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Student BookSERIES

D

Space, Shape and Position

Teacher BookSERIES

D


Copyright ©

Series D – Space, Shape and Position

Contents

Topic 1 – Lines and angles (pp. 1–5)• parallel and perpendicular lines___________________

• angles________________________________________

• angles and lines in the environment – apply_ ________

Topic 2 – Investigating 2D shapes (pp. 6–13)• properties of shapes____________________________

• quadrilaterals _________________________________

• symmetry and tessellation_ ______________________

• tangrams – investigate_ _________________________

• symmetry – solve ______________________________

Topic 3 – Investigating 3D shapes (pp. 14–21)• properties of shapes____________________________

• spheres, cones and cylinders_ ____________________

• prisms and pyramids____________________________

• cross sections_________________________________

• nets_ ________________________________________

• different views_________________________________

• net puzzle – solve_ _____________________________

Topic 4 – Position (pp. 22–28)• describing position_ ____________________________

• following directions_____________________________

• grids and coordinates_ __________________________

• compass points________________________________

• hit the points – apply ___________________________

Date_completed

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Series Author:

Nicola Herringer

Copyright ©


Series Author:

Nicola Herringer

Contents

Section 1 – Answers (pp. 1–28)• lines and angles______________________________ _1

• investigating 2D shapes________________________ _6

• investigating 3D shapes________________________ 14

• position____________________________________ 22

Section 2 – Assessment with answers (pp. 29–38)• lines and angles______________________________ 29



• position____________________________________ 37

Section 3 – Outcomes (pp. 39–43)

SERIES TOPIC

1D 1Copyright © 3P Learning


List_the_first_10_letters_of_the_alphabet_in_capitals._Circle_the_letters_that_have_either_parallel_or_perpendicular_lines.

____________________________________________________________________

Look_at_each_group_of_lines._Tick_the_perpendicular_lines.

Look_at_each_group_of_lines._Tick_the_parallel_lines.

Lines and angles – parallel and perpendicular lines

1

2

3

Perpendicular lines meet at right angles. Sometimes they intersect (cross over), sometimes they do not intersect.

Parallel lines are always the same distance away from each other at any point and can never meet. They can be any length and go in any direction.

a b c

d e f

a b c

d e f

Answers will vary.

SERIES TOPIC

D 12Copyright © 3P Learning


Follow_the_directions_about_angles.

a Tick the pair of scissors that has the largest angle.

b Place a circle around the pair of scissors that has the smallest angle.

c Find something in your classroom the has an angle larger than anything on this page and draw it below:

Look_at_the_angle_on_each_open_chest_lid._Trace_the_angle_and_then_order_the_treasure_chests’_lids_from_the_smallest_to_largest_angle.

Lines and angles – angles

An angle is the amount of turning between two lines that meet.

There are lots of angles all around us. You have probably noticed many already.

Here are two examples of angles in your classroom:

1

2

angle

angle

4 1 3 2

Answers will vary.

SERIES TOPIC




1

For_this_activity_you_will_need_a_ruler_and_a_sharp_pencil._Follow_the_directions_for_each_angle.

Copy_the_angle Draw_a__smaller_angle

Draw_a__larger_angle

a

b

c

Use_your_angle_tester_to_measure_and_compare_these_angles._Order_them_smallest_to_largest_by_writing_1_to_4_under_each_one.

An angle is the amount of turning between two lines that meet.Make an angle tester with two straight pieces of cardboard joined with a paper fastener.

3

4

corner or vertex

arms

angle

paper fastener

Answers will vary.

Answers will vary.

Answers will vary.

Answers will vary.

Answers will vary.

Answers will vary.

1 4 2 3

SERIES TOPIC



e f g

Find_some_right_angles_in_your_classroom_and_list_them_here:

____________________________________________________________________

____________________________________________________________________

____________________________________________________________________

For_each_shape,_circle_the_corners_that_are_right_angles._Write_the_number_of_right_angles_inside_each_shape.

a


A right angle is an angle where two lines meet at a square corner.Make a right angle tester by folding a piece of paper like this:

You have made the corner of a square which is a right angle. A right angle is 90 degrees (90°).

5

6

Step_1: Fold a piece of paper in half.

Step_2: Fold the same piece of paper in half again.

Step_3: Make sure that the creases are pressed down firmly.

vertex or corner arms

right angle

b c d

4

1 0

01

4

0

Answers will vary.

SERIES TOPIC



Angles and lines in the environment apply

What_to_do For this activity, you will need a ruler, a lead pencil and

two coloured pencils.

Fill the space below by following these directions. For each direction, ensure that your line goes ALL the way across the page.

1. Draw two sets of perpendicular lines.

2. Draw four sets of parallel lines. Turn your page so each set is going in a different direction.

3. Look carefully at where the lines intersect (cross over). Choose two colours. Colour angles smaller than a right angle using colour 1 and colour angles larger than a right angle using colour 2.

SERIES TOPIC



Which_shapes_can_you_see_in_this_diagram?

Complete_this_table_for_five_of_the_shapes_shown_above.

Name Number_of_sides Number_of_corners

a rhombus

b pentagon

c triangle

d octagon

e hexagon

Draw_a_line_to_match_each_shape_to_its_name.

Investigating 2D shapes – properties of shapes

In this topic, we are looking at the properties of 2D shapes.

1

2

3

square

triangle

rectangle

pentagon

hexagon

circle

octagon

rhombus

4 4

5 5

3 3

8 8

6 6

square, triangle, pentagon, trapezium

SERIES TOPIC



On_the_left_is_an_irregular_hexagon._It_has__6_sides_and_6_angles_but_its_sides_are_all_different_lengths._Name_each_of_the_irregular_shapes_below:

Join_the_dots_and_name_each_shape:


Let’s look more closely at hexagons, pentagons and octagons.A hexagon is a shape with 6 sides. ‘Hexa’ means 6. A regular hexagon has 6 equal sides and 6 equal angles.A pentagon is a shape with 5 sides. ‘Penta’ means 5. A regular pentagon has 5 equal sides and 5 equal angles.An octagon is a shape with 8 sides. ‘Octa’ means 8. A regular octagon has 8 equal sides and 8 equal angles.

4

5

a

___________________

b

___________________

1 2

6 5

3

4

8

7

1

25

34

You_can_do_this_by__counting_the_sides.

a

irregular ______________

b

irregular ______________

1 2

6 5

3

4

8

7

1

25

34

octagon pentagon

pentagon hexagon

SERIES TOPIC



Which_two_quadrilaterals_are_missing?_Add_them_to_the_dot_paper_below:

Which_quadrilateral_am_I?

a My opposite sides are equal in length and all my angles are right angles. _________________

b I have 4 sides that are all the same length with 2 different sized angles. _________________

c I have 4 sides with only 1 pair of parallel sides. _________________

d I have 4 sides with 2 pairs of parallel sides and 2 different sized angles. _________________

Investigating 2D shapes – quadrilaterals

Quadrilaterals are shapes with 4 sides.

1

2

square rectangle rhombus

trapezium parallelogram

square or rectangle

rhombus

trapezium

parallelogram

SERIES TOPIC



Use_the_line_of_symmetry_to_complete_each_shape.

Look_carefully_at_each_shape._For_any_that_are_symmetrical,_draw_in_the_line__of_symmetry.

Investigating 2D shapes – symmetry and tessellation

1

2 You_can_think_of_the_line_of_symmetry_as_a_mirror._One_half_of_a_design_or_shape__is_reflected.

Are_there_any__with_more_than_one__line_of_symmetry?

a b

An axis of symmetry is a line that divides something exactly in half. When one half of a shape or picture matches the other exactly, we say it’s symmetrical. This shape is

symmetrical.This shape is

asymmetrical.

R

SERIES TOPIC



Turn_the_design_in_each_square_to_create_a_pattern_along_the_grid.

Flip_the_design_in_each_square_to_create_a_pattern_along_the_grid.

Look_at_each_shape_and_write_whether_the_movement_is_a_flip,_slide_or_turn.


This tile demonstrates the movements of flip, slide and turn.

3

4

5

flip slide turn

a_

c_

b_

d_

turn

flip

slide

turn

SERIES TOPIC



Use_a_ruler_to_carefully_continue_this_tessellation_to_the_edges_of_the_dot_paper.


6

7

Use_four_colours_to_shade_each_tessellation_as_a_pattern.

a

b

c

A tessellation is a pattern of 2D shapes with no gaps or spaces. Shapes can be flipped or turned so they fit together.

Teacher check.

Teacher check.

SERIES TOPIC



1 Practice using the pieces with these challenges:

• Make a square using three triangles.

• Make a parallelogram using two triangles.

• Make a large triangle using the square and two triangles.

2 Now see if you can make the designs below. You must use all the pieces.

Tangrams investigate

Getting_ready

What_to_do

For this challenge, you will need to copy, colour and cut out the tangram pieces below.

copy

SERIES TOPIC



How many ways can you arrange the colours in a row so that the pattern is symmetrical? Use the cubes to decide on the symmetry and then record what you decide by shading each row.

Symmetry solve

Getting_ready

What_to_do

For this challenge, you will need two orange, two black and two white cubes (or three colours of your own choice, as long as you have two cubes of each colour).

Sample answers.

SERIES TOPIC



Jess_made_a_castle_from_some_blocks._How_many_of_each_3D_solid_can_you_see?

Match_the_label_to_each_3D_shape_by_connecting_them_with_a_line.


In this topic, we are looking at the properties of 3D shapes.

1

2

cube

cylinder

cone

sphere

triangular prism

square pyramid

rectangular prism

hexagonal prism

Cubes Rectangular prisms Square pyramids 16 5 3

SERIES TOPIC



Complete_this_table:

NameNumber_of__

facesNumber_of__

curved_surfacesNumber_of__

edgesNumber_of_corners

a cylinder

b cone

c sphere

Which_shape_has:

a Only one curved surface ______________

b One face and one curved surface ______________

c One curved surface and two faces ______________

Sean_made_this_model._How_many_of_each_shape_did_he_use?

Cylinders Cones Spheres

Connect_the_labels_to_the_part_of_each_solid_that_it_names:

Investigating 3D shapes – spheres, cones and cylinders

Let’s look more closely at these solids:

1

2

3

4

cylinder cone sphere

a bedge

face

curved surface

curved surface

edge

face

2 1 2 0

1 1 1 0

0 1 0 0

sphere

cone

cylinder

5 1 1

SERIES TOPIC



Rachel_painted_each_face_of_the_solids_below_and_then_stamped_each_face_in_a_row._Colour_match_each_shape_to_its_row_of_faces.

a

b

c

d

e

f

a b

Investigating 3D shapes – prisms and pyramids

A prism is a 3D shape where the two opposite faces are the same shape and the sides are rectangles.

1

A face of a 3D shape is a flat surface. A corner is where the edges meet.

Use_these_labels_on_each_shape_below:_ face_ corner_ edge2

Here is a triangular prism. Two faces are triangles and the rest of the sides are rectangles.

Y

Y Y Y

B

B B B B B B

O

O O O O O

P

P P P P P P

G

G G G G G G G G

R

R R R R R R R

face facecorner corner

edge edge

SERIES TOPIC



Name_each_pyramid_by_connecting_the_label_with_a_line._Look_carefully_at_the_base_of_each_pyramid.

Investigating 3D shapes – prisms and pyramids

Pyramids are all named according to their base. This diagram shows the properties of a square pyramid.

3

apex

edge

face

base/facecorner

hexagonal pyramid

pentagonal pyramid

square pyramid

rectangular pyramid

Complete_this_table_for_each_type_of_pyramid:

Pyramid Faces Edges Corners

a hexagonal pyramid

b pentagonal pyramid

c square pyramid

d rectangular pyramid

4

7 12 7

6 10 6

5 8 5

5 8 5

SERIES TOPIC



Each of these shapes represents the cross section of the solids below. Draw a line to match each shape to its cross section.

Investigating 3D shapes – cross sections

A cross section of a 3D shape is when you slice right through something.

1

SERIES TOPIC



If we were to cut out a cardboard cube along the edges and flatten it, it would be a net.

Draw_a_line_to_match_these_3D_shapes_with_their_nets_below:

Investigating 3D shapes – nets

1

SERIES TOPIC



3D shapes look different depending on whether you look at them from the top view, side view or front view.

Here_are_some_3D_models_made_from_cubes._Shade_in_the_squares_on_each_grid_to_show_the_top,_front_and_side_view_for_each_one._The_top_view_of_the_first_model_has_been_done_for_you.

Investigating 3D shapes – different views

1

side

top

front

a b c

Top_View

Fron

t_View

Side

_View

side

top

front

side

top

front

side

top

front

a b c

Top_view

Fron

t_view

Side

_view

a b c

Top_view

Fron

t_view

Side

_view

SERIES TOPIC



Net puzzle solve

Each net below will fold to make a cube.

Puzzle_1What symbol is opposite the star? Draw it here:

Puzzle_3This net is folded into a cube and then the cube is rolled over twice. Show what this cube will look like each time that it is rolled over. You need to show what each face on each cube will look like. One face has been done for you.

Puzzle_2Work out which numbers are opposite.

Opposite 1 is

Opposite 2 is

Opposite 3 is

21 3

4 65

What_to_do

6

4

5

SERIES TOPIC



a top row in the middle Add some chocolate sprinkles.

b middle row, last column Add some candles.

c bottom row, first column Dip the strawberries in melted chocolate.

d top row, first column Add a cherry.

e bottom row, last column Pour some maple syrup on the pancakes.

f middle row, first column Add a scoop of ice cream.

g bottom row, middle column Add some whipped cream.

Help_Chef_Claude_by_adding_the_finishing__touches_to_these_sweet_treats.

Position – describing position

When we describe the position of an object in a grid, we need to refer to the row and column. We use words such as left and right, top, middle and bottom. Rows go across and columns go up and down.

1

SERIES TOPIC



Will_played_this_game_on_his_own_and_flicked_three_counters._He_ended_up_with_a_total_of_20._Describe_the_position_of_each_counter:

Counter 1:

Counter 2:

Counter 3:

A_group_of_children_are_playing_a_game_called_Flickety_Winks._In_this_game,_they_flick_a_counter_twice_and_add_the_numbers_that_the_counters_land_on_to_see_who_ends__up_with_the_largest_score._Read_the_position_of_each_throw_and_name_the_winner.

1 6 7 3 11 10 210 2 8 12 3 9 25 9 11 4 12 21 23

Position – describing position

2

3

Counter_1 Counter_2 Total

Meltop row, second from the left

bottom row, third from the right

Jobottom row, third from the right

middle row, on the furthest right

Hamishmiddle row, second from the right

top row, fifth from the left

Ninabottom row, second from the right

top row, third from the left

The winner was ________________.

6 + 12 = 18

12 + 2 = 14

9 + 11 = 20

21 + 7 = 28

Nina

Answers will vary.

SERIES TOPIC



Roll_a_die_and_move_that_number_of_spaces_in_any_direction,_colouring_in_as_you_go._You_must_move_in_a_different_direction_each_time._Start_at_the_arrow.

a Your aim is get to the star in the least number of moves. Compare your number of moves with someone near you.

Aisha_is_playing_a_game_on_her_mobile_phone_where_she_has_to_move_the_snake_from_one_end_of_the_grid_to_the_other_without_bumping_into_the_black_holes._Complete_the_directions_that_she_used_for_each_game._Start_at_the_smiley_face_and_finish_at_the_star.

Position – following directions

On this page, you will practise following the directions up, down, left and right.

1

2

a b

2 up

2 left

1 up

3 left

Start_here

Start_here

Start_here

b List the number of moves and the direction here:

Teacher check.

Answers will vary.

2 up

2 left

2 up

1 left

2 up

4 right

1 down

2 right

2 up

1 up

3 left

1 up

1 left

2 up

1 left

2 up

5 right

1 up

SERIES TOPIC



Look_carefully_at_the_map_and_answer_the_questions:

a Adam crosses over Blossom Street, walks down Rosebud Road and turns left into Fig Tree Street. If he keeps walking he ends up on _____________________

b Emily walks to the end of her street and turns left into Sunny Avenue and then right into _____________________

c Max walks to the end of his street and turns left into Sunny Avenue, then right into Narree Road and left into Phillips Road and left again at Blossom Street. Who is he visiting? _____________________

d There is a shorter way he could have walked. Write him some directions below:

Colour_the_faces_according_to_where_each_person_lives:

a Libby lives on Whitley Crescent. Colour this face green.

b Max lives on Johnston Street. Colour this face blue.

c Emily lives on Narree Road. Colour this face red.

d Adam lives on the corner of Rosebud Road and Blossom Street. Colour this face orange.

A_group_of__four_friends_live_in_the_same_neighbourhood._Each_smiley_face_shows_where_someone_lives.

Position – following directions

3

4

Kerry Place

Blossom Street

Sunshine Avenue

Narree Road

Fig Tree Street

Phill

ips

Road

Rose

bud

Road

Sunn

y Av

enueFoxh

ill S

tree

t

Whitley Crescent

Johnston Street

O

R

G

B

Phillips Road

Johnston Street

Adam

Turn right into Foxhill Street, left into Fig Tree Street and right into Rosebud Road.

SERIES TOPIC



Practise_using_grid_coordinates_by_following_these_instructions:

a Write an even number in A1.

b Write the first letter of your name in D2.

c In C4, draw a 2D shape that has more than 4 sides.

d In B2, write a number that is divisible by 3.

e In D4, write your age.

f Write the answer to 6 × 4 in C1.

g List all the blank grid spaces. Remember that it is letter then number.

_________________________________________________________________

This_map_is_missing_some_places._Draw_them_in:

a A lake that covers A4 and B4.b Swings at A2.c Jet skis at C4.d A shed at D4.e Trees that cover C3 and D3.

Here_is_a_map_of_a_holiday_camping_ground._What_is_at:

a A1 ____________________

b A3 ____________________

c C2 ____________________

d D1 ____________________

Position – grids and coordinates

Maps are often set up in a grid with letters and numbers down the sides. We use these letters and numbers to pinpoint a particular part of the map. Letters always go before numbers.

1

2

3

A B C D

1

2

3

4

A B C D

1

2

3

4

Slide

Kayaks

Caravans

Tents

A2, A3, A4, B1, B3, B4, C2, C3, D1, D3

4 24

9 N

8Sample answers.

SERIES TOPIC



If_photo_1_was_taken_facing_north,_what_direction_was_the_person_facing_in_photo_2?

Sometimes_north_is_not_directly_in_front_of_us._Answer_these_questions._You_will_need_to_look_carefully_to_see_where_north_is.

What_directions_are_the_shapes_from_the_circle?

a The square is ___________ of the circle.

b The pentagon is ___________ of the circle.

c The triangle is ___________ of the circle.

d The heart is ___________ of the circle.

Position – compass points

We can use a compass to help us with direction. There are four main points on a compass – north, south, east and west.

1

2

3

N

S

W E

a Which shape is located west? b Which shape is located south?

Photo_1 Photo_2

N

west

north

south

east

east

SERIES TOPIC



Each player places the numbers and black squares on their grid without the other player seeing. Take turns to find each other’s numbers by calling out coordinates. The aim of the game is to find out where all the numbers are before the other player does. The numbers that are found make up the score. If you call out a coordinate that is a black square, then you miss a turn.

Hit the points apply

Getting_ready

What_to_do

copy

This is a game for two players. For this game, each player will need their own copy of this page. Cut out the numbers and black squares at the bottom of this page.

6

5

4

3

2

1

A B C D E F G H I J K

5 10 20 2 8

You_call_out__the_letter__before_the__number.

29Series D Topic 1 Assessment

Copyright © 3P Learning

Skills Not_yet Kind_of Got_it

• Recognises parallel and perpendicular lines

• Identifies angles in 2D shapes

• Describes angle size as a right angle, smaller or larger than a right angle

Lines and angles Name __________________

Complete_this_table_for_the_shapes_below:

Order_these_angles_from_smallest_to_largest_by_writing_1_to_4_under_each_one._Put_a_tick_next_to_the_right_angle.

Connect_each_set_of_lines_to_the_correct_name:1

2

3

perpendicularparallel

Shape_A Shape_B

a How many angles are smaller than a right angle?

b How many angles are larger than a right angle?

Shape_A Shape_B

30 Series D Topic 1 Assessment



• Recognises parallel and perpendicular lines

• Identifies angles in 2D shapes

• Describes angle size as a right angle, smaller or larger than a right angle

Lines and angles Name __________________

Complete_this_table_for_the_shapes_below:

Order_these_angles_from_smallest_to_largest_by_writing_1_to_4_under_each_one._Put_a_tick_next_to_the_right_angle.

Connect_each_set_of_lines_to_the_correct_name:1

2

3

perpendicularparallel

Shape_A Shape_B

a How many angles are smaller than a right angle?

b How many angles are larger than a right angle?

Shape_A Shape_B

4 3

1 2

1 4 3 2



Investigating 2D shapes Name __________________

Which_shape_am_I?_Circle_the_correct_answer.

I have 4 sides but I am not a square. My opposite angles are equal and not all sides are the same length. I have 2 pairs of parallel lines.

I am a parallelogram. I am a rhombus.

Complete_the_table_for_these_2D_shapes:


• Names 2D shapes: square, circle, rectangle, triangle, pentagon, hexagon, octagon, rhombus

• Describes 2D shapes by the number of sides and angles

Connect_each_of_these_2D_shapes_to_the_correct_name:1

Name Number_of_sides Number_of_angles

a

b

c

octagon hexagon rectangle square

2

3




How_has_the_tile_been_moved_each_time?_Write_flip,_slide_or_turn_in_each_box.

Create_a_symmetrical_design_in_this_grid._Shade_whole_squares.

Draw_one_line_of_symmetry_on_these_shapes:


• Classifies objects as symmetrical or not

• Identifies some lines of symmetry for a 2D shape

• Can recognise whether a shape or pattern has been turned

Tick_the_shapes_that_are_symmetrical_and_cross_the_shapes_that_are_not_in_each_box.4

a b c d

a b c d

5

6

7




Which_shape_am_I?_Circle_the_correct_answer.

I have 4 sides but I am not a square. My opposite angles are equal and not all sides are the same length. I have 2 pairs of parallel lines.

I am a parallelogram. I am a rhombus.

Complete_the_table_for_these_2D_shapes:


• Names 2D shapes: square, circle, rectangle, triangle, pentagon, hexagon, octagon, rhombus

• Describes 2D shapes by the number of sides and angles

Connect_each_of_these_2D_shapes_to_the_correct_name:1

Name Number_of_sides Number_of_angles

a

b

c

octagon hexagon rectangle square

2

3

circle 1 0

pentagon 5 5

rhombus 4 4




How_has_the_tile_been_moved_each_time?_Write_flip,_slide_or_turn_in_each_box.

Create_a_symmetrical_design_in_this_grid._Shade_whole_squares.

Draw_one_line_of_symmetry_on_these_shapes:


• Classifies objects as symmetrical or not

• Identifies some lines of symmetry for a 2D shape

• Can recognise whether a shape or pattern has been turned

Tick_the_shapes_that_are_symmetrical_and_cross_the_shapes_that_are_not_in_each_box.4

a b c d

a b c d

5

6

7

Answers will vary.

slide turn turn flip

Teacher check.



Draw_the_cross_section_of_this_shape:

Name_the_shape_for_each_net:



• Names common prisms, pyramids, cylinders, cones and spheres

• Identifies a cross section of a 3D object

• Recognises the nets of common 3D objects

Link_each_shape_to_the_correct_name_with_a_line:1

cube

cylinder

cone

sphere

triangular prism

square pyramid

rectangular prism

hexagonal prism

2

3

a

_________________

b

_________________

c

_________________

a b



Draw_the_cross_section_of_this_shape:

Name_the_shape_for_each_net:



• Names common prisms, pyramids, cylinders, cones and spheres

• Identifies a cross section of a 3D object

• Recognises the nets of common 3D objects

Link_each_shape_to_the_correct_name_with_a_line:1

cube

cylinder

cone

sphere

triangular prism

square pyramid

rectangular prism

hexagonal prism

2

3

a

_________________

b

_________________

c

_________________

a b

rectangular prism cube cylinder



Position Name __________________

Carly’s_house_is_at_A._Her_friend_Jo’s__house_is_at_B._This_is_the_way_Carly_walks__to_Jo’s_house._Is_there_a_shorter_way_she__can_go?_Describe_it_below:

Follow_the_directions_for_the_grid_on_the_right.

a Draw a large dot in B3.

b Write the first letter of your name in C1.

c Draw an arrow facing left in A2.

d Write the answer to 2 × 3 in C2.

e Which spaces are blank?

___________________________________


• Uses N, S, E and W to describe location

• Uses grid coordinates to describe position

• Describes a route on a basic map

Describe_the_position_of_these_Mathletes_using_the_compass.

a Mia is __________ of Casey.

b Dixie is __________ of Joe.

c Casey is __________ of Dixie.

d Joe is __________ of Mia.

1

2

3

3

2

1

A B C

North

South

EastWest

Dixie Casey

Joe Mia

A

B

Montana Ave

Arrow Rd Arrow Rd

Elder RdBerr

y St

Char

m S

t

Holt

St



Position Name __________________

Carly’s_house_is_at_A._Her_friend_Jo’s__house_is_at_B._This_is_the_way_Carly_walks__to_Jo’s_house._Is_there_a_shorter_way_she__can_go?_Describe_it_below:

Follow_the_directions_for_the_grid_on_the_right.

a Draw a large dot in B3.

b Write the first letter of your name in C1.

c Draw an arrow facing left in A2.

d Write the answer to 2 × 3 in C2.

e Which spaces are blank?

___________________________________


• Uses N, S, E and W to describe location

• Uses grid coordinates to describe position

• Describes a route on a basic map

Describe_the_position_of_these_Mathletes_using_the_compass.

a Mia is __________ of Casey.

b Dixie is __________ of Joe.

c Casey is __________ of Dixie.

d Joe is __________ of Mia.

1

2

3

3

2

1

A B C

North

South

EastWest

Dixie Casey

Joe Mia

A

B

Montana Ave

Arrow Rd Arrow Rd

Elder RdBerr

y St

Char

m S

t

Holt

St

south

north

east

west

A1, A3, B1, B2, C3

6

letter

Answers will vary.

39Series D Outcomes



Region Outcomes

NSW

SGS2.1_–_Makes,_compares,_describes_and_names_three-dimensional_objects_including_pyramids,_and_represents_them_in_drawings

• comparing and describing features of prisms, pyramids, cylinders, cones and spheres• identifying and naming three-dimensional objects as prisms, pyramids, cylinders, cones and

spheres• recognising similarities and differences between prisms, pyramids, cylinders, cones and spheres• identifying three-dimensional objects in the environment and from drawings, photographs

or descriptions• making models of prisms, pyramids, cylinders, cones and spheres given a three-dimensional

object, picture or photograph to view• sketching prisms, pyramids, cylinders and cones, attempting to show depth• creating nets from everyday packages• sketching three-dimensional objects from different views including top, front and side views• making and visualising the resulting cut face (plane section) when a three-dimensional object

receives a straight cut• recognising that prisms have a uniform cross-section when the section is parallel to the base• recognising that pyramids do not have a uniform cross-section

SGS2.2_–_Manipulates,_compares,_sketches_and_names_two-dimensional_shapes_and_describes_their_features

• manipulating, comparing and describing features of two-dimensional shapes, including pentagons, octagons and parallelograms

• identifying and naming pentagons, octagons, trapeziums and parallelograms presented in different orientations

• comparing and describing the features of special groups of quadrilaterals• using measurement to describe features of two-dimensional shapes e.g. the opposite sides of

a parallelogram are the same length• grouping two-dimensional shapes using multiple attributes• making representations of two-dimensional shapes in different orientations• constructing two-dimensional shapes from a variety of materials• comparing the rigidity of two-dimensional frames of three sides with those of four or more sides• making tessellating designs by reflecting (flipping), translating (sliding) and rotating (turning)

a two-dimensional shape• finding lines of symmetry for a given shape• identifies, compares and describes angles in practical situations• identifying and naming perpendicular lines• identifying angles with two arms in practical situations• identifying the arms and vertex of the angle in an opening, a slope and a turn where one arm

is visible• comparing angles using informal means such as an angle tester• describing angles using everyday language and the term ‘right’ to describe the angle formed

when perpendicular lines meet• drawing angles of various sizes by tracing along the adjacent sides of shapes and describing the

angle drawn

40 Series D Outcomes



Region Outcomes

NSW

SGS2.3_–_Uses_simple_maps_and_grids_to_represent_position_and_follow_routes

• describing the location of an object using more than one descriptor• using a key or legend to locate specific objects• constructing simple maps and plans• using given directions to follow a route on a simple map• drawing and describing a path or route on a simple map or plan• using coordinates on simple maps to describe position• plotting points at given coordinates• using a compass to find North and hence East, South and West• using an arrow to represent North on a map• determining the directions N, S, E and W, given one of the directions• using N, S, E and W to describe the location of an object on a simple map, given an arrow that

represents North• using a compass rose to indicate each of the key directions• determining the directions NE, NW, SE and SW, given one of the directions• using NE, NW, SE and SW to describe the location of an object on a simple map, given a

compass rose

VIC

Measurement_VELS__Level_3

• students recognise and describe the directions of lines as vertical, horizontal or diagonal• they recognise angles are the result of rotation of lines with a common end-point• they recognise and describe polygons• they recognise and name common three-dimensional shapes such as spheres, prisms and pyramids• they identify edges, vertices and faces• they use two-dimensional nets, cross-sections and simple projections to represent simple three-

dimensional shapes• they follow instructions to produce simple tessellations (for example, with triangles, rectangles,

hexagons) and puzzles such as tangrams• they locate and identify places on maps and diagrams• they give travel directions and describe positions using simple compass directions (for example,

N for North) and grid references on a street directory

QLD

3.S.1_Geometric_names_and_properties_are_used_to_sort,_describe_and_construct_common_2D_shapes,_including_squares,_rectangles,_triangles_and_circles,_and_3D_objects,_including_prisms,_pyramids,_cones,_cylinders_and_spheres_e.g._3D_objects_can_be_created_using_modelling_material;_pinwheels,_paper_planes_and_flowers_can_be_created_by_folding_and_cutting_paper

• flips, slides and turns are particular ways of moving shapes to explore symmetry e.g. complete simple visual puzzles; create repeat patterns

• obvious features in everyday environments can be represented and located on simple maps and plans e.g. construct a map of a simple obstacle course around the school grounds

• directions can be given for moving and for locating features within an environment e.g. instruction to move a half, full, quarter and/or three-quarter turn

41Series D Outcomes


Region Outcomes

SA

2.12_Describes_and_reports_common_characteristics_of_‘families’_of_plane_figures_(e.g._polygons,_prisms,_pyramids)

• analyses and uses spatial terms (e.g. face, edge, vertex, parallel, symmetry, angle) to describe figures and solids in their world

• describes how plane figures are different from solids (e.g. describing how a square is different from a cube)

• represents geometric figures and objects featured in everyday circumstances, including using interactive drawing software and paying attention to appropriate attributes (e.g. straight/flat or curved boundary, angle, parallel sides/faces, cross-section, line/plane symmetry, vertex, edges and faces, function)

2.13_Predicts,_describes_and_represents_the_result_of_using_combinations_of_reflections_(flips),_translations_(slides)_and_rotations_when_arranging_shapes,_searching_for_patterns_and__describing_pathways

• uses ‘flips’, ‘slides’ and rotations to describe movements when matching congruent figures, and when creating patterns with congruent figures; uses ‘rotate’ and ‘slide’ when describing movement between locations

• creates a tessellation from regular polygons (e.g. pattern blocks)• describes the repeating element of the tessellation, and how it was moved to create the tessellation• plans and predicts the result of a combination of reflections, translations and rotations

2.14_Uses_positional_language_and_measurements_to_formally_map_location_and_arrangements

• gives and follows directions from a chosen reference point, using positional language and measurements of distance (e.g. paces, metric units, directions (fractions of a rotation)). They choose the best pathway from a number of alternatives

• represents and communicates information about familiar locations and pathways between locations. They use unscaled maps that show distance and direction, or maps based on a coordinate grid

• produces electronic plans of arrangements of objects to represent different views (e.g. top, left, right and back view)

• identifies key features of maps and plan produced by peers, and uses them to locate objects or construct arrangements

WA

Level_3

Represent_location• understands a map or plan as a ‘bird’s-eye view’ and uses order, proximity and directional

language associated with quarter and half turns on maps and in descriptions of locations and pathsRepresent_shape• attends to the shape and placement of parts when matching, making and drawing things,

including matching 3D models that can be seen and handled with conventional drawings of them and with their nets

Represent_transformations• recognises repetitions of the same shape within arrangements and patterns and uses repetitions

of figures and objects systematically to produce arrangements and patterns


42 Series D Outcomes


Region Outcomes

NT

S_KGP_2.1_3D_objects_and_2D_shapes• recognise and describe 3D objects, 2D shapes and lines using everyday languageS_KGP_2.2_Lines_and_angles• identify, draw and describe lines using everyday languageS_KGP_2.3_Transformations• recognise, use and describe single transformations in 3D objects and drawingsS_KGP_2.4_Location• describe the position of nominated everyday objects in familiar locations

TAS

Standards_2–3,_Stages_4–8

• associating common 3D shapes to everyday items e.g. ball, ice cream cone, box• naming and describing common 3D shapes (e.g. cylinder, cube, rectangular prism) and their

attributes e.g. which ones roll, which ones will stack well, which would be good for storing particular items

• directions for location and movement e.g. consolidating left and right as indicators of direction• exploring what happens to shapes when they are rotated or flipped and using them to

create patterns• exploring simple symmetry by folding paper, use of pattern blocks and other materials• i ntroducing common 3D shapes and exploring how different shapes stack, pack and roll• exploring how shapes can be broken up into other shapes and how shapes can be moved

and rotated• sorting and classifying shapes by their characteristics e.g. through use of attribute and pattern

blocks and other materials (everyday items such as plates, squared paper)• making models and exploring how shapes fit together e.g. through use of pattern blocks,

geoboards and tangrams• focusing on the need for greater specificity of positional language e.g. ‘It’s between the front

door and the flagpole but it is closer to the flagpole.’• focusing on slides, flips and turns in patterning and shape investigations• discussing and demonstrating of turns (e.g. a full turn, half turn, what turns) as an introduction

to angle• using the language of shape to describe 2D and 3D shapes and their features e.g. faces, edges• drawing and constructing models of simple 3D shapes e.g. making a cube with straws and

Blu Tac• focusing on the properties of and connections between 2D shapes and 3D objects and building

the language to describe shapes e.g. sides, faces, vertices• exploring flips, slides and turns in working with shapes and patterns• experiences with a wide range of maps types and exposure to major compass points (N, S, E, W)• introduction to maps with some grid references and major compass points• further investigating symmetry using mirrors, folding and other techniques• exploring the difference between 2D and 3D shapes and how they are linked• making models and sketches of common 3D shapes• focusing on the mathematical properties of common 3D shapes and using appropriate language

to describe their features• recognising informal angles in shapes and turns e.g. in a slice of pizza, the corners of a box or the

closing of a door


43Series D Outcomes



Region Outcomes

TAS

• continuing to explore flips, slides and turns and their effects on shapes and patterns• using symmetry and/or transformations to create or continue patterns, including tessellations• giving more specific directions for moving from one point to another• exploring the two-dimensional nets of common 3D shapes e.g. a toothpaste box• investigating visual imagery of shapes and structures from different viewpoints and orientations• naming, describing, sorting and representing common 2D and 3D shapes in a range of ways

(including with technology) and describing their properties using correct mathematical language• using common language and basic compass points to describe position and location in relation

to maps, grids and plans• focusing on how 3D objects are constructed from 2D nets. Continuing to explore flips, slides and

turns and how they affect common shapes and using them to complete simple puzzles such as tangrams

• exploring symmetry and using strategies such as folding and mirrors to confirm that shapes are symmetrical

• exploring how shapes can be represented from different viewpoints and how we might represent these using technology and sketches

• continuing to build correct terminology for shapes and angles• exploring map legends and the use of grids, keys etc to move around an environment• conducting investigations and solving problems that focus on shape, including visualising,

drawing, transforming, constructing and deconstructing shapes and objects e.g. ‘Why are milk cartons shaped the way they are?’ ‘How does this structure look from above, the side, in front?

• engaging students with computer programs that allow building and visualisation of shapes and objects

• interpreting maps and plans with reference to conventions, e.g. grid references and major compass points

• focus on constructing and deconstructing shapes with materials, software packages and objects as well as visualising shapes from different perspectives

• matching nets of common 3D shapes to the shape• exploring tessellations and beginning to explain why some shapes will and will not tessellate• beginning to explore simple scales on maps

ACARA

M3MG1 Use symmetry, identifying its occurrence in the environment to create symmetrical patterns, pictures and shapesM3MG6Create angles and recognise that equivalence in angles such as two quarter turns is the same as a straight angleM3MG7Create and interpret simple maps to show position and pathways between objects

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