110 iMaths 6 Student Book ISBN 978 1 74135 181 1

Try this

Reflection, translation and rotation are transformations. They are mathematical terms for flip, slide and turn.

MG16 Transformations

Reflection

Rotation

Translation

A rotation (turn) occurs when a shape turns about a fixed point.

The F-shape slid right one square and rotated 90˚ clockwise.

A reflection (flip) is a mirror image of a shape. A shape has line symmetry if both its parts match exactly when folded.

The F-shape flipped right, across the line of symmetry.

A translation (slide) is a movement in a straight line without rotation, reflection or change of size.

The F-shape slid right one square.

a Flip the shape to the right.

b Slide the shape left one square.

c Slide the shape right one square and rotate 90˚ clockwise.

1 Transform each shape by reflection, translation or rotation as instructed.

ISBN 978 1 74135 181 1 iMaths 6 Student Book 111

Challenge

Topi

c M

G16

2 Follow the directions as each shape is transformed in five steps from one place to another on the grid. Draw the outline of the shape after each step. Colour the shape in its final location.

c Draw the outline after each step.

1. Slide left 3 squares. 2. Flip left. 3. Slide up 2 squares and rotate 180° clockwise. 4. Slide right 3 squares and flip down. 5. Colour the shape.

b Draw the outline after each step.

1. Slide down 1 square and rotate 90° clockwise. 2. Slide left 4 squares. 3. Flip right. 4. Slide down 1 square, right 1 square

and rotate 90° anticlockwise. 5. Colour the shape.

a 1. Slide right 3 squares, draw the outline, then 2. flip right, draw the outline, then 3. slide down 2 squares and left 3. 4. Draw the outline, then flip upwards. 5. Colour the shape.

Look at it this way: Draw a shape that looks the same no matter how you flip, slide or turn it. Can you draw a second shape?

MG19 Circles

iMaths 6 NSWISBN 978 174135 3167

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1 a Use a pair of compasses to draw a circle with a radius of 30 mm.

b Label the circle with the terms circumference, radius, diameter and centre.

Here are some terms given to the various parts of a circle.

The circumference (C) of a circle is its perimeter, the distance

around the boundary.

The centre (c) is the point that is an equal distance from all

points on the circumference.

The diameter (D) is the length of any line that passes through

the centre, and joins any two points on the circumference.

The radius (r) is the distance from the centre to any point on

the circumference. The plural of radius is radii.

A semicircle is a 2D shape, exactly half of a circle.

An arc is any portion of the circumference.

A sector is the part of a circle enclosed by

two radii and the arc.

A quadrant is a quarter of a circle.quadrant

sector

semicircle

arc

centre (c)

radius (r)

diameter (D)

circumference (C)

iMaths 6 NSWISBN 978 174135 3167

2 a Describe the similarities between a quadrant, a semicircle and a sector.

b Describe the differences between a quadrant, a semicircle and a sector.

3 Three circles of different diameters overlap as shown. Points B, C and D are the centres of each of the circles.

Circle X Circle Y Circle Z

Calculate the following distances using the information in the table, and without using a ruler. Show your working.

a From A to E

b From A to C

c From M to N

A B M C N D E

Circle Radius

Circle X 2 cm

Circle Y 3 cm

Circle Z 2.5 cm

Challenge A triple sector quadrant: Three sectors with the same

dimensions can be placed into a quadrant in the circle.

a Show how this is done by drawing them in the circle.

b Explain how you worked out how to do it.

26 iMaths 6 Student Book ISBN 978 1 74135 181 1

Teacher note• Comprehensive lesson notes,

suggestions and resources are available in iMaths 6 Teacher Book.

• The Investigation plan for this Investigation can be downloaded fromwww.imathsteachers.com.au.

Understanding the Investigation1 Read and plan.

Make sure you understand the meanings of: wad, justify, loot, dimensions, assumptions and bundle.

Read and discuss the rubric.

Download your Investigation plan. This will help you with the organisation and understanding of the Investigation.

Topics Before you start the Investigation you need to know…

NA7 The four operations ........................................ p44

NA8 Backtracking ................................................... p46

NA9 The distributive law ........................................ p48

NA16 Decimal multiplication ................................ p62

NA24 Order of operations .................................... p78

MG5 Packing and stacking .................................... p88

While playing with your mates in an abandoned warehouse, you discover a battered old suitcase packed with bundles and wads of $50 notes. Years ago $1 000 000 went missing from a bank and the money was never found. Could this be the loot?

Investigate whether $1 000 000 would fit into the suitcase described on the next page, and whether you would be able to carry it home.

Investigation 10I’ve found a million dollars

ISBN 978 1 74135 181 1 iMaths 6 Student Book 27

Materials

Internet access

Go to imathskids.com.au – the Investigation 10 area contains the Investigation plan and websites that you need to complete this Investigation.

InquiryIs one million Australian dollars worth more or less than one million U.S. dollars?Use an appropriate website to convert your $1 000 000 to ten di! erent currencies. Design a table to record this information.

2 The suitcase and the $50 notes.The dimensions of the suitcase are 50 cm " 40 cm " 10 cm.

A $50 note measures 15.1 cm " 6.5 cm. One wad contains 100 notes. One wad is approximately 1 cm high. Ten wads make a bundle. The approximate mass of one bundle of notes is

one kilogram (1 kg).

Using maths3 How many bundles and wads?

Work out how many wads of $50 notes are needed to make $1 000 000. Then work out how many bundles make $1 000 000

4 How heavy is a million dollars?Calculate how much $1 000 000 worth of $50 notes would weigh.

5 Will a million dollars fit into a suitcase this size?Determine how many bundles and wads of $50 notes will fit into the suitcase. You will need to know the dimensions of the $50 notes and of the suitcase. Think outside the square! The bundles and wads could be packed in different directions or on their sides. Try various arrangements.

Reasoning and reporting6 Is this the loot?

Explain whether $1 000 000 would fit into the suitcase and whether you could carry it home. Show all your calculations to justify your answers. List any assumptions you made.

Inve

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n 10

Calculator

Editing Task

1. The Path

at the end of the crumpled path the two friends came to a stop. they looked down

the left fourk, then they looked down the right. Ocnce they had gavered their

courage the f reinds held hands and started down the left path. they didn’t know

what was down their, but they were determined to find out

2. Fast Lane

Fast Lane, a new action moovie, hit cinemas last night. the movie, based on the life

of a moter racing driver, is terrible. Simon Spanner, usually a great actor, is awlful in

this movie. His co-star, danny Draper, is not much better. Maybe i am wrong, but I

dont think this movie is going too win any awards

3. Night Shadows

I lay on my comfertoble bed, enjoying the peace and quiet. suddenly I saw a shadow

pass by my bedroom door. i thought it was strange, but convinced myself that i was

imagioning things. I sat up slowly, trying to see through the darkness. I couldnt sea,

but I knew that somthing was out there.

4. Sisterly love

Wear is my big sister, whom I love and odore Julia asked “Unless I am crazy, i think

you want something!” Jenna replyed. Since you love me so much, do you think I can

come to the movies with you Julia said. even though you can be anoying

sometimes, I will let you come Jenna responded

Fast Lane