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Title: OzzieMaths Series Maths: Year 3

or eBo st r e p ok u S

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© 2017 Ready-Ed Publications Printed in Australia Author: Lisa Craig Illustrator: Alison Mutton

Acknowledgements i. Clip art images have been obtained from Microsoft Design Gallery Live and are used under the terms of the End User License Agreement for Microsoft Word 2000. Please refer to www.microsoft.com/permission.

Copyright Notice

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The Act allows a maximum of one chapter or 10% of the pages of this book, whichever is the greater, to be reproduced and/or communicated by any educational institution for its educational purposes provided that

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o c . che e r o r st super

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d.net Published by: Ready-Ed Publications PO Box 276 Greenwood WA 6024 www.readyed.net info@readyed.com.au

ISBN: 978 186 397 992 4 2

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Reproduction and Communication by others


Contents Teachers’ Notes Curriculum Links

4 5

34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

Presenting data 2 Presenting data 3 Presenting data 4 Statistics 1 Statistics 2 Probability My probability investigation Chances What’s the chance? (extension)

51 52 53 54 55 56 57 58 59 60

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

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Section 1: Number and Algebra My numbers Which number comes next? Even or odd? Abacus fun Writing numbers in words Counting on Counting back The answer is...twenty! Shapely numbers Subtraction game Thinking about subtraction Addition and subtraction facts Prove it! Arrays 1 Arrays 2 Multiplication strategies Multiplication mystery Division strategies Divide and conquer Wonder word problems What are fractions? Shady fractions Fractions on a number line Equivalent fractions Tuck shop money problems Minding your money

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Section 2: Measurement and Geometry Symmetry in nature Identifying symmetry Symmetry in the natural and built world Angles in the environment Measurement Length 1 Length 2 Mass Massive food problems Capacity 1 Capacity 2 Time word problems A Time word problems B On the grid Create your own grid map Make a 3D model

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Teachers’ Notes This book is part of the OzzieMaths Series which comprises seven books altogether. It is linked to the Australian Curriculum and each page in the book references the content descriptor/s and elaboration/s it specifically addresses.

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The activities have been designed to develop mathematical skills and reasoning in a creative way that is often connected to solving problems in real-life contexts. Students will be asked to reflect upon the strategies used to problem-solve effectively in familiar situations and expand their ideas to realise that mathematical understanding has an important role in other subject areas. Answers and additional teaching information are included at the back of the book. This book is divided into three sections as detailed below. Section One: Number and Algebra In this section, students will engage in a variety of activities that require them to demonstrate ever-increasing capability using mental and written strategies to explore number relationships and patterns. Tasks include: identifying the attributes of even and odd numbers using students’ own examples; having a race against the clock counting back in a designated number; conquering division facts in the fish tank and solving and creating problems involving wonders of the natural world.

© ReadyEdPubl i cat i ons Section Two: Measurement and Geometry f o rr ev i ewtop r pand os esofo nl y• This section• draws students’ attention theu value beauty mathematics

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in the world around them. Students will be asked to consider symmetry in the natural and built environment through observing marine life, indigenous art and the façade of Luna Park. Following an intrepid explorer across an island will help students understand the use of grid reference and scale. The importance of using standard units of measurement is explored through activities such as: estimating the mass of iconic Australian wildlife, making up milk formulae for bush babies and applying measurement in our daily lives.

. te o c Section Three: Statistics and Probability . ch e data in this Students will develop skills in collecting, organising and representing r e o t r section. Students will categorise images ofp Great Barrier Reef marine life and label s s r u e a column graph based on their decisions. The concept of probability is explained

through activities ranking the likeliness of events occurring and carrying out a chance experiment with a deck of cards to test predictions and discuss variability in results.

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Curriculum Links ALGEBRA AND NUMBER ACMNA051 Investigate the conditions required for a number to be odd or even and identify odd and even numbers

MEASUREMENT AND GEOMETRY ACMMG061 Measure, order and compare objects using familiar metric units of length, mass and capacity

ACMNA052 Recognise, model, represent and order numbers to at least 10 000

ACMMG062 Tell time to the minute and investigate the relationship between units of time

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ACMMG063 Make models of threedimensional objects and describe key features

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ACMNA053 Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems

ACMNA054 Recognise and explain the connection between addition and subtraction

ACMMG064 Identify angles as measures of turn and compare angle sizes in everyday situations

ACMNA055 Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation

ACMMG065 Create and interpret simple grid maps to show position and pathways

of two, three, five and ten and related division facts

STATISTICS AND PROBABILITY ACMSP067 Conduct chance experiments, identify and describe possible outcomes and recognise variation in results

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ACMNA057 Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies

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ACMMG066 Identify symmetry in the © ReadyEdPu b l i c a t i o n s environment •f orr evi ew pur posesonl y• ACMNA056 Recall multiplication facts

ACMSP068 Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording

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ACMNA058 Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole ACMNA059 Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents ACMNA060 Describe, continue, and create number patterns resulting from performing addition or subtraction

ACMSP069 Collect data, organise into categories and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies ACMSP070 Interpret and compare data displays

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Number and Algebra

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My numbers Use the counting grid to help you to complete the questions which follow. Keep this grid to help you with other number facts.

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Box 2 Shade in blue on the grid:

3. The first two digits of the postcode of your school.

3. The last two digits of the postcode of your school.

4. The number of children in your class.

4. The number of children if three new children join the class.

5. The number of eyes in the class now.

5. The number of eyes in the class if five children leave the room.

Box 1 Shade in red on the grid:

o c . chthis edigits of the year r 2. The last two 2. The last two digits of er o st supe r in ten years’ time year.

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1. Your age five years ago.

Curriculum Link: Recognise and explain the connection between addition and subtraction (ACMNA054)


Which number comes next? Add numbers to complete the patterns.

1 25 26 27 28 29 2 18

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o c . che e How was the number pattern made in sequence 8? r o t r s s r u e p ____________________________________________________________________ Make your own counting sequences for a classmate to complete.

9 10 Curriculum Link: Describe, continue, and create number patterns resulting from performing addition or subtraction (ACMNA060)

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Even or odd? How can you tell when a number is even or odd? You can divide an even number by 2 and there will be no numbers left over.

Remember 1

Even numbers end in the digits: 0, 2, 4, 6 and 8. Odd numbers end in the digits: 1, 3, 5, 7 and 9.

Even or Odd Quiz

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3. Number of players on the field at the start of a cricket match.

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4. Number of states and territories in the Australian Commonwealth.

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5. Number of letters in the alphabet. 6. The total number of letters in the names of months beginning with “J.”

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Take the quiz. Write E if the answer is an even number and O if the answer is an odd number.

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© ReadyEdPubl i cat i ons 60 8. Number bones ine the human body. 206 •off orr vadult i ew pu r posesonl y • 7. Number of minutes in an hour.

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10. The number many people believe is lucky.

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11. Number of rings in the Olympic logo. 12. Number of metres high of Mt. Kosciusko.

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9. Number of wings on seven butterflies.

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. te o c What happens? . che to make odd and evenr e Choose your own numbers sums below. Write o t r s s r u eanswer in green if it is ODD. pthe the answer in blue if it is EVEN and Look at the example to help you. EVEN

+

ODD

6 + 13 = 19 (ODD)

EVEN

+

ODD

____________

EVEN

+

EVEN

____________

ODD

+

ODD

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What happens when you add 10 to an even number?_ ___________ What happens when you add 100 to an odd number?____________ 10

Curriculum Link: Investigate the conditions required for a number to be odd or even and identify odd and even numbers (ACMNA051)


Abacus fun The abacus below represents the number 2543 (two thousand five hundred and forty-three).

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mischievous monkey

1. The mischievous monkey has taken some of the beads from the abacuses below! Can you draw the missing beads in each abacus so that it represents the same number in the box underneath? Colour the beads that you have added.

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a.

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2. Write the numbers below in order from smallest to largest.

3. Put a < (smaller than) or > (greater than) sign in the stars. a.

1742

1752

b.

5020

5030

c.

875

885

d.

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614

Curriculum Link: Recognise, model, represent and order numbers to at least 10 000 (ACMNA052)

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Writing numbers in words Read the identification numbers on the tagged animals. Write the numbers of the tags in words. Look at the example to help you.

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two hundred and fifteen

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Colour in the animals that have even tag numbers. 12

Curriculum Link: Recognise, model, represent and order numbers to at least 10 000 (ACMNA052) Elaboration: Reproducing numbers in words using their numerical representations and vice versa


Counting on many metres will the animals below jump to reach Jumping 1. How animals their food? Use the information below to help you count on.

information

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0

a.

A dolphin can travel 5 metres in a single jump. A cat can jump 2 metres in one pounce. A rabbit can spring 3 metres in one jump. A red kangaroo can cover 10 metres in one bound.

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challenge

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o c . 124c 130 132 136 e he128 r o t r s s r u e p 142 144 148 150 152

2. Circle the numbers that don’t fit the counting on in 4s sequence.

120 140

3. Circle the numbers that don’t fit the counting on in 6s sequence.

300

306

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318 342

324 348

326 354

Curriculum Link: Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)

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Counting back

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How far can you go back? Choose a number between 100 and 200. Write that number in the first segment of the snake. Your teacher will give you a time limit and a number to count back in, for example, “Count back in 6s.”

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What do you notice about the numbers in your counting back sequence? ____________________________________________________________________ 14

Curriculum Link: Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)


The answer is … twenty! Create as many sums as you can that total 20 by adding the digits on the grid in vertical, horizontal or diagonal lines. You cannot use a digit twice. Look at the example to help you:

E.g. 5 + 6 + 9 = 20 8

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9 + 6 + 5 = 20

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Award yourself 10 to 13 sums

Bronze medal

14 to 17 sums

silver medal

20 or more sums

gold medal

How many sums did you find? Colour the medal for your score. Curriculum Link: Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)

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Shapely numbers 1

The silly shapes are hiding some numbers! Write the correct numbers in the shapes. The first one has been done for you.

a. 265 = 200 + 60 +

5

b. 643 = 600 + 40 +

h. 936 = 900 + 30 + i. 447 = 400 + 40 +

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or eBo st r e j. 690 = 600 + 60 + c. 192 = 100 + 90 +p o k Su d. 749 = 800 - 50 -

k. 746 = 700 - 50 -

e. 885 = 800 + 80 +

l. 513 = 500 +

+

m. 186 =a 100 +o + © R e a d y E d P u b l i c t i n s f. 244 = 300 - 50 •f orr evi ew pur posesonl y•

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o c . a. 756 = 700 + 50c +6 700 + e 40 + 16 her 756 =st r super o b. 848 = 900 - 50 - 2

Write a partition that has the same total. Look at the example given.

c. 962 = 900 + 60 + 2 d. 389 = 400 – 10 - 1 e. 144 = 100 + 40 + 4 f. 1735 = 1000 + 700 + 30 + 5 g. 4586 = 4000 + 500 + 80 + 6 16

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g. 375 = 300 + 70 +

Curriculum Link: Recognise and explain the connection between addition and subtraction (ACMNA054) Elaboration: Demonstrating the connection between addition and subtraction using partitioning or by writing equivalent number sentences


Subtraction game Who’s a gem at subtraction? This game is played in pairs. The first player circles a gem in one colour. The second player circles another gem in a different colour. Players take turns circling any gem number in the grid that is the difference between any numbers that have already been circled. Keep playing until no more gems can be circled. For example: Player 1 circles 50 and Player 2 circles 10. Player 1 can now circle 40 and Player 2 could circle 30. 2

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Curriculum Link: Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (ACMNA055)

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Thinking about subtraction Try solving these subtraction word problems by drawing the problem and then writing a number sentence. Look at the example below. There is a box of 36 pencils on the desk. One child takes 9 pencils. How many pencils are left in the box? Drawing

Number sentence

36 – 9 = 27

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Drawing

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or eBo st r e p ok u Mark has 22 freckles on his face when he goes to sleep. During the S night, 8 of them disappear! How many freckles does Mark have now? Number sentence

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Forty bees leave the hive to gather pollen. At the end of the day twentysix bees return. How many bees have not returned to the hive?

Caroline buys a muesli bar for $1.65. She pays with a $2 coin. How much change does she receive?

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Number sentence

Mr. Neat has 12 pairs of blue socks. He finds big holes in 16 socks and so he throws them away. How many pairs of blue socks does he have now?

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Drawing

Number sentence

Curriculum Link: Recognise and explain the connection between addition and subtraction (ACMNA054) Elaboration: Demonstrating the connection between addition and subtraction using partitioning or by writing equivalent number sentences


Addition and subtraction facts 6

+

8

=

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14

8

=

6

We’re related.

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Solve these problems and show your working out. Some of the working out has been completed for you in problem 1. James is going to compete in a big triathlon competition. He plans to complete 25 kilometres at training today. He is going to swim 1 kilometre in the bay, then cycle 15 kilometres around the park. How many kilometres does he need to run to meet his training target today?

25 + 45 +

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Dotty earned $25 on Saturday washing cars. On Sunday she earned $45. She wants to buy a new wetsuit that costs $94. How much does she need to earn to buy the wetsuit?

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Mighty Manny weighs 110 kilograms, so he decides to go on a diet. In October he loses 6 kilograms, in November he loses 5 kilograms and in December he loses 4 kilograms. During his holidays in January, Manny gains 3 kilograms. How much does Mighty Manny weigh now?

ANSWER:

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ANSWER: Dotty needs $24 to buy the wetsuit.

Pia releases 80 racing pigeons many kilometres from home. On the first night 16 pigeons return home. On the second night 39 pigeons return. How many pigeons is Pia still waiting for?

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ANSWER:

Curriculum Link: Recognise and explain the connection between addition and subtraction (ACMNA054)

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Prove it! 1

No working out or calculators! Quickly estimate the total of these addition and subtraction facts by rounding to the nearest ten or hundred. Write the rounded numbers in the clouds. Look at the example to help you.

a.

30

50

b.

57 – 19 is about r o e t s Bo r e p ok c. d. u S 66 + 28 is about 77 + 48 is about e.

f.

261 + 116 is about

473 – 254 is about

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Can you prove that each number fact is true? To show that a number fact is true, write your proof in the second column. If the number fact is not true, write the correct number fact in the correction column. Look at the example to help you.

number fact

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a. 6 + 23 = 27

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d. 51 + 28 = 69 e. 35 + 41 = 76

proof

correction

27 – 23 = 4 (not 6)

6 + 23 = 29

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f. 16 + 62 = 82 g. 67 – 16 = 51 h. 120 – 104 = 114 i. 445 + 104 = 539 j. 2289 + 110 = 2300 20

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31 + 46 is about 80

Curriculum Link: Recognise and explain the connection between addition and subtraction (ACMNA054)


Arrays 1 An array is a set that shows equal groups in rows and columns. In the picture you can see eggs in a carton arranged into columns and rows:

}

columns rows

}

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2+2+2=6 3+3=6 3x2=6 2x3=6

1. Write 1 or 2 possible addition facts for each array shown below.

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2. On the back of this sheet draw everyday objects that show arrays. Write multiplication facts for your arrays. Curriculum Link: Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056)

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Arrays 2 Use the information on the previous page to complete the following tasks.

1

Choose 5 arrays from the previous page. Represent them by shading the grid. The egg carton has been done as an example. Annotate your grid with multiplication facts as shown.

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3 x 2 = 6 2 x 3 = 6

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Complete the table using the arrays on the previous page.

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b. bottle caps c. bugs

columns

rows

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d. chicken coop e. calculator f. coral g. coins 22

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Curriculum Link: Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056)

3x2=6


Multiplication strategies Multiplying one-digit and two-digit numbers might seem a little tricky, but there are strategies you can use without reaching for a calculator. Try this grid method to solve multiplication problems.

Example: 17 x 5 X

10

7

Total

5

50

35

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Step 1: Put the multiplier under the multiplication sign. Step 2: Partition the two-digit number. Step 3: Multiply partitioned numbers and put products in second row. Step 4: Add the two products and you have your answer.

Use the grid method to solve these multiplication problems.

a. 16 x 5 5

6 Total X 20 8 © Re ad yEdPub l i ca t i on s Total 50 5 •f orr evi ew pur posesonl y• 10

c. 37 x 2

d. 23 x 5

X

Total

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g. 13 x 5 X

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Total

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X

Total

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b. 28 x 5

Total

Total

j. 35 x 3 Total

X

Total

Curriculum Link: Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057)

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Multiplication mystery Amelia the Amazing says she can guess the number that Otto is thinking of. Discover the number that Otto is thinking of by solving all the multiplication facts and shading in the answers in the grid below. The unshaded number is the number that Otto is thinking of.

Ben

Austen

Billy 5x6

10x10

Jake 2 x 11

Otto 4x5

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or eBo st r e p9 x 10 o 5x7 2x9 3 x 12 u k S Amelia

Zoe

9x5

4x4

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• Jaydon

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8x3

Jess

Taylor

7 x 10

Lulu 33 x 2

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35

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5 x 11

o c . Sam Tian cheValentina Ollier e o t r s s r u e p 24 22 27 18 55 15 16

90

30

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The number that Otto is thinking of is: Write a multiplication fact to show Otto’s number: 24

Shay

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Lilly

Curriculum Link: Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056)

36

45


Division strategies You can have a lot of tricks up your sleeve to solve division equations. Let’s take a look at some strategies that you may already know. It does not matter which strategy you choose, to help you get the right answer. Strategy 1: Use what you know about multiplication facts to solve division equations.

or eBo st r e p ok8 lollies u Strategy 2: Make equal groups (arrays). For example: share equally among 4S friends. 40 ÷ 4 = 10 40 ÷ 10 = 4

2 x 12 = 24 12 x 2 = 24

24 ÷ 12 = 2 24 ÷ 2 = 12

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10 x 4 = 40 4 x 10 = 40

8÷4=2

Strategy 3: Skip counting (counting back).

© ReadyEdPubl i cat i ons 30 ÷ 5 = 6 20 ÷ 4 = 5 • f orr evi ew pur pose sonl y•

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… and what’s more? You know the total.

15 ÷ 3 =

4, 8, 12, 16, 20 5 4 3 2 1 skips

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5, 10, 15, 20, 25, 30 6 5 4 3 2 1 skips

The quotient is the answer.

. teYou know the number of equal o c . che groups you need to make. e r o r st super

Solve this Division Problem

Solve this division problem using one of the strategies above or another you have learned. Explain how you solved the problem to a partner. Ronaldo has scored 3 goals for his team in every soccer game he has played this season. So far, he has scored an impressive 42 goals. How many games has he played?

Curriculum Link: Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056)

25


Divide and conquer Work with a partner. Choose two different coloured pencils. Take turns choosing three bubbles from the tank to write a division fact (e.g. 35 ÷ 5 = 7). Shade in the numbers you use. You cannot use shaded numbers again. Whoever completes the most correct division facts is the conqueror.

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25 10

3

5

18

33 11

3

100

2

20

27

7

5

14

2

32 10

60

1

50

12

8

90

9

3

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4

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32

1

80

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2.

2.

3.

3.

4.

4.

5.

5.

You can continue this table on the back of this sheet. 26

Curriculum Link: Recall multiplication facts of two, three, five and ten and related division facts (ACMNA056)


Wonder word problems Have a go at solving these problems involving wonders of the natural world. lifespan of a Gentoo penguin is A javelin frog from the Kimberley, 2 1 The 20 years. It spends half its life in the WA is 2 cm long. How many javelin ocean foraging for food. How many years does the penguin spend on land?

frogs could I place in a row to fit on two 30 cm rulers?

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or eBo st r e p ok u Snails can crawlS 20 metres in one The smelly corpse plant blooms find a succulent lettuce in 6 hours?

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3 day! How far could a snail travel to 4 once every 7 years. I saw one bloom in 2016. How many times can I expect to see the same plant bloom before 2040?

© ReadyEdPubl i cat i ons •f orr vocean i ew pur p oterrarium seso nl y In my there are• 40 spiders’ moves ine the 6 5 Abyseahorse legs and 30 spiders’ eyes. How fluttering its tail fin 35 times a

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many eyes does my species of spider have?

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second. How many tail flutters would a seahorse make in 10 seconds? In 15 seconds?

o c . chone e primates A koala eats on average Gibbons arer long-armed er o 8 7 kilogram of eucalyptus leaves tswing 10 metres at a time s r as day. that can upe How many kilograms will 5 koalas through the treetops. How many eat in May?

swings would it take a gibbon to move half a kilometre?

Write a wonder word problem for a classmate to solve on the back of this sheet. Curriculum Link: Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (ACMNA057)

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What are fractions? Here is a whole pizza. Let’s cut it up into 5 equal slices (parts). The part of the pizza that’s been taken out is one part out of five. One fifth of the whole pizza is about to be eaten.

or eBo st r e p ok u S

One fifth is written as:

The top number is the numerator.

5

The bottom number is the denominator.

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1

A fraction is any part of a whole. A numerator tells you how many parts you have and a denominator tells you the total number of parts that make up the whole. 1. Can you write the fractions that the shaded parts represent on the fraction wall? Look at the examples to help you. Check your answers with a peer.

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© ReadyEdPubl i cat i ons whole •f or r evi ew pur posesonl y• 1/2

o c . che e r o 2. Look at that delicious wholer pizza again. Use the tfraction wall to help you. s su per

a. Is half the pizza a bigger share than three fifths of the pizza?__________ b. If you ate three eighths of the pizza, how many slices would be left?

___________________________________________________________

c. Is two fifths and four tenths of the pizza an equal share? Explain your answer.

28

___________________________________________________________

Curriculum Link: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (ACMNA058)


Shady fractions

a)___________

c)___________

d)___________ scrumptious pies For Sale

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or eBo st r e p ok u S

Felicity wants to sell as many slices of her scrumptious pies as possible. Look at her pie sales at lunch today. The missing parts are the slices she has sold.

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2

b)___________

chicken veggie pie pork pie ©pie ReadyE dP ubl i cat i o ns

•f orr evi ew pur posesonl y•

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seafood pie

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bacon pie

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1

Write the fraction for the shaded part of the following shapes.

apple pie

o c . Scrumptious che Pie Sales Reportr e o r st pork s per veggieu

Complete Felicity’s sales report by writing the fraction of each pie sold.

chicken seafood

bacon

apple

a. Shade in the missing parts of the pies to make them whole. b. Which was Felicity’s best-selling pie at lunch? _ _______________________ c. Which was her least popular pie today? _____________________________ Curriculum Link: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (ACMNA058)

29


Fractions on a number line 1

Label the fractions marked by the pointers on these number lines.

a. 0

1

b.

c.

0

1

It’s race day! Four children are running in a 100 metre race. After 10 seconds, the children have completed the following fractions of the distance:

© ReadyEdPubl i cat i ons Lane 1• - Jenny Lane 2e - Joel Lane -s Julia Lane 4 - Jake f orr e vi w pu r p3o eso nl y •

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Start

1 2 3 4

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2/5

3/4

3/5

o c . che e r o t rchild s r up a. Colour in the distance eachs hase run after 10 seconds. Choose a

Finish

1/2

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2

1

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0

or eBo st r e p ok u S

different colour for each lane. Be as exact as you can be when you mark each position.

b. Who is leading the race after 10 seconds?_________________________ c. What fraction of the distance does Joel have to run to finish? _____________________________________________________________ d. How many metres does Jake still have to run to finish the race? _____________________________________________________________ 30

Curriculum Link: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (ACMNA058) Elaboration: Locating unit fractions on a number line


Equivalent fractions Draw a line to match the shaded parts of the shapes in Column A with their equivalent fractions in Column B. Write the fractions on the connecting lines.

Column A

a

2

5

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b

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d

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3

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Column B

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Curriculum Link: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (ACMNA058)

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Tuck shop money problems Tuck Shop Menu For Today yoghurt

lamington

80c

$1.25

$2.20

50c

muffin

chocolate milk

$2.00

mini pizza slice r opie eB t s r e oo p k Su$2.45 80c $1.90 chicken drumstick

$1.50 fruit juice

$1.20

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Teac he r

salad sandwich

apple

1. How much does Lucas pay for a muffin and a chocolate milk?__________ How much change does he get if he pays with a $5 note? ____________ 2. How much does Noah pay for a mini pie and an apple?

© ReadyEdPubl i cat i ons 3. Yara brings her own packed lunch to school, but she wants something oratr e vi e whasp u r p os esdown onl y• to eat• andf drink recess. She $2 to spend. Write what she can

_ ___________________________________________________________

choose and how much these choices will cost.

_ ___________________________________________________________

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_ ___________________________________________________________

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4. Ivy would love a salad sandwich, a fruit juice and a lamington, but she only has $4. How much more does Ivy need?

. te o _ ___________________________________________________________ c . chcould emuch change will 5. How many pizza slices Grace buy for $6.00? How r e o she receive if she pays withr three $2 coins? st su er p

_ ___________________________________________________________

6. Finn buys three mini pies, an apple and a chocolate milk. Is there another combination on the menu that costs the same as Finn’s order?

_ ___________________________________________________________

7. Buy what you would like from the menu. How much did you pay?

32

Curriculum Link: Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents (ACMNA059)


Minding your money Jack is going to have a busy morning at the mall spending the $100 that he received for his birthday.

$100

Keep track of Jack’s spending by calculating the amount of money that he has left after each purchase that he makes. Write the total in the space under each image. Do your written addition and subtraction on the back of this sheet.

or eBo st r e game world 2 ICE CREAM 3o p k $16.00 Su PARLOUR $1.50

4

A triple choc whipple please.

$

© ReadyEdPubl i cat i ons $ •f orr evi ew pur posesonl y• half price sale

Take 50% off marked prices.

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$22.30

5

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4 curry puffs please

o c . ch e $ r $ e o r st super

I ‘ve had a great birthday and I still have _______ left!

6 cinemas

$1.50

Two tickets please!

$13.00 Curriculum Link: Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents (ACMNA059)

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Teac he r

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Section 2: r o e t s B r e oo p u k S Measurement and Geometry

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

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Information page

Symmetry in nature Nature loves symmetry! Plants and animals, the planets and even people, are beautiful examples of how a design can be repeated to produce a pattern. There are three types of symmetry: reflection, rotational and translation. Look at the examples below.

Reflection Symmetry

or eBo st r e p ok u S

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Teac he r

In reflection symmetry, you can draw a line of symmetry to divide the object in half. When you fold the image, both halves match. Look at the examples.

Rotational Symmetry An object with rotational symmetry will look the same after it has been rotated. Observe how the frangipani in image 1 looks, after rotating it 90º (image 2) and then another 90º (image 3).

© Ready EdPub i cat i on 12 l 3s •f orr evi ew pur posesonl y• 90˚

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180˚

. t e (or strip o Translation symmetry c . ch symmetry) is achieved by moving e r etor o a design a certain distance the t s s r u e p left and right from the original. Translation Symmetry

You can see the striking effects of translation symmetry in the pattern of this honeycomb and bandy bandy snake.

Think of an example of symmetry in the natural world. Draw your example on the back of this sheet. Label the type of symmetry it shows. Discuss your image with a peer. Curriculum Link: Identify symmetry in the environment (ACMMG066)

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Identifying symmetry

or eBo st r e p ok u S

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Teac he r

The ocean is awash with examples of symmetry. Can you find different kinds of symmetry in this image of the marine world? After you have filled in the table below with your examples, bring nature’s symmetry to life with colour.

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REFLECTION

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

o c . che e r o r st super

ROTATIONAL

TRANSLATION

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Curriculum Link: Identify symmetry in the environment (ACMMG066)


Symmetry in the natural and built world 1

Indigenous artists often apply symmetry in their artworks to show the process of creation.

or eBo st r e p ok u S

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Teac he r

Complete the right side of this frog so that it is symmetrical.

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

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Complete the left side of the Luna Park entrance.

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2

The symmetry of different shapes adds strength and character to the Luna Park entrance in Sydney and many other constructions.

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Curriculum Link: Identify symmetry in the environment (ACMMG066)

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Angles in the environment

or eBo st r e p ok u S

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Teac he r

1

Look around you. There are angles in your classroom, in the playground and in nature. Study the image below, then mark the angles that you find with a felt pen.

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

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90º angle (right angle)

found in the image

found in the classroom

o c . che e r o r st super

less than 90º angle (acute)

more than 90º angle (obtuse)

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2

Compare the angles that you have found in the image above with angles in your classroom. Complete the table below.

Curriculum Link: Identify angles as measures of turn and compare angle sizes in everyday situations (ACMMG064)


Measurement Believe me, that toad was as big as a hippo!

Common units of measurement help people all around the world agree on the length, the mass or the capacity of things. Common units of ? measurement for example, help us to more easily understand Olympic world records and agree on the world’s tallest man!

Teac he r

or eBo st r e pbelow and decide what is o u kmeasured: Read the 9 statements being S length, mass or capacity. Put an L, M or C next to each statement. Look at the example.

1. Mia wants to find out if she’s grown since last year.

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1

Why do we use common units of measurement?

L

2. The truck driver needs to know how much petrol will fill his truck. 3. The nurse weighs the baby. 4. The seamstress is making a wedding dress.

© ReadyEdPubl i cat i ons •f orr e i ew p uar pos eso nl y• 6. A teacher wonders if v there’s room for bigger display board. 5. The patient takes the correct dose of medicine.

7. A vet wants to know how many worm tablets to give the dog.

2

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9. Chloe wants to know how far the nearest bus stop is.

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8. I need to know if all my clothes will fit in a suitcase.

o c . che e r o r st super

Work with a partner. Make up examples like the ones above to go with: length, mass and capacity. length:

mass:

capacity:

Curriculum Link: Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061)

39


Length 1 You know that you can use a ruler to measure the length of a pencil, but did you know that a pencil can be used to estimate the length of other things?

The length of the glue stick is about 9.5cm

or eBo st r e p ok u S

Most pencils and pens are about one centimetre (1 cm) wide.

Teac he r

1 cm

E.g. You can use a pencil to estimate the length of your glue stick: *The example below has been scaled down.

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Choose and Estimate

1. Choose three small objects (e.g. eraser, crayon, sharpener) that you can lay in a vertical position on a sheet of paper.

2. Line up the end of a pencil as close to the edge of the object as you can. Label the first mark you make “0.” 3. Continue to move your pencil along the object marking off the 1cm intervals.

© ReadyEdPubl i cat i ons 4. The last labelled mark you make willu help you estimate your objects’ • f o r r e v i e w p r p o s e s o n l y• lengths. 5. Record your estimates in the table below.

ruler (actual) length (cm)

object 2

object 3

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estimated length (cm)

object 1

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6. Measure your three objects again using your ruler. Remember to put the edge of the object as close to the “0” mark on the ruler as possible. Record the lengths in the table above. 7. What did you observe about the estimated and actual lengths of your objects?

40

___________________________________________________________

___________________________________________________________ Curriculum Link: Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061)


Length 2 Would you measure the following objects in centimetres or metres? Remember there are 100 centimetres (100 cm) in one metre (1 m). Tick the correct unit.

a

b q cm

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q cm q m

g

q cm q m

q cm q m

h i © ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

q cm q m

j

q cm q m

k

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e

2

q m

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d

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q cm q m

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o c . che e r o r st su Answer these questions using your from Question 1. er panswers q cm q m

q cm q m

a. Which objects would be longer than 5 metres?_____________________ _ __________________________________________________________ b. Which objects would be shorter than 30 cm?_ _____________________ _ __________________________________________________________ c. How long do you think a blue whale is?___________________________ d. Estimate the length of a carrot. _________________________________ Curriculum Link: Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061)

41


Mass Mass tells you how light or heavy something is. The mass of light objects is measured in grams (g). The mass of heavy objects is measured in kilograms (kg).

Remember: 1000 g = 1 kg

weigh-in time at the zoo Can you estimate the mass of each animal? Write your estimates in the table below. A hint: the smallest animal is 3 g and the largest animal is 200 kg! Your teacher will tell you the average body mass for each animal later.

Teac he r Estimated mass:

Estimated mass:

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or eBo st r e p ok u S 2. Numbat 1. Hairy-nosed Wombat 3. Blue Tongue Skink Estimated mass:

Actual average mass: average mass: © Read yEdPubl i cActual at i o ns 4. Male Koala Carpet Python Frog •f orr ev5.i e wp ur pose6.sCorroboree onl y•

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Estimated mass:

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Actual average mass:

Estimated mass:

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Actual average mass:

Estimated mass:

o c . 8. Tasmanian Devil 9. Adult Green Sea che e r Turtle o r st super Actual average mass:

Actual average mass:

Estimated mass:

Estimated mass:

Estimated mass:

Actual average mass:

Actual average mass:

Actual average mass:

7. Fairy Penguin

Which combination/s of animals could sit on a see-saw to balance out the average mass of four Tasmanian Devils? Draw your solution/s on the back of this sheet. 42

Curriculum Link: Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061)


Massive food problems Put on your thinking caps to solve these problems related to mass. You can check your answers with a calculator.

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

Circle the heaviest fruit. Explain your choice in the space below.

4

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a

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b

c

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3

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2

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Mum bought a watermelon with a mass of 1 kg. She cut 3 slices from the watermelon to take on a picnic. Each slice had a mass of 150g. What was the mass of the leftover watermelon that she put in the fridge?

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1

At the Easter Show, pumpkin farmers receive a point for every gram their monster-sized vegetables weigh. The masses of the winning pumpkins are: 1st place: 735.5 kg; Runner up: 621 kg; Best in junior section: 347.2 kg. How many points did each of the winning entries receive?

Oliver wants to make brownies for both teams competing in the cricket final next week. He’s found a recipe for 20 servings that includes the following ingredients: 400g of sugar; 45g of cocoa powder; 250g of butter; 180g of flour. How much sugar, cocoa powder, butter and flour does Oliver need if he wants to make 60 servings of brownies? a coco

o c . che e r o r st super r

suga

5

A man picks up a box containing 8 cans of sliced beetroot. The total mass of the cans is 3.4 kg. How many grams does one can of sliced beetroot weigh?

Curriculum Link: Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061)

43


Capacity 1 We measure the capacity of containers to hold things in millilitres (ml) and litres (l). 1000 millilitres (1000 ml) = 1 litre (1L). Draw a line to match the volume of millilitres or litres with the containers. Think about what the containers usually hold. Look at the example to help you.

1

1. a cup of tea

a. 10 L

or eBo b. 250 ml st r e p oc.k5 ml 3. a carton of milk u S 4. a can of soft drink d. 1 L 5. a standard size bucket

e. 80 L

6. a teaspoon of medicine

f. 360 ml

A wildlife carer is preparing milk formula for baby animals. She’s written the volume of milk needed for each animal on the post-it notes below. Read the volumes in millilitres on the cylinders, then draw a line to match the correct cylinder to each baby animal.

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

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100

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50

Winnie the wallaroo 125 ml

150

150

150

100

100

100

150

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150

44

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2

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2. an average size bathtub

100

o c . che e r o r st super

50

Kendo the koala

150 ml

50

Wombles the wombat 160 ml

50

Paco the possum 85 ml

Curriculum Link: Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061)

50

Bessie the bat 5 ml


Capacity 2 1

To answer these questions, refer to your answers to the tasks on the previous page. Don’t forget to include units of measurement.

1. How many litres of water would it take to fill three bathtubs?______________ 2. What is the volume of liquid in six teaspoons of medicine?________________ 3. How many buckets of water would it take to fill two bathtubs?_____________

or eBo st r e p ok 85c. Is it cheaper 6. A can of lemonadeu costs 45c. A litre bottle of lemonade costs to buy four cansS of lemonade or two 1 L bottles?________________________ 4. Would you drink a litre of liquid if you drank three cups of tea?_____________

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5. If you wanted 3.5 L of milk, how many cartons would you open?_ __________

7. How much milk formula would the wildlife carer have to make if she had: a. three wallaroos? __________

d. eight koalas? __________

b. four bats? _______________

e. two possums? _______________

c. six wombats? ____________

f. two of each animal? ____________

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different coloured pencils to show on the measuring beaker in millilitres the ingredients in Steel Man’s tonic. How many millilitres of the “secret” ingredient does Steel Man add?

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© ReadyEdPubl i cat i ons Steel Man drinks 500 ml of his secret •f o rr evi ew ur posesonl y• 2 Shine4ever tonic every day. Usep

o c . che e Ingredients for Shine4ever r o t r s sup er 100ml of onion juice

500ml

400ml

300ml

50ml of rose water 25ml of dandruff shampoo

200ml

100ml

____ml of secret ingredient 140ml of olive oil 75ml of bath water

Curriculum Link: Measure, order and compare objects using familiar metric units of length, mass and capacity (ACMMG061)

45


Time word problems A Solve these time word problems. a full day of gardening, Mum Jian is training to be a whiz at 1 After 2 runs a big bubble bath. She hops solving a Rubik’s cube. These are the times that he took to complete the Rubik’s cube with his stopwatch today: 134 seconds, 94 seconds and 72 seconds. Write these times in minutes and seconds.

or eBo st r e p ok u S

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in at 6.30pm and she gets out of the tub at 6.57pm. How long does Mum’s bubble bath last?

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• Gigi rides her bike to and from 3 are going on a field trip 3 Year 4 school every day. It usually takes to the local nature reserve. The

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12 minutes each way. How many minutes a week does Gigi spend cycling to school?

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wildlife ranger is giving a short talk at exactly 10.15am. It is a twentyminute walk from the school to the reserve. At what time should the group leave school to be at the ranger’s talk with five minutes to spare?

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Curriculum Link: Tell time to the minute and investigate the relationship between units of time (ACMMG062)


Time word problems B Solve these time word problems. Zara is a wonderful piano Raj leaves chess club at 4.25pm. He 1 Madam 2 teacher. Yesterday she gave classes walks for 15 minutes to his cousin’s house and stays 20 minutes to have a snack and a chat. He reaches home 8 minutes later. What time does Raj arrive home?

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for one hour and forty minutes to two students. Each student gets the same amount of lesson time. How long is each piano lesson?

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• Our flight time between Darwin and has an appointment at 3 Cora 4 Brisbane was supposed to take 2.50pm with her dentist Dr. Wrench.

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three hours and forty minutes. The plane left Darwin on time at 3.25pm, but due to stormy weather, arrived twenty minutes late in Brisbane. What time did we arrive in Brisbane?

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The dentist gets caught in heavy traffic and arrives at the surgery 20 minutes late. She then spends another 3 minutes washing her hands. What time does the dentist finally see Cora?

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Curriculum Link: Tell time to the minute and investigate the relationship between units of time (ACMMG062)

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On the grid Wolf Bakes wants to trek across some very dangerous country on Hot Potato Island to see if he can survive off the land. He’s been given a grid map of the area: A

B

C

Hot Potato Island D

E

F

G

H

1 2 3 4

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© ReadyEdPubl i cat i ons 1. r Give foro Wolf’s drop-off point •f or e vthe i egrid wreference pur p se son l ymarked •

Use the information on the grid map to help you to answer the questions.

.

2. Where do orcas regularly feed offshore?________________

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3. Where is the highest peak on the island located?_ _______ 4. What can be found on the island in D8?_ _______________ 5. Give the grid reference for: a) the most southern point of the main island.__________ b) the rescue boat anchored off the coast.______________

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o c . 6. c Wolf’s pick up point is on the easterne side of the island in H4. h r Marke this pick up point on the map with an X. o t r s s r u pe 7. With a dotted line, mark the quickest route that Wolf could take from his pick up point to the boat. Estimate how far Wolf has to walk to the drop off point.__________________

8. What might force Wolf to change his course? Give the grid reference/s._ ______________________________________

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Curriculum Link: Create and interpret simple grid maps to show position and pathways (ACMMG065)


Create your own grid map Create your own grid map in the space below. The grid map could be of: • your classroom • the area where you live

• your school and playground • a local park • an imaginary place

Include a scale for your map and a key if necessary. Use the example on the previous page to help you. A

B

1

5 6 7

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Write 3 questions about grid reference locations for a peer to answer. Question 1

Question 2

Question 3 Curriculum Link: Create and interpret simple grid maps to show position and pathways (ACMMG065)

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Make a 3D model How many of the 2D faces do you need to build the 3D models? The first one has been done for you.

3D shape

Cylinder

3D shape

2D faces

or e st Bo r e Triangular p o prism k u S 6 rectangles 2 squares

Cube

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Cuboid

2D faces

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• Square-based pyramid

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hexagonal prism

. te o c What I will need to My 3D shape: . ce e make my model: h r o r st super

Make a model of one of the 3D shapes above. Name and draw the 3D shape that you have chosen in the box.

Use the back of this sheet to write instructions for a classmate to follow to make your 3D shape. 50

Curriculum Link: Make models of three-dimensional objects and describe features (ACMMG063)


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Section 3: r o e t s B r e oo p u k S Statistics and Probability

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Presenting data 1

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Oops! The box containing the seashore field trip collection has been knocked over and the objects have been mixed up. It’s your job to sort the objects. Use the images on this page to complete the tasks on the page that follows.

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seashore collection 52

Curriculum Link: Collect data, organise into categories and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies (ACMSP069) Elaboration: Collecting data to investigate features in the natural environment


Presenting data 2 1. How many of each kind of seashore item is there on the previous page? sea urchin:

pebble:

pipi:

scallop:

starfish

coral:

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2. Complete this pictograph with the data that you have sorted in Question 1. Use drawings. You need a label for the vertical axis and a title.

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pebble

pipi

scallop

starfish

coral

Curriculum Link: Collect data, organise into categories and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies (ACMSP069)

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Presenting data 3 Graphs and tables are a good way to present, describe and summarise data. Study the table below entitled, Magnus vs Mayra vs Melon the Pug.

Magnus vs Mayra vs Melon the Pug

Data

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Makes snuffling sounds when sleeping.

Likes to get up to mischief.

Can count up to 20 in Japanese.

 

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or eBo st r e p a day. Sleeps more than 10 hours  o  u k S Has large, round eyes.  

Likes blueberry  s ©muffins. ReadyEdPubl i cat i on

•f orr evi ew pur posesonl y•

1. Why is the table called, Magnus vs Mayra vs Melon the Pug?

_________________________________________________________________

_________________________________________________________________

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2. What do the ticks () and crosses () mean in the columns under the images?

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o c . _________________________________________________________________ che e r o tcan’t? s 3. What can Magnus and Mayrar dos that Melon the Pug up er

_________________________________________________________________

_________________________________________________________________

_________________________________________________________________

4. What do the children and the dog have in common?

_________________________________________________________________

_________________________________________________________________

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Curriculum Link: Interpret and compare data displays (ACMSP070)


Presenting data 4 Complete the data table below comparing something about you and two friends. You can survey each other to compare likes and dislikes, abilities or even shoe size! Use the table on the previous table to help you.

Title: Data: 1.

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2.

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3. 4. 5.

© ReadyEdPubl i cat i ons You can also present your data as a Venn diagram to show what you have and f orr evi ew p ur pinoyour ses on l y•the data don’t have • in common with another member group. Transfer

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above in the Venn diagram below.

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Curriculum Link: Interpret and compare data displays (ACMSP070)

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Statistics 1 You can collect, organise and study data to inform you about the world in which you live. During a recent dive on the Great Barrier Reef, Kirra took underwater photos of the marine life that she observed.

green turtle

butterfly fish

snubfin dolphin

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r o e t s B r e 015 021 o 038 p o u blue-spotted ray kblue clam sea snakeS 050

067

cuttlefish nautilus © ReadyE dPubl i cat i on s •f orr evi ew pur posesonl y•

lemon shark

083

092

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076

Kirra wants to organise her photographs into folders in her images file. She has decided on four categories. Which photographs will she put in the following folders? Write the photograph numbers on the folders.

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als

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Curriculum Link: Interpret and compare data displays (ACMSP070)

fish

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Statistics 2 1. Help Kirra with her observation notes Marine creature Tally by completing a tally of the marine ll creatures that she photographed on green turtle the previous page. Fill in the table butterfly fish (right). snubfin dolphin 2. How many marine animals did Kirra photograph altogether?

sea snake

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______________________________

4. Which group of animals did she see the least of?

cuttlefish

nautilus

______________________________

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r oblue-spotted e t s Boray r e 3. Which group of animals did she see p ok the most of? blue clam u S ______________________________ lemon shark

5. What did you learn from Kirra’s data about life on the Great Barrier Reef?

© ReadyEdPubl i cat i ons 6. Kirra has presented her data as ap bar graph, but she hasn’t finished • f o r r e v i e w u r p o s e s o n l y• labelling it. Complete the bar graph with labels for the bars and numbers

_________________________________________________________________

on the vertical axis. Think about the groups that Kirra has chosen to present and the number scale.

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Curriculum Link: Interpret and compare data displays (ACMSP070)

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Probability 1

Probability measures how likely it is that something will happen. How likely or unlikely is it that you will see the following things today?

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or eBo st r e p q unlikely q likely q unlikelyok q likely q unlikely q likely q likely q unlikely u S

q likely q unlikely q likely q unlikely q likely q unlikely q likely q unlikely

© ReadyEdPubl i cat i ons We can use a scale to describe probability. •f orr evi ew pur posesonl y• 2

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probability scale

0.2 0.5 0.8 1 . tecolours to shade the likeliness of you doing Use five different the things o c listed below this week. Use the Probability Scale above.. ch e r er o st running a marathon su r egame riding a horse playing ap team

impossible

unlikely

reading a text eating prawns

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even chanCe

visiting a friend

likely

certain

going to church

cuddling a pet

having a spelling test

flying to Brazil

getting a haircut

getting a pat on the back

setting the table

wearing a yellow wig

buying a telescope

Curriculum Link: Conduct chance experiments, identify and describe possible outcomes and recognise variation in results (ACMSP067)


My probability investigation You are going to carry out a probability investigation using a standard deck of 52 playing cards. Inside a pack of cards there are: 13 clubs; 13 diamonds; 13 spades; 13 hearts. In each suit there is a: 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king and ace.

Predict! 1. From a pack of 52 playing cards, what is the probability of you picking out the queen of clubs?

or eBo st r e okpicked out a card 2. After picking out u 20 p cards, how many times will you have with a heart orS diamond on it?

1.

2.

3.

4.

5.

6.

7.

8.

11.

12.

13.

14.

15.

16.

17.

18.

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My prediction:_ ___________________________________________________

My prediction:_ ___________________________________________________

Test Your Predictions!

3. Now carry out your investigation. Pick out cards from a 52 deck. Record your results in the table below. 9.

10.

19.

20.

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4. How many times did you pick:

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the queen of clubs?

the five of clubs?

a spade?

a jack?

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o c . che e r o r the two of diamonds? the six of hearts? st supe r the ace of clubs?

the three of hearts?

a king?

a queen?

the four of diamonds?

the seven of hearts?

5. Did your predictions match the results in your table? What did you find out? ________________________________________________________________ Curriculum Link: Conduct chance experiments, identify and describe possible outcomes and recognise variation in results (ACMSP067) Elaboration: Conducting repeated trials of chance experiments such as tossing a coin or drawing a ball from a bag and identifying the variations between trials

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Chances You have a mixture of blue, green, yellow and red cards in a bag. Complete the tasks below.

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or eBo st r e p ok u Shade in theS cards so

3

that it is likely that you will pick a green card out of a bag. You must show all four colours.

Shade in© theR cards soy ead EdPubl i cat i ons that it is unlikely that •f or ev i ew pur posesonl y• you will pick ar blue card out of a bag. You must show all four colours.

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Shade in the cards so that it is highly unlikely that you will pick a red card out of a bag. You must show all four colours.

5

Shade in the cards so that you have an even chance of picking a yellow card out of a bag. You must show all four colours.

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Shade in the cards so that it is highly likely that you will pick a yellow card out of a bag. Use at least three different colours.

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Curriculum Link: Conduct chance experiments, identify and describe possible outcomes and recognise variation in results (ACMSP067)


What’s the chance? (extension) Work out the chances of the following situations below happening. In the probability column, describe the likeliness of the situations happening using these terms: impossible

unlikely

even chance

likely

certain

Look at the example to help you. situation

fraction

or eB4/52 st r e oo p k 2. Being able to visit u an Australian state or S territory with more than one word in its /8

probability

name.

3. Rolling a ten-sided dice and getting a number less than 8. 4. The chance of picking a vowel in the town’s name “Oodnadatta”.

unlikely

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1. Picking an ace from a deck of cards. (There are 52 cards in a deck and 4 aces.)

© ReadyEdPubl i cat i ons 5. One thousand raffle tickets to win a bike f o rdidn’t r ev i e pWhat ur posesonl y• have been• sold. You buy aw ticket. 6. Your birthday is today.

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7. There are 16 golf balls in a bag: 6 white, 5 yellow and 4 red. What’s the chance of picking a red or white golf ball from the bag?

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is your chance of winning?

o c . cdip.e e 8. You pay $1 for a lucky h There are 50 r o r st sup prizes in the box. What’s the probability ofe r you getting a lucky dip prize? 9. What are the chances of you being born in a month that ends with the letter “y”. 10. There are 100 keys to lock the doors of the school, numbered from 1 to 100. What’s the chance of picking a key with a number 5 on it?

Curriculum Link: Conduct chance experiments, identify and describe possible outcomes and recognise variation in results (ACMSP067)

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ANSWERS p.8 Children can peer mark answers for this task. p.9 1) 30,31,32,33, 34 2) 13,12,11,10,9 3) 73,72,71,70,69 4) 58,60,62,64,66 5) 70, 65, 60, 55,50 6) 27, 30, 33,36,39 7) 59,61,63,65,67 8) 214,284,364,454 (4+10=14, 14+20=34, 34+30=64,64+40=104...)

p.17 Students’ own subtraction.

or eBo st r e p ok u S

p.10 1) 2-E 3-O 4-E 5-E 6-O 7-E 8-E 9-E 10-O 11-O 12-E 2) When you add 10 to an even number (EVEN); When you add 100 to an odd number (ODD).

p.12 2) three hundred and fifty four 3) six hundred and thirty nine 4) eight hundred and twenty eight 5) one thousand nine hundred and ninety seven 6) one thousand seven hundred and two 7) three hundred and thirteen. Coloured tags: 2,4,6

p.18 1) 22 – 8 = 14 2) 40 – 26 = 14 3) 200c – 165c = 35c 4) 24 – 16 = 8 (4 pairs) p.19 2) 1 + 15 + ? = 25, 16 + ? = 25, 25 - 16 = 9 (9km); 3) 110 – 6 – 5 – 4 + 3 = 98 (98kg); 4) 16 + 39 = 55, 80 – 55 = 25 (Pia is still waiting for 25 pigeons to return)

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p.11 1) a. Add 3 beads to T, 5 beads to TENS, 1 bead to O b. Add 1 bead to T, 4 beads to TENS, 3 beads to O c. 1 bead to T, 4 beads to H, no beads to TENS, 2 beads to O. 2) 1091, 1179, 3190, 4658, 4925 3) a. < b. < c. < d. >

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p.16 1) b. 3 c. 2 d. 1 e. 5 f. 6 g. 5 h. 6 i. 7 j. 30 k. 4 l. 10 + 3 m. 80 + 6 n. 0 + 4 o. 70 + 8 Sample answers: 2) b. 848 = 800 + 40 + 8 c. 962 = 1000 - 30 – 8 d. 389 = 300 + 80 + 9 e. 144 = 200 – 50 – 6 f. 1735 = 2000 – 200 – 60 – 5 g. 4586 = 5000 – 400 – 10 – 4

p.20 1) b. 60 – 20 = 40 c. 70 + 30 = 100 d. 80 + 50 = 130 e. 260 + 120 = 380 f. 470 – 250 = 220 Sample proof: 2) b. 26 – 18 = 8 c. 56 + 26 = 82 d. 69 – 28 = 41 e. 76 - 41 = 41 f. 82 - 62 = 20 g. 51 + 16 = 67 h. 120 – 114 = 6 i. 539 – 104 = 435 j. 2300 – 2289 = 11

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

p.14 Student’s own sequence. Possible answer: helps to solve subtraction and addition problems. p.15

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p.13 1) a. 40 b. 16 c. 24 d. 80 2) Circled numbers: 130, 142, 150 3. 326, 340.

p.21 1) a. 4+4 = 8 or 2+2+2+2 = 8 b. 5+5+5 = 15 or 3+3+3+3+3 = 15 c. 3+3+3 = 9 d. 3+3+3+3 = 12 or 4+4+4 = 12 e. 4+4+4+4 = 16 f. 8+8+8+8+8+8+8+8 = 64 g. 3+3+3+3+3 = 15 or 5+5+5 = 15 h. 3+3 = 6 or 2+2+2 = 6 i. 4+4+4+4+4 = 20 or 5+5+5+5 = 20 2) Examples of arrays that students could draw are: box of chocolates, paintbox pallets, etc.

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p.22 1) Students answers will depend on choice. 2) b. 5x3, 5x3=15 c. 3x5, 3x5=15 d. 3x3, 3x3=9 e. 4x5, 4x5=20 f. 4x4, 4x4=16 g. 3x2, 2x3=6 p.23 a. 80 b. 140 c. 74 d. 115 e. 42 f. 87 g. 65 h. 96 i. 118 j. 105 p.24 Ben:35; Austen:90; Billy:18; Jake:36; Zoe:20; Lilly:100; Jaydon:30; Taylor:22; Lulu:45; Shay:16; Jess:24; Sam:70; Valentina:66; Ollie:15; Tian:55. Otto’s number is:27 (3x9/9x3 = 27)

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p.25 42 ÷ 3 = 14 games p.26 There are approximately 20 division facts in the image. p.27 1) 20 ÷ 2 = 10 years 2) 60cm ÷ 2cm = 30 frogs 3) 6 hours is a ¼ of a day; ¼ of 20m is 5m (snail crawls 5m) 4) Counting on in 7s – 3 times (2023, 2030, 2037). 5) 35x10=350 times; 35x15=525 times 6) 5 spiders in terrarium/6 eyes each 7) 31 (days in May) x 5 (koalas) =155kg 8) 500m ÷ 10m = 50 swings

p.38 1) Sample answers - Right angles: angle of water to bank, fisherman’s knees (left); Acute angles: chef’s elbow, angle of fisherman’s rod and line (left); Obtuse angles: ballerina’s body and legs, fisherman’s leg (right). 2) Classroom angles: various answers including doors, windows (shut and ajar), foldable rulers etc.

p.29 1) a. 1/2 b. 1/2 c. 2/8 or 1/4 d. 2/3 2) a. Students need to add: chicken pie-2 slices (total=8); veggie pie-2 slices (total=4); pork pie-3 slices (total=5); seafood pie-1 slice (total=3); bacon pie-3 slices (total=10); apple pie-2 slices (total=6). b. pork c. chicken

p.39 1) 1. L 2. C 3. M 4. L 5. C 6. L 7. M 8. C 9. L 2) Examples: Length: Measure where to place markings on football field; Mass: weigh ingredients to make a cake; Capacity: chlorine doses in a pool

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p.37 Student’s drawings

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p.28 1) fraction wall: whole, 1/2, 1/3, 3/5, 4/10, 2/4 or 1/2, 6/8 2) a. No b. 5 c. Yes (2/5 and 4/10 are equivalent fractions)

p.30

p.36 Reflection: stingray, crab, crayfish; Rotational: starfish, sea anemone x2, octopus; Translation: markings on sea horse, fish, sea snake

p.40 7) Children will notice minor discrepancies between estimated and actual lengths. Ask children to explain how these could occur.

© ReadyEdPubl i cat i ons p.41 1) p a. cm b. m c.s cm o d. m e.l cm f.• cm g. m h. cm •f orr evi ew pur o s e n y i. cm j. m k. cm l. m 2) a. whale, boat, fence b.

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scissors, frog, phone, shell, ribbon (usually longer to tie), carrot c. about 25m d. about 22cm

p.31 1 = d 4/5, 8/10 2 = a 1/3, 2/6 3 = e 1/2 4 = b 2/8, 1/4 5 = c 1/4, 4/16

p.42 Average mass: 1. 35kg 2. 700g 3. 300g 4. 9kg 5. 20kg 6. 3g 7. 1kg 8. 10kg 9. 200kg 4 Tasmanian Devils 40kg = 10 Penguins/2 Pythons/a Wombat + 5 Penguins

p.32 1) $3.50, $1.50 2) $1.30 3) lamington+apple $1.75; apple+fruit juice $1.70; mini pie+fruit juice $2.00; yoghurt+mini pie $1.60; yoghurt+apple $1.30 4) 65c 5) 3, 30c 6) muffin+apple+pizza slice = $4.40 7) Student’s answer.

p.43 1) 735500 pts; 621000 pts; 347200 pts 2) 550g 3) banana (pear and lemon have equal mass, banana is heavier than the pear) 4) Ingredients X 3: 1.2 kg sugar; cocoa 135g; 750g butter; 540g flour 5) 3.4kg = 8 cans (3400g 00 8 = 425g each)

p.33 $28.45 (Children may not halve the kite’s price, giving a final answer of $17.30).

p.44 1) 2 = 80L 3 = 1L 4 = 360ml 5 = 10L 6 = 5ml 2) order: bat, wallaroo, possum, koala, wombat

p.35 Student’s answers.

p.45 1) 1. 240L 2. 30ml 3. 16 4. No 5. 4 cartons 6. 4 cans = $1.80; 2 1L bottles = $1.70 7. a. 375g b. 20g c. 960ml d. 1,200ml (1.2L) e. 170ml f. 1050ml 2) 500ml - 390ml = 110ml of secret ingredient

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p.46 1) 27 minutes 2) 134s = 2m 14s, 94s = 1m 34s, 72s = 1m 12s 3) 9.50am 4) 24m x 5 school days = 120m (2 hours) p.47 1) 50 minutes each 2) 5.08pm 3) 3.13pm 4) 7.25pm p.48 1) B7 2) G2 3) D4 4) A forest 5) a. D9 b. A8 6) Mark X at H4 7) Estimate: 65km 8) Bears at F5.

Marine creature

Tally

green turtle

ll

butterfly fish

llll llll

snubfin dolphin

l

sea snake

l

blue-spotted ray

lll

blue clam

llll l

lemon shark

l

cuttlefish

lll

nautilus

llll ll

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p.49 Students’ questions based on own grid map.

p.53 sea urchin 2; pebble 5; pipi 5; scallop shell 7; starfish 6; coral 6

2) 34 3) Nautilus (most) 4. dolphin, shark, smake (least) 5. The reef has a diversity of life with coral, plant life and marine animals. There are predators and prey. 6. The vertical axis should be labelled from 0-16 (or 18) in intervals of 2. Labels on x-axis should read from left to right: marine mammals, reptiles, molluscs and reef fish.

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p.50 cuboid (6 rectangles/2 squares; cylinder (2 circles/1 rectangle); hexagonal prism (2 hexagons/6 rectangles); triangular prism (2 triangles/3 rectangles); cube (6 squares); squarebased pyramid (4 triangles/1 square)

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p.57 1)

p.58 1. Students’ responses 2. Students’ responses

© ReadyEdP ubl i cat i ons p.59 1) 1 chance in 52 (unlikely) 2) even chance •f orr evi ew pur os es othat nl ylikelihood • of 5) p Students may notice the

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p.55 Student’s survey.

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p.56 Marine mammals: dolphin; Reef fish: blue spotted ray, butterfly fish, lemon shark; Marine reptiles: sea snake, green turtle; Marine molluscs: blue clam, nautilus, cuttlefish

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picking out a specific cards is highly unlikely compared to a complete suit.

p.60 1. Eight shaded yellow cards. 2. Seven shaded green cards. 3. Four or less shaded blue cards. 4. Three or less shaded red cards. 5. Five shaded yellow cards.

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p.54 1) Because it is comparing the abilities of three participants in a survey. 2) The ticks indicate that the participants have those abilities/behaviours. The crosses indicate that the participants can’t do certain things. 3) They can count in Japanese. 4) They all like to get up to mischief.

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p.61 2) 5/8 likely 3) 7/10 likely 4) 5/10 even chance 5) impossible 6) 1/365 unlikely 7) 10/16 likely 8) 50/50 certain 9) 4/12 unlikely 10) 10/100 unlikely

OzzieMaths Series - Year 3  

Your students will love solving these creative maths problems, many of which are set in familiar and real life situations. Written by an exp...

OzzieMaths Series - Year 3  

Your students will love solving these creative maths problems, many of which are set in familiar and real life situations. Written by an exp...