Connections Through Surfing

SurfAid International, Billabong International & Northern Sydney Region Department of Education and Training Connections through Surfing Year 9/10 Mathematics Unit of Work Stage: 4, 5 KLA: Mathematics Focus: Commercial Arithmetic and Probability Duration: 5-10 Weeks

Concept: Applying probability and consumer arithmetic to planning a surfing holiday

Key Question: Why is Mathematics essential for planning a successful surfing holiday? Context/Key Learning Ideas:  Perform operations with fractions, decimals and percentages  Solve simple probability problems with relative frequencies  Solve simple problems involving earning and spending money Assessment Task/s: Cross curricular content: (In syllabus) Outcomes: The lessons mix both summative and formative Literacy: Prescribed Focus Area/s: assessments. The emphasis is on students There are a number of worksheets that require Basic number; consumer arithmetic; simple discovering and assessing information for written responses. Appropriate metalanguage is probability themselves with the teacher acting as mentor. used. There is a mix of numerical, descriptive, creative Numeracy: Domain: and role play activities. A number of the worksheets have precise Number numerical answers that allow the teacher to carry Summative: out summative assessment. Numerical skills are Skills: Worksheets: 1.1, 1.4, 1.6, 2.1, 2.4, 3.2, 3.3, 4.1, placed within a meaningful, practical context Problem solving 4.2, 4.3, 4.4, 4.8 where possible. Research Language Modes: Applied Arithmetic Formative: The students at various times are required to read; Literacy Worksheets: 1.2, 1.3, 1.5, 1.7, 1.8, 2.2, 2.3, 2.5, write short, descriptive answers; listen to others’ 2.6, 2.7, 3.2, 3.4, 3.5, 4.5, 4.6, 4.7, 4.9, 4.10, 4.11, presentations and present work of their own. 5.1, 5.2, 5.3, 5.4, 5.5 There are also opportunities for game playing and role playing.

Rationale

The dual purpose of this unit of work is to enable students to recognise the importance of Mathematics in their lives by applying it in a real life context, and to make connections between their lives and the Mentawai people.

During the course of this unit of work the students will develop skills in interpreting problems, conducting research and independent, self-regulated learning. They develop and become familiar with metalanguage, higher order thinking and knowledge integration. These skills empower the student to continue education outside of a formal institution. Their success can be assessed in the short term by observation, questions of the teacher, speed and quality of progress through the worksheets.

of 61 Stage: 4, 5 KLA: Mathematics Focus: Commercial Arithmetic and Probability Duration: 5-10 Weeks Special thank you to:

Balgowlah Boys High School:

Dr Stephen Pickard

Galston High School:

Jason Young

Marcel Kennedy

Hunters Hill High School:

Maria Ieraci

Ben Neilsen

Northern Sydney Region:

Karen Yager

of 61 Stage: 4, 5 KLA: Mathematics Focus: Commercial Arithmetic and Probability Duration: 5-10 Weeks

Table of Contents Week 1 Travel Planning...... 2 Teaching and Learning Strategies and Activities...... 2 Lesson 1 – Introduction to the Project...... 2 Lesson 2 – Converting numbers...... 2 Lesson 3 – Internet Searching and Time to Travel...... 2 Lesson 4 – What is Probability...... 2 Lesson 5 – Harvesting Data...... 2 Lesson 6 – How Do I get There...... 2 Lesson 7 – Choice and Chance...... 2 Week One Worksheets...... 2 1.1. Conversions between Fractions, Percentages and Decimals...... 2 1.2. How to do a Boolean web Search with Google...... 2 1.3. Searching for Waves...... 2 1.4. Simple Probability...... 2 1.5. Complimentary events...... 2 1.6. Looks like Rain...... 2 1.7. How Do I get there?...... 2 1.8. Compound Events and Probability...... 2 Week 2 Balancing Budgets...... 2 Teaching and Learning Strategies and Activities...... 2 Lesson 8 Consuming Passions...... 2 Lesson 9 Current Currencies...... 2 Lesson 10 Being realistic...... 2 2. Week Two Worksheets...... 2 2.1. Worksheet Quiz...... 2 Page 4 of 61 Stage: 4, 5 KLA: Mathematics Focus: Commercial Arithmetic and Probability Duration: 5-10 Weeks 2.2. Worksheet Faculty Expenditure Budget...... 2 2.3. Worksheet Faculty Income Budget...... 2 2.4. Worksheet World Currencies...... 2 2.5. Worksheet Floating Exchange Rates...... 2 2.6. Worksheet Budget brainstorm...... 2 2.7. Worksheet Realistic budgeting...... 2 Week 3 What can go wrong will go wrong...... 2 Teaching and Learning Strategies and Activities...... 2 Lesson 11 Murphy’s law...... 2 Lesson 12 Turning data into information...... 2 Lesson 13 Insurance...... 2 3. Week Three Worksheets...... 2 3.1. Murphy’s Law: what can go wrong will go wrong...... 2 3.2. Hazard and risk...... 2 3.3. Transforming data into information...... 2 3.4. Insurance for assurance...... 2 3.5. Travel insurance...... 2 Week 4 Making it Interesting...... 2 Teaching and Learning Strategies and Activities...... 2 Lesson 14 Formula 1 Borrowing...... 2 Lesson 15 Compounding the Problem...... 2 Lesson 16 Compounding the problem...... 2 Lesson 17 Credit where credit’s due...... 2 4. Week Four Worksheets...... 2 4.1. Worksheet - It’s Simply Interest...... 2 4.2. Worksheet - Compound Interest is Simple...... 2 4.3. Worksheet - Compound Calculator...... 2 4.4. Worksheet - Pocket Calculations...... 2

of 61 Stage: 4, 5 KLA: Mathematics Focus: Commercial Arithmetic and Probability Duration: 5-10 Weeks 4.5. Worksheet - Banks and Bankers...... 2 4.6. Worksheet - Banks and Bankers...... 2 4.7. Worksheet - Adjusted Budget...... 2 4.8. Worksheet - Credit Cards, Charge Cards and Credit Charges...... 2 4.9. Worksheet - Your Credit Card...... 2 4.10. Worksheet - Online Personal Banking Services...... 2 4.11. Worksheet - Banks Credit Cards...... 2 Week 5 Ready, Steady, Go...... 2 Teaching and Learning Strategies and Activities...... 2 Lesson 18...... 2 Lesson 19...... 2 Lesson 20...... 2 Lesson 21...... 2 5. Week Five Worksheets...... 2 5.1. Your Travel Agency...... 2 5.2. Choosing an agent...... 2 5.3. Holiday requirements...... 2 5.4. Holiday proposal...... 2 5.5. Suggestion box...... 2 THE END...... 2

Week 1 Travel Planning “Once the travel bug bites there is no known antidote....” Michael Palin

This week will focus on the consumer arithmetic skills you will need to develop a budget for your trip.

Syllabus Evidence of learning conte Teaching and Learning Strategies and Activities nt Lesson 1 – Introduction to the Project Clarity of class discussion regarding the This project has several aims: video and the task . To encourage you to discover knowledge yourself through directed investigation . To give you an appreciation of how people live in our regional neighbourhood . To increase your understanding and application of commercial arithmetic

For this first lesson your teacher will play a video about SurfAid and provide an overview of the whole project. The work is structured into weeks and lessons. At the end of each week there are a number of worksheets. As you progress through the project you will complete these sheets, and after each one come back to these instruction pages. Get your teacher to check your answers at the end of each week, before starting the next.

Lesson 2 – Converting numbers Correct answers to the work sheet and the Essential to any work in probability is an ability to convert between fractions, decimals and percentages. This quality of the class lesson will be spent reviewing the stage 3/4 skills required. discussion regarding NS4.3 In Mathematics, as in other subjects, certain terms are linked together. The word fraction means a part of fractions something. It could be a fraction of one thing: “I only ate one quarter of the muffin before I was sick”; or a fraction of many things: “Only one third of the crowd of 9000 followed the Sea Eagles”. So the phrase, “a fraction of” means “a part of” something. Be careful though, when you divide something up into fractions, make sure each part is of equal size. We have all heard a younger sibling say, “but my half is smaller!”, which can’t be true – either it isn’t a half or it isn’t smaller.

A percentage is an amount out of one hundred. So for example, if on your Mathematics test you received a mark of 60%, this means that for every 100 marks given in the test, you got 60 correct. If there are fewer

of 61 Stage: 4, 5 KLA: Mathematics Focus: Commercial Arithmetic and Probability Duration: 5-10 Weeks than 100 marks you scale up to find the equivalent mark out of 100.

A decimal is a different representation of fractions and percentages that uses the place values to the right of the decimal point. Tenths, hundredths, thousandths, etc.

So a fraction can also be expressed as a decimal, for example: , or as a percentage: . This means that all these values are equivalent; just written differently. How to do convert between each format? If you are starting with a fraction it is easy to convert it to a percentage – just multiply by 100 and bung on the % symbol. For example: . If you are converting a percentage to a decimal, you simply move the decimal point two spaces to the left and drop the % symbol. For example 20.0% would be 0.200 as a decimal.

There are a few ways to convert fractions to decimals. If the denominator is a factor of 10 scale up the fraction: . Similarly if it is a factor of 100: . With other fractions it easier to convert to a percentage first and then to a decimal.

Just remember, it’s easier to convert from a percentage to either a fraction or decimal: Worksheet 1.1

Fraction Percentage Decimal

Please complete Worksheet 1.1 on page 11 and then return to this page to continue the lesson.

Lesson 3 – Internet Searching and Time to Travel Correct answers to the work sheets WMS5.2.2 You need to apply your skills from lesson 1 in planning a holiday. But before you do this in Lesson 4 you need to polish your search engine skills.

Task 1: This first part is an application of ICT skills. Specifically: “Stage 4 requires students to develop and Worksheet 1.2 refine search techniques using the Internet”. You will be exposed to using a variety of basic Boolean searches to assist in refining your searches for the rest of this unit. A Boolean expression results in a TRUE or FALSE answer. This is useful when searching for things as you only want to see the “TRUE” answers. Please turn to Worksheet 1.2 on page 13 and then return to Task 2 below.

Task 2: The remainder of this lesson will be used to investigate the weather and surfing conditions at Worksheet 1.3 Mentawai Islands making informed decisions. Please turn to Worksheet 1.3 on page 14 and then return to this page to continue the lesson.

of 61 Stage: 4, 5 KLA: Mathematics Focus: Commercial Arithmetic and Probability Duration: 5-10 Weeks Lesson 4 – What is Probability Correct answers to the work sheet and the This lesson is about probability – what is the chance of something happening? The focus of the lesson is to NS5.1.3 quality of the class assign probabilities to simple events and express the probability of an outcome as a fraction, decimal or discussion regarding percentage. Probabilities, no matter how they are expressed, vary between 0 (impossible) and 1 (certain). probability We will also cover complementary events (which can be a knotty problem). You will interpret probabilities as percentages of decimals. This work leads to the development of applying relative frequency to predict future Worksheet 1.4 experimental outcomes. You should consider and discuss the difference between experimental and theoretical probability. Please turn to Worksheets 1.4 and 1.5 on page 15 and then return to this page to Worksheet 1.5 continue the lesson.

MS3.5 Lesson 5 – Harvesting Data

Travel decisions are often based on weather statistics. Who would go skiing at Thredbo in February? We will Worksheet 1.6 research some climate data for a few cities and see how this might affect our travel choices. Please turn to Worksheets 1.6 on page 16 and then return to this page to continue the lesson.

WMS4.2 Lesson 6 – How Do I get There.

WMS4.4 It is important to now link our probability knowledge to financial skills so we can tackle the second week’s work. WMS5.1.2 During this lesson you will plan your travel arrangements from your school to the Islands. It is suggested WMS5.1.5 that a travel total of approx $3000-$4000 is set as an amount for the students to beat. This should encourage students to be more creative and competitive in their research. Worksheet 1.7 Please turn to Worksheet 1.7 on page 18 and then return to this page to continue the lesson.

Lesson 7 – Choice and Chance Choices in real life are often more complex than can be explained with simple probability. We often have to deal with multiple, independent events each with their own probabilities. For example, this morning you might have asked yourself, “What’s the chance of the bus coming before it rains?”

Choices not only consider risk but also rewards. If a lottery ticket cost $50 and there was an even chance of Worksheet 1.8 winning $5 you probably wouldn’t buy it. The risk/reward is unfavourable. But if the prize was $5000 you may well choose to buy it. Worksheet 1.8 on page 20 take you through some games to help you appreciate these concepts.

If you have completed all the worksheets for this week get them checked by your teacher before moving on to week 2.

Week One Worksheets

1.1. Conversions between Fractions, Percentages and Decimals The following exercise will involve changing percentages to decimals and fractions and vice versa. This exercise is designed to be a review of this topic; it is something you should have seen before. N.B though fractions, decimals and percentages can be any number (positive or negative) probabilities are always between 0 and 1 inclusive.

Q1 Change the following percentages to decimal a) 66% = f) 47% =

b) 23% = g) 0.3% =

c) 12.5% = h) 325% =

d) 2% = i) 200% =

e) 125% = ii) 103% =

Now turn the page and do questions 2 & 3.

Q2 Change the following percentages to fractions in their simplest form a) 30% = e) 38% =

b) 10% = f) 47% =

c) 22% = g) 200% =

d) 130% = h) 325% =

Q3 Change the following fractions to percentages Q4 Change to following decimals to fractions (Tip: make them percentages first) a) a) 0.85 =

b) b) 0.16 =

c) c) 1.56 =

Now return to page 8 to continue the lesson.

1.2. How to do a Boolean web Search with Google Sometimes web searches provide lots of irrelevant results. By using a couple of words or symbols in your search engine, you have the ability to get more relevant results. Follow these instructions for Google searches and note how many results you get. This should make your Internet research for the following sections much easier and quicker.

Basic Search

If you search for “surfing Mentawais” (omit the quotes), most search engines will look for every web page that contains the word surfing, AND the word Mentawais. This gives in about ______results.

The OR word.

Not many searches are done with the word OR in it. The reason is that the search engine will search for every page that contains the word surfing OR the word Mentawais. Try doing a search using: “surfing OR Mentawais” (use capitals for the word OR). This time you get approximately ______results.

Key words

You can tell Google to either include or exclude pages with certain words. If you put a + sign in front of Mentawais, it tells Google that the page must include the word Mentawais. This reduces the number of pages down to ______results.

You can also tell Google tell exclude pages. The way you do this is to include a – sign in front of the words that you don’t want. As we are not going to Australia, if we do a Google search of “surfing +mentawais –Australia” we are able to restrict our list down to ______results. You could reduce the number further by using more keywords with a + or a – in the search box.

Phrases

One of the most powerful ways of searching is by looking for specific phrases. If you look for a phrase by putting it inside quotation marks “surfing in Mentawais” (this time we include the quotes), it reduces the number of pages down to a mere ______results. The drawback of this method is if you get the phrase or spelling wrong, you may get no results at all.

Boolean

Your last search is to find out who George Boole was and what connection he has with search engines. Write a brief summary:

______

of 61 Stage: 4, 5 KLA: Mathematics Focus: Commercial Arithmetic and Probability Duration: 5-10 Weeks 1.3. Searching for Waves When planning a trip there are many factors that affect where we go and when we go. You will need to research on the web to respond to the following questions. Apply the skills you learnt above. (Tips: http://www.mentawai.com is a good place to start).

Which beach would you choose and why? During which months are the biggest waves likely? How big are the typical waves?

In which month would you choose to travel and why? What months are best for left hand breaks and when for right?

Paste in you favourite photo:

Paste your photo here

of 61 Stage: 4, 5 KLA: Mathematics Focus: Commercial Arithmetic and Probability Duration: 5-10 Weeks 1.4. Simple Probability What is probability and how is it used in the real world. Probability is the branch of Mathematics used to determine how likely or unlikely an event (something happening) is. A simple example is, if I roll a regular die, the probability that the die will land on a 2, is 1 out of 6. This can be expressed as , 0.1667, or 16.67 %. In general terms probability is concerned with

The probability scale runs from 0, through to 1 (0% to 100%). This means that anything with a probability of 0 cannot happen. A probability of 1 is certainty of happening and a probability of has a 50/50 chance of happening.

0______0.5______1

Impossible Even Certain

Some “real world” examples of probability are: “the chance that it will rain tomorrow is 20%”; or “there is a 50/50 chance of Mike turning up for his detention today”. Answer the following questions on simple events in probability a) A coin is tossed; write down the probability, as a fraction, of the coin showing a tail. b) The same coin is tossed again, what is the probability, as a decimal, of the coin showing a head? c) If you add your answers from (a) and (b) together, what answer do you get? (answer this as a percentage). d) What does this tell you about all the possibilities for tossing a coin?

Use a regular coin and toss it 30 times but before you start estimate the number of times you will get a heads or tails.

Theoretical Estimate Tally of Experimental Results Heads Tails Heads Tails

Theoretical probability Experimental Probability

Now continue on to Worksheet 1.5

of 61 Stage: 4, 5 KLA: Mathematics Focus: Commercial Arithmetic and Probability Duration: 5-10 Weeks 1.5. Complimentary events If I play a game of basketball and the ball goes through the hoop, the complimentary event is the ball NOT going through the hoop. Complimentary events occur in every day life. Another example, if there is an even chance that it rains on a certain day, there is an even chance that it DOES NOT rain. Given that something either will or will not happen we can write the sum of probabilities as (NB the bar above the E denotes the NOT event):

This means that both the chance of it raining and not raining will add up to 1, so if there is a 20% chance that it will rain, then there is an 80% that it will not rain. Complete the following table by listing 4 events that occur in your day. Write the probabilities as decimals.

Event Probability Complimentary Event Probability

Now return to page 9 to continue.

1.6. Looks like Rain Padang is a city in Indonesia close to Mentawai. There are a number of web sites that provide weather data but you could try http://ww.bbc.co.uk/weather/world/city_guides/ . Given your chosen month of travel, answer the questions below.

Explain the meaning of average maximum and minimum temperatures:

For the month in which you chose to travel, compare data for Padang, Sydney and a city of your choice:

City Average Sunlight Average Minimum Average Maximum Average Number of Wet Days Hours Temperature Temperature Precipitation Sydney

Padang

a) How many wet days are there in Padang over the whole year? b) For your month, what fraction of the year’s wet days are there? c) Express this fraction as a percentage d) Express this percentage as a decimal e) How many days in your chosen month? f) What is the probability that it will rain on the 4th?

of 61 Stage: 4, 5 KLA: Mathematics Focus: Commercial Arithmetic and Probability Duration: 5-10 Weeks 1.7. How Do I get there? You should know from the introduction where the Mentawai Islands are. It is just as important to know exactly how you are going to get there and back. Spend the next lesson researching how you will best get there. (You will need this information later as well). Write down your travel plan and include your best list of prices. There are several ways you can do this:

Go to a website such as www.webjet.com.au or www.bestflights.com.au and let the website find a combination of flights for you to get you to your destination. Note that this is not always the cheapest option.

Investigate booking flights on separate airlines for each flight sector. This can sometimes work out to and have shorter travel times and it can be cheaper using individual fares rather than a combined fare. You will need to know which airports you will need to stop at along the way. Airlines to try using are: Garuda; Malaysia; Thai; Cathay Pacific; Singapore; Qantas; Jetstar; etc.

Travel Plan Leg Origin Destination Duration (h) Price ($) Airline Notes

Continue on the next page

of 61 Stage: 4, 5 KLA: Mathematics Focus: Commercial Arithmetic and Probability Duration: 5-10 Weeks For each of your airplane flights, go to the website www.flightstats.com and see if you can find the following information. Your teacher should have set up an account so that you can log in. If not, then ask your teacher to do so now.

For the airports and airlines above, answer the following questions.

Airline Airport Percentage of flights that Percentage of flights that Overall on-time arrive on time depart on time percentage

Does this change the flights that you would choose to use? Why?

1.8. Compound Events and Probability A compound event in probability is an event that has more than one thing occurring. An example of this could be a game that involves a coin and a die. You toss the coin and roll the die at the same time and record what happens. You win if you get a head and an even number, and you lose if you get a tail and an odd number. If you get a head and an odd number or a tail and an even number, then the game restarts and you neither win nor lose (draw). Note that the coin outcome is independent of the die.

a) Play this game, ten times, and record the times you win, lose or draw (no result).

Game Win Lose Draw 1 2 3 4 5 6 7 8 9 10 Totals b) Now play this game a second time, however before you play it, predict the number of wins, losses and draws you will get.

Game Predicted Predicted Predicted Actual Actual Actual Wins Losses Draws Wins Losses Draws 1 2 3 4 5 6 7 8 9 10 Totals

c) Compare your totals. Was your forecast accurate? Do you have any reasons as to why you were accurate or why you were not?

Continue on the next page

of 61 Stage: 4, 5 KLA: Mathematics Focus: Commercial Arithmetic and Probability Duration: 5-10 Weeks When planning your trip to the Mentawai islands, there are numerous factors that, if you have not planned for them, could affect your trip in a negative way. You are now going to play a game using two dice. The rules of the game are as follows:

a) Roll the dice, and multiply the two faces that appear, e.g. if you roll a 5 and a 4, this will multiply to 20 (this is called your score). b) You have to roll the dice at least 10 times for the game to be complete, however if something bad happens to you in this game, you are stuck until you roll a certain number. Each roll costs $500 so keep a tally to find out the cost of your trip. c) Refer to the table below to see what happens for various scores d) Any other score means your trip has worked out ok. e) The least number of throws is 10 ($5000) but you’ll have to be lucky!

Play with up to 3 others and use the table below (and a counter or small coin) to keep track of your, and others’, status and results.

18 12 24 10 1 Missed flight. Your luggage is found You’ve caught Dengue fever. Surf is lousy, play chess. Another plane turns up Throw a 1 Throw a 2 Throw a 16 30 6 16 5 2 Lost luggage You’ve caught Malaria. Surf is great, wax the board You’ve caught Hepatitis. The doctor has cured you Throw a 12 Throw a 2 Throw a 2 Place your counter here for Player A total throws and Player B total throws and Player C total throws and Player D total throws and other scores cost: cost: cost: cost:

After playing the game try and answer these questions:

What is the chance of getting a score of 7? ______

What is the chance of missing your flight? ______

What is the chance of catching a disease? ______

Another game you might like to try is Skunk at www.//illuminations.nctm.org/LessonDetail.aspx?ID248

Week 2 Balancing Budgets “It's clearly a budget. It's got a lot of numbers in it.” GW Bush

This week we will focus on the consumer arithmetic skills you will need to develop a budget for your trip.

Syllabus Evidence of learning conte Teaching and Learning Strategies and Activities nt Correct answers to the Lesson 8 Consuming Passions work sheet and the A budget is defined as “an estimate of income and expenditure for a set period of time”. Who do you know quality of the class who produces a budget every year? ______discussion If you are going to have a successful holiday you need to be able to budget properly. But before you put your budget together it is necessary to understand some basic concepts about income and expenditure.

Task 1: Quiz Time

Use your Internet search skills to complete the quiz on worksheet 2.1 on page 24. Mark the quiz in class Worksheet 2.1 and discuss issues that come up.

Task 2: The Games Faculty

Your school has decided to create a new faculty for the study of gaming software and hardware. As its new Worksheet 2.2 Head Teacher (plus 3 other teachers) you have to draw up a list of things you will need. There is a staffroom set aside but it is bare. There are four classrooms set aside but they are also bare. Consider what you will need in the staffroom and what you might need to teach the subject. Complete worksheet 2.2 on page 25 so that you and your 3 staff can begin work next year.

Task 3: Raising Funds Worksheet 2.3 You have decided how much you need to spend but where is the money coming from? The school will meet 75% of the cost. How might the balance be raised? Complete worksheet 2.3 on page 26 and try and balance your budget.

Lesson 9 Current Currencies When travelling abroad it is important to understand the currency used in each country and how its value relates to your currency.

Task 1: What’s used where?

of 61 Stage: 4, 5 KLA: Mathematics Focus: Commercial Arithmetic and Probability Duration: 5-10 Weeks If you could create a new currency for your country what would you call it and what symbol would you

use? ______.

What denominations (coins and notes) would you have? ______. Worksheet 2.4 Use worksheet 2.4 on page 27 to list 9 of the World’s currencies including that used in the Mentawai Islands.

Task 2: Exchanging places Worksheet 2.5 Fifty years ago the value of most country’s currency was related to the price of gold. These days most countries “float” their currency. This means its value is based on what financial traders around the world buy and sell it at. Go to worksheet 2.5 on page 28 and write a short explanation of what a “floating exchange rate” means.

Task 3: Budget brainstorm For your trip you need to identify all the possible items of expenditure. For example fares, baggage charges, Worksheet 2.6 accommodation, food, tours, etc. Given that you do not have enough savings yet you also need to identify possible sources of income. Create a spreadsheet that lists these items, clearly showing whether your budget is in credit or deficit. An example to help is shown on worksheet 2.6 on page 29 which assumes you are planning 6 months ahead. Think of your own sources of income and things that you might need to buy. For the time being, just estimate what things might cost.

Lesson 10 Being realistic Is the trip affordable, and, if not, how do we make it affordable? From the last lesson you now have a rough idea of what costs might be involved. It’s time to do some research to get a more accurate idea. This will also involve finding out more about what things cost overseas. It is likely you will have to get a bank loan to balance your budget.

Task 1

Research the costs that apply to your budget and update it. Paste the updated sheet into Worksheet Worksheet 2.7 2.7. The main items of expenditure will probably be travel, accommodation and any special guided tours whilst there. How accurate was your budget estimate?

2. Week Two Worksheets

2.1. Worksheet Quiz 1. Where does the word budget come from?______

2. List five types of budget: ______

3. How big is the Australian defence budget for 2007/08?______

4. How big is the Australian aid budget for 2007/08?______

5. What things might contribute to household income?______

6. What items might be considered household expenditure?______

7. What is the difference between a wage and a salary? ______

8. How many weeks are there in a year? ______

9. If Sabrina earns $850 per week, how much does she earn in a year? ______

10. How many months are there in a year? ______

11. How much does Sabrina earn in a month? ______

12. Why does 4x the answer to Q9 give us the wrong answer for Q11? ______

of 61 Stage: 4, 5 KLA: Mathematics Focus: Commercial Arithmetic and Probability Duration: 5-10 Weeks 2.2. Worksheet Faculty Expenditure Budget Use the table below to list items you think you will need (furniture? books?), how many, the cost per item and the total costs.

Item Number Cost each Total cost

Chair 4 $120 $480

Grand Total:

2.3. Worksheet Faculty Income Budget Use the table below to list ways your new faculty can raise money. The “Number” is there in case you run an event (e.g. a raffle) more than once.

Source Number Amount Total amount

School funds 1

Grand Total:

2.4. Worksheet World Currencies Use the table below to list 15 different currencies from around the World. Also show their symbol (like we use $ for dollars).

Country Currency Symbol

1. Mentawai, Indonesia

2.5. Worksheet Floating Exchange Rates Write around 100 words summarising the floating exchange rate system.

______

of 61 Stage: 4, 5 KLA: Mathematics Focus: Commercial Arithmetic and Probability Duration: 5-10 Weeks 2.6. Worksheet Budget brainstorm Print out your budget and paste it over the brief example shown below.

Holiday Budget Holiday Income Month 1 Month 2 Month 3 Month 4 Month 5 Month 6 Month 7 Current savings 1500 Delivering papers 100 100 100 100 100 100 KFC 300 300 300 300 300 300 Loan from Granny 500 Loan from Bank Monthly total 1900 400 400 400 400 900 0 Expenditure New backpack 200 Sleeping bag 200 New surfboard 400 Clothes 200 Air tickets deposit 120 Air tickets balance 1180 Other travel tickets 500 Accommodation deposit 300 Accommodation balance 900 Spending money 500

Monthly total 120 200 300 200 1580 1100 1000

End of month balance 1780 1980 2080 2280 1100 900 -100

2.7. Worksheet Realistic budgeting Print out your revised budget and paste it in below. What were the main items that changed?

______

Week 3 What can go wrong will go wrong “Man tries to make for himself, in the fashion that suits him best, a simplified and intelligible picture of the world;” Albert Einstein

This week will investigate gathering data, analysing it, modelling it and making forecasts.

Syllabus Evidence of learning conte Teaching and Learning Strategies and Activities nt Correct answers to the Lesson 11 Murphy’s law work sheet and the Task 1: quality of the class discussion There are many chance events that could spoil your holiday. Some might be inconvenient, some might be show stoppers. First of all, please turn to Worksheet 3.1 on page 33 and summarise the weather Worksheet 3.1 and flight data you set out in Worksheet 1.6, page 16 in Week 1. Then return to Task 2.

Task 2:

Now we will add other chance events into the mix. Try and determine (or guesstimate if the data aren’t Worksheet 3.2 available) the likelihood of various things happening and their impact by completing the table in Worksheet 3.2 on page 34.

You should now appreciate that some things that are unlikely to happen may have a big financial impact and vice versa. The final column in the table helps you assess things.

Lesson 12 Turning data into information In business it is often necessary to communicate your data to others in a meaningful way. This lesson we will take a look at various ways of presenting your work.

There are two broad ways of presenting your data to make it informative: tables; and graphs. You might of course use a combination of these and put them together in a slide presentation or even a video – “An Inconvenient Truth” is a good example of the latter.

In Worksheet 2.6 on page 29 we had various items of expenditure. Use a spreadsheet, other graphing program or draw by hand to create a variety of graphs to display that data. Which is the most effective? Worksheet 3.3 Paste your graphs into the space provided on Worksheet 3.3 on page 35.

Lesson 13 Insurance Task 1

of 61 Stage: 4, 5 KLA: Mathematics Focus: Commercial Arithmetic and Probability Duration: 5-10 Weeks The insurance industry is massive. Its whole existence is due to large impact low probability events that Worksheet 3.4 might affect our lives. It exists because people are aware that even rare events can be costly. In Worksheet 3.4 we clarify some words and we investigate the industry a little.

Task 2 Worksheet 3.5 In Worksheet 3.5 we decide on whether or not to take out insurance. It is a subjective decision that very much depends on one’s risk aversion. So turn to page 36 now and complete these sheets.

3. Week Three Worksheets

3.1. Murphy’s Law: what can go wrong will go wrong For the first three lines use your chosen month of travel and your chosen airline and airport to complete the table below:

Month: Airline:

Number of wet days: Airport:

Percentage of wet days for month: On-time departures (%):

Now return to page 31 before continuing.

3.2. Hazard and risk Complete the empty cells with data or estimates. The impact column is for you to describe how the event affects the holiday. The financial impact can vary enormously. For example, if there is no surf you might decide to spend money travelling to another beach. The last row is left blank for you to think of a hazard.

Event (Hazard) Impact on holiday Financial impact Probability of it happening Financial x Risk (Risk) Severe injury before holiday (e.g. breaking a leg) Late flight (and so missed connections) Lost luggage

Severe injury during holiday

Severe illness during holiday (e.g. malaria) Wet weather

No surf

Large change in exchange rate

3.3. Transforming data into information Use the space below to paste in your examples of graphs and tables for displaying the “expanses” data from Worksheet 2.2.

Now return top page 31 before continuing.

of 61 Stage: 4, 5 KLA: Mathematics Focus: Commercial Arithmetic and Probability Duration: 5-10 Weeks 3.4. Insurance for assurance Define Insurance: ______

Define Assurance: ______

Define Reinsurance: ______

Create a list of 6 of the major insurance companies that operate in Australia and fill in the information below. The URL: http://www.insurancecompared.com.au might help.

Company name Brief description

3.5. Travel insurance

What does travel insurance typically cover?

Are extreme sports usually covered? If not why not?

What are the factors that might affect the cost of the insurance?

Select two insurance companies or websites and obtain two rough quotes for insuring your holiday: Company 1: Cost:

Company 2: Cost:

Given the financial risks that you investigated in Worksheet 3.2 explain your choice as to whether or not you will take out travel insurance.

Week 4 Making it Interesting “The case has, in some respects, been not entirely devoid of interest.” Sherlock Holmes

This week will investigate how interest is charged on loans.

Syllabus Evidence of learning cont Teaching and Learning Strategies and Activities ent Correct answers to the Lesson 14 Formula 1 Borrowing work sheet and the From your budget you prepared in Lesson 10 you will see that a loan from the bank was required to help fund quality of the class the trip. When money is borrowed a bank it is taking a risk in assuming that you will pay it back. If they take discussion a risk they want a reward, i.e. you will pay back more than you borrowed. The extra amount is called the ______.

Rather than pay a fixed extra amount the interest on a loan is calculated as a percentage of what was borrowed. Should it matter how long the loan is for? ______. Why? ______

______

One way of calculating the extra amount is the Simple Interest formula. This is a percentage based on how much is borrowed (Principal) and for how long (Period). The percentage used is called the I______R______. (complete the words)

The formula is: Interest = Principal x Rate x Number of periods I = P r n

Complete the gaps below for the following problem: You borrow $12 000 for 11 years at 10% per year. Principal (P) = ______

Rate (r) = ______which as a decimal = ______

No. Periods (n) = ______

So the extra amount you pay back (the bank’s reward for taking risk):

I = ______x ______x ______

Giving I = $______

One last term we need to know is per annum (pa). Look up the phrase in a dictionary and write its

meaning: ______

So an interest rate of 18% pa is 18% charged every ______.

Now turn to worksheet 4.1 to practice what we have learnt. Worksheet 4.1

Lesson 15 Compounding the Problem In the last lesson, you looked at simple interest calculations. Unfortunately, banks and other money lenders don’t use simple interest. You will be asked why this is the case later. Compound interest is the banks chosen method for calculating interest on a loan. The verb “to compound” means: ______

Compound interest is different from simple interest because ______

______

The formula used for compound interest is A=P(1+r)^n. (NB in Excel the ^ is used for index) where A is______, P is ______, r is ______, and n is ______.

One important point you must remember when using this formula is that the answer given also contains the P______. When finding the interest we MUST subtract the principal from this amount: I = A - P

Task 1 Using spreadsheets

The compound interest formula comes from repeated use of the simple interest formula. We can show that Worksheet 4.2 quite quickly in a spreadsheet. Open a spreadsheet, and enter the information on the following page. Copy and paste the formulae into the appropriate cells (do you know a quick way to do this?). Paste a copy of your completed spreadsheet in the space on Worksheet 4.2.

Describe what you see when you compare the Compound Interest column with the I+P column of the Simple Interest section: ______

We can also set up a spreadsheet just to calculate compound interest. In the following spreadsheet, we can change the principal, interest rate and number of periods, and our answer will be given in the interest column.

Worksheet 4.3 Use your spreadsheet calculator to answer the questions on Worksheet 4.3 and paste a copy of your spreadsheet (complete with answers) in the space on Worksheet 4.3.

Task 2 Pocketing Compound Interest To find compound interest on your pocket calculator, follow this example and check that you get the correct answer. Given a principal of $500, an interest rate of 6%, compounding annually over 5 years, we enter: 500(1+6÷100)^5= to get an answer of $669.1127888 (your particular calculator may show the above formula slightly differently and fewer decimal places in the answer). This amount is the principal + interest. So, we need to subtract the principal to get interest: Worksheet 4.4 Page 40 of 61 Stage: 4, 5 KLA: Mathematics Focus: Commercial Arithmetic and Probability Duration: 5-10 Weeks 669.11 – 500 = $169.11

Practise this and other calculations on your pocket calculator using Worksheet 4.4

Lesson 16 Compounding the problem You WILL afford this holiday, you can bank on it!

Task 1: Visit the Banks We’re going to play a game to let you practice your compound interest in preparation for your trip. We will need ten people to pair up and represent banks, they will have the power to decide on interest rates for their Worksheet 4.5 loans. But, they will be in competition with each other; their aim is to make the biggest profit! The banks should use Worksheet 4.5 and complete it in pencil so you can adjust your answers.

The rest of you will pair up and visit the banks. From Week 2 Lesson 10, when you prepared your budget, you found that you may need to borrow some money so that your trip can go ahead. You will need to use the interest rates to calculate how much you will have to repay. Your aim will be to pay as little interest as Worksheet 4.6 possible. You will have 20 minutes to visit the banks and to discuss with your partner which bank will be better for you. The clients should use Worksheet 4.6 and complete it in pencil so you can adjust your answers. RISK AND CHANCE Task 2: The Banks fight back. Worksheet 4.7 So, the bankers have spoken to each of you and given you their details. Which bank are you leaning towards Teacher: If at the moment? Who will give you the better deal? you wish introduce a OK, bankers, some of you have more prospective clients that the others. Why is this? Are you meeting your risk factor for profit quota? If not, how might you change your approach? You have a minute to alter your interest rate clients, and term length on Worksheet 4.5 before the clients get to make their final decisions. perhaps by using a dice Now that the bankers have changed their rates, you will need to make a final decision. Which bank will you roll. Risky borrow from? Adjust Worksheet 4.6. Each of you will need to have a copy of this sheet for your journal. clients may have a higher Task 3: Can it really happen? interest rate applied to Can you afford your loan? How much would you expect to repay each week? Check this amount against your them. income in the budget you wrote in Week 2, Lesson 7. Worksheet 4.7 If you cannot afford to repay your loan, what changes can be made to the loan or your budget to make the trip affordable? Paste you revised budget on Worksheet 4.7 and comment on your changes.

Lesson 17 Credit where credit’s due So far we have considered loans from banks. For consumers the most common way to get a loan is with a credit or charge card. Look up “charge card” on Wikipedia and write a short summary (in your own words) of the difference between credit and charge cards. Page 41 of 61 Stage: 4, 5 KLA: Mathematics Focus: Commercial Arithmetic and Probability Duration: 5-10 Weeks

Name two common brands of credit card (not the banks who offer them): ______

______

When was the first charge card offered? ______

In Lesson 13 we introduced the concept of Risk vs. Reward. The more risk an institution takes the more reward (interest) it wants. Consider this: you are in Harvey Norman looking at the latest 4m plasma HDTV; it costs $4999.99. The NRL final is on tonight but you don’t have the cash in your pocket or enough in your cheque account. Would you A) get out your credit card; or B) get a loan from the bank?

The advantage of A is: ______

The disadvantage of A is:______

The advantage of B is: ______

The disadvantage of B is:______

Which institution takes the most risk, bank or credit card company? ______

You teacher will issue you with a “WISA” (pronounced wiser) credit card from the “High School Worksheet 4.8 Bank” or look at Worksheet 4.8.

What is the credit card number? ______

When does the card expire? ______

Task 1: Fred’s Credit Design your own Credit Card and paste a copy of it onto Worksheet 4.9 Worksheet 4.9 Task 2: Personal Banking Online Visit the website of a bank and find out what budgeting information is available e.g. http://www.anz.com.au/aus/calculators/default.asp and select budget planner. On Worksheet 4.10 write a Worksheet 4.10 summary of typical personal banking things you can do online.

Task 3: Bank Credit Cards

of 61 Stage: 4, 5 KLA: Mathematics Focus: Commercial Arithmetic and Probability Duration: 5-10 Weeks Visit the website of a bank and find out what personal credit cards they offer. e.g. Worksheet 4.11 http://www.anz.com.au/aus/personal/credit-cards/default.asp Answer the questions on worksheet 4.11

4. Week Four Worksheets

4.1. Worksheet - It’s Simply Interest Complete the table below, applying the I = P r n formula. NB convert the rate to a decimal. Also make sure the rate and periods match. As you can see we sometimes work backwards from the Interest.

Principal Rate No. Periods Interest ($) $1000 10% pa 2 years

= ______as a decimal $1000 20% pa 2 years

= ______as a decimal $1 000 000 10% per month 2 years

= ______as a decimal = ______months $5 423 12.5% pa 1.5 years

= ______as a decimal = ______months 16% pa 2 years $320

= ______as a decimal $4 000 8% pa ______years $800

= ______as a decimal = ______months $12 500 4years $6660

______pa

= ______as a decimal

4.2. Worksheet - Compound Interest is Simple Place a printed copy of your spread sheet below:

Repeated Simple Interest Calculator

4.3. Worksheet - Compound Calculator Use your spreadsheet to answer the following questions. When complete print out the answers and paste below.

Q1) You borrow $2 000 for 2 years at 10%pa compounding annually. Q2) You borrow $2 000 for 5 years at 12%pa compounding annually. Q3) You borrow $2 000 for 5 years at 1% per month compounding monthly. (Hint: how many months in 5 years?) Q4) You borrow $500 from 1st March to 31st May at 0.2% per day compounding daily. Q5) You borrow $1 222 333 at 8% pa for 25 years, compounding annually.

Compound Interest Calculator

4.4. Worksheet - Pocket Calculations Use your pocket calculator to answer the following:

Q1) You have borrowed $20 off your friend ______who decides to charge 2% simple interest. Six weeks later you decide to pay back the money: a) what is the interest? ______b) what is the amount to be repaid? ______

Q2) Next time you need $20 for 6 weeks you decide to borrow from your other friend ______who charges 1.75% per day compounded daily. a) What is the amount to be repaid? ______b) what is the interest? ______

Q3) For how many days can you borrow $20 from your second friend so that the amount to be repaid is about the same? ______

4.5. Worksheet - Banks and Bankers

I am a banker with the ______Bank.

Our current interest rate for personal loans is % p.a. over a term of years.

In order for me to keep you job, I will need to make an average profit of per year.

In the table below, I will list my confirmed clients and find the interest my bank earns from them.

Client Principal Compound Interest Total amount repaid Interest earned calculation

From my confirmed clients, my bank will earn total interest equal to $ .

This gives me an average profit of $ ______per year.

My job at this bank will continue/terminate. (circle one)

Fortunately, regardless of your continued service with the Bank, they will be paying you a 28% commission on the interest you earn for them. (OK, seriously, they wouldn’t pay you this potentially vast sum, BUT you still need to afford your holiday, right!)

4.6. Worksheet - Banks and Bankers I am a holiday-maker seeking a loan for my trip to the Mentawai Islands.

I am after a loan of $______to cover the expenses of my trip.

In the table below, I will list the information my banks provide and calculate the amount I will need to repay (interest is to be compounded annually).

Bank Interest rate (p.a.) Term of loan Compound interest Total amount repaid calculation

I have chosen to take a loan from the ______Bank.

I will repay my loan over years with a total repayment of $ ______

The amount of interest I will be repaying is $ .

4.7. Worksheet - Adjusted Budget Print out your revised budget and paste it in below. What were the main items that changed and why?

______

Paste budget here

4.8. Worksheet - Credit Cards, Charge Cards and Credit Charges Copy and laminate this sheet so as to give each student a Credit Card.

High School Bank High School Bank High School BanK High School Bank

5490 2491 9636 4579 5490 2491 9636 4579 5490 2491 9636 4579 5490 2491 9636 4579

Valid from 05/08 until end 06/12 Valid from 05/08 until end 06/12 Valid from 05/08 until end 06/12 Valid from 05/08 until end 06/12

Dr Kerry Tightfist WISA Dr Kerry Tightfist WISA Dr Kerry Tightfist WISA Dr Kerry Tightfist WISA

High School Bank High School bank High School bank High School bank

5490 2491 9636 4579 5490 2491 9636 4579 5490 2491 9636 4579 5490 2491 9636 4579

High School bank High School bank High School bank High School bank

5490 2491 9636 4579 5490 2491 9636 4579 5490 2491 9636 4579 5490 2491 9636 4579

4.9. Worksheet - Your Credit Card Design your own credit card and paste a copy below. Consider its size; logos; necessary information; names; etc.

Your credit card

4.10. Worksheet - Online Personal Banking Services Write a summary below that describes the different things you can do through a bank’s website. For example, can you apply for a loan?

______

4.11. Worksheet - Banks Credit Cards

Q1) Which bank have you selected and what is the relevant URL? ______

Q2) How many different types of credit card does the bank offer? ______

Q3) Do any of them offer Frequent Flyer Points (FFP) and what are they? ______

______

Q4) What are the pros and cons of FFPs? ______

______

Q5) Select two different types of card and compare what they offer (interest rates; rewards; etc): ______

______

Q6) Would you like to have a credit card and why/why not? ______

Week 5 Ready, Steady, Go “Every word that is unnecessary only pours over the side of a brimming mind.” Cicero

This week we will pull all the work together and present our findings.

Syllabus Evidence of learning conte Teaching and Learning Strategies and Activities nt Teacher: Correct answers to the The travel Lesson 18 work sheet and the agents should Well done, you have worked hard to get this far. In this lesson we will split into groups of three. Half the quality of the class have access to groups will play the role of travel agent. The remaining groups will be the customers. discussion the Internet to look up Travel Agent Groups: information. You will be trying to sell a holiday to the customers. Remember there are three competing companies. Put this information on Worksheet 5.1 on page 57. Your agency must: Decide on a name; Create a logo; Think of a slogan; Etc.

Now get ready for the customers who are going to tell you what sort of holiday they want. You might suggest Worksheet 5.1 things. Once you have finished talking to a customer summarise their wants on Worksheet 5.3 so Worksheet 5.3 you can prepare a package holiday next lesson.

Customer groups:

You are going to visit two or more travel agents to decide which to use to book your holiday with your two Worksheet 5.2 mates. Decide on what is important to you when choosing an agent. Summarise your ideas on Worksheet 5.2 on page 57. Also agree in general terms what sort of surf holiday you want. And remember the budget you put together previously. Worksheet 5.3 Now need to talk to two or more agents so they can prepare quotes for your holiday. Refine what you want, in agreement with the agent, on Worksheet 5.3 and check it agrees with what the agent has completed.

Lesson 19 This is a repeat of Lesson 18 but the roles are reversed. By the end of this lesson each group should have a Worksheet 5.1 to 5.3 set of holidays that their customers want (travel agent role) and a specification of the holiday they want (customer role). Page 55 of 61 Stage: 4, 5 KLA: Mathematics Focus: Commercial Arithmetic and Probability Duration: 5-10 Weeks

Lesson 20 Task 1: Now all of the groups take on the travel agent role to put together holiday packages to offer TWO of their customers. If you only had one customer put together TWO options. Summarise your packages on Worksheet 5.4 Worksheet 5.4 on page 59. Photocopy you proposals and cut them out so that you can hand them to your customers for consideration.

Task 2: Now the groups with their agent hats on (which should be every group as they all had a go at being an agent) should hand their proposals to their customers. As customers, consider all the proposals you have been given and decide which agency and package you will take.

Task 3: The most successful agency should present themselves to the class and highlight what it is that made them such good entrepreneurs.

Lesson 21 Debrief Now that the project has been completed, you and the rest of the class should take time to discuss what was learnt; how it was learnt; what worked and what didn’t; what should be left out and what might be included. This way the project can be enhanced for future classes. Summarise your suggestions on Worksheet 5.5 Worksheet 5.5 on page 60.

of 61 Stage: KLA: Mathematics Focus: Duration:

5. Week Five Worksheets

5.1. Your Travel Agency Complete this form by coming up with a suitable name (e.g. TravelSure); a slogan (e.g. we put you in your place); a URL (e.g. www.gothere.com.au); the location (e.g. Totem Mall); consultants (i.e. your names); and a logo.

Name of business:

Slogan:

Web site address:

Location:

Consultant 1:

Consultant 2:

Consultant 3:

5.2. Choosing an agent On the following lines list some of the things that you think are important when choosing a travel agent. For example, name; location; service; dates; etc.

5.3. Holiday requirements Use the space below to summarise what is needed to make the holiday a success. Typical things might be (but are not limited to): maximum price; duration; airline; destination (somewhere in the Mentawai Islands); etc.

5.4. Holiday proposal Summarise below what you will offer two of your customers based on the information supplied above.

Name of Agent:

Summary of proposal 1 Customer name:

Summary of proposal 2 Customer name:

5.5. Suggestion box Use the space below for constructive feedback and criticism so the project can be improved upon and refined.

Marking Guidelines

A . Answers are appropriate and accurate . Sophisticated imaginative and creative responses have been given . Effort, enthusiasm and initiative are evident in the outstanding quality of the responses B . Effective answers have been given in most cases . Effective imaginative and creative responses have been given . Effort, enthusiasm and initiative are evident in the effectiveness of the responses C . Sound answers have been given in most cases . Sound responses have been given . Some effort evident in the responses D . Answers are often inaccurate, inappropriate or missing . Limited responses have been given . Limited effort evident in the responses E . Few worthwhile answers . Elementary responses . Elementary or no evidence of effort