Maths Enrichment: Measurement

- MEASUREMENT -

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Published by R.I.C. Publications http://www.ricgroup.com.au

Foreword This three book series has been written for middle to upper primary students as enrichment and extension activities. The three books cover the major areas of mathematics (number, space and measurement) and provide a variety of activities which aim to motivate and challenge young mathematical minds.

The activities in Maths Enrichment - Measurement are divided into three areas; tangrams, scale and coordinate points. While labelled as measurement activities each of the three sections has a strong link to the other major curriculum areas of space and number and this association is worth focusing on with students.

'Tangrams' uses a well-known method of problem solving to develop concepts such as mirror images, rotation and development of general problem-solving strategies to provide high-interest activities. The concept of tangrams can be expanded well outside the activities provided.

'Scale' focuses on measurement using a variety of scales which develop basic number facts as well as having application in other subject areas.

'Coordinate points' develop the concept of measuring and giving accurate directions using coordinate points.

Contents Section 1 - Tangrams Page Page Page Page Page Page Page Page

1 2 3 4 5 6 7 8

What is Tangram?

Making a Tangram Other Shapes from a Tangram Making Tangram Drawings 1 Making Tangram Drawings 2 Making Tangram Drawings 3 Making Tangram Drawings 4 Tangram Answers/Activities

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y• Section 2 - Scale Page 9 Page 10 Page 11 Page 12 Page 13 Page 14 Page 15 Page 16

Scale Pirate Island Around Town Lost Continent Around the World Fantasy Island 1 Fantasy Island 2 City Centre

Section 3 - Coordinate Points Page 17 Page 18 Page 19 Page 20 Page 21 Page 22 Page 23 Page 24

Horizontal and Vertical Messages Noughts and Crosses Grid Travels Grid Distortions 1 Grid Distortions 2 Islands World Grid

Page 25

Answers

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i

What is a Tangram?

A tangram is a Chinese shape puzzle which is thousands of years old. It consists of a square that has been cut into seven shapes. The tangram contains the following shapes: • two large triangles; • one medium triangle; • two small triangles; • a square; and • a parallelogram.

Look carefully at the tangram below. Then cut it out. You will need this tangram to complete activities on some of the following pages.

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

What can you see about the shapes that make up the tangram? How are the shapes special? How do they relate to each other?

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Concept of a tangram

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1

Making a Tangram Use the grids below to make your own tangram. Remember that a tangram is based on certain proportions; in fact you can fold a square piece of paper into a tangram. Try to draw your second tangram in a different way.

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Measuring to proportion

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2

Other Shapes from a Tangram Although the tangram is based on a square many other shapes and drawings can be made from the pieces in a tangram. Below are outlines of a rectangle, a triangle and a parallelogram. These shapes can be made from the tangram pieces. Try to make them with your tangram pieces. Mark on the drawings where each tangram shape has been placed.

rectangle

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parallelogram EXTENSION MATHS - MEASUREMENT

Making shapes with tangrams

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3

Making Tangram Drawings 1 Use the tangram pieces to construct the following drawings. Mark on the drawings where each tangram shape has been placed.

duck

© R. I .

C.Publ i cat i ons dog •f orr evi ew pur posesonl y•

cat

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Making shapes with tangrams

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4

Making Tangram Drawings 2 Use the tangram pieces to construct the following drawings. Mark on the drawings where each tangram shape has been placed.

pram

sailboat

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watering can

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Making shapes with tangrams

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5

Making Tangram Drawings 3 Use the tangram pieces to construct the following drawings. Mark on the drawings where each tangram shape has been placed.

shoe

running person

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swimming swan

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Problem solving with tangrams

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Making Tangram Drawings 4 Use the tangram pieces to construct the following drawings. Mark on the drawings where each tangram shape has been placed.

mouse

© R. I .

C.Publ i cat i ons crow •f orr evi ew pur posesonl y•

teapot

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Problem solving with tangrams

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7

Tangram Answers/Activities This sheet can be used by students for self-marking or as an activity sheet for making the tangram models represented below. More answers are possible than those provided. If all tangram pieces are used then the answer must be correct.

rectangle

triangle

duck

dog

parallelogram

cat

sailboat © R. I .

C .Publ i cat i onswatering can •f orr evi ew pur posesonl y•

pram

shoe

mouse

running person

crow

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swimming swan

teapot

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8

Scale What do each of the scales below mean when located on a map?

1.

(a) 0

150

300 km

(b)

0

60

120 m

(c)

0

2.

200 m ©100R. I .

C.Pu bl i cat i ons •f oscales rr e vi ewplace pu r p os sonl yfollowing.

• Construct you could on a map toe represent the

(a) 1 cm = 100 km

(b) 1 cm = 50 m

(c) 1 mm = 100 m

3.

What scales do you think you would find on a: (a) world map (b) street map (c) plan of a house (d) 'mud' map

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Relationship between units of measure

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9

Pirate Island Answer the questions about Pirate Island by using the scale provided.

N

Whale Point W

E S

Flat Rock Well

Tar Pit

Cave

Rocky Point

Treasure

Surf Beach © R. I .

C.Publ i ca t i ons •f or r evi ew pur posesonl y• 0 600 m 300

South Point

1.

What is the distance from the Cave to Whale Point?

2.

How far is it from South Point to the Tar Pit?

3.

If you travelled from Flat Rock to the Well and then to Rocky Point, what distance would you have covered?

4.

What is the distance from Surf Beach to Flat Rock?

5.

How far is it from the Well to South Point?

6.

(a) Which two places on the map are furthermost away from each other?

(b) How far apart are they?

EXTENSION MATHS - MEASUREMENT

Scale - meaning and conversion

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10

Around Town

N W

Look carefully at the map of a small town.

Use the scale to help you answer the questions.

E S

Bus Station

Service Station

House

Alfred Street Post Office

House

House

House

House

Page Place

House

Market Street

Sue Place

Shopping Centre

Hill Road

High Road

House

House

Smith Street

Day Avenue

© R. I .

C.Publ i cat i ons Police School •f orr evi ewStation pur poseso nl y• Park

0

150

300 m

1. What is the length of Hill Road?

4. How long is Market Street?

2. What is the area of the School?

5. What is the area of the Park?

3. What is the frontage of the Service Station?

6. What is the total length of Alfred and Smith Streets?

EXTENSION MATHS - MEASUREMENT

Scale - measure and conversion of length and area

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11

Lost Continent Below is a map of the lost continent island of 'Eera'. It is inhabited by humanlike creatures called 'Dumans'. They are a highly developed species and have invented special low-flying, all-terrain vehicles called 'Hoverpods'. These allow the Dumans to travel to their cities in straight lines without the need of roads.

Use the scale to answer the questions about travelling around Eera.

0

700

1 400 km

Dar

Tows

Boom

Bane

Can

Als

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl ySid • Pert

Mals

Ad

1. Use the scale and map to calculate the following distances. (a) Pert to Sid

(e) Ad to Dar

(b) Mals to Tows

(f)

(c) Can to Als

(g) Pert to Ad to Mals

(d) Dar to Bane to Can

(h) Pert to Als to Dar

Bane to Boom

2. If a hoverpod travels 10 kilometres on one litre of fuel, how many litres of fuel are needed to travel from Pert to Boom to Dar?

EXTENSION MATHS - MEASUREMENT

Scale - measurement and conversion

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12

Around the World Use the scale below to calculate the following distances.

(Measure to the nearest half centimetre.)

1. Perth to Sydney 2. Rio de Janeiro to Cape Town 3. Tokyo to Los Angeles 4. Sydney to New York 5. London to Singapore 6. Perth to Sydney to Los Angeles 7. Singapore to Cape Town to London 8. Tokyo to Los Angeles to New York to London 9. New York to Cape Town to Perth

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

10. Perth to Tokyo to Sydney

0

4 000

8 000 km

London

Tokyo

Los Angeles

New York

Singapore Rio de Janeiro

Cape Town

EXTENSION MATHS - MEASUREMENT

Perth

Sydney

Calculating long distances by scale

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13

Fantasy Island 1 Study the map and scale below carefully.

Long Point White Cliffs Dinosaur Cave

West End

Shelter Cove Dark Cave Diamond Beach

Gold Beach

3-km Beach

Pirate Cove N W

E S

0

4

8 km

© R. I .

C.Publ i cat i ons You are• shipwrecked atv West travel 3o kilometres overland an easterly f orr e i eEnd wand pu r p seso nl yin• 1.

Use a red pencil to mark the following route on the map.

direction. You then travel south for 1.5 kilometres and then 2 kilometres SW until you reach

. Little is found here so you travel 4

kilometres in a NE direction. At this point you can see a little distance off to the NW. You then travel ESE for 1 000 metres where you reach

2.

. A rescue ship is waiting for you here.

Use a blue pencil to mark the following route on the map.

You are shipwrecked at White Cliffs and are forced to travel in search of food and water. You travel SSE for 3 kilometres where you find

. From

here you travel ESE for 4 kilometres where you reach the coast at . Still there is no water so you travel WSW for 4 kilometres and reach

. You then travel west for 4 kilometres where

you meet a rescue party at EXTENSION MATHS - MEASUREMENT

.

Interpreting data and representing by scale

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14

Fantasy Island 2 Long Point White Cliffs Dinosaur Cave

West End

Shelter Cove Dark Cave Diamond Beach

Gold Beach

3-km Beach

Pirate Cove

N W

0

4

8 km

E S

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

1.

Give accurate instructions about how you would get from West End to 3-km Beach via Shelter Cove and White Cliffs.

2.

Give accurate instructions about how to get from Long Point to Diamond Beach via two other locations of your choice.

EXTENSION MATHS - MEASUREMENT

Using scale to provide directions

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15

,

, ,

,

, , , , ,,

, ,

,, ,,

City Centre

Look carefully at the map and scale below.

Follow the directions and complete the questions.

1.

Shops

Housing

Service Station

Housing

800 m

Use a blue pencil to trace the following route onto the map.

Walsh Street

Park

1st Ave

Industrial Area

Housing

Shopping Centre

Leanne Drive

Jones Avenue

You depart the service station and

Smith Street

2nd Ave

Government Offices

travel 800 metres south along Jones

Ave where you reach a T-junction at

Housing

the corner of

Moore Street

N

Hospital

W

left into

Street.

From here, you travel east along

E

S

Moore Street for 600 metres and turn

Street. After you travel 600 metres along this street, to

© R. I .

C.Publ i cat i ons Use a red pencil to trace the following route onto the street map.

•the f o rcorner r evofi e w pur po se so l y• From NW the industrial area you travel SWn across the park for

your east is

2.

400

Housing

Pole Street

Housing

0

.

700 metres. You are now at the corner of

and

. Travel south 400 metres and turn east into , where you travel for one kilometre. Travel north for 600 metres, where you turn east into 3.

.

Give accurate instructions about how to get from the northernmost point of Leanne Drive to the SW corner of the shopping centre. Make sure that you include distances and directions.

EXTENSION MATHS - MEASUREMENT

Identifying and constructing routes to scale

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16

Horizontal and Vertical The coordinates of a point are the two numbers which locate it on a grid. For example, the dot on the grid below has the coordinates of (4,7). The 4 shows the horizontal number and the 7 shows the vertical number.

1.

(a) Draw black dots on these coordinate points.

(7,7), (7,4), (4,4) (b) Join these points together.

What shape have you made?

10 9 8 7 6 5 4 3 2 1 0

1

2

3

4

5

6

7

8

9 10

(c) Draw another square on the grid and give the four coordinate points you use. ( , ) ( , ) ( , ) ( , ) 2.

© R. I .

C.Publ i cat i ons 3. (a) What are the coordinates for •f orr evi ew p ur pthe os es on yline • end points ofl the

How many coordinate points would you need to draw a hexagon?

10 9 8

A

B

E

7 6 5

segment GH? ( , )

C

D

3

,

)

(b) To locate any part of the line segment GH, what horizontal number will always be needed? Explain your answer.

G

4

(

2 1 0

H 1

F 2

3

4

5

6

7

8

9 10

(c) Give all the coordinate points where the line segment CD crosses the grid lines. ( , ) ( , ) ( , ) ( , ) ( , ) (d) What vertical number is needed to describe any part of line segment AB? EXTENSION MATHS - MEASUREMENT

Measurement using coordinate points

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17

Messages 1. Why did the apple turnover?

The answer to that question is hidden in the coordinate code below. Each pair of coordinate numbers stands for a letter.

A

10

O

Q

E K

9

I

8

U

D H

7

T

6

J B

5

Z

S

F

4

Y V

3

W

2

P

R

C

L

G

1 0

X

(3,5)

(6,10)

(6,2)

(1,10)

(3,8)

(8,5)

(6,10)

(8,7)

(6,10)

(8,5)

(1,10)

(1,2)

(2,6)

(8,7)

(6,10)

(8,5)

(1,10)

(9,2)

(1,10)

(5,8)

(5,8)

(3,2)

(6,10)

(8,5)

(8,5)

(1,8)

(9,1)

(4,1)

N

M

1

2

3

4

5

6

7

8

9 10

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y• Use this grid to make up your own

Answer 2.

A

10

message. Give the message to a friend to decode.

I

8

,

)

(

,

)

(

,

)

7

(

,

)

(

,

)

(

,

)

6

(

,

)

(

,

)

(

,

U

E

D H

T

J B

5

)

Q

K

9

(

O

Z

F

4

Y

(

,

)

(

,

)

(

,

)

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(

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EXTENSION MATHS - MEASUREMENT

S

V

3

W

2

P

R

C

L

G

1

X

N

M

0

1

2

Problem solving/coordinate points

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3

4

5

6

7

8

9 10

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18

Noughts and Crosses 1.

This is a game for two players.

Use coordinate points to nominate positions on the grid.

Mark each location with either an O or an X. The winner is the first person to get four positions in a row vertically, horizontally or diagonally. Write down the coordinate points you use.

10

Player 1

9

Player 2

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

8

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

7 6

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

5

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

4

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

3

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

2

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

1

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

0

2.

© R. I .

C.Publ i cat i ons • rr ev i e w pur posesonl y• This isf ao game for two players.

1

2

3

4

5

6

7

8

9 10

This game is similar to the last game but you get to nominate 2 positions every turn. However, you must get six positions in a row vertically, horizontally or diagonally. Write down the coordinate points you use.

10

Player 1

9

Player 2

8

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

7

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

6

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

5

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

4

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

3

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

2

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

1 0

( , ) ( , ) ( , ) ( , ) ( , ) ( , ) 1

2

3

4

5

6

EXTENSION MATHS - MEASUREMENT

7

8

9 10

Problem solving/coordinate points

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19

Grid Travels 1.

The dark line on the grid below shows the way a snail travelled through the grid. Describe its travels by using coordinate points to show where the snail has turned.

10

finish

Start

( , )

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

9 8

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

7 6

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

5

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

4 3

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

2

Finish ( , )

1 0

start

1

© R. I .

C.Publ i cat i ons •f orr ev eThe wdark pu r p othe se so nl y •the way 2.i line on grid below shows 2

3

4

5

6

7

8

9 10

another snail travelled through the grid. Describe its travels by using coordinate points to show where the snail has turned.

Start 10

( , )

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

start

9

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

8 7

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

6 5

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

4

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

3 2

( , ) ( , ) ( , ) ( , ) ( , ) ( , )

1 0

finish

1

2

3

4

5

6

7

8

9 10

( , ) ( , ) ( , ) ( , ) ( , )

Finish ( , ) EXTENSION MATHS - MEASUREMENT

Problem solving/coordinate points

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20

Grid Distortions 1 Grids with coordinates can be used to duplicate, enlarge, reduce and distort pictures.

The grid below with the picture of the pig is based on squares. The grid at the bottom of the page with the pig has been distorted by doubling the width of each grid square. The picture of the pig has been 10 redrawn using identical coordinates and as a result we find that the pig has been 9 distorted. The pig is still the same height but twice its original width. Distort the pig on the blank grid so that it is twice its 8 original height but retaining its original 7 width.

6

10 9

5

8 7

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y• 4

6 5

3

4 3

2

2 1 0

1 1

2

3

4

5

6

7

8

9 10

0

1

2

3

4

5

6

7

8

9 10

10 9 8 7 6 5 4 3 2 1 0

1

2

EXTENSION MATHS - MEASUREMENT

3

4

5

6

Coordinate points - manipulating area

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7

8

9

10

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21

Grid Distortions 2 10

Complete the 'pig' distortions in the blank grids.

9 8 7 6 5 4 3 2 1 0

10

1

2

3

4

5

6

7

8

9 10

9

8 7 6

5 4 3

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y•

2 1 2

1

0

3

4

5

6

7

8

9

10

10 9 8 7 6 5 4 3 2 1 0

1

2

3

4

5

6

EXTENSION MATHS - MEASUREMENT

7

8

9 10

Coordinate points - manipulating area

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22

Islands 1.

Complete the questions about the two islands below.

Treasure Island

12

(a) Draw a shipwreck at (1,3).

11

(b) Where is the dot? ( , )

10 9

(c) Draw an old pirate hut at (8,9).

8 7 6

(d) Draw a river running from (8,6) to (10,4).

5 4

(e) A lookout has been built at (2,10). Draw it.

3 2 1 0

(f)

1

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y• 2

3

4

5

6

7

8

9

10

11

12

13

14

Draw a straight line from the lookout to the dot. Where the line crosses a grid reference exactly, you will find the treasure. What are the coordinates? ( , ) 2. Give four grid references that surround these features of the island.

Secret Island

(a) The forest

12 11 10

(b) The mountains

9 8 7

(c) The swamp

6 5

(d) The rocks

4 3 2

(e) The quicksand

1 0

1

2

3

4

5

6

7

EXTENSION MATHS - MEASUREMENT

8

9

10

11

12

13

14

Measuring using coordinate points

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23

World Grid With the help of an atlas, mark in the following cities of the world. Next to each city write the grid reference.

Cape Town

(

,

)

Sydney

(

,

)

Hong Kong

(

,

)

Amsterdam

(

,

)

Lima

(

,

)

Singapore

(

,

)

New York

(

,

)

Denver

(

,

)

Los Angeles

(

,

)

Mexico City

(

,

)

Wellington

(

,

)

Johannesburg

(

,

)

Madras

(

,

)

Anchorage

(

,

)

Beijing

(

,

)

Monaco

(

,

)

New Orleans

(

,

)

Santiago

(

,

)

( , ) Montreal ( , © R .

I .

C.P ubl i cat i o n s) Athens ( , ) Oslo ( , ) •f orr evi ew pur posesonl y• Dakar

11 10 9 8 7 6 5 4 3 2 1 A

B

C

D

E

EXTENSION MATHS - MEASUREMENT

F

G

H

I

J

Plotting coordinate points

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K

L

M

N

O

P

R.I.C. Publications

Q 24

ANSWERS Page 1

Answers may vary

Page 2

Teacher check

Page 3-7

See page 8

Page 9

1. (a) 1 cm = 50 km

Page 16

2. Jones Avenue and Smith Street, Moore Street, 1st Ave 3. Answers may vary

(b) 1 cm = 20 m

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(c) 1 cm = 25 m

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2. 6

3. Answers may vary, but should be based on (a) world map - kilometres (b) street map - metres (c) house plan metres/cm/mm (d) mud map - depends on what the map represents

3. (a) (1,5) (1,1)

1. 500 m

4. 800 m

2. 1 200 m or 1.2 km

5. 900 m

(b) (1) - this is because the horizontal line is plotted first (c) (1,8) (2,7) (3,6) (4,5) (5,4) (d) (9) Page 18 Page 19

(b) 1 300 m or 1.3 km 1. 450 m

Page 20 4. 600

2

5. 37 500 m2 6. 1 400 m or 1.4 km

2. (1,7) (2,7) (2,5) (1,5) (1,4) (2,4) (2,2) (1,2) (1,1) (3,1) (3,2) (4,2) (4,1) (5,1) (5,3) (3,3) (3,8) (2,8) (2,9) (9,9) (9,8) (4,8) (4,7) (8,7) (8,6) (9,6) (9,5) (7,5) (7,6) (6,4) (4,4) (4,5) (5,5) (6,5) (6,4) (9,4) (9,3) (6,3) (6,2) (7,2) (7,1)

Scale 1cm = 350 km 1. (a) 4 375 km

(b) 2 450 km

(c) 1 050 km (d) 4 375 km

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Teacher check

(e) 3 150 km

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Teacher check

(f) 4 025 km

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1. (a) Teacher check (b) (6,4) (c) (d) (e) Teacher check (f) (4,7)

(g) 3 850 km

2. (a) (7,4) (9,4) (9,1) (7,1)

(h) 4 200 km

(b) (3,10) (6,10) (6,8) (3,8)

2. 350 litres

(d) (10,11) (12,11), (12,9) (10,9)

2. 14 000 km or 2 500 km

(e) (7,9) (10,9) (10,6) (7,6) Cape Town (C,3)

Sydney (I,3)

6. 7 500 km

Hong Kong (G,6)

Amsterdam (B,8)

8. 25 000 km or 10 500 km

Lima (O,4)

Singapore (G,5)

New York (O,7)

Denver (N,7)

3. 4 500 km

4. 8 000 km

5. 5 500 km 7. 9 500 km 9. 18 000 km

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(c) (2,5) (6,5) (6,3) (2,3)

Scale 1cm = 1 000km 1. 1 500 km

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1. (1,5) (2,5) (2,3) (3,3) (3,7) (1,7) (1,9) (2,9) (2,8) (3,8) (3,9) (4,9) (4,1) (5,1) (5,3) (6,3) (6,1) (7,1) (75,) (5,5) (5,9) (6,9) (6,6) (8,6) (8,1) (9,1) (9,8) (7,8) (8,9) (9,9)

© R. I .

C.Publ i cat i ons •f orr evi ew pur posesonl y• 3. 250 m

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1. Teacher check 2. Teacher check

Scale 1cm = 50m 2. 30 000 m

1. Because he saw the salad dressing 2. Answers may vary

6. (a) Whale Point and South Point

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1. (a) Teacher check (b) a square (c) Answers may vary

2. Teacher check

3. 700 m

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1. Moore Street, Walsh Street, Industrial area

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10. 8 000 km

Los Angeles (M,7) Mexico City (N,6)

1. Diamond Beach, Dinosaur Cave, 3-km Beach

Wellington (J,3)

Johannesburg (C,4)

Madras (F,6)

Anchorage (L,9)

2. Dark Cave, 3-km Beach, Pirate Cove, Gold Beach

Beijing (G,7)

Monaco (C,8)

1. Teacher check

New Orleans (O,7) Santiago (O,3)

2. Answers may vary

EXTENSION MATHS - MEASUREMENT

Dakar (A,6)

Montreal (O,8)

Athens (C,7)

Oslo (C,9) R.I.C. Publications

www.ricgroup.com.au

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