OzzieMaths Series - Year 4

Title: OzzieMaths Series Maths: Year 4

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.

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ISBN: 978 186 397 993 1 2

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Reproduction and Communication by others

Contents Teachers’ Notes Curriculum Links

4 5-6

36 37 38 39 40 41 42 43 44 45 46 47

Section 3: Statistics And Probability Class Pet Survey 1 Class Pet Survey 2 Presenting Data On The Data Trail Planning An Investigation Recording Data Chances Are . . . (Cards) Chances Are . . . (Ordering Task) Related And Unrelated Events

49 50 51 52 53 54 55 56 57

8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

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Section 1: Number And Algebra Even And Odd Numbers Which Number Comes Next?

Number Sequence Problems 1 Number Sequence Problems 2 Wordy Numbers Place Value With Decimals Mega Number Cards Mega Number Game Subtraction Partitions Find The Missing Numbers Division Fetch Multiple Fish Galactic Word Problems (Extension) Calculator Chaos!

Money Moments Checkout Champion Mixed Fractions Mixed Numerals On A Number Line Equivalent Fraction Word Problems Equivalent Fraction Tales

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It’s About Time Problems Time Zones What Time Is It In...?

Measuring Up 1 Measuring Up 2 Massive Problems Present Problems Fill ‘Em Up Capacity Problems 1 Fill ‘Em Up Capacity Problems 2 Calculating Volume 1 Calculating Volume 2 In The Right Direction

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Section 2: Measurement And Geometry Symmetry in Central Australian Art 29 Indigenous Art Symbols (Student Handout) 30 Symmetry In Asian Art 31 Comparing Area 32 Comparing Angles 33 Creating A 2D Skyline 34 Creating 2D Shape Objects 35

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Teachers’ Notes Maths: Year 4 is part of the OzzieMaths Series. It is linked to the Australian Curriculum and each page in the book references the content descriptor it specifically addresses.

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Section One: Number And Algebra

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The activities have been designed to develop mathematical skills and reasoning.

Creative ways that are often connected to solving problems in real-life contexts are presented. Students will be asked to reflect upon the strategies they use to problem-solve effectively in familiar situations and will begin to recognise 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 detailed below.

In this section, students will engage in a variety of activities that require them to demonstrate ever-increasing capability in using mental and written strategies to explore number relationships and patterns. Tasks include: using a number line to solve sequence problems; discovering the connection between even and odd numbers; and calculating change in shopping transactions.

© ReadyEdPubl i cat i ons f or r e vi ew pvalue ur p o ses nl y• This• section draws attention to the and beauty of o mathematics Section Two: Measurement And Geometry

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Section Three: Statistics And Probability

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in the world around them. Students will be asked to consider symmetry in Indigenous and Asian art to create their own symmetrical motifs. The skyline of a modern city activity focuses on architecture that incorporates and manipulates 2D shapes. Tasks involving measurement draw on everyday contexts.

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Students will develop skills in collecting, organising and representing data in this section. The focus is on exploring research questions and evaluating the most appropriate method of collecting and representing data. Probability activities include determining the likeliness of an event occurring and whether or not one event is affected by the occurrence of another.

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Curriculum Links Number and place value

Explore and describe number patterns resulting from performing multiplication (ACMNA081) Solve word problems by using number sentences involving multiplication or division where there is no remainder (ACMNA082)

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Find unknown quantities in number sentences involving addition and subtraction and identify equivalent number sentences involving addition and subtraction (ACMNA083)

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Investigate and use the properties of odd and even numbers (ACMNA071) Recognise, represent and order numbers to at least tens of thousands (ACMNA072) Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073) Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074) Recall multiplication facts up to 10 × 10 and related division facts (ACMNA075) Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076)

Patterns and algebra

Using units of measurement

Use scaled instruments to measure and compare lengths, masses, capacities and temperatures (ACMMG084)

© ReadyEdPubl i cat i ons objects using familiar metric •f orr evi ew pur pCompare o s e s on l y(ACMMG290) • units of area and volume

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Investigate equivalent fractions used in contexts (ACMNA077) Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (ACMNA078)

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Convert between units of time (ACMMG085) Use ‘am’ and ‘pm’ notation and solve simple time problems (ACMMG086)

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Fractions and decimals

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Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079) Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies (ACMNA080)

Shape

Compare the areas of regular and irregular shapes by informal means (ACMMG087) Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (ACMMG088)

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Curriculum Links Location and transformation Use simple scales, legends and directions to interpret information contained in basic maps (ACMMG090)

Select and trial methods for data collection, including survey questions and recording sheets (ACMSP095)

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Create symmetrical patterns, pictures and shapes with and without digital technologies (ACMMG091)

Geometric reasoning Compare angles and classify them as equal to, greater than, or less than, a right angle (ACMMG089)

Construct suitable data displays, with and without the use of digital technologies, from given or collected data. Include tables, column graphs and picture graphs where one picture can represent many data values (ACMSP096)

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Data representation and interpretation

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Chance

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Identify everyday events where one cannot happen if the other happens (ACMSP093) Identify events where the chance of one will not be affected by the occurrence of the other (ACMSP094)

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Describe possible everyday events and order their chances of occurring (ACMSP092)

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Number And Algebra

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Even And Odd Numbers 1. Complete each box with a number. Shade in the box if the number is odd.

(Hint: An odd cannot be divided evenly by two.)

My special number:

The day of the month on which I was born:

The number of pets I’ve ever had:

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The number of people who I live with:

The number of my house:

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or eBo t s r e The number of The number of letters p o kmy names: children in my classu in all S today: The number of different places I’ve lived in:

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2. Write down how many even numbers can be added together to get a total of 26? You can’t repeat numbers! (Hint: There is more than one answer.) _________________________________________________________________

_________________________________________________________________

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3. Which two odd numbers can be added together to get a total of 54? (Hint: There is more than one answer.)

. te o c 4. Circle the operation if it gives you the answer 63. . che e d. Subtracting an r a. Adding two b. Adding an odd c.

Multiplying o r st super even numbers. and an even two odd even number

_________________________________________________________________

number.

numbers together.

from an odd number.

5. Write down two facts about odd and/or even numbers.

Fact 1

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Curriculum Link: Investigate and use the properties of odd and even numbers (ACMNA071)

Fact 2

Which Number Comes Next?

Work with a partner. Cut out the cards. Put them face down on the desk. Take turns picking a card. Discuss and resolve the odd and even situations on the cards.

1

I’m thinking of two numbers. Both of them are even. When I add them together, will the answer be odd or even?

2

I’m thinking of two numbers. One is odd and one is even. When I multiply these numbers together, will the answer be odd or even?

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double it. Will the answer be an odd or even number?

4

qodd qeven

between 1 and 20. Both numbers are odd. Will the difference between them be an odd or even number?

qodd qeven

© ReadyEdPu b l i cat o snumbers I’m thinking ofi twon odd 6 less than 10. When I multiply them, •f orr evi ew pur p o se sobe nl y •or even will the answer an odd

I’m thinking of four odd numbers between 1 and 20. If I add them together, will the answer be an odd or even number?

number?

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I’m thinking of an odd number between 1 and 50. When I multiply it by ten, will the product be an odd or even number?

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I’m thinking of an even number between 1 and 20. When I divide this number by two, will the answer be an even or odd number?

qodd qeven

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ok I’m thinking of two numbers

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p u I’m thinking of S a number. Now I

I’m thinking of three numbers between 10 and 20. All of them are odd. When I add them together, will the answer be odd or even?

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qodd qeven

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If I multiply an odd number between 1 - 10 by itself and then subtract 1, will the answer be an odd or even number?

qodd qeven

Curriculum Link: Investigate and use the properties of odd and even numbers (ACMNA071)

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Number Sequence Problems 1 Solve these word problems. Annotate the number lines to show how you worked out your answers.

1.

The Olympic Games are held every four years. How many Olympic Games have been held between 1984 (Los Angeles) and 2016 (Rio de Janeiro)?

Los Angeles

Rio de Janeiro

2. The average person blinks once every 6

seconds. How many times will a person blink in 90 seconds? Draw your own number line to show your working out and answer.

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2016

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1980

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3 km. For the rest of the week he jogged 1 km che 3. On Monday, Dad jogged e r more than the day before. r o t s s r u e p How many kilometres has he jogged this week?

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9 10 11 12 13 14 15 16 17 18 19 20

0 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

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Curriculum Link: Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074)

Number Sequence Problems 2 Solve these word problems. Annotate the number lines to show how you worked out your answers.

A child usually laughs about 9 times an hour.

How many times might a child laugh in 5 hours?

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2. You collect three magic hats for successfully completing Level 1 of the

Mad Hatter game. For each new level you complete, the number of hats doubles.

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© ReadyEdPubl i cat i ons How many magic hats will you have won after completing Level 2?

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Keep Your Cool waterslide park. You love the giant slide e 3. You are visiting thec h r er ohour before lunch. It and want to cram in as many goes as you r can in one t s s u e p takes seven minutes to go down the slide and climb back up again.

How many turns on the slide will you get before Mum calls you for lunch?

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7

14

21

28

35

42

49

56

Curriculum Link: Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (ACMNA074)

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70

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Wordy Numbers 1.

Write these wordy numbers in digit form. Look at the example. two thousand and seventeen

2,017

a. six thousand four hundred and twenty-nine ____________________

or eB____________________ st r e oo p k d. 12 tens + 4 hundreds ____________________ Su + 31 ones b. fourteen thousand and forty-five

____________________

e. eight + five hundred + twelve thousand

2. What is the value of the shaded numbers?

____________________

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c. 26 hundreds + 2 tens

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3

3

b.

____________________ © ReadyEd Publ i c at i ons o7rr ev ew0 pu4r p ose sonl y• 2•f 9i ____________________

c.

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3. How many.

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c. thousands in 32, 584? d. ten thousands in 88,300? e. hundreds in 50 thousands? f. ones in 700 tens?

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Curriculum Link: Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073)

Place Value With Decimals A decimal is a fraction written using a decimal point. A number to the left of a decimal point is a whole number. The digits after a decimal point are parts of a whole number. Decimals are divided into tenths (1/10) and hundredths (1/100).

1/10 is larger than 1/100.

1.

Write the following decimal numbers as whole numbers with fractions.

Look at the example to help you. a. 15.7

r o_________ eBoe. 15.06 t c.

19.5 s r e p ok u _________ S d. 19.65 _________ f. 30.29

15 7/10

Now, order the answers above from largest to smallest.

_________

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b. 15. 45

_________

_____________________________________________________________

decimal numbers as place values. The first one has been done for 2. Write the Š ReadyEdPubl i cat i ons you.

decimal point

•f orr evi e w pur posesonl y• hundreds tens ones . tenths hundredths

Decimal number

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b. thirty five point nine c. two hundred point four

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a. six point four

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g. sixty seven point zero one h. 31.33 i. 2.67 j. 361.04 k. 108.86

Curriculum Link: Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)

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Mega Number Cards Pair up. Cut out the number cards. Then play the mega number game on the following page.

0 1 2 3 or eBo st r e p ok u S

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Curriculum Link: Recognise, represent and order numbers to at least tens of thousands (ACMNA072)

Mega Number Game How To Play Take turns to pick 4 down-turned cards each. To win, you must make the biggest number possible with your four digits. Write your numbers in the grids below.

Round 1 Player 1

Round 3

Player 1

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or eBo st r e p ok u Player Player 2 S1

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Round 2

Player 2

Player 2

© ReadyEdPubl i cat i ons Play again. This time, turn over five cards each.

•f orr evi ew pur posesonl y• Round 4

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Round 5

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1. Add 1000 to the biggest number from Round 1.________________________ 2. Add 10,000 to the smallest number in Round 4. ________________________ 3. Subtract the smallest number from the biggest in Round 1._ _____________ 4. What is the strategy for making the biggest number in this game? _________________________________________________________________ 5. How would you make the smallest numbers possible? __________________ _________________________________________________________________ Curriculum Link: Curriculum Link: Recognise, represent and order numbers to at least tens of thousands (ACMNA072)

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Subtraction Partitions Keep these hot-air balloons firmly on the ground by writing two subtraction sums that are equal to the target number written in the balloon’s basket.

Write your sums in the sandbags. An example has been done for you. Check your sums with a partner.

2.

1.

128 – 47 r o e t s Bo r e p ok u S

46

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81 - 30 - 5

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81 – 35

139

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1,000 – 320

5,178 – 2,000

680

3,178

Curriculum Link: Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (ACMNA073)

Find The Missing Numbers Put the missing digits in these addition and subtraction sums so that the answer is correct. Write the digits in the boxes. Show your working out in the space next to the sum.

1.

2.

1, 3 7 + 1, 5 5

, 2 3 + 3, 6 5

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2, 9 6

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3. 1 0,

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– 2 1, 8 3 1, 9 1

, 3 7 9

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Your Turn Make up your own addition or subtraction sum for a classmate to solve in the space provided.

Plan your sum on the back of this sheet.

Curriculum Link: Find unknown quantities in number sentences involving addition and subtraction and identify equivalent number sentences involving addition and subtraction (ACMNA083)

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Division Fetch Help Magnus fetch balls to make division number sentences. Colour in the three balls that you have used, for example: 32 ÷ 4 = 8. Shaded balls cannot be used again.

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My Division Number Sentences 1.

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16 division facts = AMAZING! 18

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Curriculum Link: Solve word problems by using number sentences involving multiplication or division where there is no remainder (ACMNA082)

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Multiple Fish It’s feeding time at the oceanarium. The marine creatures are quite fussy and will only eat fish that are multiples of certain numbers. Shade in the numbered fish in each tank that the animals will eat. Three fish in each tank will be left unshaded. Some have been done for you.

1.

120

28

30

2.

49

21

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16 122

27

36

46

44 1640

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2800 The sea snake only eats © R e a d y E d P ubl i c i ons multiples ofa 7.t The penguin only eats

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25

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The sea turtle eats multiples of 5 or 6.

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The shark eats multiples of 8 or 9.

Add 2 more fish to each tank with a correct multiple. Think big numbers!

Curriculum Link: Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076)

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Galactic Word Problems (Extension) Get your spacesuit on and solve these addition and subtraction word problems. 3,2,1…blast off! Show your working out in the spaces provided.

It takes Saturn 10,760 days to make one orbit around the Sun, and Jupiter takes 4,332 days.

How much faster is Jupiter’s orbit?

An astronaut at the International Space Station eats about 800g of food per meal, three times a day. How many grams will this astronaut eat in three days?

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people turned up to see 4. 1,200 the final eclipse of the Sun for the year. 286 people forgot to © ReadyEdPub l i cat i ons bring their eye protection. How many people were sensible •f orr evi ew pur po s e s o n l y • enough to bring their solar filter

An astronaut’s suit weighs 21kg.

She also has to wear a support pack. If the astronaut weighs 115kg with all her gear on and 84kg without all her gear on, how much does the support pack weigh?

goggles?

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o c . the astronaut weighs 70kg A day on the dwarf planet Pluto c 5. Annie 6. eto 6 days and 9 h r and Arnie the astronaute weighs is equivalent o ruper ston Earth. If you spend 3 54kg on Earth. On the Moon s hours Annie and Arnie weigh 61kg and 44kg! That’s because there is less gravity on the Moon. How much lighter are the astronauts altogether on the Moon?

20

days on Pluto, how many days and hours have gone by on Earth?

Curriculum Link: Find unknown quantities in number sentences involving addition and subtraction and identify equivalent number sentences involving addition and subtraction (ACMNA083)

Calculator Chaos!

People are in such a big hurry to snap up bargains at the sale that they keep pressing the wrong keys on their calculators. Help them calculate the correct amounts for these super sales items by ticking the operation to fix the mistake in one go. The first one has been done as an example for you.

1.

Mr. Nice has 6 nephews. He wants to buy each nephew a model helicopter that costs $44.50. He enters 7 x 44.50. He should now press:

÷6

+ 14.50

– 44.50

3.

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• Miss Sparkle wants to see how much money she has

4.

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x6

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x2

2.

or eBo st r e p ok u + 47 S+ 30p – 47

Mrs. Sweet wants to add $174 + $67. She enters 144 + 67 instead. She should now press:

+ 119

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+ 200

– 200

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Professor Merit wants to buy packs of stickers that cost $3.49, for each of the 20 children in his class. He enters 10 x 3.49. He should now press:

+ 10

5.

– 30

Mimi wanted to buy chewy snacks for her dog to give it one every day for a week. Each chewy snack costs $2.99. She entered 3.99 x 7. She should now press:

x5

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left from $987 after spending $668 on a diamond ring.

She enters 787 – 668. She should now press:

÷7

– 1.00

– 7.00

Chewy Snacks for Rover

Curriculum Link: Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies (ACMNA080)

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Money Moments Write number sentences to solve these money matters.

A customer buys a fruit smoothie for $3.30, a cheese and pickle sandwich for $3.60 and a $2.25 slice of carrot cake. How much change does he get from a ten dollar note?

3.

2.

Dad’s berry pavlovas are heavenly. He makes two every year for the school fete. Each pavlova is cut into 10 slices. Each slice is sold for $1.80. How much money does the school take from the sale of Dad’s pavlovas?

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A litre bottle of Crowning Glory hair shampoo is $4.85 more than the 500ml bottle of the same shampoo. The litre bottle costs $18.90. How much does the smaller bottle cost?

4.

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Marcus has $35.00 pocket money to spend. He spends half his money on his sister’s birthday present and he buys a new guppy fish for his aquarium that costs $8.00. How much money does he have left?

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. te o c Mr. Snap is mad about After spending $5.25 on a new .

5. note book and $2.75 6. ch e photography.

He used up 4 rolls one a metre r o t r s super of film this week! It costs $9.50 to of satin ribbon, Micaela brings $10.00 change home to her mother. How much did Micaela’s mother give her daughter to go shopping?

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develop one roll. How much will it cost Mr. Snap to have 5 rolls developed? How much change will he receive if he pays with a $50 note?

Curriculum Link: Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies (ACMNA080)

Checkout Champion Your job is to give the correct change from the till using the notes and coins shown below. First, you will calculate the bill and then give the customer the change. Write the names and amounts of coins and notes in the columns. The first one has been done for you. You can use the notes and coins more than once.

or eB st r e In o coins p ok u coffee costs S $2.95. I pay with a $5 1. My note.

Change to give

Bill:

$2.95

Change:

$2.05

In notes

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Purchase

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I had a chocolate milkshake for $2.50 and an egg and lettuce sandwich for $3.00. I’m paying with a $20 note.

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is buying two T-shirts for $14.75 2. Mark each. He is paying with two $20 notes. © ReadyEdPubl i cat i ons Bill: Change: •f orr evi ew pur posesonl y•

. te Change: o Bill: c . che e r o r st super Lola bought two pairs of earbuds for

4. $15.90 each. She paid with a $50 note.

Bill:

Change:

Compare your answers with a partner. Did you have different combinations of coins and notes to give the correct change? Make up a change problem for a partner to solve on the back of this sheet.

Curriculum Link: Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies (ACMNA080)

23

Mixed Fractions 1.

Sales at Quick Carrot Cakes are booming. The shaded parts of the diagrams show how many pans of carrot cake were sold during one week. Write the whole number and fraction of carrot cake sold. The first one has been done for you.

3 1/2

a.

c.

d.

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b.

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

e.

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2.

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f.

Draw diagrams for carrot cake sales using the mixed numerals below.

Ask a partner to check your answers.

a. 2 2/3

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b. 3 3/4

24

Curriculum Link: Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (ACMNA078)

Mixed Numerals On A Number Line Read these problems carefully. Mark your answer with a cross (x) on the number line.

Monty the bulldog sneaked around the party and managed to eat various slices of pizza. He ate a whole pepperoni pizza, half a pineapple and ham pizza and a quarter of a tomato and cheese pizza before being found out. How much pizza did Monty eat altogether?

or eBo st r e p ok u S1 3 1 1 1 3 1

0

2.

4

2

1

4

4

1

1

2

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1.

2

Milly barbecued six mouth-watering chickens for a big family lunch. She served three chickens whole, then cut up the rest into halves. At the end of lunch there were three chicken halves not eaten. How many chickens did people eat?

4

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1

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2

3

4

5

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• 6

o c . che 3. e r o read 1 novels; on Sundayr 1snovels ands after t r u e p school on Monday, he read 2 novels. How many Theo loves reading graphic novels. On Saturday, he 1 3

2 3 1 3

novels has he read in three days?

0

1

2

3

4

5

6

Curriculum Link: Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (ACMNA078)

25

Equivalent Fraction Word Problems Solve the fraction problems. Write your answers as equivalent fractions if possible.

Mum has to sew 30 buttons back on to the softball team’s shirts this week.

However, she’s been busy studying for her uni exams and has only sewn on 6 buttons. What fraction of her job has she completed?

2.

or eBo st r e p ok u S

Hannah loves her long hair, however, today it took half an hour to wash it, an hour to curl it and two and a half hours for it to dry. What fraction of Hannah’s day was taken up with looking after her long locks?

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Teac he r

1.

3.

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Ralph the baker was carrying four boxes of eggs from the storeroom. Each box contained 20 eggs. Just as he reached the kitchen a mouse scuttled across the floor and Ralph dropped the eggs in fright. Fortunately, 20 of the eggs didn’t break. What fraction of the eggs ended up in the bin?

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4.

26

m . u

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

o c . che e r o r st super

A lady decided to build a chicken coop. She calculated that she needed 160 bricks to do the job. When the truck arrived to deliver the bricks, the lady found that she was 40 bricks short. What fraction of the chicken coop was she able to build?

Curriculum Link: Investigate equivalent fractions used in contexts (ACMNA077)

Equivalent Fraction Tales Solve these fraction problems.

1.

The Tortoise, who had been in training for years, challenged the Hare to a 400 metre rematch race around the athletics track. The Hare conked out just 1 8 of the way into the race. Estimate, by shading on the track, the distance the Hare managed to run. Be as precise as you can.

300m

100m

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200m

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starting line

2.

The princess has to kiss a lot of frogs before she can find her prince. She has already kissed 10 frogs but she is only a quarter of the way to finding her man! On the number line below, indicate the number of frogs she still has to kiss to be at the halfway point in her search for love.

0

10

20

30

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

40

. te o When the c Tiddalick guzzles 360 litres of water out of the desert waterhole. .

3. eel tickles him, 130c e litres gushes from his mouth. The dancing emu manages he r o t r sand the bearded dragon to get another 80 litres out ofs the giggling frog, u per works up a sweat to get 30 litres from him. What fraction of the water does Tiddalick keep in his belly to store for future droughts?

Curriculum Link: Investigate equivalent fractions used in contexts (ACMNA077)

27

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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•

o c . che e r o r st super

Symmetry In Central Australian Art The Arrernte Peoples of the Central Desert use symbols in their art to tell stories about their Country. Symmetrical wavy lines, circles and parallel lines are all used in their rock and sand art.

Follow these steps: 1. Your teacher will give you a photocopy of indigenous symbols so that you can create in the space below your own symmetrical artwork inspired by indigenous artists. Read the meanings of the symbols to help you tell your story.

Teac he r

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or eBo st r e 2. Colour your artwork inp natural ochre tones of red, orange, brown, black, white o u k and yellow. Share your art and its story with classmates.

S

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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

Curriculum Link: Create symmetrical patterns, pictures and shapes with and without digital technologies (ACMMG091)

29

Indigenous Art Symbols (Student Handout)

resting place r o e t s B r e oo p k Su

meeting place

clouds or shelter from the wind

rain

rainbow, snake, cliff, water or honey

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waterhole, fruit, campsite, fire

emu

honey ant place

kangaroo

animal tracks

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people sitting

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sun/stars

desert landscape 30

group of trees

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

mountains

o c . che e r o r st sup r e waterholes with running water

people dancing

honey ants

snakes and tracks

Curriculum Link: Create symmetrical patterns, pictures and shapes with and without digital technologies (ACMMG091)

Symmetry In Asian Art Symmetry is an important part of Asian art. Tiles, prayer mats and pottery use simple geometric shapes and bright colours to look appealing.

The design of these wall tile panels is based on symmetry. Colour them identically.

or eBo st r e p ok u S

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Teac he r

1.

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2.

m . u

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

Create your own motifs in the space below using symmetry and geometric shapes.

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Curriculum Link: Create symmetrical patterns, pictures and shapes with and without digital technologies (ACMMG091)

31

Comparing Area 1.

Work out the area of the shaded irregular shape on this geoboard. Annotate the geoboard to show how you calculated your answer.

or eBo st r e p ok u S

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My answer is:

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

w ww

Draw and label two rectangles below that would have the same area as the shaded irregular shape above.

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32

m . u

2.

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Curriculum Link: Compare objects using familiar metric units of area and volume (ACMMG290)

Comparing Angles Classify the following angles marked on the images below as either greater than a right angle (obtuse) or less than a right angle (acute). There are also right angles too! Use ticks to show your decisions.

2.

3.

or eBo st r e p ok u S

obtuse acute right angle

obtuse acute right angle

4.

5.

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1.

obtuse acute right angle

6.

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obtuse acute right angle

7.

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obtuse acute right angle

8.

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

obtuse acute right angle

9.

o c . che e r o r st super

obtuse acute right angle

obtuse acute right angle

obtuse acute right angle

On the back of this sheet, draw your own examples of obtuse, acute and right angles that can be found in your environment. Share your ideas with the class.

Curriculum Link: Compare angles and classify them as equal to, greater than, or less than, a right angle (ACMMG089)

33

Creating A 2D Skyline

or eBo st r e p ok u S

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Teac he r

Study this skyline of a modern city to complete the questions below.

© ReadyEdPubl i cat i ons •2Df o rr e vi ew pu r p os ethe so nl y •Explain 2. Choose six shapes from the image.

Draw these in spaces below.

1. Shade in the combined or split 2D shapes you can see in the skyline above.

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1.

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4.

34

2.

3.

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how the shapes were constructed.

o c . che e r o r st super 5.

6.

Curriculum Link: Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (ACMMG088)

Creating 2D Shape Objects How have these animals been formed by combining and splitting 2D shapes? Annotate the shapes below.

or eBo st r e p ok u S

a. dog

b. owl

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1.

c. frog

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

Create your own 2D shape objects by using combined or split 2D shapes.

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2.

o c . che e r o r st super

zz Ask a peer to identify how you used 2D shapes to create your image/s.

Curriculum Link: Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (ACMMG088)

35

It’s About Time Problems Solve these time word problems. Show your written work in the space provided.

This morning Sophia arrived late to the station and saw the 8.06am train pulling out. The next train was due in 15 minutes. The train ride to Sophia’s destination takes 18 minutes. What time did she arrive at her stop?

2.

or eBo st r e p ok u S

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Teac he r

1.

Two children were squabbling about who was quicker at solving a 3D maze puzzle . Liam exclaimed, “I did it in 3 minutes and 6 seconds.” Rita replied, “Well, it only took me 194 seconds!” Which child was quicker?

“I did it in 3 minutes and 6 seconds.”

“Well, it only took me 194 seconds!”

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

Maryam is so excited. In 6 weeks and 4 days, she will be flying to Canada to visit her cousins. How many days does Maryam have to wait until her trip?

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4.

36

m . u

3.

“I can hardly wait!”

o c . che e r o r st super

Year 4 went to visit the Old Adelaide Gaol. They had a guided tour at 10.15am. The classes boarded the buses for their excursion at 9.12am and arrived at the historic building 11 minutes before the tour began. How long was the bus trip?

Curriculum Link: Convert between units of time (ACMMG085)

Time Zones Study the situations in these images. What problems can you see? Jot your ideas down under each image.

2.

It’s only 6.00pm, why aren’t they open?

or eBo st r e p ok u S

I’m hungry.

It’s daylight saving.

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1.

It’s only 9pm here.

w ww

3.

Happy New Year!

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4.

What time do we get to Melbourne?

m . u

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• We get there at 10pm Perth time.

o c . che e r o r st super

Curriculum Link: Use ‘am’ and ‘pm’ notation and solve simple time problems (ACMMG086)

37

What Time Is It In…?

Look at this map showing the time zones in Australia, then read the information in the text box below to answer the questions.

+8

+9

+10

+11

r o e t s Bo r e +8 p +9 +10 ok u S Perth

1/2

Adelaide

10:00

105˚

120˚

12:00

11:30

Sydney

165˚

150˚

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+7

165˚

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

1. When it is 4.00pm in Perth, what time is it in:

w ww

a. Sydney?

m . u

The Australian continent has three time zones. Australia is situated west of the International Date Line so it is ahead of time compared to most other countries in the world. For example, the eastern states of Australia are 10 hours ahead of London (Greenwich Mean Time - GMT), 14 hours ahead of New York, but only one hour ahead of Tokyo in Japan. ____________

b. Tasmania? ____________

c. Darwin? _____________

d. Adelaide? ____________

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o c . che e ___________ a. Darwin? _____________ b. Canberra? r o t s suwhat r 3. When it is 10pm in Londonr (GMT), time is it in Hobart, Adelaide and pe 2. If I want to ring Perth at exactly 9.15am (Australian Western Standard Time), what time do I need to ring from:

Perth?

Hobart 38

Adelaide

Curriculum Link: Use ‘am’ and ‘pm’ notation and solve simple time problems (ACMMG086)

Perth

Measuring Up 1 the scales and record the weights of the food items in grams and 1. Read kilograms.

a.

b.

c.

0

0 0.5kg

1.5kg

1kg

1.5kg

or eBo st r e p ok u S e. f.

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0

2kg

4kg

0

2kg

6kg

1kg

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0.5kg

1.5kg

1kg

d.

6kg

0 0.5kg

2kg

6kg

4kg

4kg

© ReadyEdPubl i cat i ons •measuring f orr e vi e wrecord pur pvolume oses onl y • cups and the of liquid in each.

2. Read the

. te

1000 900 800 700 600 500 400 300 200 100 50

ml

ml

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1000 900 800 700 600 500 400 300 200 100 50

ml

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1000 900 800 700 600 500 400 300 200 100 50

o c . che e r o t r s s r u e p 3. Add an additional 150ml to each measuring cup by shading. a.

a.

1000 900 800 700 600 500 400 300 200 100 50

b.

ml

b.

c.

1000 900 800 700 600 500 400 300 200 100 50

ml

c.

1000 900 800 700 600 500 400 300 200 100 50

Curriculum Link: Use scaled instruments to measure and compare lengths, masses, capacities and temperatures (ACMMG084)

ml

39

Measuring Up 2 Look at these children from different parts of the world. Read the maximum and minimum temperatures in these places today and record them. ˚C

˚C

50

50

40

40

30

30

Maximum:

or eBoMinimum: st r e p ok u S

2. Christchurch, NZ

20

20

10

10

0

0

˚C

˚C

50

50

40

40

30

30

20

20

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1. Mumbai, India

Maximum:

3. Dalarna, Sweden

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. te

4. Dubai, UAE

40

10

0

0

˚C

˚C

50

50

40

40

30

30

20

20

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Minimum: © ReadyEdPubl i ca t i ons •f orr evi ew pur posesonl y• 10

Maximum:

o c . che e r o r st super 10

10

0

0

˚C

˚C

50

50

40

40

30

30

20

20

10

10

0

0

Minimum:

Maximum: Minimum:

Curriculum Link: Use scaled instruments to measure and compare lengths, masses, capacities and temperatures (ACMMG084)

Massive Problems Work with a partner. Rank the mass of these objects from heaviest (1) to lightest (3). Circle the unit of measurement – kg or gm. Be ready to justify your choices. Your teacher will tell you the answers later. Note that images are not to scale.

1.

2.

or e leopard st Bo r hippo e p seal o u k S

qkg qgm

pair of boots

cup of rice

cake of soap

single DVD

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

w ww

qkg qgm

qkg qgm

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jeans

m . u

3.

4.

box of cereal

great white shark

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qkg qgm

o c . che e r o r st super washing refrigerator machine

piano

5. qkg qgm

chocolate bar

banana

Curriculum Link: Compare objects using familiar metric units of area and volume (ACMMG290)

orange wedge 41

Present Problems Mrs. Fernandes is posting presents to her family overseas. The weight of each box is shown below. Answer the questions that follow.

g

2 kg

11/2 k

g

1.7 kg

0.6 k

box c box d r o e t s B r espace provided. oo Do your written work p in the u of the two heaviest boxes? k 1. What is the total Sweight

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box b

Teac he r

box a

__________________________________________________

2. What is the difference in grams between box b and box c?

__________________________________________________

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

3. What is the total weight of the four boxes?

__________________________________________________

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m . u

4. In box a there are four identical books about Australia each weighing 330g. How much does the box weigh?

5. Which three boxes have a total weight of 3.8kg?

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o c . e 6. In box d there are c seven objects. Six objects are identical he r o titself weighs r s su220g. bottles of perfume each weighing The box r e p 100g. What is the mass of the seventh object?

__________________________________________________

__________________________________________________

7. For boxes up to 2kg, the post office charges $11.60 each. How could Mrs. Fernandes repack her presents to save money? How much could she save?

42

__________________________________________________ Curriculum Link: Compare objects using familiar metric units of area and volume (ACMMG290)

Fill ‘Em Up Capacity Problems 1 Solve these volume word problems with a peer. Show your written work in the space provided.

1.

The total capacity of water in these identical glasses is 870ml. How much water is in one glass?

or eB =o 870 ml s +t r e p ok u S

2.

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+

The total capacity of juice in these three jugs is 2 litres. How much juice does the larger jug contain?

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

w ww

. te

460 ml

+

460 ml

= 2 Litres

m . u

?

+

o c . larger bucket c holds six times more water than thee smaller bucket. The 3. The h r capacity of the small bucket is 3.5 litres. What would be the capacity of the er o t s s r u pe large bucket?

Curriculum Link: Compare objects using familiar metric units of area and volume (ACMMG290)

43

Fill ‘Em Up Capacity Problems 2 Solve these volume word problems with a peer. Show your written work in the space provided.

Shade in the buckets of water needed to fill an aquarium that can hold 44 litres.

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1.

or eBo st r e p ok u S

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5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 5.5 Litres Litres Litres Litres Litres Litres Litres Litres Litres

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. te

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accidentally knocked over his glass that contained 285ml of 2. Robbie lemonade. He managed to save a third of his drink. How many ml did he have left? © ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

o c . shower uses 12 litres of water per minute and e Sam’s shower uses 7 c 3. Rebel’s h r litres of water per minute. they both take a shower for 5 minutes, what is eIfr o t s s r u pe the difference in litres of water used?

44

Curriculum Link: Compare objects using familiar metric units of area and volume (ACMMG290)

Calculating Volume 1 Volume is the space taken up by a 3D or solid object. The formula for calculating volume is: length (l) x width (w) x height (h). Volume is measured in cubic centimetres and metres (cm3 and m3).

h = 4cm

l = 5cm

Look at the example in the image:

or eBo st r e p ok u S of these boxes. Show your working out.

1. Calculate the volumes

Volume of cuboid = 5cm x 4cm x 3cm

Teac he r

Answer = 60 cm3

m

w

c =4

-7

cm

-

c.

- 12c

m-

- 10cm -

b.

- 12cm -

- 18cm -

a.

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You can use digital technology to help you with your answers.

© ReadyEdPubl i cat i ons m - 24c - 18•f mp rcr evi ew p-u osesonl y• cm o 13cr m-

- 40cm -

f.

o c . che e r o r st super

-1

6cm

-

- 8cm -

- 18

cm -

- 10cm -

- 16cm -

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e.

- 8cm -

w ww

d.

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- 10

- 33c

m-

cm

- 33

-

2. Rank the volumes of the packaging from smallest to largest:

Curriculum Link: Compare objects using familiar metric units of area and volume (ACMMG290)

45

Calculating Volume 2

Tier 1: 30cm x 30cm x 10cm o eBo t s r r e Tier 2: 25cmo x 25cm x 12cm p u k S Tier 3: 18cm x 18cm x 12cm

1. Show your working out. Calculate the volume of:

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Nana has baked this beautiful birthday cake with three tiers. Study the dimensions of the cake then answer the questions that follow.

© ReadyEdPubl i cat i ons Tier 2: _________________________________________ •f orr evi ew pur posesonl y• Tier 1: _________________________________________

w ww

The total volume of the cake is:

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m . u

Tier 3: _________________________________________

2. You want to cut tier 1 into 30 equal slices to share with your class. What will be the volume of one slice? Complete the calculation:

o c .

3 c e r ÷her = cm o st super 3. You want to cut 24 equal slices from the second tier. What would be the total volume of 5 slices? Show your working out.

46

Curriculum Link: Compare objects using familiar metric units of area and volume (ACMMG290)

In The Right Direction Explore the features of the map of a national park. Answer the following questions using the map’s scale and legend.

Pardoo Point

 



Dugong Beach





Shark Inlet

or eBo st r e p ok u S Merrima National Park eek Cr r nce Spe

  Longneck Lagoon

km 0

10

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Teac he r



© ReadyE dPubl i cat i ons Legend   •f orr e vi ew pur poseso nl y• National Park

 Township

Small town

Airport Port

Camping

Walking trail Road

 Medical help

Restaurant

 Wildlife

m . u

w ww

1. Is the airport in the Merrima National Park?_ _________________________ 2. In which direction is the port from Shark Inlet?________________________

. te

3. Estimate the distance from Pardoo Point to the airport._________________

o c . che 5. What does the warning sign at Shark Inlet mean?_ ____________________ e r o r st su 6. How can you travel to Longneck Lagoon? ___________________________ pe_r 4. Estimate the distance from Pardoo Point to Shark Inlet._________________

______________________________________________________________

7. What kind of people would enjoy visiting Merrima National Park? Use the map features to support your answer.

______________________________________________________________

______________________________________________________________

______________________________________________________________ Curriculum Link: Use simple scales, legends and directions to interpret information contained in basic maps (ACMMG090)

47

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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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48

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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

Class Pet Survey 1 Abigail was put in charge of surveying the four Year 4 classes to find out the most popular choices for a class pet. Below are the results of her investigation.

Class Pet Top

5 Pet

budgie

or eBo t s r e goldfish p ok u Ssilkworms dwarf rabbit bearded dragon

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Teac he r

Choices

Tally

© ReadyEdPubl i cat i ons 1. How many children’s votes were included in this tally?_ ________________ •f orr evi ew pur posesonl y• Answer the questions based on the data in the tally table above.

2. How many children chose a budgie?________________________________

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3. How many more children chose a bearded dragon instead of

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a. a goldfish? ________________________________________________ b. silkworms?________________________________________________

. te o ______________________________________________________________ c . chAbigail’s e r 5. What do you think was survey question? er o st super 4. How many children altogether voted for a dwarf rabbit or a goldfish?

______________________________________________________________

______________________________________________________________

6. There were two other possible pets on the survey, a tarantula and a stick insect, but no-one voted for them. Should Abigail still have included them in her results table? Explain your answer.

______________________________________________________________

______________________________________________________________ Curriculum Link: Construct suitable data displays, with and without the use of digital technologies, from given or collected data.

Include tables, column graphs and picture graphs where one picture can represent many data values (ACMSP096)

49

Class Pet Survey 2 Abigail experimented with different ways of presenting the data she collected. Tick the methods that show the data she collected correctly. Explain under each method the reasons for your answers.

1

2

or eBo st r e p ok u S

goldfish silkworms dwarf rabbit bearded dragon

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budgie

______________________________

______________________________

______________________________

______________________________

______________________________

______________________________

3

4

w ww

. te

m . u

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

o c . che e r o r st super

______________________________

______________________________

______________________________

______________________________

______________________________

______________________________

______________________________

______________________________

50

Curriculum Link:

Presenting Data Fiona is mad about frogs.

She’s just spent a week camping out in the bush to complete a frog census.

This is the data in pictogram form that she collated.

Frog Census Monday

    = 2 frogs erst or eBo  p ok u S    Tuesday

Wednesday Thursday

Saturday Sunday

Present the data in the pictogram as a bar graph.

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

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Tues

Wed

Thurs

Fri

Sat

Curriculum Link: Construct suitable data displays, with and without the use of digital technologies, from given or collected data.

Include tables, column graphs and picture graphs where one picture can represent many data values (ACMSP096)

Sun

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On The Data Trail These curious children want to know more about their classmates. Read the questions these children would like answered.

A.

Who’s the tallest in the class?

B.

How many children were born in March?

or eBo st r e D. p o u How do you get Who can go the k S to school every longest without - Meena

day?

blinking?

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C.

- Carl

- Keira

- Lachlan

1. Match the collected data to the children’s investigation questions. Draw lines to do this.

© ReadyEdPubl i cat i ons a. Who’s the tallest?

1. Children’s dates of birth.

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c. How do you get to school every day?

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2. Timing eye movement.

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b. Who was born in June?

3. Heights of children in class.

o c . che e r o r 2. Help one of the children plan their investigation. stWhat does he/she need s r u e p to organise to collect the data? Use the back of the sheet if you need to. d. Who can go the longest without blinking?

4. Ways of travelling to school.

MY SUGGESTIONS TO _______________

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Curriculum Link: Select and trial methods for data collection, including survey questions and recording sheets (ACMSP095)

Planning An Investigation Work in a pair or small group.

1. Discuss what you want to investigate. our SUGGESTIONS:

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or eBo st r e p ok u 2. Agree as a groupS on an investigation question.

Our investigation question is:

© ReadyEdPubl i cat i ons our prediction: We think this because: •f orr evi ew pur p osesonl y•

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3. Predict the results of your investigation.

4. It’s time to think about how you are going to collect your data. Look at your question. Shade in the method/s of collecting data that would suit your question.

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o c . c e r asking peers h er o st super to fill out a survey.

asking questions face-to-face and recording answers.

recording results with a stopwatch, ruler, etc. in a table.

taking a class poll.

Curriculum Link: Select and trial methods for data collection, including survey questions and recording sheets (ACMSP095)

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Recording Data Now you’re ready to collect and record your data. Before you create your data sheet in the space below, here are a few things to consider: zz How many children will take part in your investigation? zz Have you got enough space to record the answers to your survey? zz Do you need to make copies of your survey questions to hand out? zz Do you need any equipment (metre-ruler, stopwatch, etc.)?

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zz How will you label your table/tally sheet?

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

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Curriculum Link: Select and trial methods for data collection, including survey questions and recording sheets (ACMSP095)

Chances Are…(Cards) Look at the events in these images, then cut out the cards.

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or eBo st r e p ok u Catching the S flu.

Meeting the Queen.

Eating a sandwich.

© ReadyEdPubl i cat i ons

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Spending time with f orr evi ew pu r poses onl y the • family.

Going fishing.

Travelling on• a plane.

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o c . ce e a wombat. r Playing on my iPad. h Cuddling o r st super

Taking a bath.

Going shopping with mum.

Being told to be quiet by the teacher.

Doing my homework.

Curriculum Link: Describe possible everyday events and order their chances of occurring (ACMSP092)

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Chances Are…(Ordering Task) Order the cards from page 55 starting with the most likely event and ending with the least likely event. Compare your choices with a peer and be ready to justify your decisions. Then glue the cards in the grid below.

2.

3.

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4.

5.

6.

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© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• 8.

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9.

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7.

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12.

Curriculum Link: Curriculum Link: Describe possible everyday events and order their chances of occurring (ACMSP092)

Related And Unrelated Events Decide if these events are related (R) or unrelated (U).

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Your neighbour bought a ticket in the million dollar lottery last week, but she didn’t win.

The ticket she bought this week won’t have the winning numbers either.

The roof in the school gym was leaking badly yesterday after two days of heavy rain. There will be no lessons in the gym today.

q related

q unrelated

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• The big prize in the lucky dip at the fete is a $100 book voucher. You buy a ticket and pick out the voucher! If you buy another ticket for the same dip, you could pick out the voucher again.

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q unrelated

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2

You throw two dice and get a double 6 so you can throw the dice again. On the second throw, you get another double 6. Will you get a double 6 on the third throw?

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q unrelated

orelated c q . che e q unrelated r o r st super

There are six marbles in a bag – four green and two red ones. If someone picks out a red marble and keeps it, you have an equal chance of picking out a red marble too.

Mr Adjani is a strong swimmer. Mr Adjani was elected president of the Parent-Teacher Association at our school.

q related q unrelated

Write your own related and unrelated events on the back of this sheet.

Curriculum Link: Identify events where the chance of one will not be affected by the occurrence of the other (ACMSP094)

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Answers Page 16 Sample answers: 1) 100-54; 86-40 2) 90-9; 120-39 3) 180 - 96; 134 - 50 4) 200 - 61; 159 - 30 5) 800 - 120; 750 - 70 6) 10,178 - 7,000; 4,000 - 822

Page 9 1)even 2)odd 3)even 4)even 5)even 6)odd 7)even 8)odd 9)even (except for 2) 10)even

Page 17 1)1,437+1,559=2,996 2)6,235 +3,665= 9,990 3)10,587- 4,208=6,379 4)23, 884 – 21,983=1,901 5)40,103+39,917=80,020 6)15,632-795=14,837 7)54,333 – 24,844=29,489 8)16,302 + 7,829=24,131

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Page 18 Sample answers: 90÷9=10, 27÷3=9, 60÷3=20, 32÷2=16, 26÷2=13, 34÷2=17, 30÷6=5, 28÷4=7, 45÷3=15, 25÷5=5, 48÷4=12, 100÷50=2, 72÷36=2, 81÷9=9, 64÷8=8, 66÷6=11

Page 10 1)7 Olympic Games 2)15 times 3)42 kilometres

Page 19 © ReadyEdP u bl i cat i ons 1)Unshaded: 30, 122, 46 2)Unshaded: 44, •f orr evi ew pu r pos e64,s150onl y• 3)Unshaded: 38, 64, 68 4)Unshaded: 25, 78, 94

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Page 12 1) a) 6,429 b)14,045 c)2,620 d) 551 e)12,508 2) a)three tens b)two tens of thousands c)six thousands 3) a)9 b)8 c)2 d)8 e)500 f)7000

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Page 13 1)b) 15 45/100 c) 19½ d) 19 65/100 e)15 6/100 f)30 29/100 Order: 30 29/100, 19 65/100, 19½, 15 7/10, 15 45/100, 15 6/100 2)a)6.4 b)35.9 c)200.4 d)4.05 e)13.08 f).75 g)67.01 h)31.33 i)2.67 j)361.04 k)108.86

Page 15 1); 2) & 3)Student can peer mark answers from rounds.

4) Put largest digit in thousands/tens of thousands place.

5)Put smallest digit (0) if possible, in thousands/ tens of thousands place.

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Page 20 1)6,428 days 2)7.2kg/7200g 3)10kg 4)914 5) 19kg 6)19 days 3 hours

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Page 11 1)45 times 2)9 magic hats 3)8 turns

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Page 8 1)Students’ own answers 2)2+4+6+8; 10+12+4; 18+6+2 3)27+27; 17+37; 7+47; 49+5; 51+3…

4)b. and c.

5) Sample responses: doubling an odd number = even number; subtracting odd numbers = even numbers

Page 21 2) -44.50 3)+200 4)x 2 5)– 7.00

Page 22 1)85 cents 2)$36 3)$14.05 4)$9.50 5)$18.00 6)$2.50

Page 23 Bill:

Change: $10.50

Bill:

Change: $14.50

Bill:

Change: $18.20

2. $29.50 3. $5.50 4. $31.80

*Other change options available. Students could share alternatives.

Page 24 b)2¼ c)2¾ d) 4¾ e)3¼ f )3¼ b) 2) a)

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Page 25 1)1¾ 2)4½ 3)5 1 3

2)Owl: hexagons, isosceles and equilateral triangles, rectangles, circles 3)Frog: ovals, circles, squares, hexagons, equilateral triangles Page 36 1)8.39 am 2)Liam was faster (3 mins 6 secs = 186 seconds) 3)46 days 4)52 minutes Page 37 1)Paris is 8 to 10 hours behind Australia – waking people up in the night with phone calls is a possibility if you do not factor in time differences.

2)Forgetting to adjust your watch/clock for daylight saving 3)Having different time zones in Australia 4)Not knowing the local time after crossing time zones in Australia; jet lag

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Page 38 1)a.6pm b.6 pm c.5 pm d.5.30 pm 2)a.10.15am b.11.15am 3)Hobart 8am, Adelaide 7.30am, Perth 6am

Page 27 1)Students should shade 50m 2)Students should mark 20 on the number line 3)240/360L returned = 1 3 stored

Page 39 1)a.250g b.100g c.400g d.3kg e.4kg f.5kg 2)a. 250ml b.75ml c.600ml 3)Add 150ml = a.400ml b.225ml c.750ml

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Page 26 1) 6 30 = 1 5 2)½ + 1 + 2½ = 4 24 = 1 6 of her day 3)60 80 = ¾ ended up in the bin 4) 120 160 = ¾ of the coop built

© ReadyEdPubl i cat i ons Page 40 1)r max 26so •f orr evi ew pu p32omin se nl y• 2) max 11 min 4

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Page 33 1)obtuse 2)right angle 3)right angle 4)acute 5)obtuse 6)acute 7)acute 8)acute 9)obtuse

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3) max 22 min 15 4) max 41 min 28

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Page 32 1)30 units 2)Rectangles could be: 7 x 4, 14 x 2 or 28 x 1 (unit)

Page 41 1)kg (average weight: hippo 1500, seal 600, great white shark 1000 ) 2)gm (cereal 350, boots 600, DVD 22) 3)gm (rice 220, soap 125, jeans 550) 4)kg (fridge 80, washing machine 65, piano 140) 5)gm (chocolate snack bar 85, banana 120, orange wedge 30)

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Page 34 1)Students could shade: circle + segments, semicircle, elliptical sphere, rectangles, isosceles, equilateral and right-angled triangles, squares 2)Students to choose from shapes in Question 1 and describe the combined and/or split 2D shapes to create buildings Page 35 1)Dog: hexagon, equilateral triangles, rectangles, square, semi-circle, circles

Page 42 1)3.7kg 2)1400g 3)5.8kg 4)180g 5)a, c, d 6)280g 7)Unpack box c and place half in box d and the other half in box a - save $11.60 Page 43

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1)290ml 2)1.08l 3)21l Page 44 1)students should shade 8 buckets 2)95ml 3)25 l Page 45 1)a.3,240cm3 b.1,092cm3 c. 2,880cm3 d.10,240cm3 e.1,152cm3 f.10,890cm3 2)b, e, c, a, d, f

Page 52 1)a = 3 b = 1 c = 4 d = 2 Suggestions should take into account the purpose of the survey, e.g. the need for measuring equipment, the method of data collection

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Page 46 1)tier 1 (9000cm3) + tier 2 (7500cm3 ) + tier 3 (3888cm3)= 20,388 cm3 2)9000 ÷ 30 = 300cm3 3. 7500 ÷ 24 = 312.5cm3 each slice, 312.5x5=1562.5cm3

Page 47 1)No 2)East 3)15km approximately 4)20km 5)No swimming 6)You can reach the lagoon using a walking trail 7)campers, bushwalkers, nature lovers, fishing enthusiasts, people who enjoy water sports boating

Page 53 Students’ responses

Page 54 Students’ reflection on the process of data collection

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3)Data for budgies and silkworms is not correct 4)Proportions for choices are correct and match tally table Page 51 Students should record the following results: Monday 8, Tuesday 10, Wednesday 6, Thursday 14, Friday 4, Saturday 12, Sunday 8. Note y-axis should be marked in intervals of 2

Page 55 & 56 Answers will vary according to students’ experiences. Events such as “Meeting the Queen” and “Travelling on a plane” will fall on the least likely continuum, whereas “Eating a sandwich” and “Taking a bath” will fall into the most likely category.

© ReadyEdPubl i cat i ons Page 57 •f orr evi ew pu r posesonl y• 1)unrelated

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Page 50 1)Data graph matches survey results in tally 2)The graph shows the data in the correct proportions, i.e., bearded dragon greatest proportion, silkworms the least

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2)unrelated 3)related 4)related 5)related 6)unrelated Ask students to explain the reasoning for their choices.

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Page 49 1)82 2)19 3)a.22 b.26 4)25 5)Which animal would you like for a class pet?

6)The survey chose “The Top 5 Pet Choices” so the omission of the other results would be acceptable

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