Understanding Everyday Maths - Book 1 by Teacher Superstore

Title: Understanding Everyday Maths - Book 1

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

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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: 978 186 397 910 8 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

7 8-9 10 11 12 13 14 15 16 17 18 19-20 21 22 23 24 25 26-27 28 29 30 31 32 33-34 35

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My First Day In Retail - Part 1 (story) My First Day In Retail - Part 1 (activity) My First Day In Retail - Part 2 (story) My First Day In Retail - Part 2 (activity) My First Day In Retail - Part 3 (story) My First Day In Retail - Part 3 (activity) My First Day In Retail - Part 4 (story) My First Day In Retail - Part 4 (activity) My First Day In Retail - Part 5 (story) My First Day In Retail - Part 5 (activity) My First Day In Retail - Part 6 (story) My First Day In Retail - Part 6 (activity) My First Day In Retail - Part 7 (story) My First Day In Retail - Part 7 (activity) My First Day In Retail - Part 8 (story) My First Day In Retail - Part 8 (activity) My First Day In Retail - Part 9 (story) My First Day In Retail - Part 9 (activity) My First Day In Retail - Part 10 (story) My First Day In Retail - Part 10 (activity) My First Day In Retail - Part 11 (story) My First Day In Retail - Part 11 (activity) My First Day In Retail - Part 12 (story) My First Day In Retail - Part 12 (activity)

4 5-6

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Youth Sports Day - Part 1 (story) Youth Sports Day - Part 1 (activity) Youth Sports Day - Part 2 (story) Youth Sports Day - Part 2 (activity) Youth Sports Day - Part 3 (story) Youth Sports Day - Part 3 (activity) Youth Sports Day - Part 4 (story) Youth Sports Day - Part 4 (activity) Youth Sports Day - Part 5 (story) Youth Sports Day - Part 5 (activity)

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36 37-39 40 41 42 43 44 45-46 47 48 49

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Section 2: Measurement and Geometry

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Section 2: Statistics and Probability

Student Council Elections - Part 1 (story) Student Council Elections - Part 1 (activity) Student Council Elections - Part 2 (story) Student Council Elections - Part 2 (activity) Student Council Elections - Part 3 (story) Student Council Elections - Part 3 (activity) Student Council Elections - Part 4 (story) Student Council Elections - Part 4 (activity) Student Council Elections - Part 5 (story) Student Council Elections - Part 5 (activity)

51 52 53 54 55 56-57 58 59 60 61

Answers

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Teachers’ Notes

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Understanding Everyday Maths - Book 1 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.

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The stories can be read aloud in the classroom followed by individual or small team attempts at the activities. 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 may structure your lessons in a way that suits your students’ needs.

o c . ch eappears in There are three stories in this resource altogether. Each story r e o a different section of the book.r The book ise sectioned staccording to the s r u p 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.

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)

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)

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)

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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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Investigate and calculate ‘best buys’, with and without digital technologies (ACMNA174) Introduce the concept of variables as a way of representing numbers using letters (ACMNA175)

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Year 7 – Statistics and Probability Construct sample spaces for singlestep experiments with equally likely outcomes(ACMSP167)

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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) Solve simple linear equations (ACMNA179) Investigate, interpret and analyse graphs from authentic data (ACMNA180)

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Assign probabilities to the outcomes of events and determine probabilities for events (ACMSP168) 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) Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data (ACMSP171) Describe and interpret data displays using median, mean and range (ACMSP172)

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Section 1: Number and Algebra

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STORY

My First Day In Retail - Part 1 Read the story and complete the maths tasks as you go. Ok, so it’s my very first day. Everyone else is slogging away in cold supermarkets, stacking shelves with incredibly glamorous products like margarine and sponges. Or worse, they’re sporting hideous visors while waiting for customers to resolve whether they want a diet soda with their greasy meal at fast food joints. But not me, uh-uh. I succeeded in scoring a job at PASH after sending 9 application letters to its head office. Persistence does pay off! Anyway, my friends are green with envy. No repulsive hats or shirts to wear, no smelling like hamburgers. I will be besieged by designer clothes and fragrances and I even get to pump my favourite tunes.

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“I will be back before closing,” Jane, my stylish boss, hollers. “Remember everything you need to know is in the manual, if you took the time to study it you will have no problems. I will be meeting with design houses and stockists all day but if you need anything please call me, and good luck,” she imparts with a smile and a wave in a cloud of perfume, leaving me to mind this entire place on my own.

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I flick through the pages of the colossal manual. It tells me that my first task before opening the shop is to set out some stock. The brown dirty stock boxes are sprawled around the dusty storeroom in no particular order. Where do I begin?

20% of the rack needs to contain formal tops 20% of the rack needs to contain skirts 35% of the rack needs to contain dresses 25% of the rack needs to contain pants

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I make racks look happy? The left side of the shop is reserved for the dressier, formal clothes. The instructions state that the 6 metre rack on that left side of the shop needs to be arranged as follows:

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Ok, that doesn’t sound too hard. I know that to make a percentage look like a decimal I need to divide it by 100. So:

20 / 100 = 0.20 35 / 100 = 0.35

25 / 100 = 0.25 It seems I just move the decimal point forward two spaces…my maths teacher would be so proud. 8

STORY

My First Day In Retail - Part 1 Ok, enough praising myself. To calculate the space I have on the rack I need to multiply these decimals by 6 metres. So:

0.20 x 6 = 1.2 metres of formal tops 0.20 x 6 = 1.2 metres of skirts

0.35 x 6 = 2.1 metres of dresses 0.25 x 6 = 1.5 metres of pants

or eBo st r e p ok Of the tops, no more than 10% are to be black. u Of the dresses, 50%S need to be short and the other 50% long.

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Easy! However just before I begin grabbing the stock to hang, I read on:

Of the pants, there needs to be 80% between sizes 8 to 14 as these are the most popular sizes.

Ok, so I guess that’s where the ‘happy rack’ part comes into it. Wow, I need to think about this:

Tops

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Dresses

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10% of 1.2 metres. I guess I just need to move the decimal forward again but this time only one place.

I know 50% is half so 0.50 x 2.1 metres = 1.05 metres of long dresses and 1.05 metres of short dresses.

Pants

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80% of 1.5 metres = 1.2 metres of size 8-14 pants and 0.3 metres of other sizes.

I quickly get to work with my calculation sheet in one hand and tape measure in the other.

ACTIVIT Y

My First Day In Retail - Part 1

Get It? Use what you have learned from Part 1 of the story to work out these problems. 1. 0.1 of 10 = 2. 10% of 50 = 3. 50% of 110 =

% of 40 = 4

% of 30 = 10

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6. If you have 50% of your sister’s share of computer time and your sister is allowed 40% of the total family computer time, how much total family computer time do you have?

7. Which container holds 100% more soda than a 1 litre jug?

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Totally Cool A. 140 pages

Teens 35 pages

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8. Which magazine has 50% less pages than your favourite mag which contains 70 pages?

All About Me

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50 pages

9. On Wednesday night you realise that you are already so tired and it is only midweek! What percentage of the school week is still left?

Curriculum Links: 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

My First Day In Retail - Part 2 Just as I catch my breath my first customer arrives. With a look of determination in her eyes she marches directly to the counter, her stomps echoing on the floating floorboards of the near empty shop. “I want to swap this size 8 top for a size 12,” she barks. Just like that, no ‘Good morning’ or ‘Hi there’. Nope. “Okaay,” I say slowly. “I guess you can take a size 12, as long as this size 8 that you are returning is not worn or um stretched,” I quiver, uncertain whether she is going to take my remark the wrong way. Fortunately she stomps over to the rack and begins hunting through the tops to locate a size 12.

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“I can only find one size 12, but the stitches are unthreading in the sleeve. I will take it only if you give me a discount,” she announces confidently as she pulls apart the sleeve and increases the damage already there. I swiftly flip through my manual as I recall setting eyes on something regarding discounts for damaged stock. Ok here it is:

No more than 1/5 discount is to be given off damaged stock.

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I scribble frantically on a piece of paper:

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Convert fraction into decimal form 1 ÷ 5 = 0.2

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Convert decimal to percentage

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1/5 = ?

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0.20 x 100 = 20%

“I can only give you 20%,” I declare firmly.

She pauses rummaging. “So how much is that off?” I keep scribbling…

Original price = $65

Find percentage of value: 65 x 0.20 = $13

“I can give you 20% off, which is $13 off the original price,” I maintain just as assertively. “Okaay,” she now utters slowly. “I will take it!”

ACTIVIT Y

My First Day In Retail - Part 2

Get It? Use what you have learned from Part 2 of the story to work out these problems. 1. 2. 3.

x 100 =

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1 = 2 1 = 5 1 = 10 1 = 3 1 = 4

6. You want to buy a new scooter for summer but you only have $40 to spend. The scooter you want is $80. Can you afford it if it is on sale with 25% off? Why/why not?

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

7. Use coloured crayons to match the percentages to the decimals.

10%

125%

50%

75%

100%

80%

160%

1.25

0.80

0.20

1.00

0.40

1.60

0.10

0.75

0.50

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40%

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20%

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8. Work these out by moving the decimals. Do not use a calculator. a. $15.00 x 10 = b. $0.45 x 10 = c. $3.95 x 10 = d. $400.00 / 10 = e. $350.10 / 10 =

Curriculum Links: 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)

STORY

My First Day In Retail - Part 3 Mid-morning and I can feel my stomach beginning to eat itself – no breakfast was a sure no-no this morning! I am tempted to run out the back for a muffin and hot chocolate while the store is empty. But I hear the clink of the front door handle once again. A woman paces aimlessly from one rack to another until she halts at the accessory stand. Her eyes - concealed under a pair of huge sunglasses which she has forgotten to remove - observes the Buy five accessories, get one free offer sign. I watch pained as she messes up the entire stand confused. I dash over to assist her.

Buy five accessories, get one free!

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“If you buy five or more items from this stand you get the cheapest item or item of the same value free,” I advise her politely. She instantly takes up the offer and presents to me 6 items to purchase. They are worth $10.50, $15.95, $10.50, $15.95, $13.50 and $19.00. I confidently put them in descending order:

The lowest valued item is free ...

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$19.00, $15.95, $15.95, $13.50, $10.50, $10.50

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She rummages within her bag and presents to me 5 different credit cards to pay for her purchases. “Could you please be a dear and use one card to purchase each item?” she asks sweetly. “You see, I have been spending quite a bit on each card and I’m trying to keep the balances as low as possible. Perhaps you could charge the smallest priced item against the largest credit card?” “Sure,” I reluctantly oblige. She lists me the balances of the cards as: AXZ $214.35; Greater Bank $214.22; Easy Bank $124.80; Town Bank $242.15 and Count Wealth $92.65

o c . c$242.15 e Town Bankh = $10.50 r er o st super AXZ $214.35 = $13.50

I put these cards in descending order and match the accessory item in ascending order.

Greater Bank $214.22 = $15.95 Easy Bank $124.80 = $15.95

Count Wealth $92.65 = $19.00

I then begin the process of charging each card one by one and handing over 5 receipts to the very appreciative accessory lady, who, to my amusement, decides to wear all six purchases together before departing the shop.

ACTIVIT Y

My First Day In Retail - Part 3

Get It? Use what you have learned from Part 3 of the story to work out these problems. 1. Sort in ascending order: 20.3, 10.9, 11.1, 8.30, 9, 7, 11

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2. Sort in descending order: 32.2, 34.5, 35, 33.5, 29.3, 32.8, 32

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1978 Uncle Frank

1971 Aunty Cecilia

1981 Mum

1958 Grandmother Maria

1941 Grandfather Luigi

1963 Grandmother Anna

1977 Dad

2003 Cousin Gabriella

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3. You have been asked to construct a family tree for a school project. The birth years of everyone in your extended family are:

1951 Grandfather Rocco © Read yEdP ubl i cat i ons 2010 Brother •f orr evi ew pur posesonl y• 2009 Sister

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Sort the dates in order to see who is the oldest. Find the ages of everyone in the family.

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4. a. Shade the city that had the coldest winter’s day and is the best skiing hot spot.

Paris -15°C

New York -10°C

Moscow-34°C

Rome -2°C

Honolulu 24°C

Brisbane 18°C

Hobart 0°C

Perth 15°C

b. Number the cities in order from warmest to coldest.

Curriculum Links: Investigate everyday situations that use integers. Locate and represent these numbers on a number line (Year 6: ACMNA124) Compare and order integers (Year 7: ACMNA280)

STORY

My First Day In Retail - Part 4 I wait for her to depart before shoving the muffin in my mouth – no time for the hot chocolate just a sip of water from my water bottle. Luckily I inhale my muffin as a man ambles in appearing lost. He examines some handbags, scratches his head and then glances at me in desperation. I am about to ask him if he is in fact lost when he blurts out, “I need a present for my girlfriend… her birthday was yesterday.” He stands there sheepishly and I lead him towards the perfumes.

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“A nice fragrance should help,” I say. I give him 5 minutes to select one. He rummages amid the bottles clumsily until he requests more assistance. He holds up three different sized bottles of perfume. One is 145 mL for $94.95, another is 210 mL for $135.95 and the other is 85 mL for $55.

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“Which is the best value for money, they are all different sizes?” he queries. Far out, you’re like double my age shouldn’t you know this?! I groan in my head – more maths! I panic for a moment knowing he is expecting me to know the answer. I think hard…I need my pen and paper again for more scribbling. “Um well if you divide each, to figure out how much they each cost per 1 mL then…”

. te o $135.95 ÷ 210 is $0.65 per mL c . ch$0.65 e r $55 ÷ 85 is per mL er o st super $94.95 ÷ 145 is $0.65 per mL

“So what does that mean?” he probes, by now utterly confused. “Well if you multiply all those amounts by 100 mL…”

0.65 x 100 mL = $65 per 100 mL “Then they are all $65 per 100 mL. That means that they are all the same price per mL,” I voice smugly that I was able to work that out. He looks at the perfumes and sings eeny-meeny-mineymo until he lands on the winner. He purchases the gift and strides out satisfied.

ACTIVIT Y

My First Day In Retail - Part 4

Get It? Use what you have learned from Part 4 of the story to work out these problems. 1. Which is the best buy - 3 bananas at $2.00 or 5 bananas at $4.50?

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2. Which is the best buy - 1 cupcake at $3.50 or 2 cupcakes at $6.00?

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3. Which is the best buy - 1 litre of soda for $2.20 or 1.5 litres of juice for $2.50? _______________________________________________________________________

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4. Your favourite singer has just released another awesome single. You have already purchased the first 4 singles released at $3.20 each. Would it have been a better decision to have not bought any singles and waited to purchase the album released next month for $22.50 with 10 tracks? What other reasons might you have for your decision?

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5. Standing in the aisle at the supermarket you can’t decide whether to purchase 4 Choc Mels for $0.90 each or a packet of 8 Choc Mels for $4.00. What is better value?

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6. You open a packet of chips at the cinema that you spent $7.00 on! You complain that there are hardly any chips in the packet and it would have been better to buy popcorn instead. You count only 31.5 chips as you are eating. How much did each chip cost you?

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7. Your mum tries to bribe you: “Pick something to cross off your chores list and receive cold hard cash.”

Wash car for 30 mins = $15

Mow lawn and clip hedges for 60 mins = $20

Clean room for 40 mins = $10 Vacuum and dust entire house for 45 mins = $15 Which job pays the best? Do any jobs pay the same rate? _______________________________________________________________________

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

STORY

My First Day In Retail - Part 5 Right on 12 noon there are no customers in the store so I seize the chance to put the Back in 30 mins! sign on the door and pop into the storeroom for a bite of lunch. I end up working through my break, pen and stock book in one hand and sandwich in the other. There are no more size 8 or size 10 Vincari & Co leather jackets and 6 customers have ordered them. I examine the stock book. There are at present already orders assigned for those sizes in the stock book, so we are way low. I subtract 2 and 4 respectively for those sizes:

or eBo t s r Size Amount e p 6 ok 8 u – 2 = -6 8 -4 S – 4 = -7 10 -3 12 14 16

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Item Vincari & Co Leather Jackets

5 12 7

The manual tells me to maintain a minimum of 8 items in storeroom stock for the designer range as they are not ordered in bulk. If I fall low on stock I must re-order. I locate the number of the fashion agency on a post-it note to arrange an order. As the phone rings I hurriedly construct a table and number line to get my maths right:

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-8

-7

-6

-5

-4

-3

Item Vincari & Co Leather Jackets

-2

-1

Size 6 8 10 12 14 16

8 8 8 8 8 8

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-10 -9

Amount –8=0 – - 6 = 14 – - 7 = 15 –5=3 – 10 = - 2 –7=1

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“Good afternoon Tempt Agencyyyy, Vicki speeaakking!”

“Good afternoon Tempt Agencyyyy, Vicki speeaakking!” squeals a voice on the other end of the line. I introduce myself and place the following order: 14 of size 8; 15 of size 10; 3 of size 12; 1 of size 16. I ask if I may dispatch back 2 size 14s as they have overstocked me. 17

ACTIVIT Y

My First Day In Retail - Part 5

Get It? Use what you have learned from Part 5 of the story to work out these problems. 1. -15 - -15 = 2. -3 + 5 = 3. -10 + -10 = 4. -1 - -4 =

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5. 5 - -3 =

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If 20/20 vision is represented by 0, how much further must your eyesight improve? b.

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6. After a visit to the optometrists you are told that your short-sightedness has got a little better. Yay! Your lenses prescription has moved from -4.25 to -3.75. How much better can you see into the distance?

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8. -6 + 4 +-5 - -80 +73 -2 =

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7. -5 - -4 - -10 – 4 + 12 + 8 =

9. Place the following on a number line: -134, -189, -100, 123, 0, 34, 89, -56, -86, -150, 143

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10. If your freezer is set at -2C and it is melting your favourite cookies and cream ice-cream what should you do? Tick. a. Increase the temperature by 2C? b. Decrease the temperature by 2C?

Curriculum Links: Investigate everyday situations that use integers. Locate and represent these numbers on a number line (Year 6: ACMNA124) Calculate answers to direct number sentences also with correct use of negatives (Year 7: ACMNA280)

STORY

My First Day In Retail - Part 6 I plonk down the phone and immediately it rings again. I answer and as a consequence on the line is my worst nightmare – a telemarketer! “Hi it’s James James from Fave Telecommunications, just wanting to talk to the owner about your phone account,” he perkily declares. “Sorry, did you say your name is James James?” I ask. “Yep James James, my friends call me James squared, get it?” he chuckles. “No,” I reply disinterested.

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“You know James to the power of two…?” he tries again.

“I’m sorry but the owner isn’t here right now, please call back tomorrow,” I apologise honestly and hang up on James squared.

Teac he r

Price – (40% of price) = $50

ew i ev Pr

One of the prerequisites of my job is that I must wear an item of stock. Ah, finally I arrive at one of the perks of this job! I glance in my wallet and uncover I have $50 to splurge on something. With a 40% staff discount off stock, I look for things that are priced at…?? Umm my brain hurts at this point. I need to do more jotting. Ok, I remember something about this in school. When I’m trying to find a value that I don’t know, I need to use a letter like ‘x’ or ‘a’ or whatever …

a - 0.4a = 50

w ww

Step 3: Insert 1 in front of a 1a – 0.4a = 50

. te

m . u

Step 2: Simplify equation

o c . che e r o st Step 5: Get ‘a’ r ons its uown per Step 4: Simplify first part of equation 0.6a = 50

0.6a/0.6 = 50/0.6

Step 6: Calculate ‘a’ a = 50/0.6

a = 83.33333 or $83.30

STORY

My First Day In Retail - Part 6 So I need to find an item of clothing that costs $83.30 or less in order to be able to afford it with the 40% discount. Cool! I head straight for the maxi dress that has been sitting there making eyes at me all day. Perfect! As I rummage through my bag I catch sight of another $40. Should I squander that too? I am tempted. I do now have a part time job I convince myself. I mean, I am getting paid for one day per week. I am getting paid like…like….wait what am I getting paid? I know that my wage is $190 per day including 9.25% superannuation. But how much is going to super and how much to me? Maybe I can use the same sort of maths method:

Teac he r

0.0925a + a = 190

0.0925a + 1a = 190 1.0925a = 190

190

ew i ev Pr

or eBo st r e p ok (9.25 % of wage) + wage = 190 u S (9.25% x a) + a = 190

=e 1.0925 ©aR adyEdaP=u173.91 bl i cat i ons

•f orr evi ew pur posesonl y•

So my wage is $173.91 per day and super must be the rest at $16.09.

w ww

0.0925 x 173.91 = 16.09

. te

m . u

I test that to make certain it’s true:

So, at this rate I can afford some more new clothes! I plunge into my bag and grab the $40. With $40 that means I have another…??? to spend. Here I go again:

o c . Price – (40% of price)e = $40 c h r o a – (0.4 x a)e =r 40 st super 1a – 0.4a = 40 0.6a = 40 0.6a 40 = 0.6 0.6

Ok $66 more to fritter! Yippee!

ACTIVIT Y

My First Day In Retail - Part 6

Get It? Use what you have learned from Part 6 of the story to work out these problems. 1. Find the value of a in the following: a. a + 4 = 5 b. a – 3 = 8 c. 3a + 9 = 15

e. 7a – 7 = 14

2. Write the brackets in the correct place for each. a. 12 + 3 x 5 = 27 b. 11 x 3 + 10 – 4 = 39

ew i ev Pr

Teac he r

d. 5a – 7 = 8

or eBo st r e p ok u S

m . u

w ww

family holiday. During the road trip, your little brother stops for a toilet break 10 times. You moan to your parents that his constant toilet breaks have added half an hour on the trip’s travel time, and this includes the 10 minutes that he spent locked in the toilet as he couldn’t unlock the door by himself. Can you prove this? For how long must each toilet break have been, for the equation to total 30 minutes? Express this in an algebraic equation.

. te

o c . che e r o r st super

Curriculum Links: 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

My First Day In Retail - Part 7 The clock strikes 4 in the shop, great one hour to go - I’m almost there. A woman sweating through her faux fur coat (yes, fur in the middle of the day!) is hovering near a sign in the corner rack that reads: Full priced items 1/2 price. Take a further 1/3 off shoes.

or eBo st r e p o u k $33.4447 for the first pair S $45.22223 for the second pair $55.66667 for the third pair “Sorry I don’t have .4447 in change, can you round up or down?” she says with a smirk on her face. I scan the manual for guidance.

ew i ev Pr

Teac he r

She brings 3 pairs of shoes to the counter and asks for 1/3 off. I plug the discount into the system and it presents me with:

It has the following rules when it comes to rounding:

If <0.04 and >0.03 then round up to 0.05

w ww

If >0.08 and <0.09 then round up to 0.10

m . u

If >0.06 and <0.08 then round down to 0.05

To round to the nearest cent I need to look at the second number before the decimal, therefore:

. te

$33.44447, $45.22223 and $55.66667

o c . che e r o r st super

So, I round up to .45 cents for the first pair, round down to .20 cents for the second pair and round down to .65 cents for the third pair. “So in total, that will be $134.30,” I declare.

$33.4447 1st pair

$45.22223 2nd pair

$55.66667 3rd pair

“Yes, I did it!” exclaims the lady to my surprise. “Huh? “ I ask. “I promised myself I would only spend $130 on shoes, and when I round $134.30 to the nearest $10, then I will still be within my budget.” She swings the bag of shoes over her shoulder and swiftly departs. 22

ACTIVIT Y

My First Day In Retail - Part 7

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

< less than

≥ greater than or equal to

≤ less than or equal to

1. Use the signs above to work out if the following are true or false. a. 5 > 3 b. 3 < 5

d. 7 < 15

ew i ev Pr

Teac he r

c. 9 > 9

or eBo st r e p ok u S

2. You and your friends go to a Mexican restaurant on Friday night. The bill at the end of the night comes to $73.50. There are four of you and you decide to split the bill evenly. What amount will you pay if you need to round the amount to the nearest 10 cents? Will this total leave a surplus or deficit? How much?

Answer:

w ww

. te

3. Your report card is given to you with the following test results:

m . u

o c . che e r o r st super

English 52.47, History 63.88, Maths 73.22, Science 49.98

Your teacher tells you that your marks will be rounded to one decimal place. After rounding all marks to one decimal place, did you pass all of your subjects? That is, did you achieve a mark of equal to or above 50% for all subjects? Report Card Report Card Ben Cousins Taylor RHeport English 52.47 ow

Answer:

ard Card glish J5a2sm History En 63.88 .4in 7 e Ha ppé HistoryEn6g3.li Maths 73.22 sh852 8 .47 H7is3.to2r aths ScienceM49. 98 2y 63.8 8 SciencMe a4th9.s 9783.2 2 Scienc e 49.9 8

Curriculum Links: Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (Year 6: ACMNA132) 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)

STORY

My First Day In Retail - Part 8 4.30pm - almost there! A fundraiser from the Dog Rescue Association walks in and politely requests a donation. I give her $15 from the petty cash tin without examining how much is left in the tin.

or eBo st r e p ok u S

“Cool, thanks!” he says - broad grin now returned. “You’re ok, I mean that’s welcome, I mean that’s ok, you’re welcome,” I stumble as he leaves. I explore the manual for petty cash instructions.

Preserve a $30 float in the petty cash tin at ALL times.

ew i ev Pr

Teac he r

The dreadlocked window washer finishes outside and arrives inside for payment, I reach into the petty cash tin for the second time in ten minutes and there is nothing at the bottom of the tin except a coin from Sri Lanka and a button. He needs twelve bucks and the situation is now becoming awkward for both of us. The broad grin he wore as he walked in, is now starting to droop. I grab $4.50 in coins from my wallet which is now EMPTY and $7.50 out of the till.

I need to deposit $30 in the tin, plus the money that is owed to me and the till.

w ww

I need to cash a cheque for:

m . u

-7.5 + -4.5 = -12

$30 plus $12 that is owed to me and the till.

. te Cash cheque = $42 o c . che e r o r st super

Therefore I should tell the bookkeeper to cash a cheque for $42 so I can put $30 in the petty cash tin, $4.50 in my wallet and $7.50 in the till. The bookkeeper does not come in until Tuesday so I write a note and put it in the petty cash tin.

Please cash a cheque for $42

Petty Cash

$30

Till

$7.50

Lana Jones

$4.50

ACTIVIT Y

My First Day In Retail - Part 8

Get It? Use what you have learned from Part 8 of the story to solve these equations without a calculator. Use the space on the right hand side of this page for working out. Time yourself to see how fast you are. Ready, set, GO! 1. 7.5 + 4.5 = 2. 30 – 12 =

ew i ev Pr

Teac he r

3. 99 + 19 =

or eBo st r e p ok u S

+ 70 = 82

5. 65 -

= 15

6. 7 x 4 =

x 11 = 121

10.

x 12 = 72

w ww

11. 12 ÷ 4 =

12. 50 ÷ 50 = 13. 80 ÷ 4 =

. te

14.

÷ 3 = 25

15.

÷ 8 = 10

m . u

o c . che e r o r st super

Score: Time:

Curriculum Links: 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)

STORY

My First Day In Retail - Part 9 5pm! I gallop to the door and swiftly flip the sign over to closed. I lock the door and turn off the music. Ah peace at last! I realise I still have some work ahead of me as the pack up process appears complicated in the manual. To close the till there are many, many steps. First I need to count what’s in the till and balance it with the cash receipt amount that the till discloses. I have a total of $1,725. My boss has asked me to keep a float of $400 in the till each night which was already in the till at the beginning of the day. So I minus $400 and I am left with $1,325. I put this in the bank envelope which is just an old cloth bag.

$1,325

or eBo st r e p ok GST bank account u 1/10 of the total sales Sneed to be banked into the GST bank account to pay for tax. Teac he r

The manual states that I need to bank the money into the following accounts:

ew i ev Pr

Trading account After this, 1/2 of cash takings that are left go into the trading account.

Term deposit Of the other half, there needs to be 1/8 of that amount placed into a term deposit that exists for staff ’s long service leave entitlements and the rest goes into paying for the loan account.

w ww

m . u

So $132.50 is to be banked into the GST account.

. te 1

Work out trading:

o c . che e r o st s r upe 1192.50r x Multiply fractions with different denominators 1

of (1325 – 132.50) is: 2

1 2

1192.50 = $596.25 2

Calculate fraction

$596.25 to bank into trading account

STORY

My First Day In Retail - Part 9 Staff entitlements:

1 1 of is 8 2

1 1 1 x = 8 2 16

Multiply fractions with different denominators

1 x 1,192.50 = $74.53 16

Calculate cash amount

or eBo st r e p ok u The S rest is to go to the loan account: $596.25 – $74.55 = $521.70

Loan account is to have $521.70

I add these amounts up to see if they total correctly:

ew i ev Pr

Teac he r

So, $74.55 is to be banked into staff entitlements account.

Trading account

$74.55

Staff entitlements account

w ww

$521.70

. te

Loan account

m . u

$596.25

o c . che e r o r st super

Total =

$1325.00

Awesome it works! I rip out the sheet in the notebook and put it in the bag with the cash for the bookkeeper to bank correctly. I check my fraction logic by recalling anything I can from school maths. The only thing I definitely remember is that a boy named Lucas who sits behind me always growls, “I am the DE-NOM-INA-TOR!” like an angry robot every time the teacher explains that the denominator is the bottom number. So that must mean that the top number is the numerator. If I try multiplying the numerator by the numerator and the denominator by the denominator it should work:

1 1 1 x = 2 2 4

That looks good to me. A half of a half is a quarter; perfect! I was right all along.

ACTIVIT Y

My First Day In Retail - Part 9

Get It? Use what you have learned from Part 9 of the story to work out these problems. 1.

1 + 1 = 5 10

1 x 1 = 5 3

1 + 1 = 3 2

1 x 8 = 10 10

or eBo st r e p ok u 1 1 1 1 S 10 5 3 2

6. Place the following fractions on this number line:

1 8

2 5

ew i ev Pr

Teac he r

1 + 9 = 3. 2 2

7. You have eaten three out of four slices of a small pizza. What fraction have you eaten and what fraction is left?

w ww Answer:

. te

m . u

o c . che e r o r st super

8. You have 8 friends who will join you to play soccer on Saturday and 1/2 are left footers. If 1/4 of those left footers score a goal, how many players is this? Express this as a fraction.

Answer:

Curriculum Links: 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)

STORY

My First Day In Retail - Part 10 The $400 float needs to be in the order specified below so I continue the table and add my calculations:

Amount 10 10 10 9 9 4 5 6 7 3 0

Calculations 0.05 x 10 0.10 x 10 0.20 x 10 0.50 x 9 1 x 9 2 x 4 5 x 5 10 x 6 20 x 7 50 x 3 100 x 0

or eBo st r e p ok u S

ew i ev Pr

Teac he r

Money 5c 10c 20c 50c $1 $2 $5 $10 $20 $50 $100

Next I write the answers to my calculations on one of the blue bank teller slips that is in the cash bag.

AXZ Bank Ltd

w ww

Coins/Notes 5c 10c 20c 50c $1 $2 $5 $10 $20 $50 $100 Total

. te

$ 0.50 1.00 2.00 4.50 9.00 8.00 25.00 60.00 140.00 150.00 0 $400.00

m . u

o c . che e r o r st super

I fold the slip in half and stuff it into the till. Another job for the bookkeeper to get to.

ACTIVIT Y

My First Day In Retail - Part 10

Get It? Use what you have learned from Part 10 of the story to solve these equations without using a calculator. Use the space on the right hand side of this page for working out. Time yourself to see how fast you are. Ready, set, GO! 1. 3.5 + 9.5 = 2. 50 – 18 =

+ 60 = 82

5. 43 -

= 13

6. 6 x 9 =

7. 3 x 8 =

ew i ev Pr

Teac he r

3. 77 + 17 =

or eBo st r e p ok u S

8. 10 x 8 = 9. 10.

w ww

11. 24 ÷ 4 =

12. 37 ÷ 37 = 13. 40 ÷ 4 =

. te

14.

÷3=7

15.

÷8=4

m . u

x 11 = 66

o c . che e r o r st super

Score: Time:

STORY

My First Day In Retail - Part 11 Once the till is balanced I stare at my list of after-work reports required.

Staff to record the demographics of the customers who have come into the store. Inlcude gender and postcode.

or eBo st r e p ok u S

ew i ev Pr

Teac he r

This is starting to feel like homework. I am told to record the demographics of the customers who have come into the store, to give the owners an improved sense of the market. I have recorded the gender of the customers all day as well as noted down their postcodes. With this data, I need to determine something called ratios. I draw up the following tally chart:

Women

Men

24 women and 6 men came into the store not including the window washer and the Dog Rescue fundraiser. If I divide 6 into 24, I get 4. This must mean that for every 1 man who came into the store today, there were 4 women. I write this in my report as 1:4.

w ww

Inside Region

. te

m . u

The postcode data seems a little trickier though. I draw up this tally chart:

Outside Region

o c . che e r o r st super

There are 19 postcodes from within our region, and 11 postcodes from outer regions. However, 11 divided into 19 = 1.727272. So it’s like for every 1 person from outside our region, there is 1.727272 people from inside our region. 1:1.727272 doesn’t look right to me, how can you have 1.727272 of a person? Nope I decide if I can’t divide it down evenly then I will leave it as 11:19.

ACTIVIT Y

My First Day In Retail - Part 11

Get It? Use what you have learned from Part 11 of the story to work out these problems. 1. I I I and I I I I = 2. OOOOO and OO = 3. 4.

and and

= and

or eBo st r e p ok u S =

Teac he r

ew i ev Pr

6. For every time you were late to school this month, you were early 4 times. Can you express this as a ratio?

w ww Answer:

. te

m . u

every 5 drops of peroxide you need to add 1 drop of hair colour and then mix. Can you express this as a ratio?

o c . che e r o r st super

Hair Colour

8. You are making your mum a chocolate cake for her birthday. The whole family is relying on you to do a great job. The recipe says that for every one cup of flour that goes into the batter mixture you need to add three tablespoons of water and one tablespoon of butter. Can you express this as a ratio?

Answer:

Curriculum Link: Recognize and solve problems involving simple ratios (Year 7: ACMNA173)

STORY

My First Day In Retail - Part 12 The last thing on my list looks the scariest. I am told to send through to head office a graph of my sales in comparison to Sienna (another employee who works on Fridays) and in comparison to the industry average. I am given this data:

Industry sales average:

Sienna’s sales look like this:

10am = $120

10am = $98

12pm = $366

or e= B 3pm $580 st r e o 5pm = $640 o p k Su 12pm = $305

3pm = $590

Teac he r

5pm = $453

ew i ev Pr

I decide to position this info in a table first and add my sales figures for today:

Sienna

Lana

Industry average

10am

357

120

12pm

305

602

366

3pm 580 422 590 © Read yEdPu bl i cat i ons 5pm 640 195 453 •f orr evi ew pur posesonl y•

. te

m . u

w ww

I then try and graph the information on a line graph using the data to plot points. I know I have to draw a giant L and label the axis. I remember my mum explaining my homework to me once where she pointed out that the vertical axis is always the y axis as the tail of the y is long . Good tip to remember mum! This means that the horizontal axis is the x. I decide to list the dollar intervals along the y axis and the time intervals along the x. I plot the points on the graph carefully where I believe they should be. I even draw a little note on the side to indicate which line represents me and which is Sienna and the industry average. Lastly using the edge of a fashion book as a ruler I connect all the points neatly just like a dot to dot. 700

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

600 Sienna

Dollars

500 400

Lana

300 200

Industry average

100 0

10am

12pm

3pm

5pm

STORY

My First Day In Retail - Part 12 Hmmm, looks like the Swiss Alps! I am advised to explain the data to management and scan and email the report to head office. Sheesh here goes, I hope they don’t think I sound like an idiot!

I begin stronger in the morning as it is Saturday and there are more shoppers around on a Saturday morning. These shoppers are mainly people wandering around having brunch at the café next door, or parents who are dropping their kids off at soccer, tennis, etc. and then have a few hours to spare.

or eBo st r e p ok u S

Teac he r

ew i ev Pr

I peak at 12 noon as the ballet school down the street finishes lessons and lots of girls are wandering the streets outside and are getting lunch at the café next door. I cross with Sienna and the industry average between 12 and 3pm and then my day gets quieter as food places begin to close early. In contrast Sienna finishes strong on Friday night. This is probably because Sienna gets a lot of teenagers come in to the shop after school on Fridays and more people are hanging around the shopping strip as there are a lot of shops open late. Also, the cinema opens for 6pm movie sessions on Friday nights so she has more traffic in the afternoon on Fridays.

As I pull the door to lock up, Jane rolls up!

m . u

w ww

“How did you go? I can’t believe you managed all day on your own today, my buyers’ meetings went way longer than expected,” she rambles. “It was ok, sales were good just a lot more maths than I was expecting!” I say.

. te

“Are you game enough to do that all again next week?” she asks sassily.

o c . che e r o r st super

“Yep, and I will start calculating my pay rise!” I reply cheekily.

ACTIVIT Y

My First Day In Retail - Part 12

Get It? Use what you have learned from Part 12 of the story to complete the task below. 1. Plot the following points on the line graph below. Make sure that you label all parts of the graph.

Y axis

23 25 26 27 r o e t s Bo r e p ok u S

8 27

ew i ev Pr

Teac he r

X axis

w ww

. te

m . u

o c . che e r o r st super

2. Pretend the x axis information above represents the number of siblings in a family and the y axis information represents the corresponding number of shoes owned by the family. Looking at your graph, what conclusions can you draw from the illustration?

______________________________________________________________________

3. On the back of this sheet, write a brief report that explains the possible reasons why the curve is the way it is. Curriculum Links: 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)

s r e p u S

Bo ok ew i ev Pr

Teac he r

Section 2: Measurement and Geometry or e t

w ww

. te

m . u

o c . che e r o r st super

STORY

Youth Sports Day - Part 1 It’s the eve of sports day at the local youth centre, Youth United. Alex and I stand at the edge of the park and grounds that we have to transform into playing fields in a matter of just a few hours. We volunteered for this as it will offer the kids from disadvantaged areas a fantastic and memorable experience. Plus its part of our Social Studies assignment. Best assignment ever – helping kids and playing sport. How hard can it be? I am the Sports Captain at school, so it’s a matter of pride that I coordinate this day perfectly. The sports part will be a blast, it’s the setup beforehand that may be a little complicated.

or eBo st r e p ok u S

ew i ev Pr

Teac he r

Read the story and complete the maths tasks as you go.

The folder in my hand marked ‘Mark and Alex’ contains instructions to create a tennis court, soccer pitch and prep an abandoned swimming pool at the local reserve. The Youth United leaders have asked us to create the court and pitch, adhering to strict measurements as the areas have to meet sport standards in order for all kids to have a ‘fair go’.

a team photo opportunity. I nominated myself as team leader and my friend Alex as my reluctant assistant.

ad court 12m

Tennis Court

m . u

doubles alley 12m

Side A

. teline service

base court 16m

doubles alley 12m

w ww

“Ok…” I say slapping sidekick Alex on the back, “…let’s start with building the tennis court.” To create the tennis court we are given a sketch.

o c . che Perimeter of deuce court eto be deuce court r o 12m ase r st 12m su r pa square. Perimeter of ad court to be 12m as a square.

Side B

Perimeter of base court to be 16m as a rectangle.

Perimeter of doubles alley to be 12m as a rectangle.

STORY

Youth Sports Day - Part 1 “Looks easy enough,” I say to Alex, who gives me a sceptical look with a measuring tape in one hand and a can of spray paint in the other. He is not confident mapping out the lines. “Ok, so according to this we need to ensure that the doubles alley lines are parallel, and that the service line is parallel to the base line,” I say. “The perimeter of each section is listed for us,” I say, showing him. Alex looks stressed. “Ok, don’t start stressing Alex, we got this. It’s just a little maths, that’s all,” I reassure him. We study the instructions one at a time.

- 3m-

Perimeter of ad court is 12m as a square.

or eBo st r e p ok u S Perimeter of deuce court is 12m as a square.

“Just do it, trust me it’s right!” I insist. When he is done I move on to the next piece.

Perimeter of base court is 16m as a rectangle.

deuce court 12m

- 3m-

I instruct Alex to begin spraying a white line for three metres in a square.

- 3m-

ew i ev Pr

Teac he r

This means that the ad court perimeter needs to be 3 x 4; this equals 12 metres.

- 3m-

ad court 12m

© ReadyEdPubl i cat i ons “Alright, perimeter of the base court is 16 square metres in a rectangle,” I voice. “Which means •forf o r evisi e u posesonl y• that the formula thisr rectangle 2aw + 2b =p 16. ” r

And when transposed 2a + 12 = 16

base court 16m

So 2a = 16-12

o c . che e r o r st super - 3m-

a=2

2a + 2b = 16.

ad court 12m

deuce court 12m

- 3m-

. t 2a =e 4

- b-

- a-

w ww

So our formula becomes 2a + (2x6) = 16

m . u

We know that the lengths of the two service courts are 3 metres + 3 metres which equals 6 metres.

Therefore the base court should be 6 metres across and 2 metres down.” I determine without any help at all. “Alrighty, get to work Alex.” He begins spraying lines while I suss out the next problem. His confidence in my abilities is now growing.

STORY

Youth Sports Day - Part 1 Lastly the perimeter of the doubles alley is 12 metres as a rectangle, which means that the formula for this rectangle is 2a + 2b = 12. We know now that the length of the service court is 3 metres down the side, plus 2 metres for the base court side which equals 5 metres.

2a + (2x5) = 12 2a + 10 = 12

- a-

- 6m -

doubles alley 12m

If we rewrite the equation with that info then:

base court 16m

or eBo t s r e 2a = 2 p ok u a = 1S

ad court 12m

deuce court 12m

- 3m-

So the lengths should be 1 metre by 5 metres.

ew i ev Pr

Teac he r

- b-

2a = 12-10

“Alex!” I shout from several metres away, “The doubles alleys are the last ones on either side.” He nods and keeps measuring and spray painting. The total surface area needs to equal 40 square metres for one side of the court and I need to prove this. I quickly add up all the sections inserting the correct measurements on the diagram. The formula for the surface area of a rectangle is length x width. So 8 m x 5 m = 40m2..

m . u

w ww

. te

o c . che e r o r st super

“Excellent Alex, all done. You passed your first challenge and it looks great! Now do it all again on the other side of the net,” I shout.

Looks great, Alex!

ACTIVIT Y

Youth Sports Day - Part 1

Get It? Use what you have learned from Part 1 of the story to work out these problems. 1. How many millimetres (mm) are there in 1 centimetre? 2. How many centimetres (cm) are there is 1 metre? 3. How many meters (m) are there in 1 kilometre?

or eBo st r e p ok u S

ew i ev Pr

Teac he r

4. Draw a diagram to show what 1 square metre would look like. Label the diagram.

5. Work out the surface areas of the following shapes using the information below.

Thes © ReadyE d P u b l i c a t i o n The rectangle parallelogram measures 5.2 metres measures 4.5 •f orr evi ew p u r p o s e s o n l y • by 9.5 metres. metres by 6.5

The square measures 2.5 centimetres by 2.5 centimetres.

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w ww Answer:

metres.

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6. You have been asked by your grandmother to mow her lawn at her country home. She promises you $1 for every square metre you mow. If the diagram below is her property map, how much money can you earn? Show your working out. 12 metres

7 metres Answer:

Curriculum Links: 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

Youth Sports Day - Part 2 “We haven’t checked for parallel lines yet. Didn’t you say something about ensuring the lines are parallel?” Alex points out. “Yes, it just means that the doubles alley lines need to be the same distance apart. So I would just measure the distance of the lines at the baseline end and then again at the net. If the distance between them is the same at both ends then they are parallel,” I explain.

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“They are parallel!” he shouts from the net.

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Alex gets out his measuring tape to see if the lines are parallel. He measures the distance between the doubles alley lines to be 1 metre at the baseline and 1 metre at the net.

“Ok, one task down. Next the water bottles need to be filled with Powerale energy drink,” I say. “What’s wrong with using the Powerale bottles?” Alex asks.

“Well, for some legal reason we cannot just give them Powerale or any other brand so we need to fill the bottles without branding on them. The bottles should just have the Youth United logo on them - ‘Believe’ which they can keep.”

© ReadyEdPubl i cat i ons “Um not quite, the bottles are different sizes. I’m not sure if one Powerale bottle will fit in one of our bottles,” I say. “It says that the Powerale bottles have ao volume of 1o litren right?” I• begin. “And • f o r r e v i e w p u r p s e s l y our rectangular prism-like Youth bottles are? How much?” I query. “Ok, so we have 20 kids coming so we need 20 bottles of Powerale right?” suggests Alex.

Alex shrugs his shoulders. I quickly measure the bottles:

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Width 10 cm

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cm 10

“I know the answer does look high,” I admit. “But if I know that 1000 cm3 = 1 litre then 1500 cm3 = 1.5 litres,” I conclude. “That means that the one litre bottles of Powerale will fill one and a half bottles of a Youth United drink bottle. So if we have 20 kids coming we will need 1.5 x 20 which is 30 bottles of Powerale to fill 20 bottles.” I say smugly.

height 15cm

Alex looks at me with grin.

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I know the formula for measuring volume of a rectangular prism is h x l x w, so to work out the volume in cubic centimetres I multiply 15 x 10 x 10 = 1500 cm3.

width 10cm

Length 10 cm

len

w ww

Height 15 cm

ACTIVIT Y

Youth Sports Day - Part 2

Get It? Use what you have learned from Part 2 of the story to work out these problems. 1. How many millilitres are there in 1 litre? 2. How many millilitres are there in 1/2 a litre?

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3. How many litres are there in 1000cm3? 4. How many litres are there in 10m3?

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Teac he r

5. You have been told by your athletics coach that you should drink 1.5 litres of water per day to stay hydrated. How much is this in millilitres?

6. How many millilitres are there in your favourite fragrance? The bottle measures 10cm tall, 8 cm wide and 5 cm thick.

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w ww

7. You are in the middle of the best peewee motor-cross rally race that you have ever attempted. You are running low on petrol on the 10th lap with only 1 litre left. Your tank holds 7 litres and your older brother offers to go get some more petrol in a cylinder. The cylinder measures 30 cm tall by 20 cm long by 10 cm wide. How much can the cylinder hold? Will it be enough to fill the tank or will your brother have to make another trip to the petrol pump?

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8. You skip breakfast most mornings but have 2 energy milk drinks on the run. How much liquid are you consuming if each carton measures 20cm x 8 cm x 4cm?

Energy Drink

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

STORY

Youth Sports Day - Part 3 “Well I hope it was easy because it looks like we have to do that again,” Alex informs. “Oh,” I reply, slightly disappointed. I stare at the instructions for filling the pool.

Fill the pool with water adding 1 litre of chlorine for every 2 litres of water.

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Teac he r

“Well get to it Alex, you know what to do now. Measure the pool so that we can figure out the volume in cubic metres,” I instruct feigning confidence. I hold the tape for Alex at one end while he measures the width and length of the pool.

The pool measures 15 m x 10 m and is 2 m deep. This means that the volume is 15 x 10 x 2 = 300 metres3 volume.

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200,000 litres of water and 100,000 litres of chlorine.

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tre

s 2 metres

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So if we need 1 litre of chlorine for every 2 litres of water then we need:

15 metres

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300 m3 = 300,000 litres.

I show my scribbled calculations to Alex, hoping for some input. “What about the lane ropes?” he asks ignoring my volume results. “Aren’t they supposed to be parallel?” he points out. He seems to have grasped this parallel line concept really well and won’t let it go. “Well it doesn’t say anything about that in my instructions but I guess we should make sure we tie the lane ropes correctly. You stand at one end and measure the distance between ropes and I will do the same at the other end. If we get the same measurements then we are ok, ok?” I bid. “Ok!” he agrees.

ACTIVIT Y

Youth Sports Day - Part 3

Get It? Use what you have learned from Part 3 of the story to work out these problems. 1. You are doing two weeks work experience with the city’s top architectural firm. Your supervisor has asked you to use a protractor to find some angles on the sketch of the development below – a street of buildings.

or eBo st r e p ok u S

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Using your protractor, find and mark as many different angles as you can on the sketch below. Pair up. Did your friend find any different angles than you?

a. acute_______________________________________________________________

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b. right________________________________________________________________

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c. obtuse______________________________________________________________ d. straight_ ____________________________________________________________

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3. Your baby brother destroys your blank music sheet on which you were going to compose an original piano piece. He seems to have created some interesting angles with his transversal scribbles. Look at the angles marked. Use your protractor to label them either: acute, right, obtuse or straight.

Curriculum Links: 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)

STORY

Youth Sports Day - Part 4 Alex and I take a break and sit on the grass in the sunshine, drinking our melted icy poles. “I wonder how well this project is going to go? I sense it will really give the kids something to look forward to and make them feel like they belong here,” I express. “Yeah, I don’t really care anymore what grade I get on this assignment I just hope that the kids have a great time,” says Alex. “We may even make the local paper!” “Well, we had better keep moving, we still have some work to do,” I say, looking at the next set of instructions.

r o e t s Bo r e The soccer pitch needs its line p ok markings set up as a u rectangle with Ssquare metres a surface area of 375 goalkeepers box

375m2

goalkeepers box

on each side. The width of the soccer pitch is to be no greater than 15 metres as the grass on the outer edges is not suitable or safe to play.

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soccer pitch

“This should be the easiest, right?” Alex asks. “We just have to draw a big rectangle in the grass.” “Hmmm, I don’t think it is that easy, I mean if you think of a soccer pitch we have to separate the two halves and mark out the goalkeeper’s box … let’s just start and give it a go,” I decide.

w ww

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surface area of the pitch needs to be 375 square metres and the width is to be 15 metres then I can calculate the length of one half using the surface area formula of width x length = surface area 2. 15 m x length = 375m2 Length = 375/15 Length = 25 metres

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o c . che e r o r st super 2l x (2x15) = 1500

25 metres each half means that the total length of the soccer pitch is to be 50 metres. The width be no greater than 15 metres. If I input this into a formula then:

And when simplified: 2l x 30 = 1500

If I were to rearrange this to get the length on its own:

2l = 1500 / 30 4

2l = 50 4

l = 50/2 4

l = 25

This means that the length of the pitch needs to be 25 metres in each half. “Have you finished scribbling in that notebook yet? We need to start actually working this out at some stage,” Alex yells at me. 45

STORY

Youth Sports Day - Part 4 “I am working this out! I’m figuring out the length and width on paper first so that we don’t stuff it up,” I retort. “Anyway I have done it, the pitch is to be 50 metres in length and 15 metres in width, which makes the halfway mark…” “I know 25 metres across!” Alex jumps in. “Yep!” I say. “What about the goal posts?” asks Alex. “Aren’t they supposed to be facing each other directly, like, you know, parallel?” says Alex. Here we go again with the parallels!

or eBo st r e p ok u S 25m

goalkeepers box

15m

25m

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“I think it’s important to figure out first how far up the side to place the goals. There needs to be the same room on either side. So like, if the width on one side is 15 metres and the goal measures 3 metres across, that means that there is 12 metres left, right?” I say looking up at Alex for confirmation. Alex is starring at a sparrow. Hopeless! I continue without his attention, “So if we divide that in half we have 6 metres on either side of the goals.”

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w ww

He marks the line markings and we put up the goals and nets together adhering to my calculations. We then make sure that both goals have the same distance of 6 metres on either end to ensure that the goals directly face each other and are in fact parallel. “And do you know what?” I add when we finish. “I reckon I could also mark in the corners for the corner kicks. The angles in the four corners are usually marked out in professional matches - we should do the same here.”

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“Ha! I just got my head around parallel lines, now you want me to figure out angles?” Alex scoffs. “Oh come on, you remember this from school don’t you? When you have two lines that meet at a right angle it’s 90 degrees.” “What if it’s a left angle?” asks Alex.

“No, no, no, a right angle as in, the interior angles of a square or a rectangle are all right angles that equal 90 degrees each. If the angles equal less than 90 then we have accidently marked out a parallelogram – your favourite!” I explain showing him a sketch of a parallelogram to illustrate my point: “If only we had a bird’s eye view, it would be easier to see what we have drawn from above,” he remarks clearly still thinking of the sparrow. “I guess we have to use the good old protractor to find the angle,” I say.

rectangle

parallelogram

ACTIVIT Y

Youth Sports Day - Part 4

Get It? Use what you have learned from Part 4 of the story to work out these problems. 1. Choose the correct mirror reflection of this triangle:

or eBo st r e p ok u S c.

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2. Which shape is a rotation of this triangle:

3. How many degrees are the angles of a square? 4. How many degrees are the angles of a triangle?

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5. Add the angles of the following shapes:

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6. Your driving test is coming up and your Learners Manual keeps referring to parallel lines. You decide to look into it further. Draw three sets of parallel lines:

7. Which cars are parked parallel to car a?

Curriculum Links: Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (Year 6: ACMMG142) 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. Investigate conditions for two lines to be parallel (Year 7: ACMMG159 & ACMMG164)

STORY

Youth Sports Day - Part 5 “Ok, last instruction on the list,” I say with a sigh.

Use wooden boxes to make a set up for a team photo for the school newsletter. “The cubes need to be stacked so that the people sitting at the back are the highest just like spectator stands,” I say as I watch Alex shift boxes around and stack them in different patterns. “No, not quite Alex, you have to sort of…well…like argh! It’s hard to explain. Hang on a sec I will draw it for you.” I cry. “So it should look something like this from the side so that the kids will be sitting on three different levels and everyone can be seen in the photograph,” I explain showing him a sketch.

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“What no questions? You get this just from a drawing? It will look different from the front you know,” I inform as he ignores me.

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Alex glances at the sketch and silently starts shifting and stacking boxes.

I sit back and wait for him to finish.

“Done!” he says proudly throwing his hands up in the air. I walk around to the front of the stack and see perfectly formed seating.

And we area finished now. © ReadyEdgood. Pu bl i c t i on sWe are ready to go for tomorrow’s sports day.” •f orr evi ew pu po e sonl yyanks • the As r I pack ups the equipment Alex “Hey you did it!” I state happily. “That looks

whistle from my neck.

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Done!

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“And you will make a splendid assistant. I think the student has overthrown the master!” he says arrogantly. “Sidekick Mark, has a lovely ring to it!”

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“Hey you did it!”

ACTIVIT Y

Youth Sports Day - Part 5

Get It? Use what you have learned from Part 5 of the story to work out these problems. 1. Draw a cube, rectangular prism and a 3D pyramid using the dot to dot. Write down the number of faces for each prism in the space provided. cube

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rectangular prism

3D pyramid

w ww

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______________________________________________________________________

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3. How many blocks are there in these building blocks?

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

s r e p u S

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Section 3: Statistics and Probability or e t

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STORY

Student Council Elections - Part 1 Read the story and complete the maths tasks as you go.

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Number of flyers printed by each candidate

Candidate 2 d Candidate 3 P Candidate 4c Candidate 5s Candidate 6 © Rea yEd ubl i a t i on 120 95 115 110 450 •f orr evi ew pur posesonl y•

Candidate 1

135

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Teac he r

Student representative council elections are finally here! I have waited a long time to be the next Julia Gillard - it is a very big deal at our school. I will listen to the students’ requests. I will push for a coffee vending machine instead of the soft drink machine. I will campaign for the students’ choice of musical school production, the students’ chosen theme for the school formal, and for the best ski location at the next retreat. Yes, I have loads to accomplish! Our school sets up the student council elections each year just like a real political ballot vote. The election process is held over 4 weeks of campaigning. I saunter into the rec room during lunch to congregate with my team; Team Eva. My team or ‘party’ as it’s known in politics, mainly includes a few close friends. They are huddled around a table deep in planning. “Hey, I’m here,” I announce. “What did I miss?” No one offers any news. “Anyone?” Serena looks up from her magazine. I target her. “Serena, I asked you yesterday to find out the average amount of flyers needed. Did you get the dirt on the other campaigns? I need to know how many I should print to keep in line with the other candidates.” “Ahh, yes,” she says slowly. “This is what I found.” She hands me a sheet:

“Amy translate this please. Advise me on the best amount to go to print.” Amy is my statistics guru! A maths wiz and the brainiest on our team, she is like a human calculator.

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The range is 355. Which is achieved when you minus the smallest number from the largest (450-95),” she says.

“What? 355 that’s the range? But that doesn’t sound right.” “Well one of the candidates, obviously Candidate 6, has a dad who runs a FastPrint store and can print as many flyers as she likes even if she doesn’t need them,” explains Serena. “I guess she is going to stuff as many as she can in lockers and hand out loads of them to flood the school with just her flyers”. “The range does not really work if there is an outlier value - it skews the result,” adds Amy. “We can use the mean for the average then. That is, you add all the values and divide by the number of values to get 1025 / 6 = 170.833. This is the average amount of flyers that the Candidates are printing and giving out. It’s a little higher than normal, but at least you won’t get swamped by Candidate 6.” “Great, done!” I determine.

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ACTIVIT Y

Student Council Elections - Part 1

Get It? Use what you have learned from Part 1 of the story to work out these problems. 1. Friday night is family board games night. Your little sister is accusing you of cheating. You explain that it is impossible to cheat. How do you prove to her that you have equal probability of landing on every colour? That is, what are the chances of landing on green, red, blue and yellow? Express the probability in fraction form and also as a percentage.

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Percentage:

2. What is the probability of rolling a six on a dice? Fraction:

3. You work the following hours at the local supermarket this week: 4 hours 3.5 hours 4.5 hours 3 hours 2.5 hours How many hours do you work on average each day?

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Teac he r

Fraction:

4. You are enjoying watching the Summer Olympics on T.V. The commentator remarks that the average speed of the 100 metre sprint is 10.359 seconds. This doesn’t seem right to you as you are sure that the Jamaicans have pushed this average under the 10 second mark. You decide to do your own calculations with the following race statistics:

9.345

9.568

10.432

9.999

10.871

9.432

9.001

10.852

10.040

9.331

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Is the commentator correct? _______________________________________________ 5. Your weekend tennis match starts in the usual way with a coin toss to decide who serves first. You win the coin toss – what are the chances of this happening? Can you express this as a fraction and a decimal?

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______________________________________________________________________ 6. a. Use the median to gain the average of the following maths test results:

88.50% 90% 56.5% 70.5% 62% 73.5% 76% 79.5% 85% 59.5% 68% ______________________________________________________________________ b. You have scored 73.5 on a maths test. How did you fare compared to the average using the range? Can you explain? ______________________________________________________________________ ______________________________________________________________________

Curriculum Links: 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)

STORY

Student Council Elections - Part 2 “Ok Anna you’re up. Your job was to research how many votes have secured past students a win in the student council elections. What’s the verdict?” Anna rummages through her notebook. “Well in past year the amount of votes that won the election were …” She presents me with a table.

Number of votes that won the Student Council Election 2006 - 2014 2006 298

2007 358

2008 247

2009 450

2010 453

2011 423

2012 425

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2013 380

2014 395

In silence we all turn to Amy with ‘What does that tell us?’ written on our faces.

Teac he r

247

298

358

380

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Without a word from us, Amy begins, “So if we put these results in numerical order they are …” Amy scribbles on a scrap piece of paper:

395 423 425 450 453

“If we use the median of the winning votes from the previous 9 years – the median being the middle number - than you will probably need, like, 395 votes to win,” Amy concludes.

w ww

“Ok, but how many chocolate bars do we need?” questions Anna. “Our budget is only, like, $47 for the whole campaign. That’s the money that we’ve raised.” We all look at Amy for the answer.

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With a look of amusement on her face Amy begins, “In the past 3 weeks we have had the following visitors to our lunchtime stand. Amy rips out a page from her notebook and pushes it under our noses.

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“Ok, great I will need to keep that in mind,” I say not so confidently - it seems like a lot. “Now what I was thinking is that I need to hand out more than just flyers, how about we bribe the votes with chocolate?” I suggest.

o c . che14, Wednesday 17, Thursday e15, Friday 12 r Monday 14, Tuesday o r st sWednesday per Monday 12, Tuesday 17, u 14, Thursday 15, Friday 14

Monday 11, Tuesday 18, Wednesday 15, Thursday 14, Friday 14 To get the mode let’s just put them in order:

11, 12, 12, 14, 14, 14, 14, 14, 14, 15, 15, 15, 17, 17, 18…”

“…and if I take the most occurring number, it is 14 right, Amy?” I ask. “Right!” confirms Amy. “Ok so about 14 chocolate bars for each day next week, first in best dressed,” I decide. 53

ACTIVIT Y

Student Council Elections - Part 2

Get It? Use what you have learned from Part 2 of the story to work out these problems. 1. You agree to help out at your Uncle’s fruit shop for some extra cash on the summer holidays. He asks you to find the average amount of watermelons sold for the week You estimate the number of watermelons sold each day to be: Monday: 18, Tuesday: 16, Wednesday: 12, Thursday: 20, Friday: 22 Find the average using the mean, median and range methods.

or eBo st r e p ok u S median:

mean:

range:

Teac he r

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2. You enter a radio competition to win a meet and greet with your favourite singer. If you know that 3,500 other people have also entered, what are the chances of you winning? Display your chance as a fraction and a decimal. _____________________________________________________________________

3. You bring home a book of raffle tickets to sell for a fundraiser. No-one seems interested in buying them as they think that there is no chance of winning. You buy the whole book of tickets and vow to share your prize with no-one when you win. If you buy 20 tickets and there are 10 books of 20 tickets available in the barrel, what chance do you have of winning? Express the answer as a fraction and percentage.

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4. You get a job waiting on tables. After counting your tips earned after a week you discover you have earned $73.40. If you worked 4 hours each night for 5 nights, how much did you earn in tips per hour on average?

w ww

_____________________________________________________________________ 5. Study these viewer phone results of the Australian Star singing contest on T.V.

James

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Sam

1653

Jessica

1345

Marcela

1565

Emilio

1376

NSW

1876

o c . che e r o r st super VIC

QLD

TAS

1562

2610

787

1277

1621

879

1765

1498

889

1301

1065

1090

1398

1423

1608

1342

1454

907

1456

1675

1027

986

1533

1690

2678

1865

1008

1453

1254

1041

a. What was the average vote of each contestant using the mean? James

Sam

Jessica

Marcela

Emilio

b. Using the totals of each contestant vote, create a bar graph on the back of this sheet.

STORY

Student Council Elections - Part 3 I gaze up at what is marked on our white board. There is the list of student groups and a bunch of numbers next to them - our target groups. There are 7 different groups to target: band members, athletes, mathletes, drama club members, environmentalists, tech wizzes and other. Each group will have its own preference for student leader according to its interests. “What’s up with our numbers?” I demand. “We did the sample,” Sarah offers. “The what?” I query.

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“The sample. You know you asked me to do a sample of each group and ask a few students from each group who they would vote for. Here are the results” She opens her notepad:

The Sample

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Athletes 5 Mathletes 6 Tech Wizzes 4 10 10 10 Drama Club Members 7 Environmentalists 5 Other 6 10 10 10

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Band members 4 10

I stare at Amy with my eyebrows raised.

She tries to enlighten me, “In percentages, this is …” I peer over her shoulder to study her notes.

Band members 40% Athletes 50% Mathletes 60%

Environmentalists 50%

Other 60%

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“I still don’t know what to make of this, what does this mean overall?” I plead for a simple answer. “Well, to find the average of your predicted votes via the sample: I add these up and divide by 7 (370/7 = 52.85) then the average total vote you will get seems to be 53%. So more than half of the total vote will be for you,” Amy declares.

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“Well why didn’t you just say so from the start.” I roll my eyes. “So, is that it?”

“There’s more. The early votes in absence for the students who will be away during Election Day show you in a race with the other 6 candidates in this dot plot. Each dot represents 1 anonymous vote. It shows the frequency that a student voted for you,” Sarah explains showing me the dot plot.

Dot Plot

  



 



“If this is indicative of the result I am doing well,” I say, pleased with what I see. 55

ACTIVIT Y

Student Council Elections - Part 3

Get It? 1 Use what you have learned from Part 3 of the story to work out these problems. 1. Look at the data below. 43.5

56.6

45.6

34.5

65.4

34.5

76.3

54.9

43.1

67.4

45.2

65.8

45.2

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a. Find the mean of the data:

c. Find the range of the data:

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b. Find the median of the data:

d. Looking at the results from the first three questions, what can you tell about the results?

______________________________________________________________________

2. Roll a dice 10 times and record your results in the table below.

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What would you expect the results to be like if you were to roll the dice 1000 times?

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______________________________________________________________________ 3. After losing two games of Seven Up, you accidently throw the pack of playing cards off the dining room table onto the floor. Your best friend tells you that if you pick up any card in the suit of spades with your eyes shut, she will let you win the next two games. Research your chances of picking up a spades suit card.

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______________________________________________________________________

4. You are at Game Galatica, your local gaming arcade. You put $1 in the big wheel to attempt to spin 500 points for a cool prize. a. What is the probability of spinning number 10? b. What is the probability of landing on a diamond?

12 1 11   2   10   3 9



4



 8  5 7 6

Curriculum Links: 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)

ACTIVIT Y

Student Council Elections - Part 3

Get It? 2 Use what you have learned from Part 3 of the story to work out these problems. 1. Study the following column graph which shows your best bowling score for the past 6 Friday nights, in comparison to your twin brother.

100

60 40 20 0

Fri 1st Oct

Fri 8th Oct

Fri 15th Oct

Fri 22nd Oct

Fri 29th Oct

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TeacBowling score he r

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Sibling

Fri 5th Nov

© ReadyEdPubl i cat i ons What can you interpret from the data display? ________________________________ •f orr evi ew pur posesonl y• ______________________________________________________________________

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______________________________________________________________________

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______________________________________________________________________ 2. You argue with your mum that people need at least 10 hours sleep each day after she almost threw you out of bed on Saturday morning. To illustrate this point you collect the following information from friends and family:

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o c . Person c e her r o st super Dad - 55 years old Aunty Etta - 67 years old Jimmy – 2.5 years old Judy – 5 years old Emily – 16 years old

Approx. hours of sleep per night 7 9 12 11 11

Represent the above information in a bar graph on the back of this sheet.

STORY

Student Council Elections - Part 4 “You are the mean! You are the mean!” squeals Ellie our Hong Kong exchange student as she races in clasping the school newspaper.

You are the mean!

“I’m not mean!” I say. “She means ‘you are the man’ or woman in this case,” offers Serena. “No, you are the mean,” Ellie insists. She explains that according to an independent survey reported in the school newspaper, out of a possible 460 votes I am to get the following votes in comparison to the other candidates:

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“How does that make me mean?” I ask.

“She’s right – you are the mean, or the average,” adds Amy. She continues,

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Eva - 65 Candidate 1 - 45 Candidate 2 - 40 Candidate 3 - 85 Candidate 4 - 90 Candidate 5 – 75 Candidate 6 – 60

“If you add all the votes together and divide by the amount of candidates, 7, then the average amount of votes that each candidate will get seems to be 65 votes. And you are right on that average. Some candidates will get more and some will get less.”

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conclude. “Ellie, did you complete the extra research that you promised?” I ask her as she unloads her papers from her backpack. “Yes,” she says proudly plonking down a dot plot for me to study.

Hair colour study of winning candidates 1994 to 2014

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Medium Brown

Light Brown

Dark Blonde

Blonde

Red

Auburn

“What is this?” I question. “Well, I went through the school year books from 1994 to 2014 and this dot plot shows that the majority of winning candidates from the past 20 years have had auburn hair!” she says proudly. “Huh?” I say. “Students with auburn hair won the election more frequently than any other colour hair,” she tries again. “Yes, but how does that help me?” I ask impatiently. “Perhaps you should colour your hair?” she says. “Thanks Ellie, that is very helpful!” I say sarcastically, ending the ridiculous conversation. 58

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Student Council Elections - Part 4

Get It? 25 20

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Months

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1. You are planning on spending the next month at your grandparent’s beach house along the peninsula. You are desperate for a month of sun after a long winter. After researching the average January temperatures for the region, you discover this graph (right) online.

Average Daily Temperature

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

Does January have the highest average temperature during the year? What other information can you deduce from the graph?

______________________________________________________________________ ______________________________________________________________________

______________________________________________________________________

Help him display this information in a bar graph below.

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parents. He asks you to help him convince them to increase his allowance. You give him some statistics that you found online (below right).

Average Weekly Allowance of Australian Children

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Age

$10

$12

$14

$16

$20

$25

$30

$35

Curriculum Links: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (Year 6: ACMSP147) Interpret secondary data presented in digital media and elsewhere (Year 6: ACMSP148) 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

Student Council Elections - Part 5 “Ok, Ok,” Ellie waves her arms around noticing my apathy. “This one I’m sure you will love. Most students in our year level have birthdays this month falling between the 20th and 29th.” She shows me what appears to be a stem and leaf graph with the days of October.

STEM LEAF “So?” I say.

0 3, 5

1 5,8,8

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

3 0,0

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“Well, that means they are mostly Scorpios born in the Year of the Rooster which means they are highly suspicious but very loyal once their trust is gained. So it is vital that your strategy is designed around gaining their trust before the voting starts next week,” she explains matter-offactly.

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“Ok Ellie, you are officially the worst researcher ever!!! What about the other students born in the other 11 months of the year?” I point out. She pauses. “Oh yeah, I didn’t think of that. But the stem and leaf plot is a nifty little graph right?” she remarks, still satisfied with her results. “Ok, I think I have something that can help,” jumps in Anna to my delight. “I did a survey sample of 100 students…” “Please don’t tell me that you asked them what their favourite colour is or how many pets they have or something equally unhelpful,” I plead.

“Ah no, my survey asked what is the single most important thing that they would like the new school captain to consider. The 100 students surveyed said that they would vote for the following.” Anna holds her notepad up. We all lean in to read it:

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18/100 20/100 15/100 11/100 10/100 26/100

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Formal theme and location: Coffee machine in senior foyer: An upgrade of the student rec room: Retreat location: New swim team caps and bathers: Healthier food options in the canteen:

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“OOHH interesting!” I say rubbing my hands together. “I should therefore focus mainly on the canteen food as this is the most frequent item voted for. Perhaps I should start writing a speech outlining my commitment to healthier food options and declaring it as one of my top priorities. Who would like to write my speech?” I ask to which immediately everyone turns away and pretends to be busy. “Oh come on, everyone knows that the speech writers are the real puppet masters of every great political victory,” I insist. Still nothing. “Ok, whoever writes my speech will receive all the left over chocolate from our lunchtime stand,” I say trying a different tactic. “I’ll do it!” everyone replies in unison. 60

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Student Council Elections - Part 5

Get It? Use what you have learned from Part 5 of the story to work out these problems. 1. Prepare a bar graph that displays the following information about the number of text messages you sent in one week. Day of the week

Number of texts

Monday

Tuesday Wednesday Friday

3 4 5 7

Saturday

Sunday

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Thursday

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

166 – 170 cm

171 – 175 cm

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161 – 165 cm

176 – 180 cm

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Height range

3. Prepare a pie graph showing the following information about the Australian cricket team’s run rate for the last 5 test matches. Opponent

West Indies England

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South Africa

560

India

470

Pakistan

394

Convert the runs into percentages and label the graph via a colour-coded system.

Curriculum Links: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (Year 6: ACMSP147) 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)

Answers - Get It

Section 1: Number and Algebra My First Day in Retail - Part 1, Page 10 1. 1 2. 5 3. 55 4. 10% 5. 33.33% 6. 20% 7. C 8. B 9. 40%

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My First Day in Retail – Part 2, Page 12 1. 1/2 = 0.50 x 100 = 50% 2. 1/5 = 0.20 x 100 = 20% 3. 1/10 = 0.10 x 100 = 10% 4. 1/3 = 0.33 x 100 = 33% 5. 1/4 = 0.25 x 100 = 25% 6. No. 25% of $80 = $20. Therefore it will cost $60. 7. 20% = 0.20; 40% = 0.40; 10% = 0.10; 125% = 1.25; 50% = 0.50; 75% = 0.75; 100% = 1.00; 80% = 0.80; 160% = 1.60 8.a.$150.00 b.$4.50 c.$39.50 d.$40.00 e.$35.01

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My First Day in Retail – Part 4, Page 16 1. The best buy is 3 bananas at $2.00 = $0.67 each because 5 bananas at $4.50 = $0.90 each. 2. 1 cupcake at $3.50 = $3.50 each and 2 cupcakes at $6.00 = $3.00 each so the latter is the best buy. 3. 1 litres of soda at $2.20 = $2.20 per litre; 1.5 litres of juice for $2.50 = $1.67 per litre so the latter is the best buy. 4. Singles = $3.20 each as opposed to $2.25 each track on the album. So album would be the best buy. One reason that may affect your decision could be that you don’t want to wait for the album release. 5. 4 Choc Mels at 0.90 each and 8 Choc Mels at $4.00 = $0.50 each. So the latter is better value. 6. 22 cents per chip. 7. $15 /30 = $0.50 per min – pays the best $10 /40 = $0.25 per min $20 /60 = $0.33 per min - same rate as vacuum $15 /45 = $0.33 per min - same rate as mowing the lawn

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My First Day in Retail – Part 3, Page 14 1. 7, 8.3, 9, 10.9, 11, 11.1, 20.3 2. 35, 34.5, 33.5, 32.8 32.2, 32, 29.3 3. 1941 Grandfather Luigi 1951 Grandfather Rocco 1958 Grandmother Maria 1963 Grandmother Anna 1971 Aunty Cecilia 1977 Dad 1978 Uncle Frank 1981 Mum 2003 Cousin Gabriella 2009 Sister 2010 Brother Age depends on current year. 4. a. Moscow -34oC b. 1st Honolulu, 2nd Brisbane, 3rd Perth, 4th Hobart, 5th Rome, 6th New York, 7th Paris, 8th Moscow

My First Day in Retail – Part 5, Page 18 1. -15 - -15 = 0 2. 2 3. -20 4. 3 5. 8 6. a. 0.50 b. 3.75 7. 25 8. 144 9. 10. b.

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My First Day in Retail – Part 6, Page 21 1. a.1 b.11 c.2 d.3 e.3 2. a.12 + (3 x 5) = 27 b.(11 x 3) + 10 – 4 = 39 c.(10 / 5) – 1 =1 d.(144 / 12) – 8 + 3 = 7

Answers - Get It 3. 10a + 10 = 30 10a = 30-10 10a = 20 a = 20/10 a = 2 minutes per toilet break

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My First Day in Retail - Part 8, Page 25 1. 12 2. 18 3. 118 4. 12 5. 50 6. 28 7. 40 8. 72 9. 11 10. 6 11. 3 12. 1 13. 20 14. 75 15. 80

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My First Day in Retail – Part 7, Page 23 1. a. True b. True c. True d. True 2. 73.50 / 4 = $18.375 each or $18.40 $18.40 x 4 = $73.60 Surplus of 10 cents 3. English 52.50% History 63.90% Maths 73.20% Science 50.00% Yes all subjects passed.

My First Day in Retail – Part 10, Page 30 1. 13 2. 32 3. 94 4. 22 5. 30 6. 54 7. 24 8. 80 9. 12 10. 6 11. 6 12. 1 13. 10 14. 21 15. 32 My First Day in Retail – Part 11, Page 32 1. 3:4 2. 5:2 3. 3:1 4. 1:1 5. 2:1 6. 1:4 7. 5:1 8. 1:3:1

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My First Day in Retail – Part 12, Page 35

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My First Day in Retail – Part 9, Page 28 1. Fractions with different denominators need to firstly have the same denominator before adding together. So convert to 10/50 + 5/50 = 15/50 or 3/10 2. Convert to 2/6 + 3/6 = 5/6 3. 10/2 or 5/1 or simply 5 4. 1/15 5. 8/100 or 4/25

1. 2. As the amount of siblings increase the amount of shoes increase. However once the sibling number exceeds 5, the number of shoes do not increase so much at all. This may be because siblings start sharing shoes and not as many need to be purchased.

6. 7. Answer: 3/4 eaten and 1/4 left 8. 1 player or 1/8 63

Answers - Get It

Section 2: Measurement and Geometry Youth Sports Day – Part 1, Page 40 1. 10 2. 100 3. 1000

Youth Sports Day – Part 5, Page 49

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4. 5. Square = 6.25 m2 Rectangle = 49.40m2 Parallelogram = 29.25m2 6. Square = length x width Square = 12 x 12 Square = 144m2 Triangle = ½ (length x width) Triangle = ½ (7 x 12) Triangle = ½ x 84 Triangle = 42m2 Total Surface area = 144 + 42 = 186m2 so you earn $186!

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5. a.360° b.180° c.180° d.360° 6. Teacher to check parallel lines 7. c and d

1. 2. c. 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 cylinder is not a prism, because it has curved sides. 3. 16 blocks.

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Section 3: Statistics and Probability Student Council Elections – Part 1, Page 52 1. Fraction: 1/4 Percentage: 25% 2. 1/6 3. 3.5 hours per day 4. No. Average time is 9.887 5. ½ or 0.5 6. a. 73.5% b. By using the median you can see that the score of 73.5% is equal to the average mark. That is, the score is not higher or lower than the average.

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Youth Sports Day – Part 3, Page 44 1. Teacher check 2. a. angle less than 90° b. angle is 90° c. angle more than 90° and less than 180° d. angle is 180° 3. Teacher check Youth Sports Day – Part 4, Page 47 1. a 2. b 3. 360° 4. 180° 64

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Youth Sports Day – Part 2, Page 42 1. 1000 2. 500 3. 1 4. 10,000 5. 1500 millilitres 6. 400cm3 is the volume which holds 400ml 7. 6000cm3 is the volume which holds 6 litres. Add 1 litre already in the tank which makes 7 litres, hence it will be enough to fill the tank. 8. 640cm3 x 2 cartons which holds 640mls each. In total 1280mls or 1.28litres

Student Council Elections – Part 2, Page 54 1. mean: 17.6; median: 18; range: 10 2. 1/3500 or 0.00029 3. 20/200 or 1/10 or 10% 4. $3.67 per hour 5. a.

Answers - Get It James

Sam

1516

1323

Jessica Marcela 1353

1418

Emilio 1525

b. 2.

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Student Council Elections – Part 3, Page 56 1. a. 52.2 b. 45.6 c. 41.8 d. The mean, median and range all give a similar approximate as to the average value for the set of data. 2. You would expect the result to show that each number from 1 to 6 will be almost evenly rolled as each number has the same probability of being rolled. That is, each number has a 1/6 chance of being rolled so over 1000 rolls of a dice, each number should be rolled approximately the same amount of times. 3. As there are four suits in a deck of cards; spades, clubs, hearts and diamonds, this means that there is a 1/4 chance of picking up a card from the suit of spades. 4. a.1/12 b. 4/12 or 1/3

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Student Council Elections – Part 4, Page 59 1. Yes, January and February appear to have the highest average temperatures for the region. December also has a higher temperature than most months, however March shows a significant drop in temperature.

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Student Council Elections – Part 3, Page 57 1. I began the month at a medium level but dropped slightly after a few weeks. I then picked up pace and finished the month strongly. In comparison to me, my brother began strong but then lost momentum mid-way through the month dropping his score significantly. He began to improve steadily after this slide, however it was not by enough to supersede me.

Pakistan

India

West Indies England

South Africa 3.

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