OzzieMaths Series - Year 5 by Teacher Superstore

Title: OzzieMaths Series Maths: Year 5

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

ISBN: 978 186 397 994 8 2

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Reproduction and Communication by others

Contents Teachers’ Notes Curriculum Links

4 5–6

7 8 9 10 11 12

Section 3: Statistics and Probability Games Of Chance - 1 Games Of Chance - 2 Games Of Chance - 3 Probability Interpreting Graphs - 1 Interpreting Graphs - 2 Reading Data

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Answers

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Section 1: Number and Algebra Investigating Factors Investigating Multiples Is It Divisible? Divisibility Rules Using Estimation Multiplication Methods: Partitioning Numbers Multiplication Methods: Area Model Multiplication Methods: Italian Lattice More Italian Lattice Understanding The Distributive Law Dividing By A Common Factor Working With Remainders Ordering Fractions Adding And Subtracting Fractions - 1 Adding And Subtracting Fractions - 2 Number Line Decimals Creating A Budget Understanding GST

42 43 44 45 46 47 48 49

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Section 2: Measurement and Geometry Which Unit Is Best? Celsius And Fahrenheit Perimeter Of Rectangles Area Of Rectangles 12 And 24 Hour Time - 1 12 And 24 Hour Time - 2 Investigating Nets - 1 Investigating Nets - 2 Investigating Nets - 3 Investigating Nets - 4 Representing Shapes Using A Grid Reference System Flip, Slide And Turn Enlarging Shapes Measuring Angles

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26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

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Teachers’ Notes This book is part of the OzzieMaths Series which consists of seven books altogether. It is linked to the Australian National Curriculum and each page in the book references the content descriptors and elaborations that it specifically addresses. This book is therefore suitable for students studying in any State or Territory in Australia.

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This book is divided into three sections, which are detailed below.

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The activities in this book allow the students to both investigate and practise a range of mathematical concepts. Student-friendly explanations of relevant concepts are included on the majority of pages. Answers are provided at the back of the book.

Section 1: Number and Algebra The activities in this section cover important skills concerning division and multiplication, allowing the students to work with factors, multiples and a range of different multiplication methods. Activities involving fractions, decimals and money calculations are also included.

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Section 2: Measurement and Geometry In this section, students will explore how to choose appropriate measurement units and will work with 12 and 24 hour time. They will also investigate concepts concerning 2D and 3D shapes, use a grid reference system, calculate perimeter and area, and construct and measure angles using protractors.

. te o Section 3: Statistics and Probability c . ch This section allows students to investigate three different egames r e o of chance, develop an understanding of probability, r st and construct supe r and interpret graphs and tables.

Curriculum Links Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098) Elaborations • exploring factors and multiples using number sequences • using simple divisibility tests

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Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100) Elaborations • exploring techniques for multiplication such as the area model, the Italian lattice method or the partitioning of numbers • applying the distributive law and using arrays to model multiplication and explain calculation strategies

Recognise that the place value system can be extended beyond hundredths (ACMNA104) Elaboration • using knowledge of place value and division by 10 to extend the number system to thousandths and beyond

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Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099) Elaborations • recognising the usefulness of estimation to check calculations • applying mental strategies to estimate the result of calculations, such as estimating the cost of a supermarket trolley load

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Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (ACMNA103) Elaboration • modelling and solving addition and subtraction problems involving fractions by using jumps on a number line, or making diagrams of fractions as parts of shapes

Compare, order and represent decimals (ACMNA105) Elaboration • locating decimals on a number line

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Solve problems involving division by a one digit number, including those that result in a remainder (ACMNA101) Elaborations • using the fact that equivalent division calculations result if both numbers are divided by the same factor • interpreting and representing the remainder in division calculations sensibly for the context

•

fundraising event identifying the GST component of invoices and receipts

Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108) Elaborations • recognising that some units of measurement are better suited for some tasks than others, for example kilometres rather than metres to measure the distance between two towns • investigating alternative measures of scale to demonstrate that these vary between

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Compare and order common unit fractions and locate and represent them on a number line (ACMNA102) Elaboration • recognising the connection between the order of unit fractions and their denominators

countries and change over time, for example temperature measurement in Australia, Indonesia, Japan and USA

Curriculum Links Calculate perimeter and area of rectangles using familiar metric units (ACMMG109) Elaborations • exploring efficient ways of calculating the

Estimate, measure and compare angles using degrees. Construct angles using a protractor (ACMMG112) Elaboration • measuring and constructing angles using both 180° and 360° protractors

•

List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116) Elaboration • commenting on the likelihood of winning simple games of chance by considering the number of possible outcomes and the consequent chance of winning in simple games of chance such as jan-ken-pon (rockpaper-scissors)

perimeters of rectangles such as adding the length and width together and doubling the result exploring efficient ways of finding the areas of rectangles

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Connect three-dimensional objects with their nets and other two-dimensional representations (ACMMG111) Elaborations • identifying the shape and relative position of each face of a solid to determine the net of the solid, including that of prisms and pyramids • representing two-dimensional shapes such as photographs, sketches and images created by digital technologies

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Compare 12- and 24-hour time systems and convert between them (ACMMG110) Elaboration • using units hours, minutes and seconds

Recognise that probabilities range from 0 to 1 (ACMSP117) Elaboration • investigating the probabilities of all outcomes for a simple chance experiment and verifying that their sum equals 1

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Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries (ACMMG114) Elaboration • identifying the effects of transformations by manually flipping, sliding and turning twodimensional shapes and by using digital technologies Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original (ACMMG115) Elaboration • using a grid system to enlarge a favourite image or cartoon

type, with and without the use of digital technologies (ACMSP119) Elaboration • identifying the best methods of presenting data to illustrate the results of investigations and justifying the choice of representations

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Use a grid reference system to describe locations. Describe routes using landmarks and directional language (ACMMG113) Elaboration • creating a grid reference system for the classroom and using it to locate objects and describe routes from one object to another

Describe and interpret different data sets in context (ACMSP120) Elaboration • using and comparing data representations for different data sets to help decision making

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Number and Algebra

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Investigating Factors Factors are whole numbers that you can multiply together to make another number. For example, the factors of 12 are 1, 2, 3, 4, 6 and 12 because: 1 x 12 = 12

2 x 6 = 12

3 x 4 = 12

Some numbers have many factors while some only have two: 1 and the number itself. Complete these questions about factors.

a. 10: 1, 2, 5, ___

c. 9: 1, ______

b. 28: ___, 2, 4, ___, 14, ___

d. 13: 1, ______

Complete the quiz about your answers to question 1.

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Write the missing factors for these numbers to complete each sequence.

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a. Which number had the least factors?______________________________________

b. Which number/s were common to all?_____________________________________ c. What differences do you notice about the factors for odd and even numbers?

_______________________________________________________________________

between any factor pairs. An example has been done for you. a. 20 1, 2, 4, 5, 10, 20

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b. 16 ___, ___ , ___, ___, ___ c. 81 ___, ___ , ___, ___

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d. 42 ___, ___ , ___, ___, ___, ___ , ___, ___

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Circle the factors in each sequence below for the number indicated, then write which factors are missing. a. 25: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 Factor missing: ___

b. 100: 4, 10, 16, 22, 28, 34, 40, 46, 52, 58, 64, 70 Factors missing: ___, ___, ___, ___, ___, ___, ___, ___ c. 63: 1, 7, 13, 19, 25, 31, 37, 42 Factors missing: ___, ___, ___ d. 90: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 Factors missing: ___, ___, ___, ___, ___, ___, 8

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Curriculum Link: Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098). Elaboration: Exploring factors and multiples using number sequences.

Investigating Multiples Multiples are closely related to factors. The multiples of a number are all the numbers in its times table. For example, the multiples of 10 are 10, 20, 30, 40, 50, 60, 70 and so on. The amount of multiples for any number is, in fact, endless! Complete these questions about multiples.

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Each sequence below shows some of the multiples of a mystery number. Write the number in the box next to each sequence.

Mystery number:

b. 14, 21, 28, 35, 42

Mystery number:

c. 26, 39, 52, 65, 78

Mystery number:

Circle the multiples of 5 in each sequence below. a . 5, 8, 11, 14, 17, 20, 23, 2 6, 29, 32

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a. 3, 6, 9, 12, 15, 18

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

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Which numbers in the sequence below are multiples of 4 and 6? Circle them in two different colours: red for multiples of 4 and blue for multiples of 6.

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Comment on any common numbers or patterns that you notice.

_ _ _ _ _ ______________________________________________________ _ _

Fill in the missing multiples of each number below to make a sequence. a . 9: 9, 18, 27 ___, ___, ___, ___, ___, b. 8: 8, ___, ___, ___, 40, ___, ___, 64, 72, ___ c. 11: 22, ___, ___, 55, ___, ___, 88, 99, ___

Curriculum Link: Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098). Elaboration: Exploring factors and multiples using number sequences.

Is It Divisible? If one number can be divided evenly by another number, we say it is divisible by that number. For example, 24 is divisible by 2 because it divides evenly into 24 exactly 12 times. However, 25 is not divisible by 2 because there is a remainder of 1. It is useful to remember that any number is always divisible by its factors.

1. A number is divisible by 2 if the last digit is an even number. For example, 12, 256, 1078. 2. A number is divisible by 3 if the sum of the digits is divisible by 3. For example, 30, 669, 5715. 3. A number is divisible by 4 if the last two digits are divisible by 4. For example, 24, 916, 7020. 4. A number is divisible by 6 if the number is divisible by both 2 and 3. For example, 60, 132, 402.

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There are also rules about divisibility. These help you to understand quickly whether a number is divisible by another. Look at the divisibility rules on the right.

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Divisibility Rules

Study each number below. Use the divisibility rules above to say which numbers they are divisible by. It may be more than one of them! Explain how you worked out each one.

Number

a) 225

Divisible by

How I worked it out

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c) 6534

d) 19036

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e) 15681

f) 212122

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b)1078

Curriculum Link: Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098). Elaboration: Using simple divisibility tests.

Divisibility Rules Find a partner to work with to answer these questions. Try to figure out some possible divisibility rules for each of the numbers below. Hint: You can think about the divisibility rules given on page 10 to help you. You should also look for any patterns that you can see. 15, 20, 105 and 200 are all divisible by 5. What might the divisibility rule for this number (5) be?

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9, 18, 27 and 900 are all divisible by 9. What might the divisibility rule for this number (9) be?

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10, 30, 60 and 2000 are all divisible by 10. What might the divisibility rule for this number (10) be?

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12, 72, 120 and 600 are all divisible by 12. What might the divisibility rule for this number (12) be? (Hint: Figure out two other smaller numbers these numbers are also divisible by.)

Curriculum Link: Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098). Elaboration: Using simple divisibility tests.

Using Estimation In Mathematics, estimation means to calculate an approximate answer. This does not mean that you make a wild guess; rather, you use logic to come up with an answer that is close to the real answer. In everyday life, estimation can help you to quickly work out such things as how much items for sale cost, how long something might take or the size of an object.

Here are a few mental estimating methods that you can use: •

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Answer the questions about estimation.

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There are many ways to estimate. Different situations may require different methods.

Rounding numbers up or down to make them easier to work with (for example, to work out 483 + 96, you could round the numbers up to make 500 + 100). Looking at the first digit of each number (for example, to work out 2755 + 5618, add 2000 and 5000, then look at the rest of the numbers: 755 and 618 is about 1300). Grouping particular numbers together that will be easier to work on (for example, to work out 156 + 822 + 45, you could group 156 and 45 together, as they make approximately 200, then add the 822).

Explain two ways when estimating could be useful during a trip to the supermarket.

_______________________________________________________________________

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Use mental calculation to estimate answers to the number problems below. Under each, explain the estimation strategy you used. It may or may not be one of the methods above. a. Tom has been given $100 for his birthday. He wants to spend it on some DVDs. He is looking at 5 DVDs, which each cost $11.95, $18, $12.80, $10 and $40. Does he have enough money? If so, approximately how much change will he get? b. A school is planning on holding a musical recital by its students. It hires out a local hall with a capacity of 950 people. Tickets are sold through four different community groups. The groups sell 523 tickets, 59 tickets, 241 tickets and 78 tickets. Approximately how many tickets have been sold so far? Approximately how many more tickets can be sold? c. A university student is about to take a 4 hour exam. There are six parts to the exam. She takes 40 minutes to do the first part, 32 minutes to do the second part, 33 minutes to do the third part, 1 hour to do the fourth part and 21 minutes to do the fifth part. Approximately how much longer does she have to complete the last part? (Hint: You may need to convert from minutes to hours or vice versa to work out this problem.)

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Curriculum Link: Use estimation and rounding to check the reasonableness of answers to calculations (ACMNA099). Elaborations: Recognising the usefulness of estimation to check calculations; Applying mental strategies to estimate the result of calculations, such as estimating the cost of a supermarket trolley load.

Multiplication Methods: Partitioning Numbers When we multiply with large numbers, we can use a method called partitioning to make the numbers easier to work with. To use partitioning, all you need is a good understanding of your times tables, as well as how to multiply by multiples of 10. Here is an example of how to solve a multiplication problem by partitioning:

908 x 7 We first work out:

900 x 7 = 6300

Then work out:

8 x 7 = 56

Then add these two numbers together to find the answer to the problem:

6300 + 56 = 6356.

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Use the partitioning method to work out these multiplication questions. The first one has been done for you.

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512 x 6

500 x 6 = 3000

462 x 7

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12 x 6 = 72

3000 + 72 = 3072

771 x 8

653 x 3

219 x 9

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971 x 4

832 x 2

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Curriculum Link: Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100). Elaboration: Exploring techniques for multiplication such as the area model, the Italian lattice method or the partitioning of numbers.

Multiplication Methods: Area Model The area model is a way of working out a multiplication problem that doesn’t involve an algorithm. This method uses expanded numbers (or partitioning) and boxes. For example, to work out 324 x 19, you would do the following:

300 +

20 +

x 10

3000

200

2700

180

In this example, you can see that each number has been expanded and multiplied separately. The results are then added together to provide the answer.

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3000 + 2700 + 200 + 180 + 40 + 36 = 6156

174 x 55

2. 923 x 17

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Use the area model to work out these multiplication questions. Look at the example above to help you.

3. 764 x 81

4. 5092 x 32

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5. 783 x 45

___ +___+___+___+___+___=____ 14

6. 333 x 33

___ +___+___+___+___+___=____

Multiplication Methods: Italian Lattice Using the Italian lattice method to solve multiplication problems is a lot of fun and easy too! This method of multiplication uses boxes with diagonal lines. You can use it to solve multiplication problems that use large numbers. All you need to do is use basic times tables and add one-digit numbers together. Here is an example:

563 x 24 5

3 2

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First do 5 x 2. Write your answer in the first square either side of the dotted diagonal line.

0 0

1 2

Then, keep multiplying. For example, work out: 6 x 2, 3 x 2, 5 x 4, 6 x 4, 3 x 4. Then add the numbers in each diagonal line. Start from the bottom right hand corner. You may need to carry numbers.

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The answer is 13512.

Use the Italian lattice method to work out these multiplication questions. Look at the example above to help you.

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3. 37 x 19

4 5 2

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Curriculum Link: Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA098). Elaboration: Exploring techniques for multiplication such as the area model, the Italian lattice method or the partitioning of numbers.

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More Italian Lattice Use the Italian lattice method to work out these multiplication questions. The first one has been done for you as an example.

2. 422 x 14

66 x 77 6

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3. 101 x 88 4. 15 x 92 © ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

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Curriculum Link: Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA098). Elaboration: Exploring techniques for multiplication such as the area model, the Italian lattice method or the partitioning of numbers.

Understanding The Distributive Law The distributive law in multiplication tells us that the answer we get when we multiply a group of numbers that have been added together is the same as multiplying each number separately and then adding these results together. This might sound confusing but it’s really quite simple if you look at these examples.

So 10 x (2 + 1) = 30 So (10 x 2) + (10 x 1) = 30

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or 10 x 3

So (5 x 4) + (5 x 5) = 45

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or 5 x 9

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10 x 3 = 30

So 5 x (4 + 5) = 45

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Fill in the missing numbers to show the distributive law.

c. 12 x 5 = __

a. 3 x 7 = __

So __ x (__ + __) = __

So 3 x (3 + __) = 21

So (__ x __) + (__ x __) = __ © ReadyEdPu bl i cat i ons d. 20 x 9 = __ b. 11 x 8 = __ •f orr evi ew pur p osesonl y• So __ x (__ + __) = __ So __ x (5 + __) = 88 So (3 x __) + (3 x __) = __

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So (__ x __) + (__ x __) = __

So (__ x __) + (__ x __) = _

2. Use the given arrays to show the distributive law for each set of numbers below. a. 15 x 4

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b. 13 x 6

c. 22 x11

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___ x ___ = ___

So ___ x (___ + ___) = ___

So (___ x ___) + (___ x ___) = ___

Curriculum Link: Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (ACMNA100). Elaboration: Applying the distributive law and using arrays to model multiplication and explain calculation strategies.

Dividing By A Common Factor Division means to divide a number into equal groups. So if you wanted to share 60 pencils between 6 people, each person would get 10 pencils each: 60 ÷ 6 = 10. It is interesting to look at how number sentences like the one above are related to other number sentences. For example, 60 ÷ 6 gives us the same answer as 30 ÷ 3. We can also write this as 60 ÷ 6 = 30 ÷ 3.

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The reason these two number sentences have the same answer is not just by chance! They are related to each other because we have divided 60 and 6 by the same factor: 2. In other words, 60 ÷ 2 = 30 and 6 ÷ 2 = 3. This would also work if we divided 60 and 6 by another of its common factors: 3. So 60 ÷ 6 = 20 ÷ 2.

Use the examples above to help you to complete the questions below.

Write which common factor has been used to create these equivalent number sentences. a. 90 ÷ 10 = 9 ÷ 1 Common factor = _____

c. 48 ÷ 8 = 24 ÷ 4 Common factor = _____

b. 30 ÷ 6 = 10 ÷ 2 Common factor = _____

d. 63 ÷ 9 = 21 ÷ 3 Common factor = _____

a. 99 ÷ 9 = 11 ÷ 3 _______________

c. 56 ÷ 8 = 14 ÷ 4 _____________

b. 200 ÷ 10 = 20 ÷ 1 _____________

d. 40 ÷ 4 = 20 ÷ 2 _____________

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Fill in the missing numbers.

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a. __ ÷ 9 = 24 ÷ 3

b. 42 ÷ 6 = 21 ÷ __

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c. __ ÷ 8 = 32 ÷ __ = 16 ÷ 2

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d. 60 ÷ __ = 10 ÷ 2 = 20 ÷ __

Complete the table with equivalent number sentences. Equivalent sentence 1 80 ÷ 8

Equivalent sentence 2

40 ÷ 4

48 ÷ 6 110 ÷ 10 108 ÷ 12

Curriculum Link: Solve problems involving division by a one digit number, including those that result in a remainder (ACMNA101). Elaboration: Using the fact that equivalent division calculations result if both numbers are divided by the same factor.

Working With Remainders Some numbers don’t divide evenly into others, so we end up with a remainder or an amount left over. For example: If we share 11 cupcakes between 2 people, we would write: 11 ÷ 2 = 5 remainder 1. So each person will get 5 ½ cupcakes.

•

If we had to share $33 between four people, we would write: 33 ÷ 4 = 8 remainder 1. So each person gets $8 and 1/4 of a dollar, which we write as $8.25.

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If we had to buy enough identical boxes to store 52 books and each box stored 12 books, we would write: 52 ÷ 12 = 4 remainder 4. Because we need 4 boxes and part of a fifth box, we need 5 boxes in total to store all 52 books.

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A zookeeper wishes to share fish among his penguins evenly. If there are 4 penguins and 29 fish, how many fish does each penguin get? Use fractions in your answer.

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Some parents need to transport their children by car to a theatre production. Each parent’s car can seat 4 passengers. If there are 23 children, how many cars will be required?

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Complete these division problems below. Show your working out. Each answer should include a remainder. Think carefully about how you express the remainder.

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10 friends earn $1451 dollars from running a craft stall. If they split the money evenly, how much will each person get?

A committee of 9 people decide to hold a raffle. The committee has 200 tickets to sell. The committee members decide to sell the same number of tickets each. How many tickets should they each receive? How many tickets will be left over?

Curriculum Link: Solve problems involving division by a one digit number, including those that result in a remainder (ACMNA101). Elaboration: Interpreting and representing the remainder in division calculations sensibly for the context.

Ordering Fractions A fraction is part of a whole number. There are two numbers in a simple fraction. The top number is called the numerator. It tells us how many parts we have. The bottom is called the denominator. It tells us how many parts the whole has been divided into. For example, a sandwich can be cut into two pieces. If we took away one piece we would be left with one out of two pieces or ½. If we cut a sandwich into four pieces and took away one piece we would be left with one out of four pieces or ¼.

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Answer these questions about fractions.

a. 1/3

c. 1/6

b. 1/8

d. 1/12

Write the fraction each of these shaded shapes represent.

e. _____

b. _____

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Colour in each of these fractions.

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c. _____

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Write the fractions in order from smallest to biggest:_ _____________________________

3. 0

Write the correct fraction represented on each number line. You can use a ruler to help you work them out. a. b.

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Label each of the following fractions on the number line: 1/2, 1/3, 1/4, 1/8

1 Curriculum Link: Compare and order common unit fractions and locate and represent them on a number line (ACMNA102). Elaboration: Recognising the connection between the order of unit fractions and their denominators.

Adding And Subtracting Fractions – 1 Use the number lines below to solve the problems involving fractions.

a. 1/8 + 2/8 =

1/8

2/8

3/8

4/8

5/8

6/8

7/8

10/12

b. 3/8 + 5/8 = c. 6/8 – 4/8 =

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2. a. 1/12 + 4/12 =

2/12

4/12

6/12

8/12

4/9

5/9

6/9

c. 5/12 + 6/12 =

3. a. 5/9 + 4/9 =

1/9

2/9

3/9

b. 8/9 – 3/9 =

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b. 9/12 – 3/12 =

7/9

8/9

1/7

2/7

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a. 5/7 – 2/7 =

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1/15

2/15

1/18

2/18

a. 9/18 + 9/18 =

5/7

6/7

4/15

5/15

6/15

7/15

8/15

9/15

10/15

b. 6/15 + 5/15 =

4/18

5/18

6/18

7/18

8/18

9/18

c. 3/7 – 2/7 =

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3/15

3/18

4/7

b. 6/7 + 1/7 =

a. 14/15 – 12/15

3/7

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10/18

b. 16/18 + 1/18 =

11/15

12/15

13/15

14/15

c. 13/15 – 8/15 =

11/18

12/18

13/18

14/18 15/18 16/18 17/18

c. 11/18 – 4/18 =

Curriculum Link: Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (ACMNA103). Elaboration: Modelling and solving addition and subtraction problems involving fractions by using jumps on a number line, or making diagrams of fractions as parts of shapes.

Adding And Subtracting Fractions – 2 Solve each problem below. a.

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Teac he r

Shade each diagram to show the fraction indicated, then complete the sum.

b. 3/9 + 3/9

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c. 2/10 + 6/10

d. 10/12 – 5/12

f. 3/4 – 2/4

g. 4/5 – 3/5

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e. 7/8 – 1/8

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Number Line Decimals

tenths

hundredths

thousandths

millionths

and

hundred-thousandths

ones

ten-thousandths

tens

hundreds

thousands

ten thousands

hundred thousands

Place Value Chart

millions

A decimal number is a number with a decimal point; for example, 46.713. Like fractions, decimals allow us to show parts of a number. The decimal point marks where the whole number portion ends and the fraction part begins. Here is 46.713 shown in a place value chart:

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On a number line, 46.713 would look like this: 46.710

46.711

46.712

46.713

46.714

46.715

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Ordering decimal numbers can seem difficult, but it is easier if you follow some simple rules. 1. First, look at the whole number. Ignore the numbers after the decimal point and work out which is bigger. For example: 57.653 is bigger than 23.7788. 2. If the whole numbers are the same, look at the numbers after the decimal point. Take one number at a time, starting with the tenths. For example, if you were asked to put 1.355, 1.358 and 1.258 on a number line, it would look like this: 1.25 1.26 1.27 1.28 1.29 1.30 1.31 1.32 1.33 1.34 1.35 1.36 1.37

ÂŠ ReadyEdPubl i cat i ons decimal number represented on each number line. 1. Tick theâ&#x20AC;˘ f orr evi ew pur posesonl yâ&#x20AC;˘ 11.857

12.6

b. 3.152

4.152

3.252

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c. 6.74

6.84

d. 9.899

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9.999

6.9

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a. 12.75

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9.7

9.8

9.9

Circle the biggest number in each set. Tick the smallest. a. 7.771

7.772

7.672

7.70

7.671

7.710

7.072

b. 2.34

2.346

2.246

2.249

2.35

2.344

2.333

c. 5.75

5.637

5.747

5.647

5.65

5.655

5.70

d. 1.101

1.111

1.10

1.001

1.011

1.11

1.12

Curriculum Link: Recognise that the place value system can be extended beyond hundredths (ACMNA104). Elaboration: Using knowledge of place value and division by 10 to extend the number system to thousandths and beyond. Curriculum Link: Compare, order and represent decimals (ACMNA105). Elaboration: locating decimals on a number line.

Creating A Budget Imagine that your class has been asked to host a breakfast for 30 parents to raise money for your school. You need to raise $300 and you have been given a maximum budget of $150 to spend on food and drinks. Look at the Food and Drink List. Write out a menu below, being as specific as you can (e.g. croissants with butter) and calculate what it will cost to buy what you need for 30 people.

Food and Drink List

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honey

coffee

1 large jar of coffee

$12.00

5 croissants

$4.00

1 loaf of bread (20 slices)

$4.00

$5.00

1 large jar of honey

$8.50

1 container of milk (2 litres)

$5.00

10 tea bags

$2.00

1 dozen eggs $6.50 (these could be boiled or scrambled with a little milk and butter)

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$1.50

1 block of butter

Menu Item

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1 serve of fruit salad

Cost

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Questions

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Total Cost:

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1. How much did you spend on the food in total?

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_ _______________________________________________________________________

2. Now use your answer to question 1 to work out how much you need to charge each parent to come to the breakfast to make $300 in profit—that is, on top of what you have already spent. (Hint: You will need to use division.)

_ _______________________________________________________________________

Curriculum Link: Create simple financial plans (ACMNA106). Elaboration: Creating a simple budget for a class fundraising event.

Understanding GST In Australia, tax is added to particular goods and services. This is known as GST (Goods and Services Tax). A tax of 10% is added on to the price of goods and a tax of 10% is added to the price of a service. For example, if a tailor charges a customer $250 for mending a jacket, he/she will add 10% GST ($25), making the total cost $275.

Complete these receipts (for goods) by adding GST, and totalling the receipt.

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Toy shop receipt

$30

Copying paper

$12

Science kit

$50

Packet of pens

$5.50

Train set

$110

Folders

$11.50

Jigsaw puzzle

$20

Stapler

$3.00

GST

_____

GST

_____

Total including GST

_____

Total including GST

_____

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Teddy bear

Guitar lessons

$310

Editing services

$565

Tiling

$1050

Carpentry

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$975

Plumbing

$650

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Roof maintenance

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Calculate the GST for these services. Write the new total cost for each service. You may need to use some scrap paper to do your calculations.

Window washing

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stationery supplies receipt

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A gardener completes some work on a large property and hands the owner the receipt (right). He says that the GST on his services is $54. Is he correct? If not, what should he be charging? Show your calculations.

Gardening receipt

Cleaning gutters

$150

Mowing lawn

$81

Planting vegetables

$99

Weeding garden

$190

Curriculum Link: Create simple financial plans (ACMNA106). Elaboration: Identifying the GST component of invoices and receipts.

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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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Which Unit Is Best? We use different units of measurement for length, area, volume, capacity and mass. In Australia, these units are based on the metric system. Some of the more common units used are shown in the table (right).

Length Area Volume

Possible units kilometre, metre, centimetre, millimetre square kilometre, square metre, square centimetre cubic metre, cubic centimetre, cubic millimetre

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kilolitres, litres, millilitres

Mass

kilograms, grams, milligrams

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We need to decide which unit of measurement is best for different tasks. For example, if you want to know the distance between two towns, you would not be likely to use a ruler and measure it in centimetres! It would be more sensible to use kilometres.

Type of measurement

Choose or write the best unit of measurement for each task below. Think carefully about what you are measuring and what would make the most sense. a. The distance between two towns: b. The height of a two year old child: c. The area of a basketball court:

h. The volume of a caravan:

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i. The capacity of a jug of water: j. The capacity of a medicine bottle:

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k. The mass of a loaf of bread:

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g. The volume of a dog kennel:

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l. The mass of a car:

m. The mass of a pen lid:

Answer each question below. If the answer is no, use the back of the sheet to explain which unit of measurement would be better used. a. Should I measure the mass of a party balloon in kilograms?

_________

b. Should I measure the length of a bicycle race in millimetres?

_________

c. Should I measure the capacity of a wheelbarrow in cubic millimetres? _________ d. Should I measure the volume of a fish bowl in kilolitres?

_________

Curriculum Link: Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108). Elaboration: Recognising that some units of measurement are better suited for some tasks than others, for example kilometres rather than metres to measure the distance between two towns.

Celsius And Fahrenheit Some countries use different measures of scale to those used in Australia. For example, to measure temperature in Australia, we use the Celsius scale. In the US, the Fahrenheit scale is used instead.

˚C

90 80 70 60 50 40 30 20 10 0 10 20 30

Look at the image (right) showing the difference between the Fahrenheit (F) and Celsius (C) temperature scales. Celsius (C)

Boiling Point 100˚C--212˚F of water

100

Freezing Point

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0˚C--32˚F

of water

Celsius (C)

1. Write the temperature at which water freezes and boils in each scale. a. Fahrenheit: freezes at ______ degrees; boils at ______ degrees

b. Celsius: freezes at ______ degrees; boils at ______ degrees

210 200 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0 10 20 30

Fahrenheit (F)

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Fahrenheit (F)

Answer these questions about the two different scales.

˚F

b. 35°C

_____

c. 62°F

_____

d. 100°F

_____

e. 96°C

_____

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2. Convert these temperatures to Fahrenheit or Celsius using the image. Approximate answers

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•

It is possible to roughly convert between the two scales by using the methods below.

•

Fahrenheit to Celsius : subtract 30 and halve the resulting number.

•

Celsius to Fahrenheit: double the number and add 30.

3. Check the methods by converting these temperatures. Use the image above to check that your answers seem correct.

a. 10°C

_____

b. 110°F

_____

c. 43°C

_____

d. 38°F

_____

e. 50°C

_____

Curriculum Link: Choose appropriate units of measurement for length, area, volume, capacity and mass (ACMMG108). Elaboration: Investigating alternative measures of scale to demonstrate that these vary between countries and change over time, for example temperature measurement in Australia, Indonesia, Japan and USA.

Perimeter Of Rectangles We can calculate the perimeter of a rectangle (the distance around it) by adding together the length of its sides. For the rectangle below, we would do the following sum: 7cm + 4cm + 7cm + 4cm = 22cm

7 cm

We can also use doubling to make this calculation more efficient. In other words, we can: zz Add the length and width together and double the result (i.e. 7cm + 4 cm = 11 cm; double 11 cm = 22 cm).

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4 cm

zz Double the length and width and add these together (i.e. double 7 cm = 14cm; double 4cm = 8 cm. 14cm + 8 cm = 22cm).

Imagine that Amy wants to decorate plain diaries to sell at a school fete. There are five different diary sizes. She decides to border each diary cover with ribbon. To do this, she needs to know the perimeter of each cover. How much ribbon does she need? Show your working out for each perimeter calculation.

length 10 cm x width 11 cm

x width 9 cm

length 17 cm x width 12 cm

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length 23 cm x width 12 cm

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Diary Design

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Use one or all of the above methods to work out the perimeter problems below.

. te o length 7 cm c . che 3 x width 6 cm e r o t r s s r u e p length 15 cm

If the ribbon costs $1.00 per metre, how much does Amy need to spend on ribbon? Write your calculation below. __________________________________________________________________________ Curriculum Link: Calculate perimeter and area of rectangles using familiar metric units (ACMMG109). Elaboration: Exploring efficient ways of calculating the perimeters of rectangles such as adding the length and width together and doubling the result.

Area Of Rectangles - 5 cm -

We can calculate the area of a rectangle by multiplying its length and width. For example, for this rectangle, we would do the following sum: 10cm x 5cm = 50 square centimetres.

or eBo st r e p ok u S - 10 cm -

Teac he r Dance Floor

Perimeter

length 4 m x width 7 m

Area

length 4 m x width 6 m

length 4 m x width 5 m

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length 7 m x width 3 m

Questions

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Working Out

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Imagine that a family are planning to hold a party for 100 people. They are trying to select a suitable venue and want the biggest dance floor possible. They visit 6 venues. They record the length and width of each dance floor in the list below. Calculate the area of each dance floor and record it in the table.

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1. Which dance floor has the greatest area?_______________________________________ 2. Which dance floor has the smallest area?_______________________________________ 3. What do you notice about dance floor 3 and dance floor 5?________________________ 4. The family decide to visit one more venue. The dance floor here is 30 square metres. Write a possible length and width for this dance floor, keeping in mind the dimensions of the others. 30

_ _______________________________________________________________________ Curriculum Link: Calculate perimeter and area of rectangles using familiar metric units (ACMMG109). Elaboration: Exploring efficient ways of finding the areas of rectangles.

12 And 24 Hour Time – 1 In most cases, people use a 12 hour clock to tell the time. 12 hour times are written in this way: 10.24 am, 2.15 pm. Am and pm notations tell us whether it is morning or afternoon.

or eBo st r e p ok u S

Use the clock face to help you to convert these times to 12 or 24 hour times. a. 1.15 pm =

d. 0027 =

b. 2210 =

e. 4.05 pm =

f. b 1856 = a © ReadyEdPu l i c t i ons •f orr evi ew pur posesonl y•

c. 7.32 am =

Draw hands on the clock faces to show the correct 12 hour clock times. Circle whether the time is am or pm.

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a. 1507

am or pm?

b. 2210

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d. 1423

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Sometimes, however, a 24 hour clock is used to tell the time. On this type of clock, the hours start at 0 and continue through to 23. For example, 0013 means 12.13 am and 2357 means 11.57 pm. You will see that am and pm are not used to write 24 hour times. The clock face on the right shows how we can convert between the 12 and 24 hour time systems.

o c . che e r o r st super am or pm?

e. 0701

am or pm?

c. 0048

f. 1650

am or pm?

am or pm? Curriculum Link: Compare 12- and 24-hour time systems and convert between them (ACMMG110). Elaboration: Using units hours, minutes and seconds.

12 And 24 Hour Time – 2 Imagine that you go on an overseas holiday. You arrive at your resort and pick up a brochure that tells you about possible activities on Monday. You also have a friend, Jo, who you would like to meet on Monday and you have scribbled down some times to meet her.

Welcome to the Castle Hotel! Our list of activities for Monday is below.

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Yoga Local history walk Photography session Scavenger hunt Local wildlife lecture Board games: meet a new friend! Monday night’s movie Ghost tour

or eBo st r e p ok u S Notes:

Jo can meet at hotel at 8.15 am, 10.45 am or 12.30 pm.

Might also do dinner in town at 7pm.

13 14

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0800–0930 1030–1100 1200–1300 1335–1415 1445–1515 1600–1730 1830–2100 2115–2215

Answer the questions using the material above. You can use the clock face picture to help you to convert from 12 to 24 hour time if you need to.

1. If you want to do yoga, can you meet Jo at 8.15 am?

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2. You decide to meet Jo for dinner. This means that you will miss one of the activities. Which one is it? _ ____________________________________________________________________________

3. Jo is interested in going on the ghost tour with you. She suggests meeting up 15 minutes beforehand. What time would this be? (Use 12 hour time.)

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_ ____________________________________________________________________________

4. Do any of Jo’s suggested meeting times clash with the wildlife lecture?

_ ____________________________________________________________________________

5. How long does the scavenger hunt take? Is it in the morning or afternoon?

_ ____________________________________________________________________________

6. If you did the local history walk, could you meet Jo at the hotel afterwards at any of her suggested times? If so, which one/ones?

_ ____________________________________________________________________________

Curriculum Link: Compare 12- and 24-hour time systems and convert between them (ACMMG110). Elaboration: Using units hours, minutes and seconds.

Investigating Nets – 1 A net is a 2D pattern. If we fold up a net, it makes a 3D shape. There is more than one net possible for each 3D shape. Cut out and construct the net below, then label it using one of the following:

cube

triangular prism

rectangular prism

fold

or eBo st r e p ok u S fold

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fold

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Curriculum Link: Connect three-dimensional objects with their nets and other two-dimensional representations (ACMMG111). Elaboration: Identifying the shape and relative position of each face of a solid to determine the net of the solid, including that of prisms and pyramids.

Investigating Nets – 2 A net is a 2D pattern. If we fold up a net, it makes a 3D shape. There is more than one net possible for each 3D shape. Cut out and construct the net below, then label it using one of the following:

triangular prism

rectangular prism

fold

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cube

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fold

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Investigating Nets – 3 A net is a 2D pattern. If we fold up a net, it makes a 3D shape. There is more than one net possible for each 3D shape. Cut out and construct the net below, then label it using one of the following:

cube

triangular prism

rectangular prism

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fold

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fold

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fold

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fold

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Investigating Nets – 4 Answer the questions about nets below.

Write the name of each 3D shape below. Use the word bank to help you. Underneath each shape, list the 2D shapes that are needed to make each 3D one. An example has been done for you. 3D word bank: square pyramid octahedron cube tetrahedron

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3D shape: cube 2D shapes needed: 6 squares

Based on your answers above, tick and label the nets that could be used to make each 3D shape above. You could draw each possibility on graph paper and try folding it first if you are not sure.

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

Representing Shapes We can represent 3D shapes by 2D drawings. To do this, we need to think about the 2D shapes that make up 3D shapes.

Below are the names of some 2D shapes that can make up 3D shapes. Draw each one.

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square

Trace each 3D shape below. Label each one and then name the 2D shapes that you can see in each.

Shape

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rectangle

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oval

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isosceles triangle

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Try drawing a rectangular prism on the back of this page. Think carefully about the 2D shapes that you will need to use. Hint: Look at a box or a book (both rectangular prisms) to help you. Curriculum Link: Connect three-dimensional objects with their nets and other two-dimensional representations (ACMMG111). Elaboration: Representing two-dimensional shapes such as photographs, sketches and images created by digital technologies.

Using A Grid Reference System A grid reference system can be used to locate objects and describe routes or pathways on a map. When we describe a location, we use the number or letter on the horizontal or x axis first. An example is to the right. On this map, the tree can be found at C1. To get from the straight bridge to the bakery, you would need to take the following path: D1 – E1 – F2 – F3.

5 4 3

kery

2 1

C A B D r o e t s B r e oo p k Su

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On the grid below, draw a map of your classroom. You should include furniture and other important objects. Use simple sketches for these objects as in the example above. Then answer the questions below.

d c

a 1

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1. Write the grid reference for your desk._ ________________________________________ 2. Write the route from a friend’s desk to your desk._ _______________________________

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3. Write two sets of directions to get from one important object to another.

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To get from ____________________ to _______________________, you would need to take the following route: _______________________________________. To get from ____________________ to _______________________, you would need to take the following route: _______________________________________. 4. Choose three other objects in your classroom. List them below. Ask a friend to write the grid reference for each. Are they correct?

object

grid reference

Curriculum Link: Use a grid reference system to describe locations. Describe routes using landmarks and directional language (ACMMG113). Elaboration: Creating a grid reference system for the classroom and using it to locate objects and describe routes from one object to another.

check

Flip, Slide And Turn When a 2D shape is moved to another position, we call the change a transformation. A transformation can be a flip, slide or turn. Look at how the 2D shape below has been transformed.

original

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slide

turn

(quarter clockwise)

Answer the questions about transformation.

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Write how the original shape has been moved.

original

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__________________________

__________________________ c. __________________________ © R eadyEdPubl i ca t i ons •f orr evi ew pur posesonl y•

slide and turn the cow on the right according to 2. Flip, the instructions below. Cut and paste the answers at

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flip down

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the bottom of this page into the correct boxes.

original

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1/4 clockwise TURN

1/2 clockwise Turn

Curriculum Link: Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries (ACMMG114). Elaboration: Identifying the effects of transformations by manually flipping, sliding and turning two-dimensional shapes and by using digital technologies.

Enlarging Shapes

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Teac he r

To enlarge a 2D shape, we can use a grid. Choose one of the pictures to enlarge below. Remember to copy carefully.

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Curriculum Link: Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original (ACMMG115). Elaboration: Using a grid system to enlarge a favourite image or cartoon.

Measuring Angles A protractor is used to measure and construct angles. The size of an angle is the amount of turn required for one arm to touch the other. For example:

45˚

90˚

225˚

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Use a 180 or 360 degree protractor to complete the activities below.

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2. Construct these angles.

. t a. 65˚ e

b. 88˚

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1. Measure and record the angles.

c. 12˚

e. 145˚ co

d. 156˚

f. 86˚

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Curriculum Link: Estimate, measure and compare angles using degrees. Construct angles using a protractor (ACMMG112). Elaboration: Measuring and constructing angles using both 180° and 360° protractors.

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Section 3: r o e t s Bo r e p ok u S Statistics and Probability

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Games Of Chance – 1 Two friends, Ben and Molly, decide to play one game of rock, paper, scissors. In this game, rock beats scissors, scissors beats paper and paper beats rock. This is a game of chance as there is no skill involved that would help Ben or Molly win (cheating doesn’t count!). Here are Ben and Molly’s possible choices for the game. Ben

Molly

rock or scissors or paper

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Answer the questions below.

1. How many choices do Ben and Molly have each?

_ _______________________________________________________________________

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2. Write the possibilities for the outcome of the game in the space below. The first one has been done for you.

Ben and Molly will draw (e.g. both choose rock) _ _______________________________________________________________________ _ _______________________________________________________________________ _ _______________________________________________________________________

© ReadyEdPubl i cat i ons 3. What is the chance that Molly will win the game? Circle the correct answer. •f or r e vi ew p ur po ses nl y•as Ben (a) more likely than Ben (b) less likely than Ben (c)o same chance

_ _______________________________________________________________________

4. What is the chance that Molly will draw with Ben? Circle the correct answer. (a) more likely than Ben

(b) less likely than Ben

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5. What is the chance that Molly will lose the game? Circle the correct answer. (a) more likely than Ben

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(b) less likely than Ben

6. Imagine that Ben and Molly decide to play another round of the game. Are their chances of winning, losing and drawing the same for this round? Explain.

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_ _______________________________________________________________________

Curriculum Link: List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116). Elaboration: Commenting on the likelihood of winning simple games of chance by considering the number of possible outcomes and the consequent chance of winning in simple games of chance such as jan-ken-pon (rock-paper-scissors).

Games Of Chance – 2 Colour the spinners below, then answer the questions.

YELLOW

RED

GREeN

YELLOW

or eBo st r e p ok u S A SPINNER SPINNER b GREEN

RED

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BLUE

1. Is Spinner A more likely to land on blue or red?__________________________________ 2. Is Spinner B more likely to land on blue or red?__________________________________ 3. Which colour is Spinner A least likely to land on?_________________________________ 4. Which colour is Spinner B most likely to land on?_ _______________________________

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• 6. Which spinner offers an equal chance of landing on yellow or red?__________________ 5. Which spinner offers the best chance of a player landing on green?_ ________________

7. How could you change Spinner A to give an equal chance of landing on each colour?

_ _______________________________________________________________________

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_ _______________________________________________________________________

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8. Imagine that both spinners belong to a board game. If you land on red, you move forward 3 spaces. If you land on blue, you move forward 1 space. If you land on green, you miss a turn. Explain which spinner would give you the best chance of winning the board game.

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_ _______________________________________________________________________

Games Of Chance – 3 Imagine that you visit a fête. You stop at a stall where you can play a game involving a jar of small toys. The stallholder says:

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“Would you like to play this game? It costs $5 to play. Close your eyes and put your hand in the jar. If you get a bird, you win nothing. If you get a cat, you win $1. If you get a mouse, you win $5. If you get a dog, you win $10. If you get a horse, you win $50! There are 24 toys in the jar. 12 are birds, 6 are cats, 3 are mice, 2 are dogs and 1 is a horse. Can’t be fairer than that!”

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Before you decide whether to play, you work out the chance of choosing each type of toy.

1. What is the chance (for example, 1 in 4) that you will pick each of the toys below?

Chance:

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Chance:

2. If you play, which toy are you most likely to pick?_ _______________________________

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3. If you play, which toy are you least likely to pick?_________________________________ 4. If you play are you more or less likely to make some money? (Remember that the game costs $5 to play.)

_ _______________________________________________________________________

5. How could this game be made fairer?

_ _______________________________________________________________________

Probability Probability is the chance that something will occur. One way that we can show the probability of an event is by using a scale from 0 to 1. A score of 0 tells us that the event cannot occur. A score of 0.5 indicates that there is an even or 50% chance of the event occurring. A score of 1 tells us that the event is certain to happen. Find a partner to work with to answer the questions.

If you were to roll a 10-sided die, what would be the probability of the events listed in the table happening? Use the scale provided to express the probability as a number.

Very Unlikely

0.2

Unlikely

Even Chances

Likely

Very Likely

Certain

0.4

0.5

0.6

0.8

Event

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Impossible

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a. rolling an even number b. rolling an odd number c. rolling a 7

d. rolling a 1 e. f.

g. rolling an even number greater than 2

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h. rolling a number less than 4

that there are 10 cats at a cat shelter, ready to be adopted. One is ginger, two are 2. Imagine white, two are grey and five are black. A customer walks in to adopt a cat.

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Impossible

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Very Unlikely

Unlikely

Even Chances

Likely

Very Likely

Certain

0.2

0.4

0.5

0.6

0.8

In pairs, mark on the scale below the likelihood of the customer choosing each colour cat. Do you and your partner agree on your answers? Explain why/why not on the back of this sheet. 46

Curriculum Link: Recognise that probabilities range from 0 to 1 (ACMSP117). Elaboration: Investigating the probabilities of all outcomes for a simple chance experiment and verifying that their sum equals 1.

Interpreting Graphs – 1 Look at the three sets of data below from the community of Vanillaville. Tick the type of graph that you think is best for recording each set of data. Hint: There should be a different answer for each. Give reasons for your choices.

Most popular sports played by 500 adults surveyed.

210

155

q column

soccer

basketball

tennis

hockey

q dot

Daily temperatures for one week in January.

q pie

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Reason:

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q column

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Reason:

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q column q dot q pie

Reason:

Curriculum Link: Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (ACMSP119). Elaboration: Identifying the best methods of presenting data to illustrate the results of investigations and justifying the choice of representations.

Interpreting Graphs – 2

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Select one set of graph data from page 47 and construct it here. Remember to label the graph clearly. You will need to turn the page to landscape.

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Title of graph:

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Reading Data Look at the three graphs and the table below and answer the questions.

Musical Instruments Played At Palmer Primary School violin

flute

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piano

No. of customers

Menu Items Chosen At Jam Café 80 60

20 0

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guitar

Gymnastics Scores By A Male Gymnast

vault floor pommel rings high parallel bar bars horse

Timetable For Bingley Ferry Time (24No. Of Hour Clock) Passengers 1000 35 1100 83 1200 92 1300 106 1400 110 1500 57 1600 23

pizza

hamburger

toasted sandwich

hot dog

sushi

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1. Which instrument is the most popular at Palmer Primary School?_____________________ 2. Which instruments have the same number of students learning how to play them?

_ _________________________________________________________________________

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3. Which menu item was the least popular at the café?________________________________ 4. Circle the approximate fraction of café customers who chose the hamburger.

a) ¼ b) ½

c) 1/8

d) 1/20

5. List the top three highest scoring events for the gymnast.

_ _________________________________________________________________________

6. How many passengers rode the Bingley Ferry between three and four o’clock?__________ 7. What are the two most popular times of day to ride the Bingley Ferry?_________________ 8. Which graph or table do you think was the easiest to read? Why?

_ _________________________________________________________________________

_ _________________________________________________________________________ Curriculum Link: Describe and interpret different data sets in context (ACMSP120). Elaboration: Using and comparing data representations for different data sets to help decision making.

Answers Section 1: Number and Algebra Investigating Factors Page 8 1.a) 10; b) 1, 7, 28; c) 3, 9; d) 13 2.a) 13; b) 1; c) There were more factors for even numbers and they included the number 2. 3.b) 1, 2, 4, 8, 16; c) 1, 3, 9, 27, 81; d) 1, 2, 3, 6, 7, 14, 21, 42 4.a) 1, 5 should be circled; 25 is missing; b) 4, 10 should be circled; 1, 2, 5, 20, 25, 50 and 100 are missing; c) 1 and 7 should be circled; 9, 3, 21 and 63 are missing; d) 3, 6, 9, 15,18 and 30 should be circled; 1, 2, 5, 10, 45 and 90 are missing.

Multiplication Methods: Area Model Page 14 1. x 50

100 +

70 +

5000

3500

200

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500

350

5000 +500+3500+350+200+20=9570

900 +

20 +

x 10

9000

200

6300

140

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Investigating Multiples Page 9 1.a) 3; b) 7; c) 13 2.a) 5 and 20 should be circled b) 10 and 45 should be circled c) 15 and 30 should be circled 3.4, 8, 12, 16, 20 and 24 should be circled in red (multiples of 4); 6, 12, 18 and 24 should be circled in blue (multiples of 6). The numbers 12 and 24 are common to both; the circled numbers are grouped in threes. 4.a) 36, 45, 54, 63, 72 b) 16, 24, 32, 48, 56, 80 c) 33, 44, 66, 77, 110

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Multiplication Methods: Partitioning Numbers Page 13 1.3072; 2.3234; 3.6168; 4.1510; 5.1959; 6.3884; 7.1971; 8.1664

9000 +6300+200+140+30+21=15691

x 80

700 +

60 +

56000

4800

320

700

56000 +4800+320+700+60+4=61884

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x 30

150000

2700

10000

180

150000 +2700+60+10000+180+4=162944

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Using Estimation Page 12 1.Answers might include the following: To quickly work out the approximate cost of a trolley load of shopping, to work out the best value items, to work out if you need a trolley or a basket for the items you intend to buy. 2.Students will come up with different methods for solving these problems; here is one possible way to solve each. a)$12 + $18 = $30; $10 + $40 = $50; added together these make $80. Add $12 to these makes $92. Tom will get approximately $8 in change. b)523 + 78 makes approximately 600; 241 + 59 is 300. Adding these together makes approximately 900, so about 50 more tickets can be sold. c)32 + 33 makes approximately 60 (minutes); 40 + 21 makes approximately 60 (minutes). Add these to 60 (the 1 hour from the fourth part) means the student has spent about 3 hours on the exam. She has approximately 1 hour or 60 minutes left. 50

90 +

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Divisibility Rules Page 11 1.The last digit is 0 or 5. 2.The sum of the digits is divisible by 9. 3.The last digit is 0. 4.The number is divisible by both 3 and 4.

5000 +

700 +

80 +

x 40

28000

3200

120

3500

400

28000 +3200+120+3500+400+15=35235

6. 300 +

30 +

x 30

9000

900

9000 +900+90+900+90+9=10989

Multiplication Methods: Italian Lattice Page 15 1. 2 6 1 0

1 2

4 2 3

0 9

3 9

0 2

1 1

2 8

0 0

1 0

1 1

2 2

1 2

More Italian Lattice Page 16 1. 6 6 4 4 0

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1 4

0 8

8 8

5 4 1

1 1

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2 2

4 4 2

2 2

1 8

1 2

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1 0

7 7

4 1

5 0

0 0

9 2

Understanding The Distributive Law Page 17 1.a) 21, 4, 3, 4, 21; b) 88, 11, 3, 11, 5, 11, 3, 88; c) 60, 12, (the rest of the answers will depend on how the students decide to break up the number 5) d) 180, 20, (the rest of the answers will depend on how the students decide to break up the number 9) 51

2.a) 15 x 4

3 1

15 x 4 = 60 So 15 x (3 + 1) = 60

So (15 x 3) + (15 x 1) = 60

Working With Remainders Page 19 1.Six cars are required (23 ÷ 4 = 5 remainder 3) 2.Each penguin gets 7 ¼ of a fish (29 ÷ 4 = 7 remainder 1) 3.Each person gets $145.10 (1451 ÷ 10 = 145 remainder 1) 4.Each person gets 22 tickets. There will be 2 left over (200 ÷ 9 = 22 remainder 2) Ordering Fractions Page 20 1. a. 1/3

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c. 1/6

13 x 6 = 78

d. 1/12

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So (13 x 3) + (13 x 3) = 78

2.c)22 x 11 3

2.The fractions in order are a) 1/8 b)1/9 c)1/2 d) 1/4 e)1/5 3. 0

1/8

1/4

4.a1/5 b)1/10

1/3

1/2

Adding And Subtracting Fractions - 1 Page 21 1.a) 3/8; b) 1; c) 2/8 2.a) 5/12; b) 6/12 or 1/2; c) 11/12 3.a) 1; b)5/9; c) 2/9 4.a) 3/7; b)1; c)1/7 5.a) 2/15; b) 11/15; c) 5/15 or 1/3 6.a) 1; b) 17/18; c) 7/18

So (22 x 3) + (22 x 8) = 242

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Adding And Subtracting Fractions - 2 Page 22 1.a) 2/3; b) 2/10 or 1/5; c) 5/6; d) 1; e) 1/5 2.a) ¾; b) 6/9 or 1/3; c) 8/10 or 4/5; d) 5/12; e) 6/8 or ¾; f) ¼; g) 1/5

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Dividing By A Common Factor Page 18 1.a) 10; b) 3; c) 2; d) 3 2.a) false; b) true; c) false; d) true 3.a) 72; b) 3; c) 64, 4; d) 12, 4 4. Possible answers are given. Equivalent Equivalent sentence 1 sentence 2 10 ÷ 1 or 20 80 ÷ 8 40 ÷ 4 ÷2 8 ÷ 1 or 24 ÷ 3 8 ÷ 1 or 24 ÷ 3 48 ÷ 6 or 16 ÷ 2 or 16 ÷ 2 11 ÷ 1 or 55 ÷ 11 ÷ 1 or 55 ÷ 110 ÷ 10 5 or 22 ÷ 2 5 or 22 ÷ 2 108 ÷ 12 36 ÷ 3 or 9 ÷ 1 36 ÷ 3 or 9 ÷ 1

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So 13 x (3 + 3) = 78

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2.b)13 x 6

Number Line Decimals Page 23 1.a)12.75; b) 3.152; c) 6.74; d) 9.899 2.a) biggest: 7.772; smallest: 7.072 b) biggest: 2.35; smallest: 2.246 c) biggest: 5.75; smallest: 5.637 d) biggest: 1.12; smallest: 1.001 Creating A Budget Page 24 Answers will vary

Understanding GST Page 25 1.Toy shop: GST: $21. Total including GST: $231. Stationery supplies: GST: $3.20. Total including GST: $35.20.

3.They both have the same area as the same numbers were multiplied. 4. 5 m x 6 m (Other answers possible.)

2. Service

Price

Added GST

Total

Guitar lessons

$310

$31

$341

Editing services

$565

$56.50

$621.50

Tiling

$1050

$105

$1155

Carpentry

$975

$97.50

$1072.50

Plumbing

$650

$65

$715

Window washing

$125

$12.50

$137.50

$87

$957

Roof maintenance $870

3.He should be charging $52 GST (10% of $520)

12 And 24 Hour Time - 1 Page 31 1.a) 1315; b) 10.10 pm; c) 0732; d) 12.27 am; e) 1605; f) 6.56 pm 2.

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b)pm

Which Unit Is Best? Page 27 1.a) kilometres; b) centimetres; c) square metres; d) square metres; e) square centimetres or square millimetres; f) cubic millimetres; g) cubic centimetres; h) cubic metres; i) litres; j) millilitres; k) grams; l) kilograms; m) milligrams 2.a) No, should be milligrams; b) No, should be kilometres; c) No, should be cubic metres; d) No, should be litres

c)pm

d)am

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a)pm

Celsius And Fahrenheit Page 28 1.a)Water freezes at 0°C/32°F and boils at 100°C/212°F. 2.(Approximate student answers are acceptable.) a) 65.5°C; b) 95°F; c) 16.7°C; d) 37.8°C; e) 203°F 3.a) 50°F; b) 40°C; c) 116°F; d) 4°C; e) 130°F

e)am

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Section 2: Measurement and Geometry

f)pm

And 24 Hour Time - 2n Page 32 © ReadyEdP121.No. u b l i c a t i o s Yoga runs from 8 am to 9.30 am. 2.The movie •f orr evi ew pur posesonl y• 3.9 pm

Area of Rectangles Page 30

Investigating Nets - 2 Page 34 Teacher to check.

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Dance Floor

Perimeter

length 4 m width 7 m

length 5 m x width 5 m

length 3 m x width 8 m

length 7 m x width 3 m

length 4 m x width 6 m

length 4 m x width 5 m

1.Dance floor 1 2.Dance floor 6

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4.No 5.The scavenger hunt takes 40 minutes. It is in the afternoon. 6.Yes. Could meet Jo at 12.30 pm. (Dinner is also possible at 7 pm.)

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Perimeter Of Rectangles Page 29 Diary design 1: 70 cm Diary design 2: 42 cm Diary design 3: 26 cm Diary design 4: 48 cm Diary design 5: 58 cm Total amount of ribbon required: 244 cm Amy needs to pay $24.40 for the ribbon

Investigating Nets - 1 Page 33 Teacher to check.

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Area

28 square metres 25 square metres 24 square metres 21 square metres 24 square metres 20 square metres

Investigating Nets - 3 Page 35 Teacher to check. Investigating Nets - 4 Page 36 1.b)tetrahedron; 4 triangles needed c)octahedron; 8 triangles needed d)square pyramid; 3 triangles and 1 square needed 2. a) square pyramid c) octahedron e) tetrahedron f) cube Representing Shapes Page 37 1.Teacher to check. 2. Cylinder = rectangle, oval (2D shapes). Square pyramid = square, isosceles triangle (2D shapes). 53

Triangular prism = rectangle, isosceles triangle (2D shapes.) Cube = square (2D shapes). Using A Grid Reference System Page 38 Teacher to check answers. Flip, Slide And Turn Page 39 1.a)flip b)slide c)turn 2.

2.Bird 3.Horse 4.It is less likely that you would make money because of the small chance of getting a dog or a horse. 5.There should be more horses and dogs and fewer of the other animals. Probability Page 46 1.a)

Event

flip down

flip up

turn a 1/4 turn

turn a 1/2 turn

flip down

flip up

turn a 1/4 turn

turn a 1/2 turn

Enlarging Shapes Page 40 Teacher to check

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Measuring Angles Page 41 1.a)17°; b)100°; c)73°; d)310°; e)208°; f)24° 2.Teacher to check

c. d. e. rolling a number between 1 and 10

1 (certain)

0.2 (very unlikely) g. rolling an even number 0.4 (unlikely)

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Probability

0.5 (even rolling an even number chance) 0.5 (even rolling an odd number chance) 0.1 rolling a 7 0.1 rolling a 1

Section 3: Statistics and Probability

f. rolling a 3 or 4

Games Of Chance - 1 Page 43 1.Three 2.Ben chooses rock, Molly chooses scissors; Ben chooses rock, Molly chooses paper, Ben chooses scissors, Molly chooses rock; Ben chooses paper, Molly chooses rock; Ben chooses paper, Molly chooses scissors. 3.Chance that Molly will win the game: c); 4.Chance that Molly will draw with Ben: c); 5.Chance that Molly will lose the game: c) 6.Their chances are the same, although the outcome might be different.

greater than 2 h. rolling a number less than 4

0.3

2. ginger: 0.1; white: 0.2; grey: 0.2; black: 0.5

Graphs -i 1o Page 47 © ReadyEdInterpreting Publ i cat n s Students should indicate that the sports graph should as column oro dotn graph, temperature •f orr evi ew pu r pbeo es l ythe• should be a column or dot graph and the pets

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Games Of Chance - 3 Page 45 1. Toy

Chance

bird

12 in 24 (1 in 2)

cat

6 in 24 (1 in 4)

mouse

3 in 24 (1 in 8)

dog

2 in 24 (1 in 12)

horse

1 in 24

Interpreting Graphs - 2 Page 48 Teacher to check

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Games Of Chance - 2 Page 44 1.Red 2.Neither; they are the same size. 3.Blue 4.Green 5.Spinner B 6.Spinner B 7.Make all the colours the same size. 8.Spinner A, because it is most likely to land on red and least likely to land on blue. There is also less chance than Spinner B of landing on green.

graph should be a pie graph.

Reading Data Page 49 1.Piano 2.Violin and flute 3.Sushi 4.b) 5.Pommel horse, vault and parallel bars 6.80 7.1300 and 1400 8.Answers will vary

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