Understanding Everyday Maths - Book 2

Title: Understanding Everyday Maths - Book 2

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© 2017 Ready-Ed Publications Printed in Australia Author: Carmel Iaria Illustrator: Alison Mutton

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

Copyright Notice

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3.

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

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Except as otherwise permitted by this blackline master licence or under the Act (for example, any fair dealing for the purposes of study, research, criticism or review) no part of this book may be reproduced, stored in a retrieval system, communicated or transmitted in any form or by any means without prior written permission. All inquiries should be made to the publisher at the address below.

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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: 978 186 397 177 5 2

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Any copying of this book by an educational institution or its staff outside of this blackline master licence may fall within the educational statutory licence under the Act.

Reproduction and Communication by others

Contents Teachers’ Notes Curriculum Links

Section 1: Number and Algebra

4 5-6

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

The Party - Part 1 (story) The Party - Part 1 (activity) The Party - Part 2 (story) The Party - Part 2 (activity) The Party - Part 3 (story) The Party - Part 3 (activity) The Party - Part 4 (story) The Party - Part 4 (activity) The Party - Part 5 (story) The Party - Part 5 (story) The Party - Part 5 (activity) The Party - Part 6 (story) The Party - Part 6 (activity) The Party - Part 7 (story) The Party - Part 7 (activity)

30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

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The Holiday - Part 1 (story) The Holiday - Part 1 (activity) The Holiday - Part 2 (story) The Holiday - Part 2 (activity) The Holiday - Part 3 (story) The Holiday - Part 3 (activity) The Holiday - Part 4 (story) The Holiday - Part 4 (activity) The Holiday - Part 5 (story) The Holiday - Part 5 (activity) The Holiday - Part 6 (story) The Holiday - Part 6 (activity) The Holiday - Part 7 (story) The Holiday - Part 7 (story) The Holiday - Part 7 (activity) The Holiday - Part 8 (story) The Holiday - Part 8 (activity) The Holiday - Part 9 (story) The Holiday - Part 9 (activity) The Holiday - Part 10 (story) The Holiday - Part 10 (activity)

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©Section Re dyE d Publ i cat ons 2:a Statistics and Probability 29i •f orr evi ew pur posesonl y•

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Section 3: Geometry and Measurement Christmas Elves - Part 1 (story) Christmas Elves - Part 1 (activity) Christmas Elves - Part 2 (story) Christmas Elves - Part 2 (story) Christmas Elves - Part 2 (activity) Christmas Elves - Part 3 (story) Christmas Elves - Part 3 (activity) Christmas Elves - Part 4 (story) Christmas Elves - Part 4 (activity)

Answers

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46 47 48 49 50 51 52 53 54

55 - 59

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Teachers’ Notes

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Understanding Everyday Maths - Book 2 is intended for Year 6 and 7 maths students. The activities in this book are linked to engaging narratives. The narratives are cleverly illustrated - some with meaningful diagrams, graphs and charts. In the narratives the teenage characters come across mathematical problems during their everyday lives and must solve the challenges presented to them. Students will immediately identify with the characters in the stories and with the everyday mathematical challenges that they face. By doing so, students will understand how maths is a part of life. This validates the purpose of this learning area. By working through the activities, students will demonstrate maths concepts as prescribed by the Australian curriculum.

This BLM will strengthen the students’ literacy skills as well as their maths skills and make maths entertaining whilst demonstrating its everyday usefulness.

The subject will never appear irrelevant again.

The stories can be read aloud in the classroom followed by individual or small team attempts at the tasks. Your students can complete the activities with only the knowledge taught throughout the story or you may wish to scaffold concepts further depending on the abilities of your students. Sometimes further research to complete a question will be required of the student. This is a valuable skill as throughout the course of their school life, students will not always be given everything they need to answer a question, rather they will need to rely on their own resourcefulness to obtain a solution. Research will occur more confidently when the students have clearly understood the problem and recognise what is required of them. You should structure your lessons in a way that suits your students’ needs.

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There are three stories in this resource altogether. Each story appears in a different section of the book. The book is sectioned according to the three maths curriculum areas of: Number and Algebra, Measurement and Geometry and Probability and Statistics. Suggested solutions are provided at the conclusion of the resource.

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Curriculum Links Year 6 – Number and Algebra Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123)

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

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)

Connect volume and capacity and their units of measurement (ACMMG138) Construct simple prisms and pyramids (ACMMG140)

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

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Year 6 – Measurement and Geometry

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

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Multiply and divide decimals by powers of 10 (ACMNA130)

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

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Year 6 - Statistics and Probability Describe probabilities using fractions, decimals and percentages (ACMSP144)

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

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

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

Explore the use of brackets and order of operations to write number sentences (ACMNA134)

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

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Curriculum Links Year 7 – Number and Algebra Compare, order, add and subtract integers (ACMNA280) Solve problems involving addition and subtraction of fractions, including those with unrelated denominators (ACMNA153)

Establish the formulas for areas of rectangles, triangles and parallelograms, and use these in problem-solving (ACMMG159) Calculate volumes of rectangular prisms (ACMMG160)

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Multiply and divide fractions and decimals using efficient written strategies and digital technologies (ACMNA154)

Express one quantity as a fraction of another, with and without the use of digital technologies (ACMNA155)

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Year 7 – Measurement and Geometry

Draw different views of prisms and solids formed from combinations of prisms (ACMMG161)

Connect fractions, decimals and percentages and carry out simple conversions (ACMNA157)

Investigate conditions for two lines to be parallel and solve simple numerical problems using reasoning (ACMMG164)

Find percentages of quantities and express one quantity as a percentage of another, with and without digital technologies.

(ACMNA158)

Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral (ACMMG166)

simple ratios (ACMNA173)

quadrilaterals (ACMMG165)

Investigate and calculate ‘best buys’, with and without digital technologies (ACMNA174)

Year 7 – Statistics and Probability

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Round decimals to a specified number of decimal places (ACMNA156)

Identify corresponding, alternate and cointerior angles when two straight lines are crossed by a transversal (ACMMG163)

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Introduce the concept of variables as a way of representing numbers using letters (ACMNA175)

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Construct sample spaces for single-step experiments with equally likely outcomes (ACMSP167) Assign probabilities to the outcomes of events and determine probabilities for events (ACMSP168)

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Create algebraic expressions and evaluate them by substituting a given value for each variable (ACMNA176) Extend and apply the laws and properties of arithmetic to algebraic terms and expressions (ACMNA177)

Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point (ACMNA178)

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© ReadyEdPubl i cat i ons Classify triangles according to their • f o r r e v i e w p ur posesonl y• side and angle properties and describe Recognise and solve problems involving

Identify and investigate issues involving numerical data collected from primary and secondary sources (ACMSP169) Construct and compare a range of data displays including stem-and-leaf plots and dot plots (ACMSP170)

Solve simple linear equations (ACMNA179)

Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data (ACMSP171)

Investigate, interpret and analyse graphs from authentic data (ACMNA180)

Describe and interpret data displays using median, mean and range (ACMSP172)

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Section 1: Numberrsand Algebra or eB t

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STORY

The Holiday - Part 1 Read the story and complete the maths tasks as you go.

Following 10 years of penned correspondence I am finally going to come face to face with my virtual friend from Hawaii, Leah. Over the past decade we have matured from composing letters on cutesy floral paper, to using sassy paper with glitter pens, to Snapchatting with plenty of emojis. We have both done a huge amount of growing up since we were six! But there has been one passion we have continually shared and that is our devotion to surfing! I return to Snapchat:

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Kiera

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I can’t believe my parents are actually letting me travel on my own!

To think I will get to enjoy a plane ride without suffering through games of eye spy or thumb wrestling with my little brothers! 

Lol  what’s the catch?

Leah

I must prove how well I am equipped. Being that my parents are both in the legal profession, I have to ‘deliberate’ and show ‘evidential research’ and ‘reasoning’ into the following: time zone differences, weather and surf conditions, packing weight, surf spot reviews, exchange rate, American taxes, hotel rates, travel insurance, tips, budget, credit card loan 

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• Lol  Notify them it’s a h-o-l-i-d-a-y!!! Good luck!

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Leah

I’m SO not kidding, they actually want a written report on all this to

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Ok, I let out a sigh of exasperation as I stare down this enormous list. I daydream of the Hawaiian surf hoping to inspire myself to attack this list. Ok I’m game, here we go with item 1:

 Time zone

There will be a time delay, I guess, and this constantly baffles me as Leah always states Hawaii is only 2 hours difference but the day before. However the Travel Guide to Hawaii stipulates that we are 22 hours in front. Huh? I resolve to adopt a number line to help me understand - it always works for me at school: 22 hours back 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 pm

Am

So according to the flight details, when I land in Honolulu it will be 12pm in Melbourne and 2pm in Hawaii but the day before. Hey, I will be a day younger!

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activity

The Holiday - Part 1

Get It? Use what you have learned from Part 1 of the story to work out these problems.

1. Fill in the number line. You might want to mark zero first.

-12 2. a. -4 + 7 =

b. -25 + -25 =

d. 6 – -2 =

c. -3 – -1 =

e. -3 – -5 - -16 – 7 + 22 + 9 =

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f. -8 + 2 +-7 – -66 +88 -2 =

3. You are an aspiring pet photographer on your weekends. While taking some adorable pics of your pet puppy you are attempting to adjust the focus with every shot. a. If the camera focus changes from -2.50mm to -4.25mm, by how much has the camera lens focus changed?

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• b. If the camera focus changes again by +3.75,

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how much further has the lens focus moved from -4.25mm?

4. Place the following on a number line: -124, -154, -100, 185, 0, 25, 97, -45, -56, -162, 130

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5. After a day skiing the Victorian Alps you get back to your cabin to find that the lemon squash you left on the porch has frozen into an icy pole. To turn it back into a drink circle which you should do: a. Put the drink in the fridge (temp 4C) b. Put the drink in the freezer (temp -4C) c. Put the drink inside the cabin (temp 18C) d. Leave it outside (temp -2C)

Curriculum Links: Investigate everyday situations that use integers. Locate and represent these numbers on a number line (Year 6: ACMNA124)

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STORY

The Holiday - Part 2 Read the story and complete the maths tasks as you go.

 Weather

I must determine the weather particulars for Hawaii to ensure it is not cyclone season or if there will be other extreme weather surprises. I locate the June temperatures for the previous year from the Hawaiian Meteorology website.

Hawaiian Weather Bureau

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Max Temp 26.5 26.5 26.8 26.3 26.9 27.3 27.5 27.9 27.1 26.9

or eBo st r e p ok u S Day 11 12 13 14 15 16 17 18 19 20

Max Temp 28.1 28.5 28.3 28.7 28.4 28.4 29.1 28.6 28.3 29.2

Day 21 22 23 24 25 26 27 28 29 30

Max Temp 29.6 29.9 30.1 29.3 29.9 29.5 29.5 29.8 29.6 29.1

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Day 1 2 3 4 5 6 7 8 9 10

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Just seems like a horde of numbers. I plot the figures to view the month in a graph. In a swift sketch I use the temperature for the y axis and the days in the month for the x axis. I plot each point accordingly and then connect them just like a dot to dot.

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Honolulu June Weather Last Year 30

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27 26 25 24 1

2

3

4

5

6

7

8

9

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

Ah that’s better! From what I can see it seems that the temperature hovers between 26.5 and 30 for most days. The start of the month is slightly cooler than the end. Overall they are pretty consistent temperatures. Awesome! This signifies there is no requirement to pack a coat ‘just in case’ as my mum would put it.

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activity

The Holiday - Part 2

Get It? Use what you have learned from Part 2 of the story to work out these problems.

1. Plot the points below on a line graph. Make sure that you label all parts of the graph.

10

20

30

40

50

60

70

80

y axis

100

150

200

250

300

350

400

450

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x axis

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2. Plot the following points on the same graph above using another colour for drawing the line graph:

x axis

10

y axis

50

o c . che 20 30 40 50 60 e 70 r o t r 75 100 s 125 s 300 400 r u pe200

80 500

3. Let’s assume the values on the x axis represent people’s ages and the values on the y axis represent the amount of days they have been sick with a cold throughout their lives. If the line graph from Question 1 is for people living in Western Europe and the line graph from Question 2 is for people living in Eastern Asia, what conclusion can you draw about the trend in people catching colds in each region throughout their lives? __________________________________________________________________________ __________________________________________________________________________

Given coordinates, plot points on the Cartesian plane, and find coordinates for a given point (Year 7: ACMNA178) Investigate, interpret and analyse graphs from authentic data (Year 7: ACMNA180)

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STORY

The Holiday - Part 3 Read the story and complete the maths tasks as you go.

Next I decipher the all-important swell of the waves. Waves that are ‘surfable’ are level 3 and over.

I acquire a chart off the Hawaiian Weather Network that exhibits last June’s swell conditions.

 Surf

Hawaiian Weather Network

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Surf Level 2 2 3 3 4 4 3 4 3 3

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Surf Level 1 3 2 4 4 5 2 4 3 3

Day 21 22 23 24 25 26 27 28 29 30

Surf Level 4 4 3 4 3 3 5 3 4 5

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Day 1 2 3 4 5 6 7 8 9 10

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Leah is forever bragging that for every bad surf day in Honolulu there will be at least 5 good ones throughout June. Well, let’s see then. I convert the chart into a tally graph to make things clearer.

Good Surf

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Ratio = 5:25 or 1:5

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Bad Surf

My tally graph tells me there are 5 days that are not surf-friendly in June and the other 25 days are great for surfing. So the ratio looks to be 5:25 or when simplified 1:5. Ratio = 5:25 or 1:5. This does indicate that for every day the surf is bad, there are 5 days when the surf is terrific! I like those numbers!

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activity

The Holiday - Part 3

Get It? Use what you have learned from Part 3 of the story to work out these problems.

Express these as ratios.

1. I I I and I I I I =

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2. OOOOO and OO = 3. and and

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5.

=

=

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4.

and

=

6. For every one charm bracelet you received for your birthday, you got 4 perfumes. Can you express this as a ratio?

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

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7. Your best friend has asked you to help start his lawn mower. He needs to earn extra cash mowing the neighbourhood’s lawns. The fuel can says that for every 20mLs of oil you need to add 100mLs of petrol and then mix. Can you express this as a ratio?

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petrol

8. You are helping your little brother prepare lolly bags for his birthday. He is very particular and insists that in every bag for every 2 chocolate bars he wants 3 lollipops and 2 balloons. Can you express this as a ratio?

Answer: Recognise and solve problems involving simple ratios (Year 7: ACMNA173)

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STORY

The Holiday - Part 4 Read the story and complete the maths tasks as you go.

I’m actually pleased with how I’m tracking; my confidence is growing with every item that gets crossed off my list.

 Packing

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Air Hawaii

Excess Luggage Weight Excess Weight

Fee

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I always seem to take oodles of clothes but not complete outfits. However my leading obstacle is my surfboard. The weight restrictions on oversized luggage is going to cost me. It’s a shame the board doesn’t fold neatly into the overhead compartment. Air Hawaii should really build compartments on its planes specifically for surfboards. I mean they are the official airline of Hawaii – I will definitely, probably, most likely write a letter of complaint or suggestion. Anyway the airline specifies the following rules in terms of fees for excess luggage weight:

$20

≥ 16kg but ≤ 20kg

$50

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≥ 11kg but ≤ 15kg

>20kg

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$5 © ReadyE dPubl i cat i ons ≥ 5kg but ≤ 10kg •f orr evi ew$10pur posesonl y• < 5kg

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To weigh my board I cart it to the bathroom scales and stand it up.

“5.3kg,” I note.

My youngest and cheekiest brother Jack notices me as he totters past the bathroom.

“Seriously Kiera, your surfboard is not overweight, you don’t have to put it on a diet,” he mocks.

“My surfboard weighs 5.3kg which means that I need to pay…?” I say to myself as I push past Jack back to my bedroom.

I study the airline baggage weight chart again and uncover that it wouldn’t be $5 as it reads less than 5kg. So, $10 then? That seems right, because at $10 my luggage needs to be greater than or equal to 5kg but less than or equal to 10kg.

Ok I need to affix $10 for excess luggage to my budget.

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activity

The Holiday - Part 4

Get It? Use what you have learned from Part 4 of the story to work out these problems. > greater than

< less than

≥ greater than or equal to

b. 19 < 9

≤ less than or equal to

1. True or False?

a. 6 > 2

c. 10 ≥ 10

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True? OR False?

d. 25 ≤ 14

a. If there are 4 tradies how much will they pay if they round the amount to the closest dollar?

b. What amount will they have to pay each if they also want to pay you a $6.45 tip (i.e 10%)?

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2. You get a holiday job as a waitress in the local café. A group of tradies that have just finished their lunch would like to split their bill of $64.50.

© ReadyEdPubl i cat i ons 3. You check your results online from last year’s little athletics summer program. The 100 •f o reach r emonth’s vi ew p ur posesonl y• metre results from PB are listed below:

Personal Best

October

15.478

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December

January

Rounded

15.883 14.226

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Month

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Round the times to one 10th of a second.

4. Your best friend is describing what would be her perfect future wedding day. She says the following conditions need to be met for it to be the perfect day: a. Her future husband needs to be less than 190cm tall but great than or equal to 175cm. b. The heel on her shoes will therefore need to be equal to or less than 9cm or greater than 6cm. c. The weather needs to be greater than or equal to 22 degrees and less than or equal to 24 degrees. d. The guest list will be greater than 100 but less than 150 people.

Express the above values using the correct symbols.

Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (Year 6: ACMNA128) Round decimals to a specified number of decimal places (Year 7: ACMNA156)

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STORY

The Holiday - Part 5 Read the story and complete the maths tasks as you go.

 Surf spot reviews

Reviews of surf spots that I have been scrutinising meticulously all have differing opinions according to their reader surveys. I note the results for Moana Surf Beach from 4 different online surf magazines.

Surf r o e t s Bo r catcher e p o u kSurf Beach Surf Spot - Moana Surf Beach Surf Spot - Moana S  8

Surf watcher

wave

 4

 7

 1 8

people gave it a thumbs up.

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Surf Rater Magazine

people gave it a thumbs up.

© ReadyEdPrider ubl i cat i ons f or r e vi ew pur po se on l y • Surf Spot -s Moana Surf Beach Surf Spot• - Moana Surf Beach 12

people gave it a thumbs up.

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people gave it a thumbs up.

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That’s a tad perplexing! I don’t know what that suggests as they surveyed different numbers of people. I remember something about ensuring that the bottom number or denominator is the same and then adding together the top lines and the bottom lines. However in this case where the surveys are all comparing the same thing, I just want to add how many people were surveyed and how many gave it a thumbs up.

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So if I attempt this it will read:

1 8 4 7 + + + = 8 9 11 12

If I add the top and bottom lines, it equals

20 2 1 or when simplified or 40 4 2

Wow that’s half! Which means that half of the people surveyed would recommend Moana Surf Beach! I would never have guessed that it would be half from just scanning the reviews. It goes to show that occasionally pictures are not always useful, now and then maths should kick in to uncover the real picture!

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activity

The Holiday - Part 5

Get It? Use what you have learned from Part 5 of the story to work out these problems.

Fractions with different denominators need to firstly have the same denominator before adding together. To do this you will need to find the lowest common denominator first. Then whatever you do to the bottom number you need to do to the top number. So multiply the top number with whatever factor you used to multiply the bottom number.

1. a. 1 + 1 =

8

5

c. 4 + 1 =

e. 1 + 6 =

2

2

10

1e 1 r o t s r 4 5B e oo p k 1 1 Su 4 3

10

b.

+

=

d.

+

=

f. 2 + 4 =

5

10 1 2. Place the following fractions on a number line: 1 10 5

2 3

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1 2

1 6

2 5

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• 3. You have eaten four squares of chocolate. What fraction have you eaten and what fraction is left?

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Answer:

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Choc

olate

Choc

olate

Choc

olate

Choc

olate

Choc

olate

Choc

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Choc

olate

Choc

olate

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olate

Choc

Choc

olate

Choc

olate

Choc

4. You are walking the neighbour’s dogs for cash on the weekend. You have 8 pooches to walk at one time and ½ are too old to walk the whole 4 blocks. a. If ¼ of those old dogs need to be returned home after 1 block, how many dogs will you have left with you?

b. What fraction of the pack are 1 block only dogs?

Solve problems involving addition and subtraction of fractions with the same or related denominators (Year 6: ACMNA126) Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies (Year 6: ACMNA127) Solve problems involving addition and subtraction of fractions, including those with unrelated denominators (Year 7: ACMNA153) Multiply and divide fractions and decimals using efficient written strategies and digital technologies (Year 7: ACMNA154) Express one quantity as a fraction of another, with and without the use of digital technologies (Year 7: ACMNA155)

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STORY

The Holiday - Part 6 Read the story and complete the maths tasks as you go.

 Jet ski spots

My eyes skim down to the next review of Moana Surf Beach, this time for a jet skiing location.

Hmmm I might do this fraction thing again and see if it’s also a recommended jet ski spot. Geez more fractions to make sense of!

Surf r o e t s B catcher r e oo p kSurf Beach Jet Ski Spot - Moanau Jet Ski Spot - Moana SSurf Beach  3 10

people gave it a thumbs up.

 5 15

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Surf Rater Magazine

people gave it a thumbs up.

wave © ReadyEdPrider ubl i cat i ons

Surf watcher

Jet Spot - Moana Surf •f orr evi ew pur pSki os es onl yBeach •

1

person gave it a thumbs up.

w ww

3

 2 5

people gave it a thumbs up.

m . u

Jet Ski Spot - Moana Surf Beach

At first glance the results don’t look remarkable, I mean, only one person recommends it from Surf Watcher magazine. Seriously, just one! Ahead of making up my mind, I opt to let maths do the talking once again – the results may not be as dire as they seem.

. te

o c . che e r o t r30% s uper Surf Rater Magazines Surf Catcher 33.33%

This time I choose to get the percentages from each, by dividing the top numerator into the bottom denominator. So:

Surf Watcher 33.33% Wave Rider 40%

Not as poor as I assumed. Although still below average, I guess it’s not a jet ski hot spot. On another note however, who would have thought 5/15 and 1/3 both equal 33.33%? Looks like I have learnt two things from this:

a. never judge a book by its cover and

b. never judge a percentage by its corresponding fraction!

18

ACTIVIT Y

The Holiday - Part 6

Get It? Use what you have learned from Part 6 of the story to work out these problems.

1. a. 1 =

x 100 =

2

c. 1 =

e. 1 =

10 8

%

b. 1 =

x 100 =

3

%

x 100 =

%

d. 1 =

x 100 =

%

x 100 =

%

f.

x 100 =

%

or e st Bo r e 1 p ok 5 u S 4

=

Teac he r

ew i ev Pr

2. You want to buy a new snowboard for the upcoming snow season but you only have $45 to spend. The board you want is $60. Can you afford it if it is on sale for 25% off?

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• 3. Match the following percentages to their corresponding decimals: Answer:

10%

175%

50%

75%

100%

80%

150%

1.75

0.80

0.25

1.00

0.40

1.50

0.10

0.75

0.50

4. Move the decimals without using a calculator:

. te

a. $35.00 x 10 = b. $0.75 x 10 =

m . u

40%

w ww

25%

o c . che e r o r st super d. $500.00 / 10 = e. $450.10 / 10 =

c. $2.95 x 10 =

5. Count how many squares there are in this grid and then colour in 25% of the squares. Of the 25% of the squares that you coloured were you able to colour in a further 50% evenly? _____________________________________________ Make connections between equivalent fractions, decimals and percentages (Year 6: ACMNA131) Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (Year 6: ACMNA132) Connect fractions, decimals and percentages and carry out simple conversions (Year 7: ACMNA157)

19

STORY

The Holiday - Part 7 Read the story and complete the maths tasks as you go.

 Exchange rate

What is the exchange rate?

Exchange rate. Ok now I wish I had paid attention to the newsreaders whenever they talked about what the Australian dollar was achieving against the US dollar. It seemed so irrelevant up until now.

If I have AU$300 as a budget and the exchange rate is currently 80 cents, then I will have…something?...to spend. I also have to pay an exchange transaction fee of AU$5.

or eBo st r e p ok u 300 xS 0.80 – 5 = ?

ew i ev Pr

Teac he r

So, if I write this out it reads:

Now I am aware I have to put brackets somewhere or I will completely stuff up the answer.

I know that I will need to pay the AU$5 fee regardless of the rate so I leave the AU$5 on the outside of the brackets:

(300 x 0.80) – 5 = $235

© ReadyEdPubl i cat i ons •f or evi e w bypquite ur ose sonly on l y• Wow, that deteriorates my r spending money ap portion!

I now have

US$235 to spend. Instantly I am wishing that the Aussie dollar climbs very swiftly.

m . u

w ww

My Dad enforces that I also must calculate my spending money factoring in the fluctuations in the exchange rate. “Nothing in finance is ever set in stone, anything can and will happen,” he tells me while showing me the stock market report.

According to the ASX, the Australian dollar can fluctuate by 10% in one month so I need to calculate for levels at 10% of either side of 80 cents.

. te

o c . che e r o r st super

10% x 80 cents = 8 cents 8 + 80 = 88 cents.

80 – 8 = 72 cents

So, if I were to use the same calculation above using the new values of 88 cents at best, and 72 cents at worst then:

300 x 0.88 – 5 = (300 x 0.88) – 5 = $259

300 x 0.72 – 5 = (300 x 0.72) – 5 = $211

So, at best I will have US$259 and at worst I will only have US$211 once I have completed the exchange of my $300 Australian dollars into US dollars. I sigh. If I was in charge of the world – I would create a unified, global currency that would make life simpler for everybody…well at least for me.

20

STORY

The Holiday - Part 7

 American taxes

Aren’t I a little young to be paying taxes? Apparently not according to the Hawaiian Travel Guide. In America most things you buy are the price listed plus taxes. So a cheeseburger at a café may display $3 on the menu except it will be say, $3.25, when you pay for it at the cashier, as taxes are added on purchase.

rger eesebu

Ch

$3. 00 + 8% TAX

So if I have $235 to spend and the tax rate is 8%, I need to include 8% in my budget which means I will have only…? dollars to spend as I need to absorb the tax within my budget.

or eBo st r e p ok u S

8% of x + x = 235

Using algebra, I can get x on its own to figure out what it is:

0.08x + x = 235

ew i ev Pr

Teac he r

Hmmm, how do I work this out? The sum I have to splurge will be…something…let’s call that something ‘x’. So if I put x into my calculation then:

©R ea dyEdPubl i cat i ons 0.08x + 1x = 235

1.08x =r 235 • f or evi ew pur posesonl y•

x = 217.59

w ww

Or when rounded up x = $218 to spend as the rest will go to 8% taxes.

. te

To test this, I resort back to my pictures:

m . u

x = 235/1.08

o c .

Total $235 che e r o r st su per $218

?

218 x 0.08 = 17.44 218 + 17 = 235

Yes it works! $17 dollars in taxes can now be added to my budget.

21

activity

The Holiday - Part 7

Get It? Use what you have learned from Part 7 of the story to work out these problems.

1. Find the value of a: a. a + 4 = 15

c. 3a + 9 = 21

e. 7a – 7 = 0

b. a – 3 = 19

or eBo st r e p ok u S

d. 5a – 7 = 18

f. 6a + 10 = 28

2. Write the brackets in the correct places:

a. 13 + 4 x 5 = 33

b. 11 x 4 + 14 – 4 = 54

c. 15 / 5 -1 = 2

d. 144 / 12 – 5 + 0 = 7

ew i ev Pr

Teac he r

3. On a walk through a sleepy coastal village your mum decides she wants to stop in every antiques store to find rare gems and knick-knacks. She drags you into 8 different stores filled with ocean-themed homewares. You argue with her that each store is costing you valuable time that could be spent at the beach. Her constant shopping has taken 90 minutes from your beach time including the 10 minutes she spent ordering a smoothie from the juice bar.

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

w ww

. te

Answer:

m . u

Can you prove this? How long must each store visit have been, plus the juice stop, for the equation to total 90 minutes? Express your argument in an algebraic equation.

o c . che e r o r st super

4. Construct an algebraic equation for the following problem and solve it: You are organising a school talent quest. If the principal instructs you that the show must go for no longer than 90 minutes including the 15 minute intermission and there are 25 acts to perform, then for how long may each act perform?

Answer:

22

Explore the use of brackets and order of operations to write number sentences (Year 6: ACMNA134) Introduce the concept of variables as a way of representing numbers using letters (Year 7: ACMNA175) Create algebraic expressions and evaluate (Year 7: ACMNA176) Extend and apply the laws and properties of arithmetic to algebraic terms and expressions (Year 7: ACMNA177)

STORY

The Holiday - Part 8 Read the story and complete the maths tasks as you go.

 Hotel rates

Hotel rates - when did it get so convoluted? I just want a room with two single beds. There are all these deals like ‘smart saver’ and ‘deal dazzlers’ and ‘upgrades and combos’. Why can’t they just give me a standard rate? The fine print at the bottom of all the hotel rates appears to show terms and conditions for extras. The fine print states:

or eBo st r e p ok u S

*Cable TV and Internet +5² per room per night. **In-room air conditioning +6² per room per night. ***Buffet breakfast +10² per room per night.

5² is 5 x 5 = 25 6² is 6 x 6 = 36 10² is 10 x 10 = 100

ew i ev Pr

Teac he r

I recall something about numbers to the power of two from school. I rummage amongst my school books until I locate a section on indices. It’s simpler than I remember. You merely multiply the number by itself concurring to how many times the little number on top declares. So:

That makes a difference!

Well! That certainly makes a difference to my accommodation expenses!

© ReadyEdPubl i cat i ons  Travel insurance

•f orr evi ew pur posesonl y•

“Travel insurance? Honestly I only have, like, $11 worth of junk jewellery and some clothes,” I moan to mum.

m . u

w ww

“It’s not just for theft or lost luggage, it’s also for medical emergencies. In America medical bills can be quite astronomical. You will be surfing near coral and reefs. What if you have an accident and cut your leg or knee on the reef? Or perhaps you could be eating at a really bad restaurant and get food poisoning. Or even…”

“Ok mum, I get it,” I stop her. The insurance plan states that I can elect one of 3 different packages.

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o c . che e r o r st super

Package 1 - 10 nights at $80

Package 2 – 6 nights at $60

Package 3 – 5 nights at $45

“But I can’t compare them easily as they have varying amount of nights, so which is the best buy?” I plead for assistance presenting mum with the information.

“Well this is easy. What you need to do is compare them each for one night,” she jumps in to assist. Clearly she was good at this when she was my age. “If you divide each down to a per night rate then:

80/10 = $8 per night 60/6 = $10 per night 45/5 = $9 per night

Well this is easy!

That means that Package 1 is the cheapest on a per night basis and Package 2 is the most expensive,” she resolves. Huh, funny that! I would have assumed Package 1 would be the most expensive at first glance. Maths changes perceptions again!

23

activity

The Holiday - Part 8

Get It? Use what you have learned from Part 8 of the story to work out these problems.

1. Which is the best buy? a. 2 mangoes at $2.40 or 4 mangoes at $4.00? ________________________________ b. 1 macaroon for $2.50 or 2 macaroons for $4.50? ____________________________

or eBo st r e p ok u S

c. 2 litre Juice for $3.20 or 1.5 litre Juice for $2.50? _____________________________

Teac he r

2. You are comparing your bus ticket prices for the next week. You can either buy a daily ticket each day for 5 days for $3.50 or buy a weekly ticket that includes the weekend for $20.

ew i ev Pr

a. Which ticket should you buy? Show your calculations and give a logical reason why you would buy either ticket. _______________________________________________________________________ _______________________________________________________________________

b. What other reasons may you have for your decision?

© ReadyEdPubl i cat i ons •decide f or r ev ew p ur po se so nl y 3. You can’t whether toi purchase 4 patterned plastic school folders for • $0.90 each _______________________________________________________________________ _______________________________________________________________________ or a packet of 8 folders for $5.50. What should you do?

_______________________________________________________________________

m . u

w ww

4. Your brother opens a packet of collector cards that he has just paid $6.00 for. He complains that 3 out of the 8 cards are doubles and are worthless. He complains most of the trip home from the shops that he should have bought action figures instead. If the 3 doubles are worthless to him, how much did each valuable card cost him?

. te

o c . che e r o r st super

_______________________________________________________________________

5. Your tennis coach gives you a choice in your cross training today: pick something to cross off your training list and receive club paid tickets to the Australian Open. Your choices are: Push-ups 20 minutes = $15 ground passes Sprint & stop on clay courts 40 minutes = $30 reserved seating day pass Exercise bike 60 minutes = $50 reserved seating night match

Medicine ball 50 minutes = $55 corporate box seating a. Which activity will pay the best for your time spent? _ ________________________ b. Did any activity pay the same rate?________________________________________

24

Investigate and calculate ‘best buys’, with and without digital technologies (Year 7: ACMNA174)

STORY

The Holiday - Part 9 Read the story and complete the maths tasks as you go.

 Tips

“Oh and tips…could you help me there too?” I request ever so sweetly to my mum.

Mum smiles, shaking her head, “This was supposed to be your research not mine,” she enlightens. “But yes, Americans do a lot of tipping and you will be using plenty of services when you consider it, like bus, taxi, bell hop, waiters…”

hawaii

or eBo st r e p ok u S

“Wait - do I need to tip them all?” I ask apprehensively.

“The book declares between 1/5 and 1/10 is standard.

Eeek that sounds like a lot! I think I will stick to only 1/5,” I determine, as I flick through the book.

Mum chuckles as she leaves the room, “Perhaps you should decipher how much that is in percentages before you elect which amount to tip.”

I punch the fractions into the calculator:

ew i ev Pr

Teac he r

“Well if you read the Hawaiian Travel Guide you would understand it is deemed impolite not to tip,” she justifies.

Travel Guide

©=R eadyEdPubl i cat i ons 1/5 20% 1/10 = 10% • f or r evi ew pur posesonl y•

m . u

Ha! I almost got rolled, I will definitely adhere to 1/10 for tips and vow to learn my fractions a little better.

w ww

Fractions have honestly always confused me – I mean Leah always says she is only three quarters native Hawaiian as she is one quarter Chinese!?! What does that even mean – is she the fraction girl? I always comment politely when she says stuff like that, having no idea what she means. I decide that if I’m going to meet her and possibly her family than I should look into this fraction business a little more.

. te

o c . che e r o r st super

So to divide something into quarters you divide by 4 right? She has only two parents but 4 grandparents.

Now if she is three quarters Hawaiian than that probably means 3/4. So, if she has 4 grandparents, 3 of those 4 are native Hawaiian. The other grandparent must be Chinese so 1 out of the 4 or 1/4.

She also always talks about her extended family owning one fifth of the Hawaiian pineapple production industry. I always found this peculiar as one fifth sounds like she owns half of Hawaii!!

To check what one fifth means I write it as 1/5. To calculate the percentage again I divide 1 by 5 and times by 100 to get the percentage:

1 / 5 = 0.2 x 100 = 20%

Oh ok that’s 20% of the pineapple industry. Still pretty cool!

25

ACTIVIT Y

The Holiday - Part 9

Get It? Use what you have learned from Part 9 of the story to work out these problems.

1. a. 1% of 20 =

c. 50% of 220 =

e.

b. 10% of 40 =

d.

% of 80 = 8

or eBo st r e p ok u S f. 25% of

% of 30 = 6

= 75

ew i ev Pr

Teac he r

2. If you have 40% of your sister’s share of household closet space and your sister is allowed 25% of the total family closet space, then how much total family closet space do you have?

Answer:

3. Which USB stick holds 100% more data than a 1 gigabyte hard drive?

© ReadyEdPubl i cat i ons 1w p orr evi e pos sonl y• 1• GBf 2eGB GB ur

w ww

m . u

2

4. Which school club has 50% less members than the chess club, which has 30 members?

. te

Environment Club

Reading Club

o c . che e r o r st super

15 members

Answer:

Photography Club 45 members

60 members

5. You finally made it past spring, which means no more allergies! What percentage of the year do you have allergy free?

Answer:

26

Multiply and divide decimals by powers of 10 (Year 6: ACMNA130) Make connections between equivalent fractions, decimals and percentages (Year 6: ACMNA131) Find percentages of quantities and express one quantity as a percentage of another, with and without digital technologies. (Year 7: ACMNA158)

STORY

The Holiday - Part 10 Read the story and complete the maths tasks as you go.

 Budget

For my budget, I assemble all my research into a table and stare at my calculations.

Cost -10 -65 -17 -25 -36 -80

Balance 300 290 225 208 183 147 67

Oh dear, I have like, no money!

or eBo st r e p ok u S

ew i ev Pr

Teac he r

Description Spending money Excess baggage Exchange rate American taxes Cable TV and Internet Air conditioning Insurance

Oh dear, I have like, no money! How can that be? Only $67 dollars left. $300 seemed like so much in the beginning that I scoffed at the idea of a credit card loan when my parents suggested it.

But now it seems like it may have to be. I dread the thought of paying off a credit card debt for the rest of my life! Not to be dramatic or anything but I heard that they can be impossible to pay off because the interest rate or something is so high. I stomp into the lounge room where my parents are sitting.

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• “Alright, alright everyone save your mocking, just tell me how to go about a credit card loan for a “I need money!” I declare.

“See, things cost money dear,” Dad says gleefully as he can now finally prove his point to me after 16 years of repeating himself. holiday,” I request. “I need about $700 max!” I determine.

m . u

w ww

“Well you have to pay for the $700 including the, say, 15% interest you will get charged on the balance remaining each month. So, you earn $90 per week at your part-time job, right? You can work the rest out yourself,” Dad answers setting me a challenge.

I head back to my room to commence my calculations. Ok, so I need a table or something – here I go again - pictures and maths together.

. te Month 1 July

31 July 31 August 30 September 31 October

o c . che e r o r st super Interest at 15% of balance

Balance plus interest

$700

$90

$790

$430 $134.50 $0

$64.50 $20.18

$494.50 $154.68

Balance $700

Less payments I make per month

($90 x 4 weeks) = $360 $360 $154.68

Total Interest $174.68

Wow, so that will take me 4 months to pay off and cost me $174.68 in interest over that time. I have learnt so much about money, I need to start being more frugal. I get back online to Leah.

Kiera

Ok I think I’m done. And the verdict is that I should be allowed to take the trip to Hawaii. The bad news is I will be broke when I get home! Lol I think I will have to cancel my internet connection and go back to writing to you on floral paper!  27

ACTIVIT Y

The Holiday - Part 10

Get It? Try these equations without a calculator. Time yourself to see how fast you are. Ready, set, go!

1. 3.5 + 11.5 = 2. 26 – 14 = 3. 99 + 9 = 4.

or eBo st r e p ok u S

5. 55 -

= 18

6. 8 x 3 =

7. 9 x 7 =

© ReadyEdPubl i cat i ons 9o = 45 •xf rr evi ew pur posesonl y•

8. 11 x 6 = 9.

10.

12 = 3 30 = 30

60 = 13.

4 14.

3

= 25

15.

5

= 11

. te

m . u

12.

x 12 = 72

w ww

11.

ew i ev Pr

Teac he r

+ 73 = 82

o c . che e r o r st super

Score: Time:

28

Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (Year 6: ACMNA123) Compare, order, add and subtract integers (Year 7: ACMNA280)

Teac he r

ew i ev Pr

Section 2: Statistics and or eBo st r e p ok u SProbability

w ww

. te

m . u

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

o c . che e r o r st super

29

STORY

The Party - Part 1 Read the story and complete the maths tasks as you go.

65

© ReadyEdPubl i cat i ons Number of people atp each party •f orr e vi ew pur os esonl y• Michael’s Party

73

Ella’s Party

52

Lucas’ Party

71

Sienna’s Party

71

Christian’s Jordan’s Party Party

55

66

Grace’s Party

79

Megan’s Party

w ww

m . u

Simon’s Party

or eBo st r e p ok u S

ew i ev Pr

Teac he r

I’ve stood waiting for this for a long time; 16 years in fact. Everyone is envisioning big things from me. I have been talking up my 16th birthday bash for so long that now I must deliver the goods. And I will.

I am going for an old school hip hop hustle theme. You know, with boom box candy wrappers, bling necklace invitations, graffiti brick wall decoration stands, $100 American bills littering the floor in addition (and only if my finances permit) a low rider parked in the party room or perhaps a replica.

“Don’t overlook the table centrepieces…” adds my enthusiastic, younger sister Penny.

“What centrepieces? What tables?” I ask exasperated. Being merely a year younger than me she is especially engrossed in this party, as a good deal of her friends from her year level will be invited too.

“I don’t think you have contemplated this at all. There is so much to resolve and we barely have 2 weeks left to do it,” she nags then rips out a page from her notebook and shoves it under my nose.

Her first item on the list is to determine how many people to invite based on the probability of the number who showed up to the previous 9 parties held this year.

All 9 bashes invited approximately 80 people. Hmmm I didn’t weigh up that one. What if scores of people show up, or worse …not enough? I examine the statistics from her research. The following data is penned in her neat handwriting:

44

She asks me to work out the average so I’m aware how many people might turn up. Average … average … I know this. I grab my statistics book from school. I look for methods to work out averages. I get given the mean, median, mode and range. I select the range method. I single out the greatest number of 79 and subtract from it the lowest number of 44.

. te o 79 – 44 = 35 c . che e r o r st super

That’s it? Hmmm that doesn’t seem like a good representation of the average. I mean 35 is even less than the smallest attendance statistic! Perhaps the range isn’t very useful if there are too many outliers. The result becomes a little distorted. Nope, not good in this instance. I attempt the mean method this time by adding all the numbers and dividing the sum by the number of parties, and I get:

65+73+52+71+71+55+66+79+44 = 576 576/9 = 64

That appears a little better. Ok so I should expect around 64 people to show up, based on previous parties held this year. That’s not bad. Should be epic!

30

activity

The Party - Part 1

Get It? Use what you have learned from Part 1 of the story to work out these problems.

1. Friday night is slumber party night. During a game of Truth, Dare, Make-up, Hair your best friend argues that you are cheating. You explain that the spinner cannot cheat. How do you prove to her that you have equal probability of landing on every option? That is, what are the chances of landing on Truth, Dare, Make-Up or Hair? Express the probability in fraction form and also as a percentage.

or eBo st r e p ok u S

Truth

Dare

Make-up Hair

_______________________________________________________________________

Teac he r

a. selecting an odd number? �����������������������������������������������

b. selecting a number that begins with a 4? �����������������������������������������������

ew i ev Pr

2. Your Aunty Jen has convinced you to attend her weekly bingo night. As the youngest attendee you are asked to pick the numbers out of the barrel. If there are numbers 1-100 in the barrel what is the probability of:

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

3. Your Dad has asked you to keep your shower time shorter to lower the water bill. He argues that your showers are 40 minutes on average! You know that can’t be right so you record your shower times over the next 5 days. How many minutes do your showers take on average using the mean?

w ww

33.58 min

42.56 min

45.11 min

29.10 min

m . u

38.22 min

________________________________________________________________________

4. You are reading an article in The World Game soccer magazine about the rise in the average height of players in last year’s World Cup in comparison to 20 years ago. You decide to check this out for yourself. Analysing the player statistics for the Italian team you note that the starting eleven had the following heights:

. te

o c . che e r o r st super

A. Marcetti 193cm

M. Fazzi 194cm

N. Vento 195cm

L. Mazzagatti 191cm

M. Matteo 192cm

V. Bel’Uomo 196cm

P. Panutti 187cm

R. Aleppi 188cm

C. Betelli 185cm

A. Del Marco 189cm

V. Lettere 194cm

a. What is the average height using the mean and the median? _______________________________________________________________________ b. How does this compare to the average height of the Italian team in 1990 of 184cm? _______________________________________________________________________ Describe probabilities using fractions, decimals and percentages (Year 6: ACMSP144) Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data (Year 7: ACMSP171) Describe and interpret data displays using median, mean and range (Year 7: ACMSP172)

31

STORY

The Party - Part 2 Read the story and complete the maths tasks as you go.

How do you know this?

My sister’s next request is to ensure that an equal amount of girls and guys show up in order to keep the gender dynamics balanced.

Well that’s pretty straightforward isn’t it? If I drive out equal invitations to both guys and girls, there is no reason one gender would accept or decline more than the other, so the probability of getting a male is ½ and the probability of getting a female is ½. This seems right as there can only really be two outcomes. I scribble this down to make sure that I am not going crazy…

Yes that’s what I thought, juussst checking!

ew i ev Pr

Teac he r

or eBo t s r e P (male) =p ½ P (female) = ½ ok u S

Alright I strike that one off the list, content that I am making some headway on this and feeling much more organised. My sister asks whether I have enough cases of soft drink for the amount of people attending. She has given me details again from the last 9 parties:

Number of cases of soft drink at The last Nine parties

5

Michael’s Party

Ella’s Party

Lucas’ Party

Sienna’s Party

Christian’s Jordan’s Party Party

Grace’s Party

© ReadyEdPubl i cat i ons 6 4 7 7 3 3 5 •f orr evi ew pur posesonl y•

Ok now I am beginning to query her data. I mean how does she even know this?

I asked around!

“How do you even know all this?” I shout from my room.

w ww

“I asked around,” she shouts back matter-of-factly.

I sigh. The list isn’t enough to give me a picture in my head. The statistics textbook illustrates methods of data representation. I choose to rearrange the statistics into a dot plot to see it better, I hate numbers in a list.

. te

Megan’s Party

4

m . u

Simon’s Party

o c . eparty Number c ofh cases of soft drink at each r er o st super 























































































Simon’s

Michael’s

Ella’s

Lucas’

Sienna’s

Christian’s

Jordan’s

Grace’s

Megan’s

Ok that looks better. I can see clearly that Christian’s and Jordan’s were way under the rest, and that most were scattered around the 6 or 7 mark. I’ll order 7 cases of soft drink just to be on the safe side.

32

activity

The Party - Part 2

Get It? Use what you have learned from Part 2 of the story to work out these problems.

1. Prepare a bar graph that displays the following information about the number of books read during the last school holidays.

Number of books read on the school holidays

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Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 3

4

5

4

2

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1

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

2. Prepare a line graph showing the following information that relates to the number of pets people in your class own.

Number of pets my classmates have

Cats

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8

Fish

4

7

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Rabbits 6

Horses 3

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Dogs

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3. On the back of this sheet, prepare a pie graph showing the information below about the votes for TV’s best comedy show on the Australian People’s Choice Awards.

Convert the votes into percentages and label the pie graph using a colour coded system.

Al’s House 455 votes

votes for tv’s best comedy show Crazy Couple 320 votes

All The Family Parents & More The Silverburgs 550 votes

400 votes

Prepare observed frequencies across experiments with expected frequencies (Year 6: ACMSP146) Identify and investigate issues involving numerical data collected from primary and secondary sources (Year 7: ACMSP169) Construct and compare a range of data displays including stem-and-leaf plots and dot plots (Year 7: ACMSP170)

775 votes

33

STORY

The Party - Part 3 Read the story and complete the maths tasks as you go.

Penny walks past my bedroom door on her way to the kitchen (in her quest for another tiny piece of chocolate no doubt). I don’t know why she just doesn’t take half the packet at once. She ambles past, halts and backpedals to my doorway.

“How long have you booked the venue for?” she tests, knowing fairly well that I have not even thought about it.

“Does anyone care how long we stay?” Apparently yes, as she gives me a look of disapproval.

or eBo st r e p ok u S

“You are paying for the venue per hour so you should consider that in your budget,” she points out.

He picks up after just one ring.

“Yello, Ron’s Enterprises,” he says in a thick Scottish accent.

“Hi it’s Dean, I just was wondering…” I begin.

“Who?” he barks.

“Dean,” I try again.

Hi it’s Dean ...

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“Well how long does the average party go for?” I wonder out loud. She hands me the phone with the number of Ron the manager of my party venue.

I sigh. I’m evidently not high on his list of priorities. I clarify politely who I am and probe whether he can give me any information on how long parties usually last at his

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© ReadyEdPubl i cat i ons •f orr evi ew pur po se sonl y• Dean who?

“Dean who?” he barks.

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venue. As I talk I hear him rummaging through his invoices for the past few months. I gather that it must be a frequently asked question. He begins rattling off information from the last lot of invoices. I furiously scribble the information down trying not to let his accent muddle me:

. te o3: 5 hours c Party 1: 5 hours Party 2: 4.5 hours Party . che Party 5: 3.5 hours r eParty 6: 6 hours Party 4: 3 hours o r st s per Party 7: 5.5 hours u

“Ok, Ok that’s heaps to go off,” I interrupt him.

I use the mean method again to determine the average, so:

5 + 4.5 + 5 + 3 + 3.5 + 6 + 5.5 = 32.5 32.5 / 7 = 4.6 hours

Sounds good! I can start the whole thing at 7.30pm and it is possible that we can be out of there before midnight. I don’t fancy paying the extra surcharge for post-midnight rates.

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activity

The Party - Part 3

Get It? Use what you have learned from Part 3 of the story to work out these problems.

1. You are on a nutritious vitamin boost plan this week to increase your healthy food intake. Your mum asks you how many pieces of fruit you have eaten this week. You estimate the number of fruits eaten including dried fruit and glasses of fruit juices to be:

Monday 9

Tuesday

Wednesday

Thursday

Friday

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6

8

6

a. Find the average using the mean, median and range methods.

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_______________________________________________________________________ b. What does the range measure in comparison to the mean and median?

_______________________________________________________________________ _______________________________________________________________________

2. You enter a competition to win a pass to the latest action movie. If you know the organisers have reached their limit of 2,500 entrants, what are your chances of winning? Display your chances as a percentage.

© ReadyEdPubl i cat i ons • f o rflip r e i e wMonday pur se n l y• 3. You and your sister av coin every top seeo who wills geto the worst

_______________________________________________________________________

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chore for the week – bin duty! If you do this every week for 52 weeks what would you expect the result to be for you and your sister? Explain why you have come to your conclusion.

_______________________________________________________________________

_______________________________________________________________________

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4. You and your Dad entered this year’s City Fun Run for charity. Approximately 15,000 people entered the event and you were told that $330,000 was raised for the cause.

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a. How much money was raised by each participant on average?

_______________________________________________________________________ b. The participant finish times were recorded in 30 minute intervals. Using the information below, prepare a line graph on the back of this sheet.

Finish Time Interval 30-60min 60-90min 90-120min 120-150min 150-180min

Participants 500 2500 6000 4500 2000

Describe probabilities using fractions, decimals and percentages (Year 6: ACMSP144) Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (Year 6: ACMSP145) Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data (Year 7: ACMSP171)

35

STORY

The Party - Part 4 Read the story and complete the maths tasks as you go.

Music! Ok now that I do have covered. Yesterday I shot out a Facebook post asking people to vote for the best 80s and 90s rap albums to grow our song base for the night. The results are looking good. Some fast replies – everyone has an opinion on this:

Rap City: 12 votes American Beat Box: 5 votes In Your Head: 6 votes

In The Crib: 7 votes American Rap Story: 9 votes Street Noise: 9 votes

or eBo st r e p ok u S best 80s and 90s rap albums

12

Votes

10

9

8 6 4 2 0

7

6 n © ReadyEdPubl i cat i o s 5 •f orr evi ew pur posesonl y•

Rap City

In The Crib

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American Beat American Rap Box Story

That looks smashing. I send out another Facebook post and break for a few minutes surveying the parade of likes and smiley faces as they come filtering in.

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s

In Your Head

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Rap City

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9

Street Noise

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12

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I need to reply with a cool graphic to illustrate to everyone the results. I reckon it will get people excited about the party. I use a column graph as my starting point:

ACTIVIT Y

The Party - Part 4

Get It? Use what you have learned from Part 4 of the story to work out these problems.

1. Study the following column graph which displays your best score in the Crash Force video game for the past 6 Friday nights, in comparison to your online gaming pal Louie from Singapore.

crash force

5000 4000

2000

1000 0

Fri 1st Oct

Fri 8th Oct

Fri 15th Oct

Fri 22nd Oct

Fri 29th Oct

me louiE

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3000

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Fri 5th Nov

What can you interpret from the data display?__________________________________

© ReadyEdPubl i cat i ons •f o rr e vi ew pare ur p os esonl y• 2. Your teacher points out that your grades not going to

_______________________________________________________________________

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improve unless you put in more effort and time with your homework. To illustrate her point she shows you the below table which she says is the amount of time 13 year old children spend doing homework in different states in Australia.

Convert the following information into a bar graph.

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Approximate hours of homework per night for each Australian State.

Victoria Northern Territory

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2.5 2.0

Tasmania

1.7

New South Wales

2.2

Queensland

3.2

Western Australia

1.3

South Australia

1.7

Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (Year 6: ACMSP147) Identify and investigate issues involving numerical data collected from primary and secondary sources (Year 7: ACMSP169) Construct and compare a range of data displays including stem-and-leaf plots and dot plots (Year 7: ACMSP170)

37

STORY

The Party - Part 5 Read the story and complete the maths tasks as you go.

“You mustn’t forget the heaters!! We need the heaters, girls won’t show up without heaters, girls won’t stand out on the balcony without heaters, order the heaters!!!” my sister yells.

I roll my eyes, she is always cold. She has a point though - girls are forever huddling around the heaters at school. It seems such a misuse of money in September. I mean, how cold will it be?

Hmmm, how do I check? I google ‘Melbourne weather statistics.’ I get led to the Australian Bureau of Meteorology. Finally some primary data that does not come from my sister’s mouth.

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Average temperature for September evenings between 6pm and midnight

September 1 September 2 September 3 September 4 September 5 September 6 September 7 September 8 September 9

14.3° 12.3° 12.0° 11.3° 12.5° 15.2° 16.1° 14.2° 12.8°

I resolve to trial this median thing myself. With my stats maths book in hand it advises fairly quickly that the median is the middle number when the numbers are placed in order. That’s simple enough. I rearrange the amounts in ascending order in the chart:

September 16 September 17 September 18 September 19 September 20 September 21 September 22 September 23 September 24

13.4° 14.5° 14.3° 15.6° 11.3° 11.9° 12.5° 14.6° 14.8°

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The site reveals that the median temperature for September evenings between 6pm and midnight is 13.5 degrees. Doesn’t seem right.

Really? Only 13.5 degrees? I find a link to a list of temperatures for each September night last year.

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Australian Bureau of Meteorology

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• Average temperature for September evenings between

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6pm and midnight arranged in ascending order

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11.2° 11.2° 11.3° 11.3° 11.3° 11.9° 12.0° 12.3° 12.5° 12.5° 12.5° 12.5° 12.8° 13.5° 13.5° 13.6° 13.9° 14.0° 14.2° 14.3° 14.3° 14.3° 14.5° 14.6° 14.8° 15.2° 15.6° 16.1° 16.5° 16.5°

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… and 13.5 + 13.6 divided into 2 = 13.55 degrees! Ha. Funny. That actually works. The BOM are right. Too easy. If only it had seemed this relevant in maths class!

My eyes wander down to the next section in the maths book that demonstrates a stem and leaf plot and I have a canny idea. To annoy my sister and show her up I quickly construct a stem and leaf plot using the September temperature data.

STEM 0 1

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2

LEAF 1, 1.2, 1.3, 1.3, 1.3, 1.9, 2, 2.3, 2.5, 2.5, 2.5, 2.5, 2.8, 3.5, 3.5, 3.6, 3.9, 4, 4.2, 4.3, 4.3, 4.3, 4.5, 4.6, 4.8, 5.2, 5.6, 6.1, 6.5, 6.5

story

The Party - Part 5 I dart into her room and this time I shove a piece of paper with data under her nose.

“See, most nights it’s between 10 and 20 degrees in September!” I proclaim proudly.

She glimpses at the graph over her black framed glasses.

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“A stem and leaf plot has its limitations you know.

Especially when you have many stems with no leaves - that can be a problem if there are outliers.

It’s furthermore difficult to use if decimal leaves are used. Moreover stem and leaf plots simply show the frequency that certain classes of values occur. Between 10 and 20 is not much help to us the values don’t span many 10s of values.”

I leave the room silent and stunned. That is the last time I try to show off with maths stuff.

I order the heaters.

Later Penny drops by my room again. Tiny square of chocolate in hand. “Actually, your stem and leaf plot was pretty good,” she says. “But let me show you where it can be really useful.” She flips through her ballet magazine until she finds a list of top 20 ballet dancers and their individual career performances.

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

She continues, “So you already know that the stem of the graph is listed on the left hand side and represents the tens digits and the leaves are in the right hand side of the graph and represent the ones digits for each of the categories of tens, twenties, thirties, forties and so on. So with the following data of performances: I can arrange them together in a stem and leaf plot.”

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She sketches the following:

STEM

. te01

LEAF

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35, 25, 56, 45, 11, 13, 24, 26, 27, 46, 34, 36, 39, 33, 25, 12, 14, 8, 6, 3

o c . e 2 c her r o st super 3 4 5

3, 6, 8 1, 2, 3, 4 5, 5, 6, 7 3,4,5,6,9 5, 6 6

“So as you can see it shows us a picture of the data that illustrates the information. Now you can see the frequency of different classes of values occur,” she concludes and leaves.

It actually does make more sense now that I know that it is a frequency graph. “Thanks,” I mumble.

“No problem,” she shouts.

How did she even hear me?

39

ACTIVIT Y

The Party - Part 5

Get It? Use what you have learned from Part 5 of the story to work out these problems.

1. Have a look at the following data that lists the birth dates of all your classmates: 8, 9, 11, 11, 11, 14, 15, 15, 15, 15, 19, 19, 23, 24, 25, 25, 25, 25, 27, 28, 28, 29, 31, 31

Teac he r

STEM

LEAF

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Arrange the above data in a stem and leaf plot and explain what the graph is telling us about frequency. _______________________________________________________________________ _______________________________________________________________________

2. Your parents have decided to upgrade the family car! They are insisting (once again) on buying another boring white car. You argue with them that over 50% of the cars on the road are white and it will be dull!! To prove your point you stand out the front of your street and tally the amount of cars and their colours. Results are:

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

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blue

silver

green

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black

o c . che e r o r st sup r CHOOSE Ae TOPIC

Present this data in a dot plot.

3. Research one of the following topics online and find a table of primary data statistics that you can use to draw a line graph on the back of this sheet.

a. b. c. d. e. f. g. h.

40

Households in Australia that own cars (e.g. 0, 1, 2, 3, 4, 5 + cars) Marriage rate over the past 50 years Common baby names over the past year Countries in the top 10 of the Olympic Medal Tally at the last Olympics Top 10 migrant groups by size in Australia Top 10 highest grossing movies of all time Top 10 music artists (according to most number 1 hits) of all time Rainfall days in different capital cities for each month last year Interpret secondary data presented in digital media and elsewhere (Year 6: ACMSP148) Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data (Year 7: ACMSP171) Identify and investigate issues involving numerical data collected from primary and secondary sources. (Year 7: ACMSP169) Construct and compare a range of data displays including stem-and-leaf plots and dot plots. (Year 7: ACMSP170)

STORY

The Party - Part 6 Read the story and complete the maths tasks as you go.

Back in my room I spy a half-eaten packet of popcorn behind my laptop. As I nibble on the stale snack I realise the chow situation hasn’t been addressed. 4.6 hours sounds like a long time - what if people want to eat something? I can hear my mother telling me I’m a bad host for not providing food. She thinks it’s a dinner party.

… I sent out a tweet to the soccer girls …

“Ok need your help again,” I holler to Penny.

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“Give me 10 or 12 minutes,” she scoffs.

10 or 12 minutes later she delivers another list - another little square of chocolate in hand.

“A sample of how many people would eat the following foods.”

She hands me a piece of scented paper.

2 9

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“What’s this?” I query.

3 9

© ReadyEdPubl i cat i ons •f orr evi ew pur posesonl y• 16

9 9

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4 9

o c . che e r … must order o r st super cake and stuff!

“What do you mean a ‘sample’? Who did you ask?”

I say amazed at her work ethic.

“I sent out a tweet to the soccer girls, 9 of them participated in the sample,” she says.

“There’s that word again, ‘sample’. Just say 9 of them replied,” I plead.

“Ok 9 of them replied. I will dumb it down for you,” she grouses.

So if the ‘sample’ is anything to go by everyone will want and expect cake! Mental note: must order cake and stuff!

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ACTIVIT Y

The Party - Part 6

Get It? Use what you have learned from Part 6 of the story to work out these problems.

1. After watching the latest cooking show competition on TV you are certain that everyone in Australia will be a fan of your famous honey and blueberry pancakes. You decide to test your theory by conducting an experiment with a sample of taste testers. You draw up a key and record the results.

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Ratings KEY:

terrible 

ok 

lovely 

superb 

Mum = 

Nanna Carla = 

Dad = 

Sister = 

Neighbour Jim = 

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Taste Test RESULTS

Bobby (Dog) =

a. From the above results what percentage of the sample think the pancakes are superb?

______________________________________________________________________

© ReadyEdPubl i cat i ons ______________________________________________________________________ •f orr evi ew pur posesonl y• b. Does this sample size give a good indication of the rest of the Australian population? Why/why not?

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2. You have been asked to take care of the background music at your sister’s party. You have organised a whole stack of tracks and selected ‘Random’ on the music player. If your sister has 5 favourite tracks and there are 25 songs altogether, what are the chances of her hearing one of her favourites? Express the answer as a fraction and a percentage.

______________________________________________________________________

______________________________________________________________________

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3. You have been assigned the job of magician for your little brother’s birthday party. You ask one of the kids to pick a card from a deck of snap playing cards and then you have to guess the picture as well as the colour. If there are four colours to choose from and 12 pictures in a deck of 48 cards then: a. what are the chances of guessing the right colour?

______________________________________________________________________ b. what are the chances of selecting the right picture? ______________________________________________________________________ c. what are the chances of selecting both the right colour and the right picture? ______________________________________________________________________ 42

Describe probabilities using fractions, decimals and percentages (Year 6: ACMSP144) Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (Year 6: ACMSP145) Construct sample spaces for single-step experiments with equally likely outcomes (Year 7: ACMSP167) Assign probabilities to the outcomes of events and determine probabilities for events (Year 7: ACMSP168)

STORY

The Party - Part 7 Read the story and complete the maths tasks as you go.

Suddenly I have a thought.

“Hey Penny do the sample thing again and this time ask at what time should I stop the party to cut the cake,” I say.

“Done,” she says as she promptly gets to work. Half an hour later, she is in my room.

“Ok so here are the results for a larger sample population of 22,” she says with a wink now loading on the jargon on purpose. She hands me her research.

or eBo t s r e 8pm p 9pm 10pm 11pm o k 2 votes Su 3 votes 8 votes 7 votes 2 22

3 22

8 22

7 22

12am

2 votes

2 22

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What time should I stop the party to cut the cake?

“Ok, that’s great but I’m no closer to deciding what time to choose,” I point out.

“Well I’m glad you asked…there is one more method of analysing a list of data that can give you the most popular or frequent value”, she explains.

© ReadyEdPubl i cat i ons “Yes, it’s called the mode,” she says ignoring my sarcasm. “You select the value that appears the •f orr evi ew pur posesonl y• most frequently. In this case it is 10pm.”

“Oh really?” I remark sarcastically.

I realise as she is talking that I actually remember the mode method from school. I recall the teacher saying that the word mode means ‘most popular’.

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Penny looks at me confused. Her face looks like she is thinking hard. She reaches for her maths book, as I wave my arms to stop her.

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“Alrighty, I declare that I shall cut the cake at 10pm,” I say in a silly regal voice. “But you have to tell me this…what would be the mode if there were two or more most popular or frequent values? That is, what if 10pm and 9pm got the same amount of votes?”

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“It would be bimodal if there are two modes and multimodal if there are more than two modes,” I explain to her this time. “Easy huh?” I pose to her.

She smiles.

“I think I have done well,” I say.

“I?” she queries.

“I think I have thought of all the necessities,” I say ignoring her.

“I?” she asks again.

“I feel excited about what will be the BEST party ever! That is until I turn 17,” I tell her with a sly smile.

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ACTIVIT Y

The Party - Part 7

Get It? Use what you have learned from Part 7 of the story to work out these problems.

1. Describe the following terms: a. Mode_________________________________________________________________ b. Bimodal_______________________________________________________________

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c. Multimodal____________________________________________________________

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a. What is the mode? ______________________________________

chocolate bars icy poles popcorn lollies soft drink water muesli bars

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2. You get a summer job at the candy bar in the local cinema. Your boss has asked you to record the sales of each product over one afternoon and figure out the mode.

Here is the data:

b. Why do you think the boss asked for the mode to be found? How could she use this information?

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

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a. the amount of students with birthdays in each month. b. the various ethnic backgrounds of students.

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3. Record the following information regarding the students in your class and find the mode for each:

Consider whether you were able to find the mode or whether the results were bimodal or multimodal.

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4. Your student careers’ counsellor has directed you to a career in advertising. She explains to you that there will be some maths, involved especially finding the mode, median and mean. Can you think of examples when, whilst working on research for an advertising campaign, you may need to determine the mode, median or mean of a set of data: a. for a campaign for a particular brand of milk? ________________________________________________________________________ b. for the latest video game? ________________________________________________________________________ c. for a new sports car? ________________________________________________________________________

44

Compare observed frequencies across experiments with expected frequencies (ACMSP146) Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data (ACMSP171)

Teac he r

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Section 3: Geometry and or eBo st r e p ok u Measurement S

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

o c . che e r o r st super

45

STORY

Christmas Elves - Part 1 Read the story and complete the maths tasks as you go.

or eBo st r e p ok u S

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I re-attach the pom-pom balls that keep falling off my elf shoes and loosen the giant belt buckle around my waist. As far as summer jobs go I thought this would be the easiest - how hard is it to dress up as an elf and take photos of kids on Santa’s knee in the local shopping mall?

I am not feeling very relaxed and neither are the other elves. I didn’t know we were required to set up the display and Santa’s sleigh. I sigh as I stare at my reflection in the mirror of the shopping centre bathroom. I head back to the centre court exhibit that we have been trying to set up in vain the whole morning. One of the elves is scratching his head over some giant wooden letter blocks. As head elf, I try to help.

“These are supposed to be stacked in the corner to make a wooden toy display,” he says to me, desperation etched on his face. “I have 12 blocks to use,” he tells.

“So what’s the problem?” I query inspecting his display. “It looks good.”

“It’s stupid,” he answers.

“It’s not stupid at all, the kids will love it,” I protest.

“No it’s stupid!” he repeats yanking my arm to follow him up the escalators onto the second floor balcony. I stare down at the display. The 6 blocks spell STUPID from above.

Okay I see his point. People gazing down onto the display will only view the blocks from above.

The letters on the top side of the boxes will only be visible. As we hurriedly dash back we notice another problem with the display.

“Oh BUM,” we both say in unison viewing the blocks from the left side as we ride back down the escalator.

“Did you notice anything else?” another elf raises as we arrive back.

We stare at the front of the blocks. Nothing seems obvious for a moment - then I finally see it.

POO! “I don’t know how I did that. I couldn’t have come up with those three words if I tried,” the elf says, shaking his head apologetically.

“Well, we can’t leave it like that. Can you imagine what people’s photos will look like from the front and the side? They will only see the blocks two-dimensionally and they will pick up the typos straight away,” I lament.

Suddenly I have an idea.

“Okay, let’s wrap some of the blocks with Christmas paper to cover the letters and they can be pretend gifts,” I suggest.

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

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ACTIVIT Y

Christmas Elves - Part 1

Get It? Use what you have learned from Part 1 of the story to work out these problems.

or eBo st r e p ok u S

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Teac he r

1. You enter a graphic design competition to design the cover of the program for the school production. You decide to draw 3D square, triangular and rectangular prisms for an art deco style look. Use the dotted paper below to draw these diagrams.

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

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2. Not all cylinders are prisms. Is this statement true or false? Give a reason for your answer and provide an example.

______________________________________________________________________

______________________________________________________________________

______________________________________________________________________

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3. Your grandparents just got back from a holiday in Egypt. They brought you back souvenirs of their trip to the pyramids including a crystal pyramid for your bedroom.

Draw a 3D triangular prism to show what it would look like. How many faces does it have?

Construct simple prisms and pyramids (Year 6: ACMMG140) Draw different views of prisms and solids formed from combinations of prisms (Year 7: ACMMG161)

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STORY

Christmas Elves - Part 2 Read the story and complete the maths tasks as you go.

“Wrapping boxes is harder than it looks,” screeches elf number 4 sitting buried in wrapping paper, sticky tape and tinsel. Her job of wrapping empty boxes to fill in Santa’s sleigh is proving difficult.

“What’s so hard about this?” I pose.

“The company has pre-cut the paper for me!” she says angrily, her face the colour of Santa’s suit. “And they don’t FIT!” she shrieks.

Paper 1

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Paper 2

60cm x 30cm = 1800cm surface area

Paper 3

60cm x 40cm = 2400cm surface area

Paper 4

60cm x 50cm = 3000cm surface area

Paper 5

60cm x 60cm = 3600cm surface area

60cm x 20cm = 1200cm surface area

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I wrangle the sizing guide out of her clenched fist. It reads:

© ReadyEdPubl i cat i ons The look of complete confusion on elf 4’s annoyed face tells me to attempt again. I quickly jot •f orr evi ew pur posesonl y• down the following formula for her:

“It’s not so hard,” I say convincingly. “You simply work out the surface area of a box by calculating the surface area of a cube.”

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surface area of cube = 6a²

I show her. Still nothing on the face of elf 4.

“The surface area of a cube is the area of the 6 squares that cover it. The area of one of them is a².

Since these are all the same, you can multiply one of them by 6, so the surface area of a cube is 6 times one of the sides squared,” I impart on my final attempt. “You can use that figure to decide which size paper to use. I can’t make it any clearer,” I say as I begin to walk away.

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“Ok but, but…what the heck do I use for this?” she cries, showing me a rectangular box.

“It’s also a prism,” I tell her scribbling down a different formula:

surface area of rectangular prism = 2ac + 2ba + 2bc

“There are 2 equal sides on a rectangular box 3 times,” I say.

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a

b

c

story

Christmas Elves - Part 2 I hang around as she gives the measurements a go. She measures one side of the cubed box to be 15cm and uses the calculator to square the number to equal 225cm. Then she multiplies the 225 by 6 to get 1350cm2. I wait for her to look up at me confused. However to her credit she confidently grabs the size 2 sheet of paper and begins wrapping. Before I have a chance to make my escape she apprehends me by the elf shirt.

“Before you run away from me could you please show me how to measure the books?” she pleads in a slightly less angry voice. My eyes set upon a stack of different shaped flat books that need to be wrapped and given away to children. I create some rules for her on the back of a screwed up piece of wrapping paper that she had previously ripped apart in defeat.

or eBo st r e pcalculation ok u Surface area S

Square area = a² a = length of side

a

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She peers at my diagrams with a look of scepticism.

rectangle h area = w x h w = width © Re adyEdPubl i cat i on sI Trust me h = height w am actually pretty

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trapezium area = ½ (a + b) × h h = vertical height

good at this stuff.

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triangle area = ½ × b × h b = base h = vertical height

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“Trust me I am actually pretty good at this stuff. All the books are paperback so they are fairly flat.

Just remember to multiply your answer by 2 as there are 2 sides, the front of the book and the back of the book,” I tell her.

“So the first one will be 30cm, but because there are 2 sides you will need to multiply your answer by 2. So, 30cm² = 900cm and multiplied by 2 = 1800cm. So use paper size 2. This should be all you need to determine paper size and ribbon size and everything else. Ok?” I ask.

She doesn’t reply as she busily endeavours measuring one side of a book and plugs that figure into a calculator. I smile as I walk away.

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ACTIVIT Y

Christmas Elves - Part 2

Get It? Use what you have learned from Part 2 of the story to work out these problems.

1. Solve these: a. How many millimetres (mm) are there in 10 centimetres?

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b. How many centimetres (cm) are there is 10 metres?

c. How many metres (m) are there in 1000 kilometres?

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2. You book a table at the local restaurant for your upcoming birthday. You are told by the restaurant that they have one size square table which is 9m2 that fits all the dishes they serve for everyone to share. If you are inviting 8 friends and yourself, how much room is that per person: a. in square metres? b. in perimeter/metres?

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3. You have been asked by your grandmother to wash and iron all her table linen before she moves house. She offers to pay you $1 per square metre which you politely refuse.

If you would have accepted her payment how much would you have earned?

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1.5m

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5 x square table cloths

0.3m 0.5m

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4 x rectangular table cloths 10 x rectangular tea towels

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Answer:________________________________________________________________

4. Your parents have agreed to upgrade your bedroom with some new furnishings. They firstly ask you to sketch your bedroom with measurements so that they know what to buy when you get to the homewares store. Using what you know about the rules of surface area, sketch the following on the back of this sheet: a. square room with surface area of 25m2 b. rectangular bed with surface area of 2m2 c. rectangular rug with surface area of 6m2 d. rectangular desk with surface area of 0.75m2

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Solve problems involving the comparison of lengths and areas using appropriate units (Year 6: ACMMG137) Establish the formulas for areas of rectangles, triangles and parallelograms and use these in problem solving (Year 7: ACMMG159)

STORY

Christmas Elves - Part 3 Read the story and complete the maths tasks as you go.

Just as I catch my breath my attention veers to another calamity.

“Wow, we are overflowing dude!” cry elf 5 and elf 6.

I watch as the lollies that they are pouring into the huge glass lolly jars overflow and tip all over the floor.

“Don’t empty the whole sack of lollies in,” I plead annoyed.

“Determine whether they fit first,” I grumble at the elves who quickly start picking up the lollies in response.

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“Look it isn’t hard, this is how you measure the volume of a cylinder,” I say feigning calmness.

volume = length x width x height

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… this is how you measure the volume of a cylinder

height

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“Oh yeah I totally remember that from school,” says elf 5.

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“Just remember to check the sack of lollies before tipping them in. It will tell you the volume on the bottom of the sack. So if there are too many, don’t pour them all in,” I command.

o c . che e r o t r s s r u e p Loosen that belt

“Sheesh dude! Why are you so totally grumpy? Loosen that belt buckle a smidgen will ya, and chill,” he replies with a wink while he stuffs a handful of lollies into his pocket. I sigh, some people are just too casual!

buckle a smidgen will ya, and chill

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ACTIVIT Y

Christmas Elves - Part 3

Get It? Use what you have learned from Part 3 of the story to work out these problems.

1. Solve these: a. How many millilitres are there in 1 litre? b. How many millilitres are there in ½ a litre?

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c. How many litres are there in 1000cm3? d. How many litres are there in 1m3?

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2. Your American neighbour asks you how many litres will approximately fit in his 1 gallon water can. You measure the watering can and note that the rectangular can measures 25cm tall x 10cm thick x 15cm wide.

Answer:

3. Its backyard water balloon time! The packet says to not fill them with any more than 450 millilitres. How much is that in litres?

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Answer:

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4. You are working as a junior lifeguard at the local pool. Your boss has asked you to inflate and fill a small paddling pool for the toddlers, as the water in the toddler’s pool has turned a funny shade of green! You inflate the pool and measure it to be 6 metres long x 4 metres wide and 0.75 metres high. However you are told not to fill it more than 0.4 metres deep. How much water will you need?

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Answer:

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5. As a concerned environmentalist you are trying to convince everyone in your street to purchase a water tank to conserve water usage. To argue your case you calculate how much volume each of the 3 top selling tanks hold in cubic metres and in litres.

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Tank 1: 3.5m(h) x 2m(w) x 1m(l)

cubic metres

litres =

Tank 2: 4.25m(h) x 2.75m(w) x 1.5m(l)

cubic metres

litres =

Tank 3: 3m(h) x 1.5m(w) x 0.75m(l)

cubic metres

litres =

Connect volume and capacity and their units of measurement (Year 6: ACMMG138) Calculate volumes of rectangular prisms (Year 7: ACMMG160)

STORY

Christmas Elves - Part 4 Read the story and complete the maths tasks as you go.

“Finally done!” I say throwing my hands up in the air in victory.

“Not yet!” pipes up elf 7 without taking her eyes off her compact mirror she is staring into. “Have you seen the Christmas trees?” she asks with a flick of her long black hair.

“What’s wrong with them,” I ask fearfully. But as I turn my head to look at the cardboard cut-outs that are to decorate the edge of the area, I see the problem.

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“They look ridiculous” elf 7 says, stating the obvious as she points to the green equilateral triangles stuck to brown rectangles.

“They are equilateral acute triangles - the angles are the same,” I point out.

“No, they are not cute, and I know cute,” she declares adjusting her chandelier earnings. They look like arrow signs pointing up,” she states.

“That’s because the angles are the same hence equilateral and less than 90 degrees – a-c-u-t-e,” I repeat. “Every angle must be 60 degrees as the total degrees of the interior angles of a triangle is always 180 degrees,” I ramble.

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I quickly redesign the trees using an isosceles triangle for the tree. I select the bottom two angles to be 75 degrees each and the top angle to be 30 degrees.

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“Oh I love her! Isla Sossi designs like the hottest shoes!” she interrupts as she applies even more lip gloss to her already super shiny lips.

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“…making it look less like an arrow and more like a pine tree,” I explain. “And that wasn’t a designer – I said i-s-o-s-c-e-l-e-s!!”

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“See, now that the angles are different the triangle becomes isosceles…” I begin.

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I make sure I illustrate where the equal sides are using / / and where the equal angles are using .

I instruct them to re-cut the board for the trees and using the following formula for drawing the triangles: X = 75

y = 75

z = 30.

“Ok are we done now? Can we finally open the exhibit and start letting people in to see Santa?” I beg.

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y

“Ready head elf,” all my elves grumble grudgingly.

3 hours and 45 minutes of unsmiling toddlers later and I am truly ready to throw in my elf hat - tomorrow I’m hitting the beach!

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activity

Christmas Elves - Part 4

Get It? Use what you have learned from Part 5 of the story to work out these problems.

1. Name the following triangles: a.

b.

c.

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a. acute

b. right

c. obtuse

d. straight

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2. Draw the following angles:

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12pm

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6am

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3. You are trying to grow a tomato plant for a school science project. You want to ensure plenty of sunshine to grow your plant. At what angle is the plant to the Sun at the different times of the day?

6pm

Convert between common metric units of length, mass and capacity (Year 6: ACMMG136) Connect volume and capacity and their units of measurement (Year 6: ACMMG138) Calculate volumes of rectangular prisms (Year 7: ACMMG160)

Answers - Get It

The Holiday – Part 5, Page 17 1. a. 5/40 + 8/40 = 13/40 b. 5/20 + 4/20 = 9/20 c. 5/2 d. 3/12 + 4/12 = 7/12 e. 7/10 f. 4/10 + 4/10 = 8/10 2. 1/10, 1/6, 1/5, 2/5, ½, 2/3 3. 4/12 eaten and 8/12 left, or 1/3 eaten and 2/3 left.

4. a. 7 b. 1/8

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The Holiday – Part 2, Page 11

The Holiday – Part 6, Page 19 1. a. 0.5 = 50% b. 0.3333 = 33.33% c. 0.1 = 10% d. 0.25 = 25% e. 0.125 = 12.5% f. 0.20 = 20% 2. Yes. 25% of $60 = $15 off 3. 25% = 0.25 40% = 0.40 10% = 0.10 175% = 1.75 50% = 0.50 75% = 0.75 100% = 1.00 80% = 0.80 150% = 1.50 4. a. $350.00 b. $7.50 c. $29.50 d. $50.00 e. $45.01

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2.

3. Teacher to check

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The Holiday – Part 3, Page 13 1. 3:4 2. 5:2 3. 2:1 4. 1:3 5. 1:1 6. 1:4 7. 20:100 or 1:5 8. 2:3:2

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14.2 14.0 4. a. ≥ 175cm and < 190cm b. ≤ 9cm and > 6cm c. ≥ 22 degrees and ≤ 24 degrees d. > 100 people and < 150 people

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The Holiday – Part 1, Page 9 1. -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 2. a. 3 b. -50 c. -2 d. 8 e. 42 f. 139 3. a. -1.75 b. -0.5 4. -162, -154, -124, -100, -56, -45, 0, 25, 97, 130, 185 5. c

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The Holiday – Part 4, Page 15 1. a. True b. False c. True d. False 2. a. $16.00 b. $17.75 3. 15.5 15.9

5.

12 squares 25% of 12 = 3 squares No, you cannot colour in 50% of three squares evenly as 50% of 3 is 1.5 55

Answers - Get It The Holiday – Part 9, Page 26 1. a. 0.2 b. 4 c. 110 d. 10% e. 20% f. 300 2. 10% 3. 2GB 4. Environment Club 15 members 5. 75%

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The Holiday – Part 8, Page 24 1. a. 2 mangoes at $1.20 each or 4 mangoes at $1.00 each. So best buy is 4 mangoes for $4.00. b. 1 macaroon at $2.50 each or 2 macaroons at $2.25 each. So best buy is 2 macaroon for $4.50. c. 2 litre Juice at $1.60 per litre or 1.5 litre Juice for $1.65 per litre. So best buy is 2 litre juice for $3.20.

2. a. $3.50 each day trip or $2.85 each day.

Best buy is $20 weekly ticket which will make each daily trip $2.85. b. You may not need to use the bus ticket on the weekend or perhaps you get a lift from your parents for a few days per week and may not need the weekly ticket.

3. $0.90 each or $0.68 each for a packet of 8.

So, best buy is packet of 8 for $5.50.

4. $6.00 / 5 cards = $1.20 per card 5. a. $15 / 20min = $0.75 per min $30 / 40min = $0.75 per min $50 / 60min = $0.83 per min $55 / 50min = $1.10 per min – Medicine ball will pay the best for the time spent b. Push ups and sprint/stop on clay courts will pay the same rate per minute

The Holiday – Part 10, Page 28 1. 15 2. 12 3. 108 4. 9 5. 37 6. 24 7. 63 8. 66 9. 5 10. 6 11. 4 12. 1 13. 15 14. 75 15. 55

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The Holiday – Part 7, Page 22 1. a.11 b.22 c.4 d.5 e.1 f.3 2. a. 13 + (4 x 5) = 33 b. (11 x 4) + 14 – 4 = 54 c. (15 / 5) -1 = 2 d. (144 / 12) – 5 + 0 = 7 3. 8a +10 = 90 8a = 90 -10 8a = 80 a = 80/8 a = 10 min 4. 25a + 15 = 90 25a = 90 – 15 25a = 75 a = 75/25 a = 3 min

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The Party – Part 1, Page 31 1. ¼ or 25% 2. a. 50% b. 11/100 or 11% 3. 37.71 min 4. a. mean = 191.3cm median = 192cm b. The average height of the team has increased from 1990 by approx. 7 or 8 cm

o c . che e r o r st super The Party – Part 2, Page 33 1.

Answers - Get It 2.

The Party – Part 4, Page 37 1. My score begins high but begins to drop after the first week. In comparison Louie begins on a low score but climbs steadily until his score peaks in the third week.

Louie’s score begins to drop slightly each week after that as mine stops its decline and begins to rise again. We end on the final week on the same score.

2.

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3.

The Party – Part 5, Page 40 1. 8, 9, 11, 11, 11, 14, 15, 15, 15, 15, 19, 19, 23, 24, 25, 25, 25, 25, 27, 28, 28, 29, 31, 31 2.

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The Party – Part 3, Page 35 1. a. mean = 7.2, median = 7, range = 3 b. The range measures the degree of spread in the statistics. That is, the range or spread of the values from the smallest to the largest is 3. Whereas the mean and median attempt to determine the average or middle value.

2. 1/2500 or 0.04% 3. You would expect that over 52 weeks there would be approximately half of the coins tossed resulting in heads and half in tails.

This is because there are two possible outcomes that have the same probability of occurring.

4. a. $22 per person b.

The graph is telling us that numbers between 10 and 30 are the most frequently occurring classes of numbers.

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3. Teacher to check solutions The Party – Part 6, Page 42 1. a. 4/6 or 66.67% b. No, the sample size does not give a good indication of the rest of the population as the Australian population is approximately 24 million and the sample size is 0.000026086% of the Australian 57

Answers - Get It population.

2. 5/25 or 1/5 or 20% 3. a. ¼ b. 1/12 c. 1/48

3.

The triangular cylinder has 5 flat surfaces including the bottom.

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Christmas Elves – Part 2, Page 50 1. a. 100 b. 1000 c. 1,000,000 2. a. 1 square meter per person b. 1.33 meters per person 3. 4 x 3.15m2 and 10 x 0.15m2 and 5 x 2.25m2 = 25.35m2 So $25.35 4.

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The Party – Part 7, Page 44 1. a. Mode is number that appears most frequently in a set of values. b. Bimodal is the term used when there is more than one value that occurs most frequently c. Multimodal is the term used when there is more than two values that occur most frequently in a set of values.

2. a. The mode is popcorn. b. The boss will want to know the mode to find out what kinds of snacks are most popular at the movies during your afternoon shift. She can use this information to restock snack products more efficiently.

3. a. Teacher to check solutions b. Teacher to check solutions 4. a. Teacher to check solutions b. Teacher to check solutions c. Teacher to check solutions

because it has curved sides. Therefore the answer is True: not all cylinders are prisms.

Christmas Elves – Part 1, Page 47 1.

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2. A circular cylinder is not a prism as to be a prism the two parallel ends need to be polygons. Which means that all faces need to be flat. A circular cylinder is not a prism, 58

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The Christmas Elves – Part 3, Page 52 1. a. 1000 b. 500 c. 1 d. 1000 2. 1 gallon = 3750 cm3 = 3.75 litres 3. 0.45 litres 4. 6m x 4m x 0.4m = 9.6m3 This equals 9,600 litres of water 5. Tank 1 = 7m3 = 7,000 litres Tank 2 = 17.5m3 = 17,500 litres Tank 3 = 3.4m3 = 3,400 litres

Answers - Get It Christmas Elves – Part 5, Page 54 1. a. equilateral (all sides equal) b. scalene (no sides equal) c. isosceles (2 sides equal) 2. Teacher to check drawn angles. a. acute - Less than 90° b. right - 90° c. obtuse - More than 90° d. straight - 180°

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3. 6am = 0 degrees 9am = 45 degrees 12pm = 90 degrees 3pm = 45 degrees 6pm = 0 degrees

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