book 1 3d postcards year 5 feedback and solutions...book 1 3d postcards year 5 feedback and...

Book 1

3D Postcards

Year 5 Feedback and Solutions

MATHEMATICS

MATHEMATICS

First published 2012

ISBN 978-1-74205-782-8 SCIS 1535401

First published 2012

© Department of Education WA

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the Western Australian Department of Education, unless copied under the Statutory Education Licences.

Whilst every effort has been made to ensure the accuracy of the information contained in this publication, no guarantee can be given that all errors and omissions have been excluded. No responsibility for loss occasioned to any person acting or refraining from action as a result of the material in this publication can be accepted by the Department.

Requests and enquiries concerning copyright should be addressed to:

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Department of Education

This resource contains information from the Western Australian Curriculum Version 8.1. © School Curriculum and Standards Authority. The unaltered and most up to date version of this material is located at http://wacurriculum.scsa.wa.edu.au

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3D Postcards

© WestOne Services 2012 – MATHS1862

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3D Postcards

Feedback and Solutions

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TUNE IN

DAY 1 2D allsorts

1 Complete the following patterns

a) 3 723, 3 733, 3 743, 3 753, 3 763, 3 773 The rule is add 10

b) 1 065, 1 115, 1 165, 1 215, 1 265, 1 315 The rule is add 50

c) 6.4, 6.1, 5.8, 5.5, 5.2, 4.9 The rule is subtract 0.3

d) 43 179, 43 289, 43 399, 43 509, 43 619, 43 729 The rule is add 110

e) 832.6, 822.6, 812.6, 802.6, 792.6, 782.6 The rule is subtract 10

2 Off to the pool

9 cars would be needed to take the 26 students.

8 3 = 24 (not enough room for all students)

9 3 = 27 (this is enough cars with one seat to spare)

3 Not so simple flags

c)

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SWITCH ON

4 Happy holidays!

The Duncan family come back from their holiday to Darwin on the 6th of September. 5 What's the chance?

a) Spinner D would give you the best chance of spinning a 1.

b) Spinner C would give you the best chance of spinning a 2.

c) Spinner A would give you the best chance of spinning a 3.

d) Spinner C would give you the smallest chance of spinning a 1.

e) Spinner B would give you a chance of spinning a 4.

f) Spinner D would give you an equal chance of spinning a 1, 2 and 3.

Activity 11.1

A polygon is a closed two-dimensional shape made using only straight lines.

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1.2

Shape Polygon Not a polygon

1.3

Shape Polygon Not a polygon

Drawings will vary. The drawing will have a curved line or is an unclosed 2D shape or both.

Drawings will vary. The drawing will have only straight lines and be a closed 2D shape.

Drawings will vary. The drawing will have only straight lines and be a closed 2D shape.

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Activity 22.1

2D shape Name Number of sides

Triangle 3

Square 4

Rectangle 4

Pentagon 5

Hexagon 6

Octagon 8

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2.2

2D shape Name Number of sides

Heptagon 7

Nonagon 9

Decagon 10

Hendecagon 11

Dodecagon 12

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2.3 and 2.4

a) The polygons are both octagons. They both have eight sides.

They are different because one octagon has sides of even lengths and the other has sides of different lengths.

b) The polygons are both hexagons. They both have six sides.

They are different because one hexagon has sides of even lengths and the other has sides of different lengths.

c) The polygons are both pentagons. They both have five sides.

They are different because one pentagon has sides of even lengths and the other has sides of different lengths.

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2.5

Regular octogon Irregular pentagon

2.6

Drawings may vary. These are examples.

Regular triangle Irregular triangle

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Activity 33.1

Squares and rectangles are polygons, parallelograms and quadrilaterals.

Squares and rectangles both have four right angles measuring 90°.

Squares and rectangles have the same number of sides, angles and corners.

Opposite sides are parallel to each other.

Opposite angles are also equal. The four 90° angles inside a square or rectangle total 360°.

3.2

Squares have four sides of equal length and rectangles have two pairs of sides of equal length.

3.3

No

Rectangles can't be called squares because all the sides are not of equal length

3.4

Yes

Squares can be called rectangles because opposite sides are of equal length.

Regular heptgon Irregular hexagon

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3.5a)

A B C

D E F

b) The lines in example E are not parallel because parallel lines will never meet and the two lines already cross over each other.

3.6

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3.7

Yes

Squares and rectangles are parallelograms because their opposite sides are parallel and equal in length and the opposite angles are equal.

3.8

POWER UP

1.1

Answers will vary. This is one example of a complex, concave octagon.

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1.2

a)

acute right reflex straight obtuse

b)


c)


d)


e)


f)


g)


h)


i)


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1 Divisibility by 3

DAY 2 Polyhedrons and non-polyhedrons

TUNE IN

23 89 105 187

32 90 123 267

24 95 144 275

2 Fruit for sale

a)

b)

c) ○ an apple and an orange ● a banana and an apple

○ an orange and a banana ○ two apples

80c 50c 20c 60c

○ ○ ● ○80c 70c 90c 30c

● ○ ○ ○

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3 Looking at angles

4 How long? a) The pencil is 30 mm long.

b) The sticky note pad is 45 mm wide.

c) The paper clip is 35 mm long.

5 Favourite colours

a) There are more students who like red than students who like purple.

○ True ● False

There are fewer students who like green than students who like yellow.

● True ○ False

There are more students who like blue than students who like green.

○ True ● False

There are fewer students who like yellow than students who like purple.

○ True ● False

b) 28 students were surveyed for this information.

Acute angle Reflex angle Straight angle Right angle

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Activity 11.1

The three dimensions of a 3D object are width, length and height.

SWITCH ON

width

height

length

1.2

Answers will vary. These are just a few examples from an endless possibility.

Tissue box, book, ice-cream container, cool drink can, pencil case, computer, apple, ball stereo, television, vase, bottle, eraser, pillow, photo frame, telephone book and calculator.

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Activity 22.1

Cone Cylinder Sphere Torus

2.2

Examples include:

▪ Cones – ice-cream cone, traffic cone, party hat, fir tree, pine cone, candle, carrot.

▪ Cylinders – aluminium can, roll of lollies, spray cans, water tank, pipe, postertube, glass, felt tip pen, salami.

▪ Spheres – world globe, ball, grapefruit, pearl, ball of string, lolly.

▪ Tori – inner tube from tyre, swimming ring, doughnut, life saving ring, teethingring, wheel of a car or bicycle.

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Activity 33.1All other faces of a rectangular prism are rectangles.

3.2

heptagonal prism triangular prism cube

pentagonal prism decagonal prism hexagonal prism

3.3

a) A square prism has two parallel end face shaped like squares. It also has four side face shaped like rectangles.

b) A cube has all six faces shaped like squares.

3.4 The other faces of the square-based pyramid are triangles.

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3.5

hexagonal pyramid octagonal pyramid triangular pyramid

nonagonal pyramid square-based pyramid pentagonal pyramid

3.6

Pyramids and prisms

Similarities Differences

Pyramids and prisms are made up of flat shapes.

Pyramids are named by their base. Prisms are named by their ends.

They are made of plane faces.

Most faces in a pyramid are triangular in shape.

Most faces in a prism are rectangular in shape.

They both have faces, edges and vertices.

Only pyramids have triangular faces that meet at an apex.

They are both three-dimensional objects with length, width and height.

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Activity 44.1

a)

Name of object pentagonal pyramid

Number of faces 6

Number of edges 10

Number of vertices 6

Shapes of all faces

1 5

b)

Name of object octagonal prism

Number of faces 10

Number of edges 24


Shapes of all faces

2 8

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c)

Name of object square pyramid

Number of faces 4

Number of edges 8


Shapes of all faces

1 4

d)

Name of object triangular pyramid

Number of faces 4

Number of edges 6


Shapes of all faces

4

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e)

Name of object quadrilateral prism (kite-shaped prism)

Number of faces 6

Number of edges 12


Shapes of all faces

2 2

2

4.2

Polyhedral formula is F + V – E = 2

a) Pentagonal pyramid: 6 + 6 – 10 = 12 – 10 = 2

b) Octagonal prism: 10 + 16 – 24 = 26 – 24 = 2

c) Square pyramid: 5 + 5 – 8 = 2

d) Triangular pyramid: 4 + 4 – 6 = 8 – 6 = 2

e) Quadrilateral prism: 6 + 8 – 12 = 14 – 12 = 2

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4.3

a)

b)

c)

Draw a picture of the object.

I have 8 rectangular faces, 24 edges and 16 vertices.

I also have 2 faces which are octogons.

What am I?

Draw a picture of the object.I have 5 vertices and my base is rectangular in shape.

What am I?


Although 3D, I am not a polyhedron. I have a circular base, one curved surface and an apex.

What am I?

Octogonal prism

Rectangular pyramid

Cone

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Answers will vary. These are some examples:

▪ the Pentagon building in Washington DC (pentagon)

▪ the pyramid at the Louvre in Paris (pyramid)

▪ the Eiffel tower (pyramid)

▪ Ell Castillo (the castle) in Chichen Itza (pyramid)

▪ segments from the Great Wall of China (square and rectangular prisms)

▪ Nelson’s column in London (cylinder)

▪ pyramids of Egypt (pyramid)

▪ Colosseum in Rome (circular)

▪ Taj Mahal in India (prism with a sphere on top)

▪ Empire State building (tall square prism).

POWER UP

1 Tickets please

There are 14 children on the bus.

36 + 28 = 64

78 – 64 = 14

DAY 3 Cross sections of 3D objects

TUNE IN

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2 Fraction grid

a) or any 6 squares are shaded

b) or any 16 squares are shaded

c) or any 18 squares are shaded

3 That's symmetrical

4 A glass of juice

a) There is 1 650 mL of juice left in the carton.

This can also be written as 1.650L

Convert litres to millilitres to solve this problem 2 L = 2 000 mL

2 000 mL – 350 mL = 1 650 mL

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b) From the remaining 1 650 mL, 4 other people can have a 350 mL glass from this carton.

23 5 0 mL

4

1 4 0 0 mL

5 Purple or black?

a) ○ 3 out of 5 ○ 2 out of 3 ● 2 out of 5 ○ 1 out of 4

b) ○ 1 out of 3 ○ 4 out of 7 ● 1 out of 4 ○ 3 out of 4

c) ○ 3 out of 7 ● 4 out of 7 ○ 1 out of 7 ○ 3 out of 4

d) ● 3 out of 4 ○ 1 out of 3 ○ 1 out of 4 ○ 2 out of 4

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Activity 11.1

SWITCH ON

Model Cross-section

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1.2

Make the following 3D objects out of modelling clay or play dough.

Use a blunt knife, dental floss or fishing line to cut the models in the same way as the images. Draw both cross-sections for each object.

ModelCross-section

A B

a)

b)

c)

d)

A

B

B

A

B

A

B

A

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1.3

Cross-section Cube

triangle B and D

parallelogram E

rectangle C

square A

DAY 4 Investigating nets

TUNE IN

1 Four card shuffle a) Thomas’s number is 574.

b) 10 574

c) 75.41

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2 Don't be late

a) b)

The time is 4:05 or 5 past 4 The time is 5:10 or ten past 5 c)

d) Sarah’s father arrives home 3 hours and 28 minutes after her.

3 Rock solid!

a) The solids used to make the model are a square prism and a triangular prism.

b) There are 7 faces.

c) There are 10 vertices.

d) There are 15 edges.

4 Mass

a) ○ 2 g ○ 20 g ● 200 g ○ 2 kg

b) There would be approximately 15 oranges in a 3 kg box.

200 g 5 = 1 kg so about 5 oranges have a mass of 1 kg

3 5 oranges = 15 oranges.

6

9 3

12

78

1011

54

21

6

9 3

12

78

1011

54

21

6

9 3

12

78

1011

54

21

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5 It's a goal!

a) Adrian scored 6 more goals than Robin.

b) Karina scored more goals than Daniel and Robin combined or Gayle and Robin combined or Adrian and Robin combined.

c) The total number of goals scored for the year was 60.

d) 21 goals were scored by Karina.

e) On average, 12 goals were scored by each player. (60 ÷ 5 = 12)

SWITCH ON

Activity 11.1

Answers will vary.

a) The ends are more likely to be squares or rectangles.

b) The prism will be called a square prism or a rectangular prism.

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1.2

3D object2D shapes used

circle square rectangle triangle

cube 0 6 0 0

square prism 0 2 4 0

triangular prism 0 0 3 2

cylinder 2 0 1 0

triangular pyramid 0 0 0 4

square pyramid 0 1 0 4

rectangular pyramid 0 0 1 4

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1.3

3D o

bjec

t2D

figu

res

used

rect

angl

etr

iang

lepe

ntag

onhe

xago

nhe

ptag

onoc

tago

n

pent

agon

al p

rism

50

20

00

octa

gona

l pyr

amid

08

00

01

hept

agon

al p

rism

70

00

20

hexa

gona

l pyr

amid

06

01

00

octa

gona

l pris

m8

00

00

2

hept

agon

al p

yram

id0

70

01

0

hexa

gona

l pris

m6

00

20

0

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1.4

a) A net always has the same number of faces as the 3D object it represents.

b) A net always has the same sized faces as the 3D object it represents. 1.5

triangular pyramid

octagonal prism

triangular prism

square pyramid

pentagonal prism

cylinder

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Activity 22.1

A cube has six faces so its net will have six faces.

All faces of the net will be shaped like a square.

2.2

a) Answers will vary for this task.

You probably arranged your six squares into one of the arrangements shown in the answers for 2.3.

b) Answers will vary. 2.3

a) b) c) d)

e) f) g) h)

i) j) k) l)

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POWER UP

▪ 2 end faces – (3 cm 1 cm)

▪ 1 base face – (8 cm 3 cm)

▪ 1 top face – (8 cm 3 cm)

▪ 2 side faces – (8 cm 1 cm)

This is one way the rectangular prism could be drawn.

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DAY 5Review

TUNE IN

1 What is the value?

3 PlaceValue

TotalValue

a) 923.65 ones 3

b) 2 481 536 tens 30

c) 83 156.4 thousands 3 000

d) 12 625.30 tenths 0.3 or

e) 436 851.45 ten thousands 30 000

f) 546.83 hundredths 0.03 or

3 10

3 100

2 Hundredths grid

There are 7 out of 100 squares or 7 100 left white.

This is written as 0.07.

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3 Point me in the right direction

a) The new direction is NW (north-west).

b) The new direction is NE (north-east).

c) You can move from a SW to a SE direction by moving a three-quarter turn in a clockwise direction or moving a quarter turn in an anti-clockwise direction.

4 Round the garden

a) The perimeter of the grassed area is (12 m + 12 m + 12 m + 12 m) or 12 m 4 = 48 m

b) The area of the grass is 12 m 12 m = 144 m²

5 The marble's in the bag

a)

A B C D

b) Gregor has a 1 out 2 chance of choosing a red marble from bags A and B.

c) Gregor has a 5 out of 5 chance choosing a red marble from bag D. Gregor can be 100% certain of choosing a red marble from bag D.

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Activity 11.1

Polygons are 2D closed shapes made using straight lines.

1.2

a)

SWITCH ON

Irregular, complex, convex polygon

Regular, simple, convex polygon


Irregular, simple, convex polygon

A B C D

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Irregular, simple, concave polygon

Irregular, complex, convex polygon

Irregular, simple, convex polygon

b) All of these polygons are pentagons.

c) What shape is Figure B? Rhombus (or a parallelogram)

d) What shape is Figure C? Decagon

e) What shape is Figure H? Octagon

1.3

Answers will vary. These are just examples.

Regular quadrilateral Irregular quadrilateral Complex quadrilateral

1.4

a)

E F G H

square

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rectangle

rhombus

b) These three shapes are parallelograms because their opposite sides are parallel and equal in length and their opposite angles are equal.

Activity 22.1

This is one possible way to label the diagram. The terms edge, vertex and face may be in different positions.

Edge

Vertex

Apex

Face

Base

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2.2

2.3

triangular prism

cylinder

sphere

square pyramid

pentagonal prism

octagonal pyramid

Pyramids and prisms

Prisms only Prisms and pyramids Pyramids only

opposite end faces that are parallel polyhedron a single apex

named by the shape of its end faces flat (plane) faces base at one end

rectangular shaped side faces straight edges

faces made by connecting the base

to the apex

a pair of congruent faces have vertices named by its

base shape

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2.4

ObjectNumber of Drawings of 2D

shapes used to make the objectFaces Edges Vertices

rectangular prism 6 12 8 6

heptagonal pyramid 8 14 8 1 7

square pyramid 5 8 5 1 4

pentagonal prism 7 15 10 2 5

octagonal pyramid 9 16 9 1 8

2.5


I have two circular end faces, no edges and no vertices.

I also have one curved surface.

What am I?

Cylinder

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Activity 33.1

Draw the cross-sections you would see if each of these 3D objects were cut vertically.

3D object Cross-section view Name of 2D shape

octagon

triangle

square

pentagon

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3.2

A prism has the same cross-sections all the way along its length.

The cross-sections of a prism are the same shape as its end faces.

The cross-sections of a prism are always two–dimensional shapes.

The cross-sections of pyramids have the same shape as the base but different sizes.

Activity 44.1

Answer T for true or F for false for these statements about nets.

True False

a) A net is a flat pattern that can be folded to make a 3D object. T

b) There is only one net for each 3D object. F

c)A net has the same number of faces as the 3D object it is representing.

T

d)The faces of the net must be the same shape as the faces of the 3D object it is representing.

T

e) The faces of a net can be joined together in any order. F

f)The faces of a net can be any size as long as they are the same shape.

F

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4.2

triangular pyramid

cube

hexagonal pyramid

cone

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4.3

a) b) c)

d) e) f)

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4.4

7 cm

7 cm

7 cm

7 cm

4 cm4 cm

4 cm4 cm

3 cm 3 cm4 cm 4 cm

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4.5 You should have used four grid squares to represent one 2 cm cubed crystal.

Mr Grey’s prism net

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= ≠ = =

1 Football fever

○ 18 + 6 + 5 ○ 18 5 6 ● 18 + 5 6 ○ 18 5 + 6 18 + 5 6 = 18 + 30 = 48 Melody has 48 cards in total.

2 Equal or not?

a) 2 3 8

12 b) 6 10 1

2 c) 3 4 12

16 d) 3 5 12

20

3 3D object

a) The 3D object is an octagonal prism.

b) The object is made up of 2 octagons and 8 rectangles.

4 Balance it out

a) Remora would need twenty-five 100-gram discs to make the arm balance even.

25 100 = 2 500 g = 2.5 kg

b) Five 500-gram discs are needed to make the arm balance even.

DAY 6Constructing 3D objects

TUNE IN

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5 Holiday activities

a) If there are 30 in a half, then there will be 15 in a quarter.

▪ 15 students like going to the beach.

▪ One third of 15 is 5. 5 students like to read.

▪ Two-thirds of 15 is 10. 10 students like riding their bikes.

d) There are 30 students in half the group so the whole group is double 30. 60 students took part in the survey.

SWITCH ON

Activity 11.1

a) The two 3D objects used to draw this image are a sphere and a cone.

b) The image looks like an ice cream cone.

c) If the image was flipped it looks like a clown's head.

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1.2

3D objects used Geometric model Real-life object

4 rectangular prisms

1 cone

1 rectangular prism

1 triangular prism

1 cylinder

6 cylinders

1 pentagonal prism

1.3

Answers will vary.

reading

movies

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Activity 22.1

This is one example of what a square prism looks like.

a) 12 lengths of straw are used to make this model.

b) This tells you the number of edges in a square prism.

c) 8 blobs of playdough are used to make this model.

d) This tells you the number of vertices in a square prism.

2.2

a) 9 matchsticks are used to make the skeletal model.

b) This tells you the number of edges in a triangular prism.


d) This tells you the number of vertices in a triangular prism.

2.3

a) 17 lengths of straw are used to make this skeletal model.

b) This tells you the number of edges used to build the model.


d) This tells you the number of vertices in the model.

e) As the two objects were combined, the base of the triangular prism was shared by the top of the square prism. This means that the model used four less straws and four less blobs of dough than was needed to make each object individually.

Square prism Triangular prism

Combined model

Number of straws 12 9 17

Blobs of dough 8 6 10

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Activity 33.1

Skeletal objectBlobs of

playdough used

Number of straws

used

Length of all straws when laid out in a

straight line

pentagonal prism 10 15 80 cm + 25 cm = 105 cm

octagonal pyramid 9 16 40 cm + 64 cm = 104 cm

square pyramid 5 8 20 cm + 32 cm = 52 cm

hexagonal prism 12 18 96 cm + 30 cm = 126 cm

POWER UP

Models will vary.

Answers will vary.

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1 Prime and composite numbers

Number Factors Prime or composite?

7 1, 7 prime

8 1, 2, 4, 8 composite

9 1, 3, 9 composite

18 1, 2, 3, 6, 9, 18 composite

19 1, 19 prime

23 1, 23 prime

35 1, 5, 7, 35 composite

47 1, 47 prime

64 1, 2, 4, 8, 16, 32, 64 composite

2 Follow the pattern

a) The fifth diagram would have 17 squares.

b) The sixth diagram would have 21 squares.

c) The tenth diagram would have 37 squares.

The rule is ‘add 4 more squares each time.’

DAY 7 Looking at 3D objects from different views

TUNE IN

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3 Unfolding symmetry

4 Saw away

2 500 mm or 2.5 m of timber remains after cutting 1 500 mm from a 4 m length.

34 10 0 0 –

1 5 0 0

2 5 0 0

4 000 – 1 500 = 2 500 mm = 2.5 m

5 Pick a ball

a) 5 is the number least likely to be chosen because there is only 1 chance out of 9.

b) 6 is the number most likely to be chosen because it had 4 chances out of 9.

c) The numbers 3 and 4 have an equal chance of being chosen. They both have 2 chances in 9 of being chosen.

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Activity 11.1

SWITCH ON

1.2

front view side view rear or back view

1.3

a) The mystery item is a top view of a cool drink can.

Answers will vary. The side view of a cool drink can looks like this image.

Your drawing may also include pictures and words.

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b) The mystery item is a side view of a book.

Answers will vary. The front view of a book looks like this image.

Your drawing may also include pictures and words

1.4

View top view side view back view front view

Item sneakers/shoes camera high heeled shoe jet/plane

View top view front view side view back view

Item tomato barbecue chair/seat computer screen

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1.5

Answers will vary.

Activity 22.1

Top view Side view

2.2

a)

Front view Side view

Top view

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b)

Top view


c)


Top view

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d)


Top view

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Top view Front view Right side view L R

a)

b)

c)

POWER UP

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DAY 8 Drawing 3D objects using paper-and-pencil methods

TUNE IN

1 Solve these problems

a) (5 4) – 10 = 10 f) 4 (5 6) = 120

b) (6 – 3) 12 = 36 g) 30 – (8 2) = 14

c) 15 – (20 ÷ 4) = 10 h) (30 2) ÷ (5 3) = 4

d) 50 ÷ (100 ÷ 10) = 5 i) (12 2) ÷ (24 ÷ 6) = 6

e) (3 4) (3 2) = 72 j) (2 3) (4 5) = 120

2 Write two equivalent fractions for each of these

a) 1 5 = 2

10 = 3 15 = 4

20 = 5 25 c) 2

3 = 4 6 = 6

9 = 8 12 = 10

15

b) 3 4 = 6

8 = 9 12 = 12

16 = 15 20 d) 2

10 = 4 20 = 6

30 = 8 40 = 10

50

3 Flipping out!

a)

Slide or translation Flip or reflection

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b) The imaged turned (rotated).

4 Both the same

a) The perimeter of the rectangle is 6 cm + 4 cm + 6 cm + 4 cm = 20 cm

b) This means that the perimeter of the square is 20 cm.

20 ÷ 4 (number of sides) = 5

Each side of the square is 5 cm long.

5 Basketball points

a) The difference between the highest and the lowest number of points scored is 13 points.

b) 2 people scored more points than Gail.

c) Jehanne and Kyle scored 23 points together.

d) The difference between the number of points scored by Elijah and Gail is 2 points.

e) If you average out the score, each person would have 7 points. The average is calculated by dividing the total number of points by the number of players.

35 ÷ 5 = 7

f) Kyle and Jehanne scored more points than the average.

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SWITCH ON

Activity 1 Drawings will vary. These are just examples.

cube triangular pyramid hexagonal prism rectangular prism

Activity 22.1

Check the isometric drawings against the examples given.

2.2

Check the isometric drawings against the examples given.

Answers will vary for the own choice isometric drawing.

2.3

Check the oblique drawings against the examples given.

POWER UP

Answers will vary.

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1 Don't put all your eggs in one basket! There are 44 eggs in total.

For the baskets to hold the same number of eggs, each basket needs 22 eggs.

Take 7 eggs from the basket containing 29 eggs and place them in the basket containing 15 eggs: 29 – 7 = 22 and 15 + 7 = 22

2 Numbers on a line

a) ○ 0.28 ○ 0.3 ● 0.4 ○ 0.195 b) 0.195, 0.28 and 0.3

3 Don’t get lost

a) Give the grid references to show where each person lives.

Alan (3, 3) Bob (1, 5) Carol (5, 4)

Dave (2, 1) Eve (4, 5)

b) Bob, Carol and Eve live north of Alan.

c) Eve and Bob live north-west of Carol.

d) Alan and Dave live south-west of Carol.

e) Eve lives directly east of Bob.

DAY 9Using technology to draw 3D objects

TUNE IN

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4 Arm balance

○ ○ ● ○

5 Flip over a card

a) ○ 1 out of 4 ● 1 out of 6 ○ 2 out of 4 ○ 1 out of 12

b) The chance of Marlon choosing a blue card is 3 out of 12 or 1 out of 4.

c) Green is the colour that has the same chance as being chosen as blue.

d) The chance of Marlon choosing a red card is 4 out of 12 or 1 out of 3.

Activity 11.1

Answers will vary.

1.2

Answers will vary.

1.3

Answers will vary.

1.4

Answers will vary.

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Activity 22.1

Answers will vary. Here is one example of a rectangular prism.

2.2 Answers will vary. Here is one example of a hexagonal prism and a triangular prism.

2.3 Answers will vary. Here is one example of a hexagonal pyramid.

Activity 3

3.1

Answers will vary.

3.2

Answers will vary.

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POWER UP

Answers will vary. Here is one example.

DAY 10Review

TUNE IN

1 Working with place value

Begin with the start number and add on.

Add 1 000 Add 100 Add 10 Start number Add 0.1

7 178.5 6 278.5 6 188.5 6 178.5 6 178.6

20 989.3 20 089.3 19 999.3 19 989.3 19 989.4

4 074.8 3 174.8 3 084.8 3 074.8 3 074.9

1 876.05 976.05 886.05 876.05 876.15

51 984.2 51 084.2 50 994.2 50 984.2 50 984.3

24 590.9 23 690.9 23 600.9 23 590.9 23 591

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2 Fundraising

a) ○ $27 ○ $36 ● $46 ○ $45 b) $77

c) Room 5 can buy 6 cows.

d) ○ $3 ● $8 ○ $5 ○ $46

3 Cutting corners

a) There are 7 faces on the new solid.

b) There are 15 edges on the new solid.

c) There are 10 vertices on the new solid.

4 Measuring up

a) Which container has the most liquid? D

b) Which containers have the least liquid? B and C

c) Which two containers have the same amount of liquid? B and C

d) Each mark on Container A shows how many millilitres? 2.5 mL

e) How much liquid is in Container A? 12.5 mL

f) How much liquid is in Container B? 10 mL

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5 All in our family

Cousins

Num

ber o

f cou

sins

10

8

6

4

2

Activity 11.1

Cylinders, rectangular prisms and a cube were used to make this mode.

This model looks like a truck.

1.2

a) Answers will vary.

Some possibilities are cylinders, cone, triangular prisms and rectangular prisms.

b)

Quentin Peter Ricky Stephen

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Activity 22.1

a) The object is a triangular prism.

It has 9 edges and 6 vertices.

b) The object is a hexagonal prism.

It has 18 edges and 12 vertices.

Activity 33.1

Object: cockroach

View: bottom

Object: camera

View: side

Object: chest of drawers

View: front

Object: shoe

View: side

Object: pizza

View: top

Object: car with boot open

View: back

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3.2Side view Top view

3.3

Top view

or

Side viewFront view

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3.4

a)

b)

Activity 44.1

Answers will vary. These are examples.

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4.2


4.3


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Activity 55.1


5.2

Submit your answers to your teacher.

3D postcards Overview

© Department of Education WA 2020 –MATHEMATICSYR5

1

Overview Year 5: 3D Postcards

Western Australian Curriculum

Year 5 Mathematics Content strands

Number and Algebra

Measurement and Geometry

Statistics and Probability

Content Descriptions

Number and Algebra

Number and Place Value

Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098)

Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099)

Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100)

Solve problems involving division by a one digit number, including those that result in a remainder (ACMNA101)

Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (ACMNA291)

Fractions and Decimals

Compare and order common unit fractions and locate and represent them on a number line (ACMNA102)

https://k10outline.scsa.wa.edu.au/home/teaching/codes/mathematics/year-5/acmna098

https://k10outline.scsa.wa.edu.au/home/teaching/curriculum-browser/mathematics-v8/overview/glossary/rounding


https://k10outline.scsa.wa.edu.au/home/teaching/curriculum-browser/mathematics-v8/overview/glossary/multiplication


https://k10outline.scsa.wa.edu.au/home/teaching/curriculum-browser/mathematics-v8/overview/glossary/number

https://k10outline.scsa.wa.edu.au/home/teaching/curriculum-browser/mathematics-v8/overview/glossary/remainder







2

Fractions and Decimals

Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (ACMNA103)

Recognise that the place value system can be extended beyond hundredths (ACMNA104)

Compare, order and represent decimals (ACMNA105)

Money and Financial Matters

Create simple financial plans (ACMNA106)

Patterns and Algebra

Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction (ACMNA107)

Find unknown quantities in number sentences involving multiplication and division and identify equivalent number sentences involving multiplication and division (ACMNA121)

Measurement and Geometry

Using Units of Measurement

Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108)

Calculate perimeter and area of rectangles using familiar metric units (ACMMG109)

Compare 12- and 24-hour time systems and convert between them (ACMMG110)

Shape

Connect three-dimensional objects with their nets and other two-dimensional representations (ACMMG111)

https://k10outline.scsa.wa.edu.au/home/teaching/curriculum-browser/mathematics-v8/overview/glossary/denominator


https://k10outline.scsa.wa.edu.au/home/teaching/curriculum-browser/mathematics-v8/overview/glossary/place-value










https://k10outline.scsa.wa.edu.au/home/teaching/curriculum-browser/mathematics-v8/overview/glossary/volume

https://k10outline.scsa.wa.edu.au/home/teaching/curriculum-browser/mathematics-v8/overview/glossary/capacity

https://k10outline.scsa.wa.edu.au/home/teaching/codes/mathematics/year-5/acmmg108

https://k10outline.scsa.wa.edu.au/home/teaching/curriculum-browser/mathematics-v8/overview/glossary/perimeter






3

Location and Transformation

Use a grid reference system to describe locations. Describe routes using landmarks and directional language (ACMMG113)

Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries (ACMMG114)

Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original (ACMMG115)

Geometric Reasoning

Estimate, measure and compare angles using degrees. Construct angles using a protractor (ACMMG112)

Statistics and Probability

Chance

List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116)

Recognise that probabilities range from 0 to 1 (ACMSP117)

Data Representation and Interpretation

Pose questions and collect categorical or numerical data by observation or survey (ACMSP118)

Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (ACMSP119)

Describe and interpret different data sets in context (ACMSP120)



https://k10outline.scsa.wa.edu.au/home/teaching/curriculum-browser/mathematics-v8/overview/glossary/transformation



https://k10outline.scsa.wa.edu.au/home/teaching/curriculum-browser/mathematics-v8/overview/glossary/equally-likely-outcomes

https://k10outline.scsa.wa.edu.au/home/teaching/codes/mathematics/year-5/acmsp116


https://k10outline.scsa.wa.edu.au/home/teaching/curriculum-browser/mathematics-v8/overview/glossary/data








4

General Capabilities and Cross Curriculum Priorities General capabilities

Literacy

Numeracy

Information and communication technology (ICT) capability

Critical and creative thinking

Personal and social capability

Ethical understanding

Intercultural understanding

Cross-curriculum priorities

Aboriginal and Torres Strait Islander histories and cultures

Asia and Australia’s engagement with Asia

Sustainability

This resource contains extracts from The Western Australian Curriculum Version 8.1. © School Curriculum and Standards Authority.

The unaltered and most up to date version of this material is located at http://wacurriculum.scsa.wa.edu.au/

creativecommons.org/licenses/by-nc-sa/3.0/au/

http://creativecommons.org/licenses/by-nc-sa/3.0/au/

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9 7 8 1 7 4 2 0 5 7 8 2 8

MATHS18623D POSTCARDS

FEEDBACK AND SOLUTIONS ISBN 978-1-74205-782-8

Department of Education

© Department of Education WA

Year 5

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