RIC-6940 The Maths Box Series - Year 5 – Sample cards

Card 1 

Number and Algebra — Number and place value 

Fun with factors 

One-to-12 multiplication fact table 

× 1 2 3 4 5 6 7 8 9 10 11 12 

1 1 2 3 4 5 6 7 8 9 10 11 12 

2 2 4 6 8 10 12 14 16 18 20 22 24 

3 3 6 9 12 15 18 21 24 27 30 33 36 

4 4 8 12 16 20 24 28 32 36 40 44 48 

5 5 10 15 20 25 30 35 40 45 50 55 60 

6 6 12 18 24 30 36 42 48 54 60 66 72 

7 7 14 21 28 35 42 49 56 63 70 77 84 

8 8 16 24 32 40 48 56 64 72 80 88 96 

9 9 18 27 36 45 54 63 72 81 90 99 108 

10 10 20 30 40 50 60 70 80 90 100 110 120 

11 11 22 33 44 55 66 77 88 99 110 121 132 

12 12 24 36 48 60 72 84 96 108 120 132 144 

The arrows show two factors of 28. They are 4 and 7 (or 7 and 4). 

1 Two factors of 56 are: 

(a) 8 and 7 (or 7 and 8) 

(b) 5 and 6 (or 6 and 5) 

(c) 12 and 3 (or 3 and 12) 

3 Two factors of 81 are 9 and . 

(a) 11 

(b) 8 

(c) 9 

A factor is a number 

that divides into 

a larger number 

without leaving a 

remainder. 

©R.I.C. Publications 

Low Resolution Images 

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2 Two factors of 72 are: 

(a) 7 and 2 (or 2 and 7) 

(b) 9 and 8 (or 8 and 9) 

(c) 3 and 9 (or 9 and 3) 


(a) 6 

(b) 5 

(c) 12 

Maths box 5 

(01) 

R.I.C. Publications ® — ricpublications.com.au

Card 1 

5 Which statement is true? 

(a) Two factors of 132 are 11 and 

12. 

(b) Two factors of 132 are 10 and 

13. 

(c) Two factors of 132 are 8 and 9. 



Look at the sequence below. 

24, 27, 30, 33, 35 

8 One number does not belong 

because it does not continue the 

sequence and does not have 3 as 

one factor. Which one is it? 

(a) 24 

(b) 30 

(c) 35 

9 Which number in the sequence has 

9 as one factor? 

(a) 27 

(b) 24 

(c) 33 

10 Which number in the sequence has 

10 as one factor? 

(a) 24 

(b) 30 

(c) 35 

11 A factor is a number that divides 

into a larger number without 

leaving a . 

Solve the problems. 

12 Bob is a carpenter who is 

making stools for a client. 

If one stool has four legs, 

how many stools will Bob 

be making if he needs to 

make forty-eight legs? 

13 Each week, Tim receives 

twelve dollars pocket 

money for doing jobs 

around the house. He has 

saved one hundred and 

forty-four dollars towards a 

new computer game. How 

many weeks has he taken 

to save this amount of 

money? 

14 Tasmyn is helping her 

aunt fold serviettes at her 

cafe. If each table needs 

eight serviettes, how many 

serviettes in total will she 

need to fold for seven 

tables? 

ADDitional activity 

• Did you know that you only need 

to know half of the facts in the oneto-12 

multiplication fact table to 

know them all? This is because, for 

example, 3 × 4 is the same as 4 × 3, 

so you only need to know one of the 

pair of factors. 



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• Write your own one-to-12 

multiplication chart. Look at all the 

pairs of factors like the one above. 

Cross out one of each pair in the 

bottom half of the chart. When you 

have crossed out one of each pair, 

you will have half of the factors left to 

learn.

Card 1 

Number and Algebra — Fractions and decimals 



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1 Whose pizza is cut into the greatest 

number of slices? 

(a) Tyson (b) Andre (c) Lucy 

2 True or False? 

1 

16 

is the smallest unit fraction that 

one slice of pizza represents. 


(19) 


Card 1 

3 What fraction is one slice of Jack’s 

pizza? 

(a) 

1 

(b) 

1 

(c) 

1 

6 

5 

4 

4 Yes or No? 

Are Max and Ella’s pizzas both cut 

into eighths? 

5 Who ordered a pizza where one 

slice represents 1 16 ? 

6 One slice of ’s pizza is 1 7 . 

Greater than or less than? 

7 One slice of Max’s pizza as a fraction 

is 

one slice of Melissa’s 

pizza as a fraction. 

8 One slice of Tyson’s pizza as a 

fraction is 

one slice of 

Jamie’s pizza as a fraction. 

9 One slice of Nino’s pizza as a 

fraction is 

one slice of 

Ella’s pizza as a fraction. 

10 One slice of Andre’s pizza as a 

fraction is 

one slice of 

Lucy’s pizza as a fraction. 

11 How many slices of pizza is 1 of 4 

Tyson’s pizza? 

12 How many slices of pizza is 1 of 2 

Andre’s pizza? 

13 Using the friends’ names, which is the 

correct order of pizza fractions from 

smallest to largest fraction? 

(a) Amanda, Jack, Nino 

(b) Max, Melissa, Nat 

(c) 

• Write the names of all the pizza 

owners from greatest fraction 

to smallest fraction. 

• Work out the patterns below, 

and solve each missing fraction: 

1 

, 1 , , 1 3 6 24 

, 1 , 1 , 1 8 16 32 

1 

Lucy, Andre, Tommy 

14 Using the friends’ names, which is the 

correct order of pizza fractions from 

largest to smallest fraction? 

(a) Andre, Jack, Nat 

(b) Ella, Tommy, Lucy 

(c) Melissa, Max, Jamie 

, , 1 , 1 

40 10 5 

1 

, 1 , 1 , 

56 28 14 



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Card 1 

Number and Algebra — Money and financial mathematics 

School fete finances 

Merrick Valley School is planning a school fete to raise 

funds to buy equipment for the school. 

As part of the fundraising activities, all classes will 

have a stall which they will stock with saleable goods. 

Some stalls will be stocked with donated goods. All 

money raised from these stalls will be income with 

no expenditure for materials or ingredients. All the 

money raised from these stalls becomes the profit. 

Other stalls, however, will be stocked with goods that have been 

made with materials bought by the students. The amount of 

money raised will depend on the cost of buying materials and 

how much the goods are sold for. These stalls will have some 

expenditure and some income. The profit is the income minus 

any expenditure. 

Mrs Bowen’s Year 5 class are making iced cupcakes for the cake 

stall. They are buying all the ingredients and making them in 

class on the morning of the fete. 

They have decided to package 

and sell the cupcakes 

individually, in pairs, and in 

boxes of six. They plan to 

make six dozen cupcakes. 

The total cost of the 

ingredients was $18.60. 



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1 If the total income from the sale of 

all the cupcakes was $36.00, what 

profit was made? 

(a) $17.40 

(b) $54.60 

(c) $48.20 

2 If all the cupcakes were sold 

individually for 60c each, what 

would the income be? 

3 If all the cupcakes were sold in pairs 

for $1, what would the income be? 

(a) $43.20 

(b) $36.00 

(c) $54.80 

4 Which method of selling would 

provide the greatest income from 

the cupcakes—selling individually or 

selling in packs of two? 


(34) 


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5 If all the cupcakes were sold in 

boxes of six for $2.40 per box, 

what would the income be? 

(a) $44.50 

(b) $36.20 

(c) $28.80 

If all the ingredients were donated by the 

parents, ... 

6 ... what would the income be for 

individual cupcakes sold for 60c 

each? 

7 ... what would the profit be? 

8 ... what would the profit be if all 

cupcakes were sold in pairs for 

$1.50 a pair? 

9 ... what would the profit be if all 

the cupcakes were sold in boxes 

of six for $3.50 per box? 

(a) $28.80 

(b) $252.00 

(c) $42.00 

10 More or less? 

Using donated ingredients is 

profitable than 

purchasing ingredients. 

Some of the parents cooked and donated 

large cakes and loaves to support the school. 

11 If sixteen parents donated one large 

cake each, which sold for $5.50 each, 

how much income did this contribute 

to the profit for the class cake stall? 

12 What profit would the cake stall make 

if the class bought the ingredients, 

sold all the cupcakes individually for 

60c each, and twenty parents each 

donated one large cake or loaf which 

sold for $5.50 each? 

13 The parents and citizens association 

agreed to finance each class stall with 

an initial donation of $20.00 towards 

the cost of materials or ingredients. 

Any excess not used was added to the 

profit for that stall. What amount did 

the cake stall have to add to it? 

14 What extra cost 

was included 

in the cost of 

the ingredients 

when they 

were purchased 

by the teacher 

for the class? 



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ADDitional activities 

✘ Review Question 12. List the different operations and written and mental strategies you used 

to calculate your answer. 

✘ Select ten different amounts mentioned in the questions. Draw up a decimal money table with 

the headings tens, ones, tenths and hundredths at the top of the columns. Write the amounts 

in order from largest to smallest in the correct columns. (Don’t forget to add a column for the 

decimal point!)

Card 1 

Number and Algebra — Patterns and algebra 

Equivalent number 

sentences are like 

weighing scales— 

both sides must 

balance. 

1 

6 x 8 

63 ÷ 7 

To solve an equivalent number sentence and find the value of a missing number, 

first solve one side. 

18 ÷ 9 4 ÷ 

Find the unknown number. 

12 x 4 84 ÷ 7 

3 x 3 8 x 4 

18 ÷ 9 = 2 

so 4 ÷ 

2 

must equal 2 as well. 

4 ÷ 2 = 2 

so the missing number is 2. 

5 x 7 7 x x 9 

9 x 8 

36 ÷ 3 

64 ÷ 2 



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3 

÷ 5 42 ÷ 7 

10 x 4 x 8 

4 


(37) 


Card 1 

5 

6 

7 

8 

9 

10 

18 ÷ 6 

x 5 

4 x 3 

÷ 4 

165 ÷ 3 

x 10 

3 x 

120 ÷ 2 

9 x 9 

11 x 

÷ 8 

240 ÷ 4 

Which answer makes each number sentence 

equivalent? 

11 

12 

13 

14 

36 ÷ 4 = 

(a) 12 × 2 

(b) 27 ÷ 3 

(c) 5 × 2 

9 × 4 = 

(a) 7 × 8 

(b) 12 × 3 

(c) 20 ÷ 10 

(a) 11 × 10 

(b) 112 ÷ 2 

(c) 12 × 7 

(a) 6 × 11 

(b) 84 ÷ 12 

(c) 24 ÷ 2 

= 7 × 8 

= 28 ÷ 4 



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Review all the equivalent number 

sentences in Questions 1 to 14. On a 

sheet of paper, record what operation 

(multiplication, division, subtraction or 

addition) was used to find the missing 

number. 

Select any number between 

80 and 100 and write as many 

multiplication, division, addition 

and subtraction operations that 

equal the number selected.

Card 1 

Bumbling Merv Measure was such a mess. 

He didn’t know how to measure and he really couldn’t care less! 

He’d initially made some attempt to learn but the results were far from pleasing. 

What happened was so comical that his friends couldn’t resist some teasing. 

Merv was quite a clever fellow, but when it came to measuring, he just didn’t get it! 

Finally, I think he said to himself, ‘I’ll choose what I like, and I won’t regret it!’ 

So, in his bumbling fashion, he chose whatever unit came to mind 

To measure whatever he needed to at that particular time. 

Now Merv can say with pride he has possessions like no other— 

A shaggy toothbrush 190 kilometres long, a 1828-metre brother, 

A garden fence 20 millimetres wide, a fluffy cat 350 metres tall 

And a colourful painting 60 kilometres wide decorating his bedroom wall. 

Please take my advice and don’t be like Merv Measure 

Who chooses any measurement unit at his leisure! 

Don’t be a buffoon like this bumbling fool! 

To measure correctly, use the correct unit and tool! 

1 Which unit of measurement would 

be the most appropriate to use to 

measure a person’s stride? 

(a) millimetres 

(b) centimetres 

(c) kilometres 

Measurement and Geometry — Using units of measurement 

Messy Merv Measure 



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3 Which unit of measurement would be 

the most appropriate to use to measure 

the distance between two towns? 


(b) metres 

(c) kilometres 

2 Large or small? 

A large object or distance should 

be measured using a unit 

of measurement. 

4 Large or small? 

A small object or distance should be 

measured using a unit of 

measurement. 


(45) 


Card 1 

Millimetre, centimetre, metre or kilometre? 

5 Which unit of measurement is 

approximately the width of a sewing 

needle? 

6 Which unit of measurement is 

approximately the width of your small 

finger? 

7 A (unit of measurement) is 

approximately the length of a grown 

person’s stride. 

8 A kilometre would be an appropriate 

unit to use to measure the: 

(a) distance a delivery truck travels. 

(b) height of a school child. 

(c) length of a permanent marker. 

9 Which is the best object of the 

following to measure in millimetres? 

(a) room 

(b) hand 

(c) swimming pool 

10 One thousand millimetres is 

equivalent to one: 

(a) metre. 

(b) centimetre. 

(c) kilometre. 

11 One kilometre is equivalent to 

one thousand: 

(a) millimetres. 

(b) centimetres. 

(c) metres. 

12 One metre is equivalent to one 

hundred: 

(a) centimetres. 

(b) kilometres. 

(c) millimetres. 

13 One centimetre is equivalent 

to ten: 

(a) kilometres. 

(b) metres. 

(c) millimetres. 


The number of centimetres in 

a kilometre can be calculated 

by multiplying the number of 

metres in a kilometre (1000) by 

the number of centimetres in a 

metre (100). 




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Research to find out the meanings of 

the prefixes ‘milli-’, ‘centi-’ and ‘kilo-’, 

then write the dictionary meaning of 

the words ‘millimetre’, ‘centimetre’, 

‘metre’ and ‘kilometre’. 

Draw up a table with four columns headed 

‘Kilometres’, ‘Metres’, ‘Centimetres’ and 

‘Millimetres’. In each column write three or four 

objects that could be measured using each unit of 

measurement.

Card 1 

Measurement and Geometry — Shape 

Nigel’s favourite hobby is constructing models from various materials. 

One day, Nigel wants to be an engineer or an architect. 

Yesterday, he downloaded a 3D net from an internet site and created a wacky 

character. Consider the wacky character 

he made and the net he downloaded. 

A net is a 

flat twodimensional 

pattern that 

can be folded to 

make a model 

of a threedimensional 

object. 

1 If the face of the net numbered 

1 is the face of the wacky 3D 

character, then the face numbered 

6 will be the: 

(a) back of the head. 

(b) base of the feet. 

(c) arms. 

2 The face of the net numbered 7 

is the: 

(a) sides of the body. 

(b) top of the head. 

(c) front of the body. 



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3 The faces of the net numbered 8 

are the: 

(a) back of the body. 

(b) arms. 

(c) sides of the head. 

4 The face of the net numbered 2 

is the: 

(a) base of the feet. 

(b) sides of the body. 

(c) back of the body. 


(52) 


Card 1 

5 Which number indicates the face of 

the net that represents the base of 

the feet? 

(a) 4 (b) 5 (c) 3 

6 Which number indicates the face of 

the net that represents the front of 

the body? 

(a) 3 (b) 5 (c) 2 

7 The number 3 indicates the face of 

the net that forms the of 

the wacky 3D character. 

8 The number 9 indicates the face of 

the net that forms the sides of the 

of the wacky 3D character. 

9 Which two 2D shapes make up most 

faces of the wacky 3D character net? 

(a) rectangles and squares 

(b) cubes and prisms 

(c) circles and triangles 

10 All the nets below can be used to 

construct which 3D object? 


construct which 3D object? 


construct prisms. 

13 The base of this net indicates that the 

3D object that can 

be constructed from 

it is a pyramid. 

14 What type of pyramid can be 

constructed from the net below? 



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Experiment with Polydrons or Geoshapes 

to investigate different nets for a tetrahedron, 

then sketch the nets onto paper. 

Conduct an internet search of 3D nets to fold 

and create your own wacky characters like 

those at

Surprising symmetry 

Nature displays a surprising number of mathematical elements, symmetry being one of 

them. Consider the reflectional (line) symmetry of the butterfly and the avenue of trees, 

and the rotational symmetry of the fern and palm frond. 

Where else can reflectional and rotational symmetry be found? 

Do the lines show reflectional and/or rotational 

symmetry? 

1 

2 

Card 1 

Measurement and Geometry — Location and transformation 



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3 

4 

REMEMBER! 

Reflectional (line) symmetry 

occurs when the size, form and 

arrangement of parts of a shape 

or object on opposite sides of 

a line correspond. Each half is a 

mirror image of the other. 

Rotational symmetry occurs 

when an object, figure or shape 

matches itself when it has been 

rotated around a fixed point. 


(55) 


Card 1 

5 Which figure with reflectional 

symmetry shows the correct lines of 

symmetry? 

(a) 

6 Which figure does not have the 

property of rotational symmetry? 

7 Yes or No? 

Figure A exhibits 

rotational symmetry. 


Figure B exhibits both 

reflectional and rotational 

symmetry. 

9 Which five capital letters of those 

below have reflectional symmetry? 

A, F, G, M, P, T, E, K, R, Z 

10 Five of the capital letters below 

have rotational symmetry. Which 

ones are they? 

B, Y, U, H, N, W, S, Z, X, V 

11 Which statement is false? 

(b) 

(a) (b) (c) 

(a) Some capital letters have both 

reflectional and rotational 

symmetry. 

(b) Some capital letters only 

have rotational or reflectional 

symmetry. 

(c) All capital letters have some 

type of symmetry. 

A 

B 

12 Which figure shows an example of 

horizontal line symmetry? 

4. 

1. 

2. 

13 Two of the shapes below have 

multiple lines of symmetry. Which are 

they? 

2. 

1. 

3. 


3. 

5. 

Shapes that are turned 90°, 180°, 

270° or 360° on a central point and 

still appear exactly the same have 

rotational symmetry. 



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• Make a list of words written in block capital 

letters like ICEBOX, DECIDED, EXCEEDED, 

HIDE and CHOICE that have horizontal 

symmetry. 

• Make a list of words written in block 

capital letters like MUM that have vertical 

symmetry. 

• Investigate the longest word with 180º 

rotational symmetry.

Card 1 

Measurement and Geometry — Geometric reasoning 

What’s your angle? 

Angles are all around us. Have you noticed any like these ... or others? 

All angles are classified by their size and how they relate to a 90° right angle. 

1 Which angle is described as ‘an 

angle measuring 90°’? 

(a) an acute angle 

(b) a right angle 

(c) an obtuse angle 



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3 An angle is greater than 

90° but less than 180°. 

(a) obtuse 

(b) acute 

(c) right 

2 Which angle is described as ‘an 

angle measuring less than 90°’? 

(a) a straight angle 

(b) a reflex angle 

(c) an acute angle 

4 A angle measures 

exactly 180°. 

(a) right 

(b) reflex 

(c) straight 


(63) 


Card 1 

5 Which angle is described as ‘greater 

than 180° but less than 360°’? 

(a) an obtuse angle 

(b) a reflex angle 

(c) an acute angle 

6 One rotation (a full turn which ends 

up at the starting point) measures 

degrees. 

What is the name of the angle? 

7 

8 

9 

10 

11 

(a) right 

(a) reflex 

(b) straight (c) acute 

(b) obtuse (c) acute 

(a) obtuse (b) right (c) acute 

(a) acute (b) reflex (c) obtuse 

(a) reflex 

(b) straight (c) right 

12 What is the diagram showing? 

(a) a right angle 

(b) a straight angle 

(c) one rotation 

Which word best completes these 

statements? 

13 All angles are measured in 

. 


(b) degrees 

(c) kilograms 

14 The angle does not change even 

if the 

are different 

lengths. 

(a) arms 

(b) degrees 

(c) angles 


• Compare the 

size of angles 

in a set of 

pattern blocks. 

The angles in 

pattern block 

shapes are 

related. If the 

angles in a square block are 90º, work out 

the angles of the other blocks. Record your 

findings in a table. 



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• Draw each block and write 

the angle of each shape. 

60° 

For example: 

60° 60°

Card 1 

Statistics and Probability — Chance 

1 Six different fantasy images appear 

on the dice. The chance of throwing a 

dragon, expressed as a fraction, is: 

(a) 

1 

3 

(b) 

1 

2 

(c) 

1 

6 

2 What is the chance of throwing a 

soldier? 

(a) 

1 

6 


(b) 

1 

2 

(c) 

1 

4 

Players have a one-in-six chance 

of throwing one of the different 

fantasy images. 

4 If the images are grouped as people 

(soldier and wizard), fantasy creatures 

(dragon and goblin) and fantasy 

objects (crown and skull), what is the 

chance of throwing a person? 



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If the groupings in Question 4 are 

observed, players have the same 

chance of throwing a person, fantasy 

creature or object. 


(66) 


Card 1 

The boys traded their six-sided dice for an eightsided 

dice that showed the following images: 

• people (wizard, soldier, king), 

• fantasy creatures (goblin and dragon), and 

• fantasy objects (crown, skull; and 

sword and shield). 

6 The chance of throwing a king is: 

(a) 

1 

8 

(b) 

1 

6 

(c) 

1 

7 What is the chance of throwing an 

image of a fantasy creature? 

(a) 

1 

8 

(b) 

2 

8 

4 

(c) 

4 

8 The chance of throwing an image of 

a fantasy object is: 

(a) 

1 

8 


(b) 

2 

8 

8 

(c) 

3 

Players have 3 chance of throwing 

8 

an image of a person. 

10 The chance of throwing either a 

person or a fantasy object is: 

(a) 

4 

8 

(b) 

6 

8 

8 

(c) 

1 

11 What is the chance of throwing 

either a fantasy creature or a 

person? 

(a) 

5 

8 

(b) 

4 

8 

8 

(c) 

2 

8 

12 Which word makes this sentence 

correct? 

Players have a 

in 

eight chance of throwing any one of 

the eight images on the dice. 

(a) two (b) three (c) one 

13 Which statement is incorrect? 

(a) Players have an equal chance of 

throwing an image of a person or 

a fantasy object. 

(b) Players have an equal chance of 

throwing an image of a person or 

a fantasy creature. 

(c) Players have less chance of 

throwing a fantasy creature than 

a fantasy object. 

14 Likely or Unlikely? 

It is highly 

that a player 

will throw the same image every time. 



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Additional 

ACTIVITY 

Using a ten-sided dice, work out 

the chance of throwing any of the 

numbers one to ten. Then work out 

the chances of throwing an odd or 

even number, a number between 

five and ten, a number less than 

four, any number greater than two; 

and multiples of three.

Card 1 

Statistics and Probability — Data representation and interpretation 

1 Which question could you collect data about by observing this spider web? 



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(a) What type of insects get caught in the web? 

(b) How many birds build a nest? 

(c) How many insects get caught in the web? 

(d) Both (a) and (c) 

Categorical or numerical? 

2 The type of insect observed would be data. 

3 How many insects observed would be data. 

4 The number of insect legs observed would be data. 

5 The variety of colours of the insects would be data. 


(70) 


Card 1 

At the end of Day 1 the following observations were tallied: 

Day 1 

Day 2 

Day 3 

Day 4 

6 What categories of insects was the 

data arranged into? 

(a) flying insects and crawling 

insects 

(b) yellow insects and green 

insects 

(c) grasshoppers and moths 

ADDitional activity 

Crawling insects 

11 If you were at the zoo and saw the 

animals on the left, which animal category 

would you see the most of? 

12 Which category do these tally marks 

belong to? 


It is not useful to tally the number of 

each individual animal at the zoo, but it is 

useful to see how many of each category 

there are. 

14 Yes or No? 

Flying insects 

Ant Grasshopper Beetle Cricket Moth Dragonfly Fly 

7 How many flying insects were observed 

on Day 1? 

8 Which category was the most popular on 

Day 3? 

9 How many crawling insects were 

observed on Day 2? 

10 Which category was caught in the web 

the most overall? 



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Would the data for the most popular 

animal at the zoo be the same as the data 

for the most common type of animal 

found at the zoo? 

• Draw a table and tally your observations at the zoo as shown above. Go to and research other animals and categories 

you might come across at a zoo, and add them to your tally.

RIC-6940 The Maths Box Series - Year 5 – Sample cards

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