OzzieMaths Series - Year 6

Title: OzzieMaths Series Maths: Year 6

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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: 978 186 397 999 3 2

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Reproduction and Communication by others

Contents Teachers’ Notes Curriculum Links

4 5–6

Section 1: Number and Algebra

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

Interpreting Graphs (Student A) Interpreting Graphs (Student B) Interpreting Line Graphs Tall Story Column Graphs 1 Tall Story Column Graphs 2 What’s Up With These Graphs?

Games Of Chance It’s Likely That…

True Or False (Chance Problems) How Lucky Can You Be? Holiday Spin 1 Holiday Spin 2 Conduct A Probability Experiment 1 Conduct A Probability Experiment 2

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Answers

46 47 48 49 50 51 52 53 54 55 56 57 58 59

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Odd Fruit Out Are You Primed To Go? Triangular Numbers Mathematically Minded 1 Mathematically Minded 2 Adding And Subtracting Integers Equivalent Fractions Match 1 Equivalent Fractions Match 2 Fraction Problems 1 Fraction Problems 2 Adding And Subtracting Decimals Multiplying And Dividing Decimals The Powers Of 10 Jigsaw Number Values More Or Less Problems Super Saver Shopper Bullseye!

Sequences

Section 3: Statistics and Probability

60-64

Section 2: Measurement and Geometry

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Metric Conversions Cubby House Conversions Fish Tank Volumes Fish Tank Volumes (Extension) Comparing Lengths And Areas Don’t Miss The Boat!

Angles In Action Looking For X Transformations Design A Logo Know Your Cartesian Plane Fast Delivery (Student A) Fast Delivery (Student B) Fast Delivery (Response Sheet) Prisms Around Us Ancient 3D Shape Constructions Build A 3D Shape House 1 Build A 3D Shape House 2

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Teachers’ Notes Maths: Year 6 is part of The OzzieMaths Series which comprises seven books altogether. It is linked to the Australian Curriculum and each page in the book references the content descriptor/s and elaboration/s being addressed.

The activities have been designed to develop mathematical skills and reasoning in a creative way that is connected to solving problems in real-life contexts.

Students will be asked to reflect upon the strategies used to problem-solve effectively in familiar situations and expand their ideas to realise that mathematical understanding has an important role in other subject areas. Answers and additional teaching information are included at the back of the book. This book is divided into three sections as detailed below.

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Section One: Number and Algebra

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: identifying and explaining the odd one out in a number series, exploring integers above and below sea level, playing equivalent fraction dominoes and writing number sentences with the powers of 10 to burst balloons.

© ReadyEdPubl i cat i ons f or r e vi ew pur o sesoofnl y• This• section draws students’ attention top the applications Section Two: Measurement and Geometry

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calculating and comparing measurements of mass, length and capacity in our daily lives. Students will engage in activities such as: converting metric units of everyday objects, finding the correct dose of water conditioner for fish tanks and planning a ferry trip to the zoo by reading a timetable. Tasks investigating the Cartesian Plane include a pizza delivery race and designing a logo for the community.

. te Statistics and Probability o Section Three: c . che Students will develop skills in interpreting and comparing edata r o displays based on an extreme bike race and changes t in height for r s s uper women and men over the last century. They will consider how data can be skewed in displays to give a biased viewpoint and identify what to be on the lookout for. Tasks to describe probability focus on real-life examples and carrying out chance experiments with a small and large sample.

4

Curriculum Links Number and Algebra Identify and describe properties of prime, composite, square and triangular numbers (ACMNA122) Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123)

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Investigate everyday situations that use integers. Locate and represent these numbers on a number line (ACMNA124)

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Compare fractions with related denominators and locate and represent them on a number line (ACMNA125) Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126)

Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies (ACMNA127) Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128)

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Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without digital technologies (ACMNA129) Multiply and divide decimals by powers of 10 (ACMNA130)

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Make connections between equivalent fractions, decimals and percentages (ACMNA131)

Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (ACMNA132)

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Explore the use of brackets and order of operations to write number sentences c e h r (ACMNA134) er o st super

Continue and create sequences involving whole numbers, fractions and decimals.

Describe the rule used to create the sequence (ACMNA133)

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Curriculum Links Measurement and Geometry Connect decimal representations to the metric system (ACMMG135) Convert between common metric units of length, mass and capacity (ACMMG136) Solve problems involving the comparison of lengths and areas using appropriate units (ACMMG137)

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Connect volume and capacity and their units of measurement (ACMMG138) Interpret and use timetables (ACMMG139)

Construct simple prisms and pyramids (ACMMG140)

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Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142) Introduce the Cartesian coordinate system using all four quadrants (ACMMG143)

Investigate, with and without digital technologies, angles on a straight line, angles at a point and vertically opposite angles. Use results to find unknown angles (ACMMG141)

Statistics and ©Probability ReadyEdPubl i cat i ons

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Describe probabilities using fractions, decimals and percentages (ACMSP144)

Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145)

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Compare observed frequencies across experiments with expected frequencies (ACMSP146)

Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)

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Interpret secondary data presented in digital media and elsewhere (ACMSP148)

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Number and Algebra

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Odd Fruit Out 5

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A prime whole number is greater than 1 and can only be divided by 1 and itself.

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42 20 A composite number can always be divided evenly.

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A square number is the product of a number multiplied by itself.

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r o e t s Bousing a colouring r e Choose the 'odd fruit out' in each set of numbers below pin the column on the right. ok pencil. Explain your choice u S

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__________________________ __________________________

__________________________

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__________________________ __________________________

Curriculum Link: Identify and describe properties of prime, composite, square and triangular numbers (ACMNA122)

Are You Primed To Go? Help the numbat find the safety of its log by creating a sequence path of prime numbers between 1 - 150.

The starting point has been given to you.

5

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Curriculum Link: Identify and describe properties of prime, composite, square and triangular numbers (ACMNA122)

113 101

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Triangular Numbers Triangular numbers can be shown as stacked triangles of dots. Here are some examples:

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1. Write the number of dots you see in each triangle above. The first two have been done for you.

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Triangular number

T1 = 1

1

T2 = 1 + 2

3

T3 = 1 + 2 + T4 = T5 =

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2. Describe the number pattern that is forming.

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Number of triangles (T) in the stack

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4. Think ahead to complete the table below.

Number of triangles (T) in the stack T6 T7 T8

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3. On the back of this sheet or in your workbook, draw the 6th dot triangle in the sequence above. Complete the T6 triangular number.

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T9 T10 T11

5. Can you predict the triangular number for T15? How did you work this out?

_______________________________________________________________________

_______________________________________________________________________

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Curriculum Link: Identify and describe properties of prime, composite, square and triangular numbers (ACMNA122)

Mathematically Minded 1 Solve these mixed operation (+ - x ÷) problems. Do your written work in the spaces provided.

1. There are 68 students in Year 6. Your job is to set up enough chairs for an assembly in rows of 15. How many rows will there be? How many seats will be empty?

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2. Cabbage Tree Primary School orders 2,232 exercise books to kick off the school year. If each child receives 9 books, how many students are enrolled at the school?

3. The local postie delivered 928 letters on her route today. Yesterday she delivered 147 more letters. How many letters did she deliver yesterday?

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4. Rosie feeds her two dogs 250g of dry kibble each a day. If she buys a 3kg bag of kibble, will this be enough food for a week?

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5. It is Grand Final Day and 6,735 fans turn up for the match. At half-time the score is 44 – 2 so 2,849 disappointed fans leave the stadium. How many people stay until full-time?

o c . che e 6. It takes Lawrence 14 minutes to walk home from school each day. If he leaves school r o r at 3.56pm, what time does he arrive home? st s uper 7. Axel makes 28 hand-shaped surfboards a month. He takes January, February and March off each year to go surfing. How many boards does Axel produce in a year?

Curriculum Link: Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123)

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Mathematically Minded 2 Solve these word problems by thinking about the type of operations you need to perform. Number the order of operations that you use to find the solution.

1. Coral collects 214 bunya nuts. She gives half to her aunty and she eats 10. How many nuts does Coral have left?

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-

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2. Ned borrows the latest Percival Johnson book that has 956 pages. He can’t put it down. He’s only got 127 pages to read until he reaches the end. How many pages has Ned read?

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3. The Sales family have a 565km drive home. They stop for lunch after driving 182km and again for a rest 171km from home. How far has the family travelled so far?

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4. A farmer lets 296 goats out to graze. At the end of the day, her kelpie herds 215 goats back into the pen. The farmer collects another 12. How many stragglers are left in the paddock?

5. Three buses are hired to take Year 5 and 6 classes on a trip. Each bus seats 47 people.

The last bus has 9 vacant seats. How many children went on the trip?

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a bigger batch of 100 muffins, how many cups of flour will she need?

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7. The teacher puts 76 pieces of fruit on a platter for the Kindy class. Each child eats 3 pieces. There are 4 pieces of fruit left over. How many Kindy kids are in the class?

+ 12

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Curriculum Link: Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123)

Adding And Subtracting Integers

20 18 16 14 12 10 8 6 4 2

0

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-2 -4 -6 -8 -10 -12 -14 -16 -18 -20

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A real life example of how we add and subtract integers can be seen in the diagram below that explores activities: above (+), at (0) and below (-) sea level.

sea floor

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1. Write an integer for the following, then mark the integer on the number line above.

e. water skier:

f. scuba diver:

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d. paraglider:

2. The integer for the turtle is -10. The turtle is _____ __________ below ____________.

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3. What are the new positions for the following?

o c . ch b. the bird lands on the deck of the boat _______________________________ e r e o t r s su er p 4. Write a story problem using sea level that includes the integers 10 and -2.

a. the scuba diver ascends 13m ______________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

_______________________________________________________________________

Curriculum Link: Investigate everyday situations that use integers. Locate and represent these numbers on a number line (ACMNA124)

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Equivalent Fractions Match 1 Create dominoes by cutting along the dotted lines only on this page and page 15. Pair up or get into groups of three. Shuffle, then divide the dominoes between you equally. Take turns to match the end of each domino with its equivalent fraction (written or visual). If you don’t have a matching fraction equivalent, say “pass”. Continue until you reach the finish line.

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Curriculum Link: Make connections between equivalent fractions, decimals and percentages (ACMNA131)

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Equivalent Fractions Match 2 Cut out these dominoes and add them to the stack on page 14.

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Curriculum Link: Make connections between equivalent fractions, decimals and percentages (ACMNA131)

finish

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Fraction Problems 1 Read the word problems below which involve the addition and subtraction of fractions. Mark your answers on the number lines.

1. Mack drinks 3/8 of a carton of milk. How much milk is left?

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2. After an hour, Dad has assembled 1/5 of a bookcase. Mum takes over and another 3/5 of the bookcase is erected. How much of the bookcase is still unfinished?

1

3. Jade orders two pizzas to share with three friends. Jade eats 1/2 a pepperoni pizza, Cassie eats 1/4 of a marinara and a 1/4 of the pepperoni. Toby eats 3/4 of the marinara. There is no pizza left over. How much pizza did Lucinda eat?

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4. Sian bakes a batch of 32 chocolate chip cookies. She can’t resist eating 8 of them.

What fraction of the cookies are left?

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5. The class is preparing a display for Diwali out of sheets of coloured cardboard. One group uses 3/4 of a green sheet of cardboard, another group uses 1 1/2 sheets of red cardboard and a third group cuts up 3/4 of a sheet of gold cardboard. How much cardboard does the class use altogether?

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Curriculum Link: Compare fractions with related denominators and locate and represent them on a number line (ACMNA125)

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Fraction Problems 2 Solve the word problems below about fractions of whole numbers. Show your working out in the spaces provided.

1. Bella and James hold a bake sale to raise money for the local animal shelter. They raise $125. Bella and James keep 1/5 of the money to pay Mum for her cooking ingredients.

How much do they donate to the animal shelter?

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2. Two boxes containing 48 books each, arrive in the library. By morning break the librarian has placed 3/8 of the books on the shelves. How many books are still in the boxes?

3. Henry buys 40 litres of bright green paint on sale. If it takes 5 litres to paint one room, how many rooms in the house can he paint bright green?

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4. Anna has 1 3/4 hours to do her homework, practise her drums and play with her cat.

If she wants to divide her time equally among the three activities, how much time will she spend on each?

5. Mr. Picky only chooses perfect cherries to make his pies. Out of 500 cherries, he rejects 3/10. How many cherries do not end up in Mr. Picky’s pies?

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o c . che e r o tHe needs 240g of butter, but 6. Kieren wants to make a surprise r birthday cakee forr his Dad. s sup he can only find 2/3 of that amount in the fridge. How much butter does Kieren have?

7. Chloe receives a new camera for Christmas. On Boxing Day she takes 28 photos, but only 3/4 of them are in focus. How many photos are too fuzzy to print?

Curriculum Link: Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies (ACMNA127)

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Adding And Subtracting Decimals Before you add or subtract these sums, round the decimals to estimate a reasonable answer.

1. What is the difference in weight between the two envelopes?

0.229g

0.25g

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25.85mm 11.6mm 11.6mm 3. By how many points did gymnast A win the competition?

Scoreboard

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2. Add the diameters of the three buttons.

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9.25 points

gymnast B 8.537

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Front nine holes 3,307.25m Back nine holes 2,866.186m

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4. What is the total length of this 18-hole golf course?

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5. If someone pumps 4740.96L out of a full rainwater tank to water the veggie garden, how much water is left in the tank?

9000L

6. How many grams of cheese must be added, to balance the weight of the bacon?

230.56g 18

313.88g

Curriculum Link: Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (ACMNA128)

Multiplying And Dividing Decimals Solve the supermarket problems below by multiplying and dividing decimals using whole numbers. Do your working out in the spaces provided.

1. Each pallet weighs 18.15kg. How much do 4 pallets weigh?

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2. A medium tomato has 9.25mg of sodium (salt). How much sodium would 6 tomatoes contain?

3. A watermelon weighs 3.58kg. If it were cut into 8 slices, how many grams would each slice weigh?

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4. A uni student works part-time as a shelf stacker in a supermarket. She earns $18.86 an hour. How much does she earn after working 7 hours?

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5. A chocolate cake weighing 750g has 2,805 calories. If the cake is cut into 12 equal slices, how many calories would each slice have?

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6. An employee has beenc wrapping gifts. She cuts 15 pieces ofe ribbon with a length of h r 20.68cm each. How much ribbon has she cut altogether? er o st s uper 7. Someone mops the floor in the seafood section and uses 6 buckets of soapy water. If each bucket holds 9.605L, how much water has been used?

Curriculum Link: Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without digital technologies (ACMNA129)

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The Powers Of 10 Step right up! See if you can burst all the balloons at the sideshow. All you have to do is write number sentences that multiply or divide by powers of 10 (10, 100 and 1000). If they match the numbers on the balloons, you’re a winner. Look at this example: 61.4 = 614 ÷ 10 or 0.614 x 100

Step Right Up

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Curriculum Link: Multiply and divide decimals by powers of 10 (ACMNA130)

Jigsaw Number Values Complete the equivalent missing number values in the jigsaw pieces below.

These will help you to answer the word problems on page 22. The first one has been done for you.

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Curriculum Link: Make connections between equivalent fractions, decimals and percentages (ACMNA131)

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More Or Less Problems Solve the word problems below that include fractions, decimals and percentages. Do your written work in the spaces provided.

1. Marie has 25% of $500 and Gregory has 2/5 of $550. Who has more?

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2. After the end-of-year class party, 2 out of 8 children have tummy ache. What percentage of children feel unwell?

3. Which is bigger: 0.125 or 15%?

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4. Our maths test had 60 questions. I got 4/5 of the questions correct. You got 85% correct. Who got more questions correct?

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5. It’s sale time at the department store. Shade in the price tag that gives the better discount for A and B.

A.

3 5 off

8 off

80%

6. David’s drink bottle is 0.5 full and contains 360ml of water. Diana’s drink bottle is 60% full and contains 390ml. Whose water bottle has the greater capacity?

22

Curriculum Link: Make connections between equivalent fractions, decimals and percentages (ACMNA131)

Super Saver Shopper How much have I saved today?

1.

Penny Crown is a clever shopper. She finds all the best discounts. Calculate how much money Penny has saved on her big shopping spree today. Use the back of this sheet to do your working out.

2.

3.

or e st Bo r $14.99 e p ok u S

4.

5.

6.

$22.75

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$96.00

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7.

$38.50

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m . u

$250

o c . che e r o r st super $59.90 8.

9.

$450

Total cost of full price items: $997.24

$23.10

Penny saved:

Curriculum Link: Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (ACMNA132)

23

Bullseye!

Help the three Williams write number sentences that are equivalent to the target numbers (written inside the apples). Write the missing numbers or operations in the number sentences and help them score some bullseyes.

1.

14

3.

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23

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2.

(12 - ___ ) x 11 + 3 = ___

___ - 10 + (9 ÷ 3) = ___

___ ÷ 4 + 32 -18 = ___

4.

5.

6.

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45 ___ (5 x 3) + 12 =

7.

7

c 8.

36 – (2 x ___) ÷ 2 =

24

(60 ___ 5) + 25 x 3 =

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•f orr evi ew pur posesonl y•

52 ÷ (16 ___ 3) + 8 =

her 228 st r o super

42 ÷ 7 x (___ x 2) =

Curriculum Link: Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123)

o

c .

9.e

29

6 + (2 ___ 16) – 9 =

Sequences Write the missing whole numbers, fractions and decimals to complete the sequences below. Describe the pattern in each sequence.

1.

1 12

2 12

3 12

4 12

5 12

Describe the pattern:________________________________________________________

4.25

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2.

3.

392

380

368

356

344

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Describe the pattern:________________________________________________________

Describe the pattern:________________________________________________________

4.

6 14

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0.15

0.19

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0.23

0.27

0.31

m . u

Describe the pattern:________________________________________________________

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Describe the pattern:________________________________________________________

6.

9 13

9

Describe the pattern:________________________________________________________

7.

225

196

169

144

121

Describe the pattern:________________________________________________________

Extra! Create a sequence for a peer to solve on the back of this sheet.

Curriculum Link: Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence (ACMNA133)

25

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Section 2: r o e t s Bo r e p ok u S Measurement and Geometry

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Metric Conversions Convert the measurements of length, mass and capacity below to the unit indicated. The first one has been done as an example.

1. A basketball player is 213cm tall.

2.13 ______________m

2. The Sydney Harbour Bridge is 1.149km long.

______________m

3. An adult leopard seal can weigh 0.5 tonnes.

_____________ kg

or eBo st r e p ok u S

______________ L

5. An elephant’s tusks can grow up to 3500mm.

_____________ cm

6. Someone squirted 0.016L of tomato sauce on their hotdog.

_____________ ml

7. An athlete threw a shotput 2319cm.

______________m

8. A meteorite weighing 4.074kg was discovered in the park.

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4. The capacity of an Olympic swimming pool is 2.5Ml.

______________ g

9. The Burj Khalifa building in Dubai is 0.829km high.

______________m

10. On average, a cow produces 30280ml of milk a day.

______________ L

11. The length of an amazing person’s foot measures 0.426m.

_____________ cm

_____________ kg © ReadyEdPubl i cat i on s 13. The capacity of the water reservoir is 45,000,000L. _____________ Ml •f orr evi ew pur poseson l y• 14. The diameter of a strand of human hair is about 0.018cm. ____________ mm 12. Scientists think the dinosaur, Sibirosaurus, weighed 50 tonnes.

_______________t

16. The length of a door is 2345mm.

______________m

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15. A car weighs 1086.45kg.

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4.074 kg

1086.45 kg

50 tonnes

0.829 km

Curriculum Link: Convert between common metric units of length, mass and capacity (ACMMG136)

213 cm 27

Cubby House Conversions Study the builder's drawing below. He has jotted down the materials needed (including dimensions) to build a cubby house. Convert the units of measurement to the units indicated in the boxes. An example has been done for you.

roofline 287cm

baton screws 1.25cm

roof nails 28mm

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Teac he r

2.8cm m r o e t s Bo r e mm p ok u S slate tiles

290mm x 445mm

boards 240cm x 120cm

cm

mm

© ReadyEdPubl i cat i ons lattice baton 4.2cm x 0.8cm • f o r r e v i e w p u r p o s e s o n l y• m

support pole 112cm

mm

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Questions

hardwood timber 12.7cm x 12.7cm

m . u

w ww

width of verandah 1.94m

pickets 1.2 m

o c . che e r o r st super cm

cm

mm

1. What would be the total length of support poles needed? ________ m 2. What is the total length of six pickets?

________ cm

3. How many baton screws would fit end to end on a metre rule? ________ 4. Calculate the area of: i. one slate tile ___ (cm2) ii. five slate tiles ___ (cm2)

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Curriculum Link: Connect decimal representations to the metric system (ACMMG135)

Fish Tank Volumes Calculate (with or without digital technology) the volume of water in litres in the fish tanks below (volume = l x h x w). Note that the water line is 5cm below the rim of the tank (height = 5cm). Remember: 1000 cm3 = 1 litre.

2.

25

40

or eBo st r e p ok u S 45

25

1.

65

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Teac he r

40

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80

55

4.

45

w ww

60

3.

55

m . u

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Curriculum Link: Connect volume and capacity and their units of measurement (ACMMG138)

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Fish Tank Volumes (extension) Use the information and your answers to the task on page 29 to answer the following questions.

1. You have calculated the volume of water in each tank on page 29. Now calculate the capacity of each tank. Do your written work in the space provided.

Fish tank (a)

Fish tank (b)

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Fish tank (d)

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Fish tank (c)

2. Water conditioner is added to aquariums to keep the fish healthy. The dose is 0.25ml for every 20 litres. How many ml of water conditioner should be added to the fish tanks below? (i)

(ii)

(iii)

(iv)

180 l260 lc 330 l © Rea dy EdPu bl i at i ons •f orr evi ew pur posesonl y• How many trips would it take to fill Tank O using each water container?

3.

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1000 900 800 700 600 500 400 300 200 100 50

m . u

60 l

ml

= ______ trips

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A. 500 ml

tank O

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= ______ trips B. 8.5 L

= ______ trips

Volume = 198 Litres

c. 15 L

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Curriculum Link: Connect volume and capacity and their units of measurement (ACMMG138)

Comparing Lengths And Areas Study the floor plan for each child’s bedroom below.

Bronte 2 m

3m

3 m

Kyle

1.5 m

2 m

6m

1.5 m

6.5 m

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2.5 m

1.5 m

3m

4.5 m

© Rea2dmyEdPub l i cat i ons 2m •f orr evi ew pur posesonl y1.5 •m

4m

1 m

4.5 m

Cullen

3.5 m

2.5 m

Lin

5 m

3m

5.5 m

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Teac he r

1.7 m

or eBo st r e p ok u S 3 m

5 m

2.5 m

4.7 m

1. Explain how you are going to calculate the areas of these compound shapes.

. te o _ _____________________________________________________________________ c . che e r _ _____________________________________________________________________ o t r s s r u e p _ _____________________________________________________________________

2. Calculate the areas of the bedrooms and record your answers in m2 below.

Kyle:

Bronte:

Lin:

Cullen:

Curriculum Link: Solve problems involving the comparison of lengths and areas using appropriate units (ACMMG137)

31

Don’t Miss The Boat!

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Teac he r

You have planned a day out with friends on a public holiday to visit the Paroo Park Zoo. To get there, you have to catch a ferry. Study the timetable below.

© ReadyEdPubl i cat i ons f o rr ev i ewPicnic pu r p oPitt’s sePier? so nl y• 2. How long• is the ferry ride between Point and _____________________

1. What time does the first ferry to the Zoo leave from Main Quay?___________________

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3. You plan to catch the 9.45 ferry from Main Quay. If you want to stop off at Wattle Bay for a quick dip at the beach, at what time would you be able catch the next ferry to the Zoo? ________________________________________________________________________

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4. How long is the return ferry ride to Main Quay on the all stops ferry?_ ______________

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6. Your Dad is meeting you at 17.15 at Pitt’s Pier to drive you home.

What is the latest ferry c e h r you should catch from the Zoo be there in time? o etor t s s r u e p ________________________________________________________________________ 5. How long is the return ferry ride to Main Quay on the express ferry?________________

7. It’s a 20 minute brisk walk from the Zoo’s exit to the ferry terminal. What time would you recommend that a person leaves the Zoo to catch the last ferry of the day to Main Quay? Explain your answer.

________________________________________________________________________

________________________________________________________________________

________________________________________________________________________

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Curriculum Link: Interpret and use timetables (ACMMG139)

Angles in Action Look at these images of athletes in action. Observe the angles that their bodies form.

E

C A

or eBo st r e p ok u S B

F

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Teac he r

D

G

H

© ReadyEdPubl i cat i ons •f orr evi e w pur poseso nl y• right angle 90º acute (< 90º) obtuse (>90º)

w ww

2. Estimate the size of the angles.

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1. Classify the types of angles in the images. Complete the table with the lettered angles.

o c . che e r o r st super 3. Measure the angles with a protractor. How close were your estimates? a.

b.

c.

d.

e.

f.

g.

h.

a.

b.

c.

d.

e.

f.

g.

h.

Extra! Draw a stick figure athlete in action on the back of this sheet. Mark some angles on your athlete. Ask a peer to measure the size of the angles.

Curriculum Link: Investigate, with and without digital technologies, angles on a straight line, angles at a point and vertically opposite angles. Use results to find unknown angles (ACMMG141) Elaboration: Identifying the size of a right angle as 90° and defining acute, obtuse, straight and reflex angles.

33

Looking For X Finding x is a breeze if you follow these clues: zz Angles on a straight line equal 180º. zz Angles in a triangle equal 180º. zz When two lines intersect, they form two pairs of opposite angles that are congruent. zz When a line intersects two parallel lines, the interior angles are congruent.

Teac he r x

60˚

x

22˚

© ReadyEdP ubl i cat i ons 4.

•f orr evi ew pur poses60˚ onl y• 65˚

x

w ww x

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x

m . u

3.

5.

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or eBo st r e pof these? ok What does x equal in each u S 1.

2.

6.

o c . che e x r o r st super 110˚

52˚

7.

8.

110

x

˚ x

34

40˚

Curriculum Link: Investigate, with and without digital technologies, angles on a straight line, angles at a point and vertically opposite angles. Use results to find unknown angles (ACMMG141)

35˚

Transformations Identify the transformation of shape A in each grid below. For example, reflection rotation to the left.

a.

b.

y C

y

B

A

C

or eBo st r e p ok u S x

B

c.

D

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Teac he r

A

d.

y

x

y

D

© ReadyEdPubl i cat i ons •f orr evi e ur posesonl y•x xw p

C

A

C

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A

e.

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B

B

m . u

B

o c . y yc e her r o st super D f.

C

C

x A

B

x

A

Curriculum Link: Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142)

35

Design A Logo Designs for eye-catching logos are often created by transforming shapes through translation, rotation and reflection. Logos and their choice of shapes can symbolise what companies, sports teams and organisations represent.

1. Study the logo below with a partner and make notes next to the logo about: the symbols in the logo

who or what the logo might represent

the effectiveness of the logo

or eBo st r e p ok u S midcoast minnows

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use of transformation in the logo

2. In the space below, create a logo that could be connected to your school or local community. Remember: keep it simple and use striking colours.

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m . u

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Curriculum Link: Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142) Elaboration: Designing a school or brand logo using transformation of one or more shapes.

Know Your Cartesian Plane Complete the questions below based on this Cartesian plane.



axis)

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 (9,-4)



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or eBo st r e p oaxis) u ( k S  (-5, 5)

(

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

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2. Label the plane’s quadrants in the boxes.

3. What does the arrow (

) indicate at the intersection of the x- and y-axis?

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1. Label the x- and y-axis.

________________________________________________________________________

o c . ________________________________________________________________________ che e r o t r 5. Write the coordinates for the positions ofp thee icons on the plane. s su r 4. How do you order and write the coordinates of a point on the plane?



________________

 _________________



________________

 _________________

6. Plot a point on the plane in Quadrant 1 and write its coordinates.__________________ 7. What will this point’s mirror coordinates be in Quadrant 4?_ ______________________ 8. What do the arrows mean on the x- and y-axis?

________________________________________________________________________ Curriculum Link: Introduce the Cartesian coordinate system using all four quadrants (ACMMG143)

37

Fast Delivery (Student A) You are going to call out coordinates to your partner so he/she can deliver pizzas to the houses in the correct order. If you take too long, the pizza is free!

or yeBo st r e p ok u S

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Teac he r

zz Before you send your partner out to deliver pizzas, make sure you can identify the coordinates of the houses on the plane below (write them at the bottom of the page). Number the order (1 – 12) of the deliveries, too, on the plane next to the houses. (Don't show your partner your sheet - they have their own!)

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

o c . che e r o r st super

Coordinates a.

b.

c.

d.

e.

f.

g.

h.

i.

j.

k.

l.

38

Curriculum Link: Introduce the Cartesian coordinate system using all four quadrants (ACMMG143)

Fast Delivery (Student B) You are going to call out coordinates to your partner so he/she can deliver pizzas to the houses in the correct order. If you take too long, the pizza is free!

or yeBo st r e p ok u S

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Teac he r

zz Before you send your partner out to deliver pizzas, make sure you can identify the coordinates of the houses on the plane below (write them at the bottom of the page). Number the order (1 – 12) of the deliveries, too, on the plane next to the houses. (Don't show your partner your sheet - they have their own!)

w ww

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m . u

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

o c . che e r o r st super

Coordinates a.

b.

c.

d.

e.

f.

g.

h.

i.

j.

k.

l.

Curriculum Link: Introduce the Cartesian coordinate system using all four quadrants (ACMMG143)

39

Fast Delivery (Response Sheet) Your partner is going to call out 12 coordinates on this Cartesian plane. Your job is to find the positions as quickly as you can and make 12 pizza deliveries.

y r o t s r eBo e p ok u S

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Teac he r

zz Mark the position of the house with a cross (x) on the grid. Be as accurate as you can. After you have completed your deliveries, your partner will assess your pizza delivery skills.

x

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12/12 Employee of the Month

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Curriculum Link: Introduce the Cartesian coordinate system using all four quadrants (ACMMG143)

6 or less get another job!

Prisms Around Us Prisms are everywhere - from the pyramids of Egypt and China, to packets on supermarket shelves. zz Match the list of prisms/pyramids (below) with the images, then complete the missing information about the features of each one.

List of prisms/pyramids hexagonal prism triangular prism octagonal prism pentagonal prism square-based pyramid cuboid square prism hexagonal pyramid

vertices:

type:___________________

faces:

type:___________________

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6

edges:

type:___________________

f.

faces:

faces:

vertices:

12

type:___________________

faces:

vertices: type:___________________

8

edges:

o c . cedges: edges: e her9 r o st super h. vertices:

type:___________________

g.

d.

edges:

faces: © ReadyEdPubl i cat i ons vertices: vertices: •f orr e vi ew pur posesonl y •

type:___________________

e.

edges:

7

vertices:

m . u

c.

8

faces:

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a.

or eBo st r e p ok b. u S faces:

edges:

faces:

16

vertices: type:___________________

edges:

8

Extra! Find a net of one of these 3D prisms or pyramids and construct it. To download a variety of nets online go to: www.korthalsaltes.com/ Curriculum Link: Construct simple prisms and pyramids (ACMMG140)

41

Ancient 3D Shape Constructions Do your own research to discover remarkable constructions of the ancient world that used 3D shapes. Below are some examples.

or eBo st r e p ok u S

great wall of china

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Teac he r

Mohenjo Daro, PAKISTAN

My Research On An Ancient Construction Name:

Location:

Date:

© ReadyEdPubl i cat i ons Shape and ofi purpose: •dimensions f orr ev ew Construction’s pur pose sonl y•

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the construction:

. t e o Building materials: c . che e r o r st super Sketch or image:

42

Other interesting information:

Curriculum Link: Construct simple prisms and pyramids (ACMMG140) Elaboration: Considering the history and significance of pyramids from a range of cultural perspectives including those structures found in China, Korea and Indonesia.

Build A 3D Shape House 1

or eBo st r e p ok u S

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Teac he r

zz In small groups, try your hand at building a model of this house out of 3D shapes. Study the floor plan below first, then follow the instructions on the next page.

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Curriculum Link: Construct simple prisms and pyramids (ACMMG140)

43

Build A 3D Shape House 2 Decide how to divide the floor plan on page 43 into 3D modules using prisms in order to build your model.

1. How will the group divide the house into modules? Mark the divisions with a ruler in a different colour on the floor plan on page 43.

2. This floor plan has been drawn to scale. Mark the dimensions of your modules on the floor plan to help you visualise the size of the nets you need to make.

or eBo st r e p ok u S

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Teac he r

3. Sketch and label the 3D prisms and pyramids that you need to construct your modules.

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

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4. Which 3D shape/s will you need to build the roof of the house? Remember that the roof line will extend beyond the walls of the house. Sketch your roof.

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o c .

5. 3D nets we need: Materials we need: che e r o r st super _ _______________________________ _ _______________________________ _ _______________________________

_ _______________________________

_ _______________________________

_ _______________________________

_ _______________________________

_ _______________________________

_ _______________________________

_ _______________________________

_ _______________________________

_ _______________________________

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Curriculum Link: Construct simple prisms and pyramids (ACMMG140)

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

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Interpreting Graphs (Student A) zz Your partner (Student B) is going to ask you questions about the graph below and will record your answers. You can peer mark your answers later.

Year 6 conducted a class survey to find out the least popular jobs children were asked to do to earn pocket money. Look at the results.

Teac he r

looking after little kids

10

other

6

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or eBo t s r e entertaining guests 17o p u k S tidying bedroom 21

© ReadyEdPubl i cat i ons •tof o r evi wp ur p osesonl y• Questions askr Student Be about his/her graph.

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1. How many students took part in this survey?

2. How many students prefer action films?

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o c . che e 4. How many students prefer comedy and action films altogether? r o r st super 3. How many more students prefer comedy films to scary films?

5. What fraction of students prefer sci-fi and scary films?

well done!

46

Curriculum Link: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)

Interpreting Graphs (Student B) zz Your partner (Student A) is going to ask you questions about the graph below and will record your answers. You can peer mark your answers later.

Year 6 were polled to find out the types of films they liked to see. Look at the results in this pictogram.

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Teac he r

Favourite Types of Films or eBo st r   e p o u k  S             = 2 people     action sci-fi comedy scary © ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y•

Questions to ask Student A about his/her graph.

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1. What would be an appropriate title for your graph? __________________________________________________________________

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2. How many students took part in the survey?

o c .

3. How many studentsc don’t like entertaining guests? e her r o st super 4. How many students don’t like tidying or babysitting?

5. What fraction of students chose other jobs they didn’t like?

well done!

Curriculum Link: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)

47

Interpreting Line Graphs zz Two cyclists were training for an extreme ten hour road race. Study the graph below that shows the distance covered in 10 hours by Cyclist 1.

Distance travelled in training session

200

Legend

180 160

kilometres

120 100

Teac he r

80 60 40 20

0

1

2

3

4

5

6

7

8

9

10

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or eBo st r e p ok u S

140

Cyclist 1:

© Readhours yEdPubl i cat i ons 1. Complete• thisf table Cyclist 1’sw training statistics using above. orforr e vi e pu r po sethe sgraph onl y• Distance (km)

16

2

3

4

5

6

7

8

9

10

m . u

1

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Time (hours)

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o c . che e r o ttable shows Cyclist 2’s statistics. r s s 4. Cyclist 2 took a route that was more mountainous.

This r u e p Plot Cyclist 2’s data using a different coloured pencil on the graph above. Add to the

2. How far did Cyclist 1 ride in 10 hours?_________________________________________

3. What distance did Cyclist 1 cover during the 4th hour?____________________________

legend.

Time (hours)

1

2

3

4

5

6

7

8

9

10

Distance (km)

10

25

34

50

62

75

88

105

124

140

5. How much further did Cyclist 1 ride than Cyclist 2? ______________________________ 48

Curriculum Link: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)

Tall Story Column Graphs 1 A study has shown that the average height of men and women has steadily increased globally over the last hundred years. zz Look at the two double-column graphs below that compare changes in height for men and women in selected countries and complete the questions and task on page 50.

or eBo st r e p ok u S

Graph 1 : Mean height change since 1914 - Women

200 160

ew i ev Pr

cm Tea ch er

180 140

Legend

120

1914

100 80

2014

© ReadyEdPubl i cat i ons 40 •f orr evi ew pur posesonl y• 20 0

Australia

w ww 200 180 160 140

cm

120

Kenya

South Korea

m . u

60

Graph 2 : Mean height change since 1914 - Men

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o c . che e r o r Legend st super

100

1914

80

2014

60 40 20 0

Australia

Kenya

South Korea

Curriculum Link: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)

49

Tall Story Column Graphs 2 zz Use the graphs on page 49 to answer these questions.

1. According to the graph, what was the mean tallest height in 1914: a. for women? __________

b. for men?

__________

2. According to the graph, what was the mean shortest height in 2014: a. for women? __________

b. for men?

__________

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3. How tall on average are Kenyan men today?_ _________________________________ 4. How much taller on average are Australian men than Korean men? _ ______________

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5. What is the mean increase in height for Australian women since 1914?_____________

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6. What is the increase in height for Kenyan men since 1914?_______________________ 7. Who has had the highest mean increase in height since 1914?____________________ 8. Who has had the lowest mean increase since 1914?_ ___________________________

9. Study these statistics from the same height study.

Mean height of women © R e a d y E dPubl i c at i ons Country Year - 1914 Year - 2014 •f orr evi ew r poses nl y• Latvia 156 p cmu 170o cm Brazil

150 cm

161 cm

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In the space below, construct your own double column graph to represent the information in the table above. Don’t forget to add a title and legend.

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cm

120 100 80 60 40 20 0

50

Australia

Brazil

Latvia

Curriculum Link: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)

Legend

What’s Up With These Graphs?

Presenting data in graphs can make a point more convincing without taking up too much space. However, some graphs you might find online can be very misleading. This can be accidental or intentional. zz Study the graphs below. Identify in the space provided on the right how these graphs could be misleading.

Graph 1

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Earthquakes Recorded In Wattle Flat 2000 - 2010 4

_ _______________________________ _ _______________________________

2

_ _______________________________

0

_ _______________________________

2000

2001

2002

2005

2006

2009

_ _______________________________

_ _______________________________

84

_ _______________________________

82

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2010

© ReadyEdP bl i cat i ons _u _______________________________ Life Expectancy Of Australian _p _______________________________ •f or r eInv i ew pur osesonl y• Men And Women 2013

Graph 2

80

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78

_ _______________________________

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years

_ _______________________________

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_ _______________________________

76 0

Graph 3

. t Mene

o c . che e r o r _ _______________________________ st supe r Women

_ _______________________________

_ _______________________________ _ _______________________________ _ _______________________________ _ _______________________________ _ _______________________________ _ _______________________________

Curriculum Link: Interpret secondary data presented in digital media and elsewhere (ACMSP148) Elaboration: Identifying potentially misleading data representations in the media, such as graphs with broken axes or non-linear scales, graphics not drawn to scale, data not related to the population about which the claims are made, and pie charts in which the whole pie does not represent the entire population about which the claims are made.

51

Games Of Chance 1. Match the games of chance with their rules for playing. If you know, write the name of the game of chance under each image.

Chance Game 1

Chance Game 2 62

7

99

23

*

*

40

*

4

5

66

*

11

26

13

*

21

12

84

33

77

29

*

1

62

5

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Chance Game 3

99

11

Chance Game 4

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34

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a. Players have 26 cards each placed face down. Both top cards are turned over. Whoever has the higher card, wins both cards and adds them (face down) to the bottom of his/ her pile. The goal is to win all the cards. b. Players have a card with numbers on it. A caller announces a number and if the player has that number, he/she marks it off the card. When someone’s numbers are all called, he/she is declared the winner.

o c . c. A player decides the winner is going to be “odds”. On the count of three, players show c e h r a number of fingers on one hand.

If the sum of fingers is an odd number, then the e o t r s s r u pe player who called “odds” has won. d. On the count of three, players make a gesture with their fists. Rock breaks scissors, scissors cut paper, and paper covers rock. Players then decide who has won.

2. Do all the players in the games above have an equal chance of winning?

Explain your answer. __________________________________________________________________ __________________________________________________________________ 52

Curriculum Link: Describe probabilities using fractions, decimals and percentages (ACMSP144) Elaboration: Investigating games of chance popular in different cultures and evaluating the relative benefits to the organisers and participants.

It’s Likely That… zz Discuss the statements on these cards in a small group. Your task is to come to a group decision about whether you agree or disagree with the statements. Be ready to stand by your decisions when you compare your answers with another group.

Statement 1

Statement 2

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It’s impossible to pick an ace first time from a deck of cards.

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You have a fair chance of winning a game if no-one cheats.

Statement 3

Statement 4

It always rains just after the car’s been washed.

Nothing is ever 100% certain.

Statement 5

Statement 6

The more tickets you buy in a lottery, the greater the chance you have of winning.

There’s always someone in our year group with the same birthday.

Statement 7

Statement 8

Someone will smile at me today.

It’s better to choose heads when you’re flipping a coin.

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Curriculum Link: Describe probabilities using fractions, decimals and percentages (ACMSP144)

53

True Or False (Chance Problems) zz Decide whether the probability of an event occurring in these chance problems is true or false. Do your written work in the space provided.

Correct false answers.

1.

cricket club is raising money for 2. Our new equipment. It is holding a raffle.

The prize is a dinner for two. The club has sold 500 tickets. Mum has bought 15 tickets. Her probability of winning a night out is 0.05.

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qTRUE

qFALSE

C.046

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Ethan forgot to do his homework.

Students are being called on randomly to give answers. If there are 30 students in the class, and 10 students have already given an answer, the chance of Ethan being asked next is 5%.

qTRUE

qFALSE

A bag contains 17 green jubes, 18 balls numbered from 1 4.

3. Coloured red jubes and 15 yellow jubes. The to 50 are put into a bingo pot. The probability of picking out a yellow probability that the first ball that © R e a d y E d P u bl i cat i ons comes out is a multiple of 4 is 25%. jube is 3/5.

•f orr evi ew pur posesonl y•

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12 45

qTRUE qFALSE . te qFALSE oone card from c If you roll two dice once, the chance Kiara is going to pick .

6. a standardr 5. of getting an even number che eof 52 cards. The on both deck o r st that the card Kiara picks super dice is 1/4 . probability will be a red ace card is 0.21.

3

qTRUE

qTRUE 54

qFALSE

Curriculum Link: Describe probabilities using fractions, decimals and percentages (ACMSP144)

qTRUE

qFALSE

How Lucky Can You Be? Discover how lucky the following people could be by solving these probability word problems. Show your working out in the space provided.

1. Ellie has a chance of winning a car on a quiz show. All she has to do is avoid choosing a black ball from a bag containing 5 white balls and 10 black balls. What is the chance expressed as a fraction of Ellie winning the car?

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2. Two brothers flip a 10c coin each to decide who's going to wash the dog. Bailey calls HEAD-HEAD and his brother calls HEAD-TAIL. What is Bailey's chance (expressed as a percentage) of not washing the dog?

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3. Mr. Curry has 24 cards with 4 different symbols on them. He shuffles and deals the cards to place students in equal groups of 6 for ball games. What’s the chance (expressed as a decimal) that the first student receives a card with a star on it?

4. There are fifty numbers marked on a fortune wheel at a fete. If the wheel stops at number 1, 25 or 50, the player wins a giant plush toy. What’s the chance (expressed as a percentage) of winning a toy when the wheel is spun?

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5. Evan and Seth are going to pick a card each from a deck of 52 cards to decide who gets to ride the BMX bike for the afternoon. Whoever picks the highest card gets the bike. Seth goes first. What’s the chance (as a fraction) of Seth picking an ace or a king?

Curriculum Link: Describe probabilities using fractions, decimals and percentages (ACMSP144)

55

Holiday Spin 1 sur

f

far m

F

CAM

SUR

P

ing

faR M

ski

The 8 members of the Barney family have been arguing for weeks about how to spend their next holiday. Mrs. Barney decides that a spinner with the five holiday preferences on it will make the decision for them. Each person’s choice is represented on the spinner.

or eBo st r e p ok u S farm stay surfing boating skiing

BOAT

FAR

M

camping

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1. What is the probability of the spinner landing on each holiday activity after one spin?

Complete the table.

fraction %

decimal

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

2. Mrs. Barney’s preference of skiing ends up being the winner. However, the rest of the family demand that to be fair, it should be the best of 20 spins and the activity with the highest frequency should be the undisputed choice.

Predict the outcome. Explain your prediction.

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o c . e Outcomes Of 20c Spins her r o st su _p ____________________________________ er

3. The bar graph below represents the outcomes of 20 spins.

7

a. Is the holiday decided on after 20 spins?

Why/why not?

6 4

56

____________________________________

_

____________________________________

b. Do the scores for each activity fit your prediction?

2 0

_

skiing

farm stay

surfing

boating

camping

_

____________________________________

_

____________________________________

_

____________________________________

Curriculum Link: Describe probabilities using fractions, decimals and percentages (ACMSP144)

Holiday Spin 2 The Barney’s next holiday is finally decided after more spins. Study the graph below.

skiing

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surfing

boating

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45 40 35 30 25 20 15 10 5 0

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frequency

HOLIDAY CHOICE RESULTS

camping

1. Can you determine how many spins were made by studying the frequency bar graph above? Explain your answer in the space below.

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

faR M

P

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CAM

BOAT

FAR

M

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F

__________________________________________________

SUR

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__________________________________________________

far m

ing

__________________________________________________

f

ski

__________________________________________________

sur

o c . che e ________________________________________________________________________ r o r st super ________________________________________________________________________ 2. Were the outcomes after _______ spins different from the expectations in the probability table you completed in Question 1 on page 56?

3. Express the outcomes for the holiday activities as percentages. Use digital technology to help you. Round to two decimal places.

skiing

farm stay

surfing

boating

Curriculum Link: Describe probabilities using fractions, decimals and percentages (ACMSP144)

camping

57

Conduct A Probability Experiment 1 Grab a six-sided die and a partner. You are going to conduct an experiment to find out what the probability is of an event, where the outcome is a multiple of 3 (3, 6).

You already know the probability in theory of rolling a 3 or a 6.

The probability is: _____________________.

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Design your results

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1. Design your results table in the space below. A good sample to begin with is 10 rolls of the die. If you choose more, design your table on the back of the sheet. Conduct your experiment.

© ReadyEdPubl i cat i ons •f orr evi ew p uyour r pexpectation? osesonl y• 2. How did your sample results compare with

________________________________________________________________________

________________________________________________________________________

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3. Draw a frequency bar graph of your sample results here.

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Frequency Bar Graph …

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4. Discuss your results with other peers. Do the results vary?

58

Curriculum Link: Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145)

Conduct A Probability Experiment 2 You have observed from your experiment on page 58 that the frequency of rolling a multiple of 3 with a die is just an estimate of the true probability. The true probability of this event is 2/6 or 1/3 (33.33%).

1. Your task is to collect more sample results from other classmates to see how the frequency of 3s and 6s would trend towards the true probability of 1/3.

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Draw a results table to record at least 100 rolls of a die.

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2. Draw the frequency table of the larger sample’s results. Calculate the probability with the help of digital technology.

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Curriculum Link: Compare observed frequencies across experiments with expected frequencies (ACMSP146)

59

Answers p.8 1.33 is not prime 2.140 is not a square number 3.75 is not even 4.323 is not even 5.54 is not a multiple of 7

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p.13 1.a. 0 b. -20 c.14 d.10 e.0 f.-14 2.10 metres below sea level 3.a. -1 b.2 4. Sample answer: The paraglider released him/herself from the harness and dropped 10m into the sea. He/she narrowly missed a jellyfish drifting by 2 metres under the surface.

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p.9

6.3.56pm + 14 minutes = 4.10pm 7.28x9=252 surfboards p.12 1.214÷2, 107-10 /97 nuts 2. 956-127=829 pages read 3.182+171=353 km travelled 4.215+12=227/296-227=69 stragglers 5.47x3=141, 141-9=132, 132-5=127 children 6.3 cups x 2 = 80 muffins, 3 ÷ 2 = 1 ½ cups for another 20 muffins, 6 + 1 ½ = 7 ½ cups 7.76 – 4 = 72, 72 ÷ 3 = 24 children

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

p.11 1.5 complete rows of 15 chairs(75), 7 empty chairs 2.2232÷9=248 children 3.928+147=1075 letters 4.No. Needs 500g per day x 7 = 3.5kg 5.6735-2849=3886 fans

p.16 1.Mark 5/8 2.Mark 1/5 3.Mark 1/4 4.Mark 6/8 (3/4) 5.Mark 3

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p.14 & 15 Sequence solution with card ending in: 9/12 3/4, 6/10 3/5, whole octagon 5/5, 2/3 shaded triangle 8/12,5/6 10/12,4/5 8/10 shaded circle, 1/2 3/6,3/9 1/3,9/10 18/20,5/8 10/16, diamond with ¼ shaded 5/20, 3/8 6/16, pentagon with 2/5 shaded 6/15, 1/7 2/14, 1/2 4/8, 7/8 of octagon shaded 14/16, 2/4 6/12, 3/4 15/20, 11/12 22/24, 4/14 2/7, 6/9 2/3, 4/40 1/10, 2/12 shaded on dodecagon 1/6 shaded on hexagon FINISH

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p.10 1.T3=1+2+3 (6), T4=1+2+3+4 (10), T5=1+2+3+4+5 (15) 2.By adding another row of dots and counting all the dots, you can find the next number of the sequence.

3.T6=1+2+3+4+5+6 (21) 4.T6 21, T7 28, T8 36, T9 45, T10 55, T11 66 5.T15 120 (T12 - 66+12, T13 -78+13, T14 91+14, T15 - 105+15)

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Answers p.17 1.125÷5=25 Donation: $100 2.3/8 of 96 = 36 books, 60 books left in boxes 3.40÷5=8 rooms 4.Total=105m, 105÷3=35m each activity 5.3/10 of 500 = 150 cherries 6.2/3 of 240g = 160g 7.3/4 of 28=21, 28-21=7 fuzzy photos

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p.23 1.$24 2.$1.49 3.$4.55 4.$4.20 5.$19.25 6.$62.50 7.$29.95 8.$90 9.$2.31 $997.24 - $238.25 (savings) = $758.99

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p.19 1.72.60kg 2.55.50mg 3.447.5g 4.$132.02 5.233.75 calories 6.310.2cm 7.57.63L

p.24 1.(12-8) 2.21 3.36 4.÷ sign 5. x 6. – sign 7. 11 8. (19x2) 9. X sign

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p.18 1.0.021g 2.47.97mm 3..713 points 4.6,173.436m 5.4,259.04L 6.83.32g

p.22 1.Marie $125, Gregory $220 2.25% 3.15% 4.Me 48 correct, You 51 correct 5.A. 3/5 B.80% 6.David 720ml, Diana 624ml

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p.20 Sample answers: 2.7471÷10=747.1 3..4576x10=4.576 4.13÷100=0.13 5.5482÷10=548.2 6.9.31x1000=9310 7. 4.58x10=45.8 8.55÷1000=0.055 9.20.17x100=2017 10.0.132x10=1.32 11.639.2÷1000=0.6394 12.800÷100=8 13.3.456x10=34.56 14.1556÷10=155.6 15.77.6÷100=0.776 16. 919÷1000=0.919

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p.25 1.6 1/2, 7 1/2, 8 1/2 (+ 1) 2.3, 2.75, 2.5 (counting back by 0.25) 3.332, 320, 308 (counting back by 12) 4.8 3/4, 9 1/4, 9 3/4 (+ 1/2) 5.0.35, 0.39, 0.43 (+ 0.4) 6.7 2/3, 7 13 , 7, 7 (counting back by 13 ) 7.100, 81, 64 (counting back in square numbers)

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p.21 (fractions simplified) b.1/4 c..75, 75% d.0.10, 1/10, e.1/3, 33.3% f.0.8, 80% g.0.6, 3/5 h.1/20, 5% i.0.125, 12.5% j.0.4, 2/5

p.27 2.1,149m 3.500kg 4.2,500,000 L 5.350cm 6.16ml 7.23.19m 8.4074g

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Answers 9.829m 10. 30.28L 11.42.6cm 12.50,000kg 13. 45,000,000,000 ml 14.0.18mm 15.1.80645 (rounded 1.81t) 16.2.345m

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p.33 1.Right angle: E, H Acute: A,C,D,F,G Obtuse: B 2.Student’s estimate within 15º 3.A. 85º B. 110º C. 60º D. 85º E. 90º F. 45º G. 55º H. 90º

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p.28 boards: 2400x1200mm lattice baton: 42x8mm hardwood timber: 127x127mm pickets: 120cm width of verandah: 194cm support pole: 1.12m slate tiles: 29x44.5cm baton screws: 12.5mm roofline: 2.87m 1.Support poles 2.24m 2.Length of 6 pickets 720cm 3.80 screws 4.Area of 1 tile 1.209.5cm2 Area of 5 tiles 6,452.5cm2

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p.32 1.8.05am 2.15 minutes 3.12.42pm 4.62 minutes (1h 2m) 5.48 minutes 6.Departs zoo at approximately 16.51 7.The last ferry leaves the zoo at approximately 17.39 so to be on time, a person should leave about 17.05-17.10 taking into account the 20minute brisk walk. Students could explain their reasoning to peers.

p.34 1.120º 2.68º 3.65º 4.120º 5.38º 6.35º 7.70º 8.40º p.35 a.translation reflection over x-axis b.rotation reflection c. translation reflection translation d.rotation reflection reflection reflection over y-axis e.90 degree rotation reflection f.rotation reflection rotation

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p.29 1.20x25x40=22,500cm3 22.5L 2.104,000cm3 104L 3.198,000cm3 198L 4. 330,000cm3 330L

p.30 1. Calculations are based on the tanks’ volumes from p.29 and not being filled to the rim.

Tank A: 22.5L Tank B: 104L Tank C: 198L Tank D: 330L 2.i)0.75ml ii)2.25ml iii)3.25ml iv)4.125ml 3.A.396 trips B.23.3(24 trips) C.13.2(14 trips)

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p.31 1.Students will describe how they can divide composite shapes to calculate area by dividing the bedrooms into smaller rectangles. Ask students to mark divisions on floor plans.

Kyle: 22.5m2 Bronte: 20.1m2 Lin: 34.5m2 Cullen: 24.75 m2

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p.36 1. Notes could include: use of transformation and reflection of circles; the connection of minnows to small fish seen in logo; intersecting circles form fish shapes; connection to a sporting team; evaluation of effectiveness.

Answers p.37 1&2

Quadrant 2

Quadrant 1



(-5, 5)

p.42 Students’ own research.

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  (y axis)



Quadrant 4

3.The (0,0) coordinate 4. The x coordinate is written first, separated by a comma from the y coordinate. The coordinates are enclosed in brackets.

5.star (5,7); heart (-7, -2); cross (1,-9); diamond (0, -10) 6.Example: (8,2) 7. mirror coordinate in Quadrant 4 (8, -2) Ask students to peer correct coordinates.

8.The arrows indicate that the numbers are increasing in the direction shown on the x- and y-axes.

p.43 & 44 The floor plan acts as a springboard for students to improvise and change the dimensions as they see fit. It is a basic design made up of three cuboids and a triangular prism. The roof could be constructed from a larger triangular prism or one or two squarebased pyramids (extending to include the carport roof and the covered patio).

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(9,-4)

Quadrant 3

d.cuboid: faces 6, edges 12 e.triangular prism: faces 5, vertices 6 f.hexagonal prism: faces 8, edges 18 g.octagonal prism: faces 10, edges 24 h.square-based pyramid: faces 5, vertices 5

p. 46 Student A: 1.36 2.12 3.4 4.24 5.1/3

p.47 © ReadyEdPu bl i cat i ons Student B: 1.E.g. “Jobs children don’t like doing/Least liked jobs at home” 2.54 3.17 •f orr evi ew pur p o s e s o n l y • 4.31 5.1/9

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p.38 & 39 Student A: Students can order the coordinates in any order. Coordinates in Quadrant 1: (7,0), (4,2), (0,5), (8,6), (2,7); Quadrant 2: (-3,3), (-2,9); Quadrant 3: (-3,-1), (-9,-2), (-4, -7); Quadrant 4: (3, -2), (5, -9).

Student B: Quadrant 1: (2,2), (4,5), (0,7), (9,8); Quadrant 2: (-7,2), (-7,9), (0,-9); Quadrant 3: (-5,-1), (-8,-8); Quadrant 4: (9, -1), (6, -4), (1, -9)

p.48 1.Accept small variations in reading the graph’s data. Distance(km): 16, 30, 40, 55, 80, 98, 118, 138, 160, 180 2.180 km 3.About 25km 4. Teacher to check graphs 5.40km

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p.40 Students will peer mark coordinates. p.41 a.square prism: faces 6, edges 12 b.hexagonal pyramid: vertices 7, edges 12 c.pentagonal prism: vertices 10, edges 15

p. 50 Allow for small variations in answers 1.a.155cm b.165cm 2.a.140cm b.158cm 3.168cm 4.22cm 5.9cm 6.2cm 7.South Korean women 8.Kenyan men and women (about 2cm) 9.Teacher to check.

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Answers p.51 Graph 1: not in sequential years - does not show that earthquakes were not recorded during 5 years in the decade Graph 2: intervals on y-axis make the difference between men and women’s ages disproportionate Graph 3: pie chart does not add up to 100%

skiing

farm stay

surfing

boating

camping

fraction

1/8

3/8

1/4

1/8

1/8

%

12.5

37.5

25

12.5

12.5

decimal

0.125

0.375

0.25

0.125

0.125

2.It is more likely that the farm stay and surfing choices will be more frequent if the spins are carried out fairly.

3.a. No. Camping and farm stay are tied. b.Camping has appeared more frequently than surfing and other choices with equal probability.

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p.53 The discussion cards are designed for students to reflect on the probability of events occurring if the conditions are fair. There are opportunities to determine whether or not events are related or unrelated, to describe probability as a fraction, decimal or percentage and to discuss folkloric notions of likely outcomes e.g. it always rains after the car’s been washed or there’s always someone in my year with the same birthday (interestingly, the probability of a match in a class of 25 is 56.09%; in a year group of 72, it’s 99.01%).

p.57 1.You can determine the number of spins by adding the results for each holiday choice. The total is 120 spins.

2.After more spins, the frequency of the farm stay and surfing choices was closer to the true probability.

3. skiing 16.67%; farm stay 33.33%; surfing 25%; boating 14.17%; camping 10.83%

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p.52 Game 1: bingo (b) Game 2: odds or evens (c) Game 3: rock, paper, scissors (d) Game 4: war (a) 2. In theory, players have a fair chance of winning in all games. However, with “rock, paper, scissors” and “odds or evens,” body language and previous results could influence the games’ results.

p.56 1.

© ReadyEdPubl i cat i ons •f orr evi ew pp.58 ur pose nl y• The probability is s 2/6 o 1/3.

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p.54 1.True 2.False 0.003 3.False 0.24 (There are 12 multiples of 4 between 1 and 50 = 12/50) 4.False (15/50 = 3/10) 5.True 1/2 x 1/2 = 1/4 6.False (1/52 = 0.019) p.55 1.Chance of winning 5/15 = 1/3 2.There are four possible outcomes: HH, HT, TH, TT. The chance of getting out of washing the dog is 1/4 = 25% 3.4/24 = 1/6 = 0.166 4.3/50 = 6% 5.8/52 = 2/13 64

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1. Teacher could model first results table with class to help students with format for collecting data on larger sample.

2.Students’ results compared with true probability of 1/3.

3.Sample frequency bar graph could be generated on IWB for discussion. p.59 1. & 2.

The objective of these tasks is to illustrate that in a greater sample, the results will trend towards true probability of 1/3. This example frequency graph was generated with 100 die rolls. The frequency for rolling 3s and 6s was 37/100 = 37%.