallel lines b 2 lines perpendicular to each other

c a horizontal line d averticalline

right angle

yes

parallel

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SERIES TOPIC

F 12Copyright © 3P Learning

Geometry

A circle is a full turn and is 360°. Think of it as a clock – from 12:00 round to 12:00. Copy this page and then cut out the circle below and try the following:

a Fold the circle in half. How many degrees are in a half circle? ___________________

b Fold it in half again. You now have a quarter circle. How many degrees are in a quarter of a circle? ___________________

c Fold it in half once more. You have an eighth of a circle. How many degreesare in one eighth of a circle? ___________________

What is an angle?Look at where these two lines meet. The angle is the amount of space betweenwheretheyjoin.It’salsotheamountofturnbetweenthem.

Ifweimaginethatthesetwolinesarejoinedattheirmeetingpoint,wecouldrotatethelinesaroundthispoint.They’llstayjoinedbut the amount of turn will change.

We measure angles using degrees – the symbol for this is °. We use a protractor as our measuring tool.

Lines and angles – lines

3

FOLDFOLD

FOLD

FOLD

FOLD

FOLD

FOLD

FOLD

copy

180o

90o

45o

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SERIES TOPIC

3F 1Copyright © 3P Learning

Geometry

Draw the other line to create an angle that is:

Wally the work experience boy made some mistakes labelling these angles. Correct any mistakes you see.

Label each of these angles as right, acute or obtuse:

Lines and angles – introducing angles

Whenanangleislessthanaquarterturnof90°wesayit’sacute.Whenit’sexactly90°wesayit’saright angle. Whenit’sbetween90°and180°wesayit’sobtuse.Whenit’sexactly180°wesayit’sastraight angle.Whenit’smorethan180°wesayit’sareflex angle.

We use an arc toshowwherewe’remeasuring.

Withrightangles,weuseasquaresymbollikethis .

90°

270°

180° 360°0°

1

a

angle

d

angle

b

angle

e

angle

c

angle

f

angle

a

angle

b

angle

c

angle

d

angle

2

3

obtuse straight reflex acute

a

acute

b

right

c

obtuse

Remember to mark your angles with or !

acute

obtuse

right

acute

obtuse

acute

reflex acute obtuse

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SERIES TOPIC

F 14Copyright © 3P Learning

Geometry

Use a protractor to measure all of these marked angles. Write the answers in the angles:

Sometimesweneedtobemoreprecisewhennamingangles,insteadofjustusingtermssuchasacuteorobtuse. This is where a protractor comes in handy. To measure an angle using a protractor we:lfitthebaselineoftheprotractortoonelineoftheangle,liningupthecentrepointof the protractor with the vertex of the angle

l look where the other line intersects the numbers,makingsurewereadroundfrom0°.

Lines and angles – measuring angles

baseline centre point

This is an angle of50°

50°

1

____°

____°

____°

____°

____°

____°

____°

____°

____°

___°

____° ____°

____°

____°

____°

____°

____°

____°

____°

225o

80

100

120

120

120 120

105

70

75

90

90

90

90

115

130

120

120

100

80

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SERIES TOPIC

5F 1Copyright © 3P Learning

Geometry

Can you think of a way to measure the exterior angles of these 2 figures? Maybe a full (360°) protractor would help or is there another way to calculate that outside angle without actually measuring it? What else could you measure?

Lines and angles – measuring angles

Use a protractor to complete these angles. One line is drawn for you. You need to measure and draw the other line. Draw it about the same length as the other line. Mark the angles with the measurements.

2

3

a

45°

d

110°

b

60°

e

10°

c

90°

______°

______°

Line the middle of your protractor up with the dot at the end of the line.

When we talk about measuring angles we usually mean the interior angle. We can also measure the exterior angle – the one on the outside.

How many degrees in a full turn? How could this help me?

35°

325

270

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SERIES TOPIC

F 16Copyright © 3P Learning

Geometry

What to do next

What to do

Iftheminutehandmoves180°,howmanydegreeshasthehourhand‘passed’?

Usetheclockstocalculatehowmanydegreeshave‘passed’betweentheminutehands:

a

b

c

Time passes investigate

Nowconsiderthehourhands–howmanydegreeshave‘passed’betweenthe 2 hour hands?

a

b

________°

________°

________°

________°

________°

Getting ready Inthisactivityyouwillmeasurethepassingoftimenot

inminutesandhours,butindegrees.

You can work with a partner and you may like to use a clockface with movable hands to help you work out the answers.

How many degrees are there in an hour? How many degrees are there in 5 minutes?

60

120

180

60

330

15o

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SERIES TOPIC

7FCopyright © 3P Learning

Geometry 2

Look at these polygons. Are they regular or irregular? Label them. You may use a ruler and a protractor to help you make your decision.

Use the rules and examples in the box above to decide if the following shapes are polygons. Circle the polygons:

2D shapes – polygons

Apolygonisa2D(flat)shapewith3ormorestraightsides.ThewordcomesfromtheGreekwords,poly and gonia,meaningmanyangles.Allpolygonsareclosed–theyhavenobreakintheirboundaries.Theyhavenocurvedsides.

These are polygons. These are not polygons.

1

2

Polygonscanberegularorirregular.Regular polygons have all sides of equal length and all angles of equal size. Irregularpolygonshavesidesofunequallengthandanglesofunequalsize.Sometimeswecanthinkirregularshapesarenot‘proper’astheylookdifferenttothemorecommonones. These shapes are both hexagons because they both have six sides – but one is regular and one is irregular .

a _____________

b __________

c _____________

d __________

f _____________e __________

Do any of your answers surprise you? Why do you think this is?

regular

regular irregular

irregular

irregular

regular

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SERIES TOPIC

F8Copyright © 3P Learning

Geometry2

What have you called the 4 sided shape? Compare your answer with those of 3 others. Do they agree with you? Why might there be differences?

2D shapes – polygons

Polygons are classified and named differently depending upon their sides and angles. Label and draw at least one example of each of the following. Remember they don’t have to be regular. Research the names of any you don’t know:

a 3 angles and 3 sides _________________ b 4anglesand4sides _________________

c 5 angles and 5 sides _________________ d 6 angles and 6 sides _________________

e 7 angles and 7 sides _________________ f 8anglesand8sides _________________

g 9anglesand9sides _________________ h 10anglesand10sides ________________

i 11 angles and 11 sides _________________ j 12 angles and 12 sides ________________

4

3

triangle quadrilateral

hexagonpentagon

octagonheptagon

decagonnonagon

dodecagonhendecagon

Answers will vary and may include: square, rectangle, quadrilateral, rhombus, kite and arrowhead.

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SERIES TOPIC

9FCopyright © 3P Learning

Geometry 2

Use the information above and the dot paper below to create a square, a rectangle, a rhombus and a trapezium. Check them against the criteria. Do they match? Swap with a partner and label each other’s shapes.

Aquadrilateralisakindofpolygon.It’saclosed,flatshapewith4straightsidesand4angles. ThenamecomesfromtheLatin,quad and latus,meaning4sides.Oneofthethingsthatcanbeconfusingaboutquadrilateralsisthatthereareanumberofclassifications,andshapescanbecalleddifferentnames.Thisishowtheyallfittogether:

SoasquareisakindofrhombusANDarectangleANDaparallelogramANDaquadrilateralAND apolygon.It’skindoflikeaGardener’sDelightisacherrytomatoANDatomatoANDafruitAND isconsideredavegetableANDisafood.

2D shapes – quadrilaterals

quadrilateral4sidesand4angles

polygonclosed shape with straight sides

squareall angles are right angles

all sides are equal

trapeziumhas 1 pair of parallel sides

parallelogramhas 2 pairs of parallel sides

irregularhas no parallel sides

kiterectangleall angles are right angles

opposite sides are equal and parallel

rhombusall sides are equal

opposite sides are parallel opposite angles are equal

arrowhead

1

square

trapezium

rhombus

rectangle

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SERIES TOPIC

F10Copyright © 3P Learning

Geometry2

2D shapes – quadrilaterals

Use the information below to draw the following quadrilaterals. Check your drawings with other pupils. Do they agree with you? Is it possible your drawings may be different and still correct? Why?

As well as always having 4 sides, quadrilaterals have one other feature in common. Use a protractor to carefully measure the angles of these quadrilaterals. Add the 4 angles of each shape together. What do you find?

a The angles of a quadrilateral always add to __________________________.

b Find4morequadrilateralsaroundtheroomandtestoutthetheory.

a Ihave4sidesofequallength.Ihave4equalangles.They’reallrightangles. Ifyoudrawmydiagonals,thelinesform right angles where they intersect.

I’ma_________________________________

b SometimesI’mcalledanoblong.Ihave4sides. My opposite sides are equal. Ifyoudrawmydiagonals,theanglesoppositeeachotherattheintersectionareequal.

I’ma_________________________________

3

2

c Ihave2pairsofequalsides.My opposite sides are equal in length. My opposite angles are equal. Noneofmyanglesare90o.

I’ma_________________________________

d SometimesI’mknownasatrapezoid.Ihaveonepairofoppositeparallellines.

I’ma_________________________________

360 o

square

rhombus

rectangle

trapezium

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SERIES TOPIC

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Geometry 2

What do you notice about the relationship between the angles and the sides of a triangle? (This is always the case. They’re a consequence of each other.)

What do you notice? Complete the following statements:

a Isoscelestriangleshave_________equalangles.

b Equilateral triangles have _________ equal angles.

c Scalene triangles have _________ equal angles.

Now measure the lengths of the sides. Mark any lines that are the same length in a triangle with a little line. The first triangle has been marked for you in Question 1. What do you notice? Complete the following statements:

a Isoscelestriangleshave_________equalsides.

b Equilateral triangles have _________ equal sides.

c Scalene triangles have _________ equal sides.

Triangles are classified into the 3 different groups depending upon their angles. Below is an example of each group. Use a protractor to measure the angles of the triangles. Mark any angles that are the same in a triangle with an arc. The first triangle has been done for you.

2D shapes – triangles

Atriangleisatypeofpolygon.Ithasthreesidesandthreeangles.Thethreeinterioranglesalwaysaddto180°.Herearethe3maintypesoftriangles:

isosceles equilateral scalene

isosceles equilateral scalene

1

3

2

4

60o

85o

60o 35o60o 60o

2

2

3

3

0

0

The number of equal angles is the same as the number of equal sides.

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SERIES TOPIC

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Geometry2

Using a protractor to help you, draw an example of a right angled, equilateral, isosceles and scalene triangle below. Don’t label them or mark the angles or sides as equal. Switch papers with a partner and measure and label each other’s triangles. Switch back and check.

Measure the sides of both triangles to the nearest 12 cm and mark any equal sides.

a Basedonyourmeasurements,canrightangledtrianglesbeeitherisoscelesorscalene? ____________

b Can they be equilateral? Why or why not?

____________________________________________________________________________________

____________________________________________________________________________________

Thereisanothertypeoftriangleyouwillcomeacross.It’scalledtherightangledtriangle.Lookatthese examples. How many degrees are the marked angles? What symbol tells you this?

2D shapes – triangles

6

5

Since same sides equal same angles, I just have to make sure the sides are equal! The angles will follow.

Yes

No. Because in an equilateral triangle, each angle is always 60o.

Answers will vary.

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SERIES TOPIC

13FCopyright © 3P Learning

Geometry 2

2D shapes – circles

Acircleisalsoa2Dshape.It’saclosedcurvethathasallofitspointsafixeddistancefromthecentre. Lateron,youwilllearnabouttheformalmathsofcircles–they’remorecomplexthantheylook!Rightnow,it’simportanttorecognisethedifferentpartsandtoexploretherelationshipsbetweenthe parts.

centre – this is the point in the middle

radius – the distance from thecentretothecircle’sedge

diameter – the distance from the edge of a circle through the middle to the opposite edge

circumference – the distance around the circle

arc – part of the circumference

sector–a‘slice’ofthecircle

Below are some circles. Each radius is marked.

a Extend the radius through the midpoint to the opposite edge of each circle. You have now marked the diameters.

b The diameter of each circle is twice its radius. Write the diameter of each circle in the boxes above.

1

diameter diameter diameter

2 cm1 cm

112 cm

4 cm 2 cm 3 cm

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SERIES TOPIC

F14Copyright © 3P Learning

Geometry2

What to do next

What to do Readthequestionsbelowandchoosethe10questionsyouthinkwillscoreyou

thehighestnumberofpoints.Onceyou’vedecidedonyourquestions,tickthem.They’renowlockedin.

Onceyouandyourpartnerhavebothfinished,askyourteacherorthedesignatedcheckertocheckyouranswers.AsGameMaster,theirdecisionisfinal.Whowon?

Circle sense apply

You’llplaythisgamewithapartner.You’lleachneedacopyofthispageanditmaypaytostudytheinformationonthepreviouspage.Theaimistoscorethehighestnumberofpointsyoucanbyanswering10questions.Theharderquestionsscoremorepointsbutofcourse,thereisagreaterriskofgettingthemwrong!

Playagainchoosingdifferentquestions.Youcanreuseaquestionifyougotitwrongbutnotifyouanswereditcorrectlythefirsttime.Ifyourunoutofquestions,designsome of your own.

What is the distance around a circle called? ................................................................... __________________

What is the name given to a small part of the distance around a circle? ....................... __________________

Name the distance from the centre of a circle to its edge. ............................................. __________________

What is the distance from the edge of a circle through the middle to the opposite edge called? ............................................................................................... __________________

What is the point in the middle of a circle called? .......................................................... __________________

What do we call a slice of a circle? ................................................................................. __________________

Namea3Dobjectthatiscircular. .................................................................................... __________________

FOR 5 POINTS

Istheradiusofacircletwiceitsdiameter? ..................................................................... __________________

Everypartofacircle’scircumferenceisanequaldistancefromitscentre. Isthisstatementcorrect? ................................................................................................ __________________

Namea3Dobjectthatwouldn’tworkifitwasn’tcircularandexplainwhy. ___________________________

Isacircleapolygon?Whyorwhynot? ________________________________________________________

Anothernameforthecircumferenceofacircleisitsperimeter.Isthisstatementcorrect? .. __________________

Acirclebelongstothequadrilateralfamily.Isthisstatementcorrect? .......................... __________________

Ifacirclehasadiameterof10cm,whatisitsradius? .................................................... __________________

Thecircumferenceofacircleistwiceitsradius.Isthisstatementcorrect? ................... __________________

Ifacirclehasaradiusof15cm,whatisitsdiameter? .................................................... __________________

FOR 10 POINTS

Getting ready

circumference

arc

radius

centre

diameter

sector

ball

No

Yes

Yes

No

5 cm

No

30 cm

No. A polygon has straight sides.

A ball wouldn’t roll.

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SERIES TOPIC

15FCopyright © 3P Learning

Geometry 2

What to do Recordyourfindingsinthetable.Doyouseeanypatterns?

Shape Number of sides Number of triangles Sum of angles

square

pentagon

hexagon

octagon

decagon

dodecagon

How many triangles? investigate

Usetheshapesbelow.Yourtaskistosectioneachshapeintotriangles. Your lines must go from corner (vertex) to corner and can’tcrossovereachother.

Getting ready

How can I work out the sum of all the angles? Well, I know that all triangles have an angle sum of 180˚ so I can add how many triangles I have …

4

5

6

8

10

12

2

3

4

6

8

10

360o

540o

720o

1 080o

1 440o

1 800o

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SERIES TOPIC

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Geometry3

Transformation, tessellation and symmetry – symmetry

What do you notice about lines of symmetry in regular polygons?

Find and mark any lines of symmetry on these regular polygons. These can be vertical, horizontal or diagonal. If it’s easier, cut out copies of the shapes and fold them to test them.

a Asquarehas_____linesofsymmetry. b Anequilateraltrianglehas_____linesofsymmetry.

c Anoctagonhas_____linesofsymmetry. d Ahexagonhas_____linesofsymmetry.

1

2

Reflectiveorlinesymmetrydescribesmirrorimage,whenonehalfofashapeorpicturematchesthe other exactly. The middle line that divides the two halves is called the line of symmetry.Shapes may have: more than no line of symmetry one line of symmetry one line of symmetry

4 3

68

A regular polygon has the same number of lines of symmetry as it has sides.

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SERIES TOPIC

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Geometry 3

Compare your list with that of another group. Do they agree? If there are any letters you disagree on, present your cases to each other and see if you can reach a consensus.

Transformation, tessellation and symmetry – symmetry

Look at these letters of the alphabet. Work with a partner to decide which ones have lines of symmetry when written in this font. Which ones have more than one? Which ones have none? Record them in the table below:

3

4

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Vertical line of symmetry

Horizontal line of symmetry

More than one line of symmetry

No lines of symmetry

A

H

I

M

O

T

U

V

W

X

Y

B

C

D

E

H

I

K

O

X

H

I

O

X

F

G

J

L

N

P

Q

R

S

Z

Answers will vary.

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Geometry3

Colour the other half of these pictures so that they’re symmetrical:

Using the vertical line as the line of symmetry, draw the mirror image in the top right square. Now reflect the picture on the other side of the horizontal line of symmetry.

Transformation, tessellation and symmetry – symmetry

These shapes are called pentominoes. Some have lines of symmetry. Draw them in. The first one has been done for you.

5

7

6

HINT: A small mirror on the line of symmetry will help.

We humans like symmetry.People who are considered beautiful usually have symmetrical faces.Top racehorses are very symmetrical too – this helps them run smoothly and fast!

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SERIES TOPIC

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Geometry 3

Transform these letters:

Look at this trapezium. Flip it in your head and then record what it looks like. Then turn it 180˚ clockwise (a half turn) in your head and record what it looks like now. Turn it another 90˚ clockwise (a quarter turn) and record.

What has been done to this tile? Describe each transformation as either a flip, slide or turn:

Transformation, tessellation and symmetry – transformation

Whenwemoveashape,wetransformit.Thistileshowsthreewayswecandothis:

Whenwe’reaskedtoflip,slideorturn,ithelpstovisualisethemoveinourheads.

reflect(flip)

translate(slide)

rotate(turn)

1

3

2

a

turn90°clockwise

d

flip

b

flip

e

flip

c

slide

f

turn180°

T

N

H

Q

J

W

slide slideturn turnflip flip

H

Q

T

N

J

W

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Geometry3

Rotate each shape and record the new position. Starting from the original position each time, rotate each shape by a quarter turn, half turn, three quarter and full turn and record each new position.

a

b

c

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

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� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

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� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

Thesearecommonrotations:

original quarter turn half turn three quarter turn full turn position 90˚ 180˚ 270˚ 360˚

Whatdoyounoticeaboutafullturn?

Transformation, tessellation and symmetry – transformation

4

5

Think of the name of a capital city somewhere in the world. Disguise its name by choosing to either flip, slide or turn each capital letter. Ask a partner to decode it. For example, PARIS could be disguised as .

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

Answers will vary.

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Use pattern blocks to find shape pairs that tessellate. Record them here. How many can you find? Here’s one to get you started:

b Whichofthe3regularpolygonstessellatedwithoutflippingorturning? __________________________

c Whichregularpolygonsdoyouneedtofliporturntogetthemtotessellate?

____________________________________________________________________________________

We bet you’ve been tessellating with pattern blocks since you were a little kid. Now we want you to work out which shapes tessellate and which don’t.

a Workwithapartnerandusepatternblockstofind3regularpolygonsthattessellateontheirown.Remember,aregularpolygonhassidesofequallength.Recordyourproofbelow:

TessellationcomesfromtheGreekword,tessere,whichmeanssquaretablet.Itmeanscoveringasurfacewithapatternof2Dshapeswithnogapsorspaces.Whenwetessellateashape,weoftenfliporturntheshapessothattheyfittogether.Someshapeswilltessellateontheirown.Wecallthisregulartessellation.Someshapestessellatewhenyouuse2shapesinthepattern.Wecallthissemi-regulartessellation.Tessellationiscloselylinkedwithart.Mosaics,patchworkandpavingusetessellation.Canyouthink of others?

Transformation, tessellation and symmetry – tessellation

1

2

square

triangle and hexagon

hexagons and triangles

squares and triangles

octagons and triangles

octagons and squares

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Tessellations usually involve creating a pattern and repeating it over and over. A famous mathematician named Roger Penrose was obsessed with finding a tessellation that was created without repeating any large patterns. It took him a while but he got there. It’s often called “Kites and Darts” as the two parallelograms in the pattern resemble these.Colour the pattern in colours of your choice on the right to recreate his discovery. While you’re doing that, check – can you see any large repeated patterns?

Transformation, tessellation and symmetry – tessellation

It’s said that all quadrilaterals tessellate. Is this true? Work with a partner to test this theory out. Use blocks or tessellation shapes such as those below. Record your findings below then tick the ones that tessellate once you know:

3

5

4 Do you agree with the statement that all quadrilaterals tessellate? Why or why not?

Answers will vary.

Yes– all will tessellate.

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What to do Recreateoneofthedesignsbelowbyrulingovercertainlines.Pickacolourscheme

and complete your design.

Tessellate and create create

Manyculturesandartstylesusetessellationsasabasisforcreatingintricateandbeautifulpatterns.Islamicartisonesuchartform.Lookattheexamplesbelow.

Getting ready

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What to do

Dig it, Dr Jones create

You have 14 oftheplate.Youneedtofindawaytorecreatetherestofit.Howwill

youdothis?Wouldacompasshelp?Howwillyoufindtherightcentrepoint?

Then,useyourknowledgeofsymmetryandtessellationtocompletethedesign.

WhileworkingonanarchaeologicaldigwiththefamousDrJones,youcomeacross aportionofabeautifuloldplate.

DrJonesthinksitmaybe14 oftheLostPlateofIcarus,apricelessfind.Heasksyou

torecreatewhatyouthinktheentireplatemayhavelookedlike.

Getting ready

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2Dshapeshave2dimensions–widthandheight.They’reflat.

3Dshapeshave3dimensions–height,widthanddepth.Sometimeswecallthemsolids.Whenwedrawthem,weoftenshow themastransparentorasskeletonssowecan‘see’alltheirsides.3Dshapescanhaveallflatsides,allcurvedsides,oramixtureofboth.

Look at these 3D shapes. Which 2D shapes form their sides? If it helps, find the solids in your classroom and study them.

Have these questions been answered correctly? Correct any mistakes:

a How many surfaces does this shape have?

b Howmanyvertices?

c How many edges?

Study the shape and answer the following:

a How many surfaces does this shape have?

b Howmanyvertices?

c How many edges?

3D shapes – introduction

a This is made of:

____ squares

b This is made of:

2 ______________

4______________

c This is made of:

1 ______________

____ ___________

d This is made of:

____ ___________

____ triangles

height

height

width

width

depth

1

3

2

The 2D shapes are the surfaces of a 3D shape. The edge is where 2 surfaces meet. The point where 2 or more surfaces meet is called the vertex.Ifwe’retalkingaboutmorethanonevertex,wecallthem vertices.

6

12

8

squares6 1

54

rectangle

rectangles triangles

pentagon

4

4

6

8

12

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Use classroom equipment such as geoshapes, polydrons or straws and plasticine to create 2 different prisms. Name them here and record how many vertices, edges and surfaces they have.

Count the number of sides on each grey face. Now count the number of rectangular faces each shape has. What do you notice?

Finish these prisms by ruling the missing edges. Name them according to their faces. The first one has been done for you.

3D shapes – polyhedrons

Some 3D shapes are polyhedrons. This means each surface is a polygon. The polyhedrons we most commonly come across are pyramids and prisms.

Prismshaveidenticalparallelfacesjoinedbyrectangles.Boxesareagoodexampleofprisms–have a look in your kitchen cupboard at home at the cereal and pasta boxes.Mostprismsarenamedaftertheirendfaces(e.g.rectangularprism,triangularprism).

a ________________ prism

b ________________ prism

c ________________ prism

d ________________ prism

1

2

3

cube or square

3D shapes

polyhedrons

pyramids otherprisms

rectangular triangular pentagonal

They’re the same.

Answers will vary.

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What kind of pyramids are these? Remember a pyramid is named after its base.

Pyramidshaveabasewith3ormorestraightsides.Theyhavetriangularfaceswhichmeetat apoint.They’renamedaftertheirbases.

What do you notice about the number of sides on the base and the number of triangular faces?

Pretend you’ve cut apart a hexagonal pyramid. Draw all its faces. What shape will the base be? How many triangular sides will you draw?

3D shapes – polyhedrons

a ________________ pyramid b ________________ pyramid c ________________ pyramid

4

5

6

7 What are 3 things pyramids and prisms have in common? What is something that makes them different?

hexagonal triangular rectangular

They’re the same.

Answers will vary and may include:

– Pyramids and prisms are made up of polygons/flat sides.

– Pyramids and prisms have angles, vertices and edges.

– Pyramids and prisms have straight edges.

– Pyramids have 1 point at the top, prisms don’t.

– The sides of a pyramid are triangular, prisms have rectangular sides.

Hexagon base

6 triangular faces

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Many polyhedrons are named according to the number of faces they have. Colour match the information with the shape and the name. You may need to do some research! The first one has been done for you.

3D shapes – polyhedrons

Thereareotherkindsofpolyhedrons.They’realsomadeupofpolygonsandhavestraightsides,buttheydon’tfittherules for pyramids and prisms. Here are some examples:

Change these shapes so they’re still polyhedrons but no longer regular prisms or pyramids. Maybe you could draw in a dotted line to show a cut or add some extra faces.

Create a polyhedron out of polydrons or geoshapes. Count how many faces it has. Can you find out what it should be called?

8

9

10

3Dshapesdon’thavetoberegular.Theycanbemadeupofdifferentshapesandhaveanglesandsidesofdifferentsizes.

Thisisstillapolyhedron:Thisisstillapentagonalprism:

octahedron

tetrahedron

4faces,6edges,4vertices

dodecahedron

icosahedron

8faces,12edges,6vertices

12faces,30edges,20vertices

cube or hexahedron

6faces,12edges,8vertices

20faces,30edges,12vertices

¤

¤

#

##

**

Answers will vary.

Possible answer: Answers

will vary.

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3D shapes – spheres, cones and cylinders

Anothergroupof3Dshapeshasoneormorecurvedsurfaces.Examplesincludespheres,conesand cylinders.

What am I? Use the clues to decide which shape I am:

a Ihave1curvedsurface.That’sit,Iliketokeepthingssimple. _____________________________

b Whenyoucutacrosssectionfromme,bothpartskeepthe same number of edges and surfaces. _____________________________

c Ihavenoverticesand3surfaces. _____________________________

d Ihave1edgeand2surfaces. _____________________________

Pretend you have to describe these shapes to someone who can’t see or feel them. Make sure you talk about their surfaces, their vertices and their edges and anything else you think would help them build a picture.

1

2

3

When we cut through a solid parallel to the base, we make a cross section.

a Draw how these shapes would look like in 2 pieces:

b Howhasthischangedthesphere?Explainthisintermsofsurfaces,edgesandvertices.

a b c

Answers will vary.

It now has 2 surfaces. One is flat. It has one edge and no vertices.

sphere

cube or retangular prism

cylinder

cone

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Draw dotted lines to reveal missing edges, surfaces or vertices:

Draw some 3D shapes:

Use a ruler to join the bases of these pyramids with their points:

Whenwedraw3Dshapes,wecandrawdottedlines toshowthesurfaces,edgesandverticeswecan’tsee.

3D shapes – drawing 3D shapes

1

2

3

a

d

b

e

c

f

a b c d

If you draw lightly with a sharp pencil, you can rub mistakes out easily!

Answers will vary.

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Copy these irregular 3D shapes:

Use the dot paper to help you finish these shapes. We have helped you with the first one.

We can use dot paper or hexagonal grids to guide us when we draw 3D shapes.

3D shapes – drawing 3D shapes

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

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SERIES TOPIC

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triangular prism

Answers will vary.

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SERIES TOPIC

33FCopyright © 3P Learning

Geometry 4

What to do Colour match the correct parts. Your teacher has a list of the shapes if it would help

toknowwhichshapesyou’relookingfor.

2 halves make a whole … apply

Thenetsof5solidsarebelow–theproblemisthatthey’vebeenseparatedinto twoparts.Yourjobistomatchthepartscorrectly.Seeifyoucandoitinyourhead.Ifthisprovestoodifficult,youcancutthenetsoutandphysicallyjointhemtoformthe solid.

Getting ready

¤

¤

#

#

*

*

List of shapes: pentagonal prism,

cube, hexagonal pyramid, triangular pyramid,

triangular prism

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SERIES TOPIC

F34Copyright © 3P Learning

Geometry4

What to do next

What to do

Tomb Raider investigate

You’retrappedinatombfarunderground.Thereare6keyzonesinthetomb.

PresentyourfindingstotheGuardianofPower(thatwouldbeyourteacher).Ifthey’recorrect,youmayescapescotfree.Ifnot?Well,onlytheyknowwhatpunishmentisinstore.Thereare28routesintotal.Foranextrachallenge,youcouldtryandfindthemall.

Toescape,youmustfind 10differentwaystogetfrom the ledge to the gold.

Record them below. We have given you one route to get you started: ledge coffin gold.

Getting ready

Answers will vary.

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35Series F Topic 1 Assessment

Copyright © 3P Learning

a

55°

b

90°

c

110°

Lines and angles Name ____________________

Draw:

2

3

1

Draw an angle that is:

Label each of these angles as right, acute, reflex or obtuse:

a

angle

b

angle

c

angle

d

angle

Skills Not yet Kind of Got it

• Knowstermsparallel,perpendicular,horizontal,vertical

• Recognisesandlabelsacute,obtuse,rightangledandreflexangles

• Draws angles to 5o markers

a 2 parallel lines b 2 lines perpendicular to each other

c a horizontal line d averticalline

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36 Series F Topic 1 Assessment

Copyright © 3P Learning

a

55°

b

90°

c

110°

Lines and angles Name ____________________

Draw:

2

3

1

Draw an angle that is:

Label each of these angles as right, acute, reflex or obtuse:

a

angle

b

angle

c

angle

d

angle

Skills Not yet Kind of Got it

• Knowstermsparallel,perpendicular,horizontal,vertical

• Recognisesandlabelsacute,obtuse,rightangledandreflexangles

• Draws angles to 5o markers

a 2 parallel lines b 2 lines perpendicular to each other

c a horizontal line d averticalline

reflex right obtuse acute

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37

Copyright © 3P Learning

Series F Topic 2 Assessment

a b c d

2D shapes Name ____________________

Draw a line from the label to the correct triangle:

Look at the following two quadrilaterals. Name them and list their properties:

Circle the polygons:

2

3

4

1

Name these polygons:

equilateral triangleright angled triangleisosceles triangle scalene triangle

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38

Copyright © 3P Learning

Series F Topic 2 Assessment

Label the following parts of the circles below:

a b

c d

Name and draw this mystery shape:Ihave4sides.Allofmyanglesareequal.Ifyoudrawinmydiagonals,thelinesformrightangleswhere they intersect.

If I drew a shape and the sum of the angles was 180˚, what shape could I have drawn? Draw it.

2D shapes Name ____________________

5

6

7

Skills Not yet Kind of Got it

• Recognises and names simple polygons

• Namespropertiesofsimplequadrilaterals

• Recognisesandnamesdifferenttypesoftriangles

• Namesdifferentpartsofcircles

• Usesknowledgeofshapepropertiestoidentifysimplepolygons

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39

Copyright © 3P Learning

Series F Topic 2 Assessment

a b c d

2D shapes Name ____________________

Draw a line from the label to the correct triangle:

Look at the following two quadrilaterals. Name them and list their properties:

Circle the polygons:

2

3

4

1

Name these polygons:

equilateral triangleright angled triangleisosceles triangle scalene triangle

hexagon rectangle pentagon octagon

trapezium

4 straight sides.

1 pair parallel sides.

2 acute angles (equal).

2 obtuse angles (equal).

square

4 straight equal sides.

2 sets of parallel sides and all angles are right angles.

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40

Copyright © 3P Learning

Series F Topic 2 Assessment

Name and draw this mystery shape:Ihave4sides.Allofmyanglesareequal.Ifyoudrawinmydiagonals,thelinesformrightangleswhere they intersect.

If I drew a shape and the sum of the angles was 180˚, what shape could I have drawn? Draw it.

2D shapes Name ____________________

5

6

7

Skills Not yet Kind of Got it

• Recognises and names simple polygons

• Namespropertiesofsimplequadrilaterals

• Recognisesandnamesdifferenttypesoftriangles

• Namesdifferentpartsofcircles

• Usesknowledgeofshapepropertiestoidentifysimplepolygons

Label the following parts of the circles below:

a b

c d

radius diameter

arc circumference

triangle

square

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41

Copyright © 3P Learning

Series F Topic 3 Assessment

Transformation, tessellation and symmetry Name ____________________

Rotate this shape and record the new position. Do a quarter turn, half turn, three quarter and full turn.

Transform these letters:

Complete this picture so it’s symmetrical:

Draw the lines of symmetry on these shapes:

2

3

4

1

a b c

a

turn180°

d

flip

b

turn90°

e

flip

c

slide

f

turn180°

T

N

M

Q

L

Y

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

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42

Copyright © 3P Learning

Series F Topic 3 Assessment

Which of these shapes tessellate on their own? Remember you can flip or turn them. Use the dot paper to help work this out. Colour any shapes that will tessellate and cross out the shapes that won’t.

Continue this tessellation across the page:

Transformation, tessellation and symmetry Name ____________________

What is tessellation? Pretend you’re explaining it to a younger pupil. What would you say and/or draw?

6

7

5

Skills Not yet Kind of Got it

• Identifiesanddrawslinesofsymmetry

• Visualisesandrepresentstransformations–flips,slides,turns

• Understandsanddescribestessellation

• Continuessimpletessellations

• Makesjudgmentsaboutwhichsimplepolygonswilltessellate

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

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43

Copyright © 3P Learning

Series F Topic 3 Assessment

Transformation, tessellation and symmetry Name ____________________

Rotate this shape and record the new position. Do a quarter turn, half turn, three quarter and full turn.

Transform these letters:

Complete this picture so it’s symmetrical:

Draw the lines of symmetry on these shapes:

2

3

4

1

a b c

a

turn180°

d

flip

b

turn90°

e

flip

c

slide

f

turn180°

T

N

M

Q

L

Y

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

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� � � � � � � � � � � � � � � � � � � � � � � � � � �

Q

T

YM

L

N

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

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� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � �

Page 46: SERIES Geometry - Grade 5 ASW - UNIT 1 Decimalsgrade5asw.weebly.com/uploads/2/2/4/1/22418994/... · Lines and angles – measuring angles Use a protractor to complete these angles

44

Copyright © 3P Learning

Series F Topic 3 Assessment

Which of these shapes tessellate on their own? Remember you can flip or turn them. Use the dot paper to help work this out. Colour any shapes that will tessellate and cross out the shapes that won’t.

Continue this tessellation across the page:

Transformation, tessellation and symmetry Name ____________________

What is tessellation? Pretend you’re explaining it to a younger pupil. What would you say and/or draw?

6

7

5

Skills Not yet Kind of Got it

• Identifiesanddrawslinesofsymmetry

• Visualisesandrepresentstransformations–flips,slides,turns

• Understandsanddescribestessellation

• Continuessimpletessellations

• Makesjudgmentsaboutwhichsimplepolygonswilltessellate

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

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� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

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� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

Answers will vary.

Answers will vary and may include:

Page 47: SERIES Geometry - Grade 5 ASW - UNIT 1 Decimalsgrade5asw.weebly.com/uploads/2/2/4/1/22418994/... · Lines and angles – measuring angles Use a protractor to complete these angles

45

Copyright © 3P Learning

Series F Topic 4 Assessment

3D shapes Name ____________________

Draw a line of cross section across this shape and then draw what the two pieces would look like if the shape was cut:

Label each of these 3D shapes:

Name this shape and list the properties. Make sure you identify how many edges, faces and vertices it has:

How are prisms and pyramids similar? How are they different? Explain using words and/or diagrams:

Name these 3D shapes:

2

3

5

4

1

a b c d

a b c

Page 48: SERIES Geometry - Grade 5 ASW - UNIT 1 Decimalsgrade5asw.weebly.com/uploads/2/2/4/1/22418994/... · Lines and angles – measuring angles Use a protractor to complete these angles

46

Copyright © 3P Learning

Series F Topic 4 Assessment

Draw in dotted lines to reveal the missing edges, sides and vertices of these shapes:

Complete these 3D shape drawings:

Draw lines to match the nets to the correct shape names:

3D shapes Name ____________________

What is a net? Explain it using words. (We mean the mathematical kind, not the catching butterflies kind.)

7

8

9

6

triangular prism triangular pyramid pentagonal prism

a b c

a b� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

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� � � � � � � � � � � � � � � � � � � � � � � � � � � �

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� � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � �

Skills Not yet Kind of Got it

• Identifiesandnamessimplepolyhedrons

• Identifiespropertiesofasquarebasedpyramid,includingfaces,edgesandvertices

• Describessimilaritiesanddifferencesbetweenpyramidsandprisms

• Visualisesandrepresentscrosssectionsofpolygons

• Visualises and describes nets

• Sketches 3D models

Page 49: SERIES Geometry - Grade 5 ASW - UNIT 1 Decimalsgrade5asw.weebly.com/uploads/2/2/4/1/22418994/... · Lines and angles – measuring angles Use a protractor to complete these angles

47

Copyright © 3P Learning

Series F Topic 4 Assessment

3D shapes Name ____________________

Draw a line of cross section across this shape and then draw what the two pieces would look like if the shape was cut:

Label each of these 3D shapes:

Name this shape and list the properties. Make sure you identify how many edges, faces and vertices it has:

How are prisms and pyramids similar? How are they different? Explain using words and/or diagrams:

Name these 3D shapes:

2

3

5

4

1

a b c d

a b c

hexagonal pyramid

cube or hexahedron

Square based pyramid

– 1 square base

– 4 triangular faces

– 5 vertices

– 8 edges

– 5 faces

Answers will vary and may include:

Similiarities:

– straight edges

– 3D shapes

Differences:

– pyramids come to 1 point at the top

– prisms have 2 matching ends

– the faces of a pyramid are triangles, the faces of a prism are rectangles

triangular pyramid

rectangular prism

sphere cone cylinder

Page 50: SERIES Geometry - Grade 5 ASW - UNIT 1 Decimalsgrade5asw.weebly.com/uploads/2/2/4/1/22418994/... · Lines and angles – measuring angles Use a protractor to complete these angles

48

Copyright © 3P Learning

Series F Topic 4 Assessment

Draw in dotted lines to reveal the missing edges, sides and vertices of these shapes:

Complete these 3D shape drawings:

Draw lines to match the nets to the correct shape names:

3D shapes Name ____________________

What is a net? Explain it using words. (We mean the mathematical kind, not the catching butterflies kind.)

7

8

9

6

triangular prism triangular pyramid pentagonal prism

a b c

a b� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

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� � � � � � � � � � � � � � � � � � � � � � � � � � � �

Skills Not yet Kind of Got it

• Identifiesandnamessimplepolyhedrons

• Identifiespropertiesofasquarebasedpyramid,includingfaces,edgesandvertices

• Describessimilaritiesanddifferencesbetweenpyramidsandprisms

• Visualisesandrepresentscrosssectionsofpolygons

• Visualises and describes nets

• Sketches 3D models

Answers will vary.

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

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49

Copyright © 3P Learning

Series F Objectives

Series F – Geometry

2006 Primary Framework Core Objectives

Topic 1Lines and angles

Usingandapplyingmathematics• explorepatterns,propertiesandrelationshipsandproposeageneralstatementinvolvingnumbersorshape;identifyexamplesforwhichthestatementistrueorfalse

Understanding shape• readandplotco-ordinatesinthefirstquadrant;recogniseparalleland

perpendicular lines in grids and shapes; use a set square and ruler to draw shapes with perpendicular or parallel sides

• estimate,drawandmeasureacuteandobtuseanglesusingananglemeasurerorprotractor to a suitable degree of accuracy; calculate angles in a straight line

Topic 22D Shapes

Usingandapplyingmathematics• explorepatterns,propertiesandrelationshipsandproposeageneralstatementinvolvingnumbersorshape;identifyexamplesforwhichthestatementistrueorfalse

Understanding shape• identify,visualiseanddescribepropertiesofrectangles,triangles,regularpolygonsand3Dsolids;useknowledgeofpropertiestodraw2Dshapesandidentifyanddraw nets of 3D shapes

• estimate,drawandmeasureacuteandobtuseanglesusingananglemeasurerorprotractor to a suitable degree of accuracy; calculate angles in a straight line

Topic 3Transformation, tessellation and symmetry

Usingandapplyingmathematics• explorepatterns,propertiesandrelationshipsandproposeageneralstatement

involvingnumbersorshape;identifyexamplesforwhichthestatementistrueorfalse

Understanding shape• completepatternswithuptotwolinesofsymmetryanddrawthepositionofa

shapeafterreflectionortranslation

Topic 4 3D Shapes

Usingandapplyingmathematics• explorepatterns,propertiesandrelationshipsandproposeageneralstatementinvolvingnumbersorshape;identifyexamplesforwhichthestatementistrueorfalse

Understanding shape• identify,visualiseanddescribepropertiesofrectangles,triangles,regularpolygonsand3Dsolids;useknowledgeofpropertiestodraw2Dshapesandidentifyanddraw nets of 3D shapes