Money Matters

RIC-6011 6.2/73

Money matters: A teachers handbook for developing money concepts Published by R.I.C. Publications® Pty Ltd PO Box 332, Greenwood Western Australia 6924 Published 2009 ISBN 978-1-74126-851-5 RIC–6011

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Paul Swan and Linda Marshall

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Grateful acknowledgment is given to Kellee Williams and the students at Woodvale Primary School for their support and comments on drafts of this book.

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Only the blackline masters contained within this publication may only be reproduced by the original purchaser for use with their class(es).

The publisher prohibits the loaning or onselling of these blackline masters for purposes of reproduction. No other part of this publication may be reproduced in any form or by any means, electronic or mechanical, including photocopying or recording, or by any information storage and retrieval system, without written permission from the publisher.

FOREW0RD We all use money and to some extent take it for granted. Students may see money coming into the household and be oblivious as to how their caregivers receive, save, spend and invest it. Much of the mathematics related to finances can seem quite complex and, at times, daunting.

To support teachers help their students gain a sense about money, we decided to produce a handbook for teachers to use when working on the various concepts associated with money. The book starts with early money concepts such as coin recognition and counting coins, and continues through to concepts such as financial literacy that are more suited to teachers of older students. This is not a book about performing calculations with money but rather a book that integrates the mathematical ideas associated with money with societal issues. Suggestions are made for handling discussions about money-related issues in a sensitive manner. Ideas for activities, scenarios for role-plays, teacher tips, project ideas and games are included, along with blackline masters (BLMs) where appropriate.

r o e t s Bo r e p ok u S CONTENTS

GENERAL TEACHER INFORMATION Introduction........................................................... 4 Key skills/concepts needed..................................... 5 Finding out what students know............................... 6 Parents as partners................................................. 7 Letter to parents..................................................... 8 Issues to consider..............................................9–13 The barter system................................................. 14 Bartering............................................................. 15 Language associated with money......................16–17

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‘Toss to $10’ – game.............................................. 69 Counting coins – Assessment 1................................ 70 Counting coins – Assessment 2 and checklist........71–72 Counting coins – Assessment 3................................ 73 Counting coins – Individual assessment record........... 74 COIN EQUIVALENCE

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Coin recognition – activities.............................20–24 Coin reference sheet – blackline............................ 25 Coin cut-out templates......................................26–27 ‘Coin match’ – game............................................ 28 ‘Money bags’ – game.......................................... 29 ‘Fill my board’ – game and game board............30–31 ‘Money concentration (game and card templates)...............................32–34 ‘Money dominoes’ (game and domino templates)..........................35–38 Coin spinner template......................................39–41 Background information: Notes on coins............42–43 Background information: Notes on notes............44–46 Coin recognition assessment checklist..................... 47

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MONEY FRAMES Money frames – activities and money frames templates............................................... 86–98

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MONEY RECOGNITION

Changing and exchanging coins activities........... 76–79 ‘Pay the person’ – game.......................................... 80 Vending machine – information and problem cards.................................................. 81–82 Coin equivalence checklist....................................... 83

INTEGRATION AND SHOPPING

Integration and shopping............................... 100–101 Setting up a class shop.................................. 102–104 Transactions................................................. 105–106 Catalogue shopping.............................................. 107 Sharing money..................................................... 108

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COUNTING COINS Strategies for counting coins – activities............ 50–52 Counting and weighing coins – activites.................53 ‘Count coins’ – game and game board............. 54–57 ‘Money star’ – game, game board and cards.... 58–63 ‘Coin match’ – game and coin cards................ 64–65 ‘Go for broke’ – game, game board and spinners........................................................66–68 R.I.C. Publications® – www.ricpublications.com.au

FINANCIAL LITERACY

Financial literacy activities............................... 110-116 Blank cheque templates......................................... 117 Blank deposit slip templates.................................... 118 Blank withdrawal slip templates.............................. 119 Blank balance sheet template ‘How much do I have?’.......................................... 120 Blank bank statement template ‘Keeping track of your money’................................ 121 GST (Goods and Services Tax)............................... 122

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Introduction Of interest

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Historically, money has taken many forms, beginning with bartering, where nothing was exchanged but the goods or services themselves.

From there, items agreed upon within a particular community became the ‘go between’; for example, conch shells were used in some island communities. This has evolved to the use of coins and notes, as we know them, in most communities in the civilised world. These ideas are expanded upon later in the book.

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In the Yap islands of the South Pacific they once used stones as money. The stones, called ‘rai’, were more than just stones—they were stones that were made in the shape of a wheel. What makes this more interesting is that the stone wheels varied in size from just a few centimetres to around three metres in diameter and weighing thousands of kilograms.

Imagine trying to carry some loose change in your pocket!

In fact, the locals would roll the larger ‘rai’ around the island.

The stones were not necessarily valued by size but rather by the danger and adventure that was involved in paddling to nearby islands to obtain the stone.

While we all know what money is, and can recognise it, defining money is quite difficult. Basically, money is a measure. It measures the value of something. Money may be exchanged for something. The value of that thing, item or service (goods or services) needs to be agreed at a particular point in time. Consider for a moment how the value of a bottle of water might change depending on the circumstances, such as how thirsty the person is, whether there is an alternative source etc. In fact, in the middle of a desert, a bottle of water might be considered priceless (meaning it cannot be given a value).

Money can be exchanged for something.

Using money as a medium of exchange is only one of its many functions. As mentioned earlier, money acts as a measure of value. Also it is a store of value—consider bank balances. In addition, it can be used as a means of paying for an item or a service. This payment may take place in a single transaction or over a period of time, such as when you are paying something off.

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Has the same value as

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The concepts related to money can be difficult to teach, because the relationship between coins and notes cannot easily be seen. For example, when using Base Ten Blocks (MAB), there is a proportional relationship between each of the pieces. A student can literally see that ten small cubes make a long, ten longs make a flat and so on.

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When using money, the coins and notes are not physically proportional. So the 10c coin is not twice as big or twice as heavy as a 5c coin. Similarly, two 20c coins and one 10c coin bear no physical resemblance to a 50c coin. Even more confusing, the $1 coin is larger than the $2.

Money matters: A teachers handbook for developing money concepts

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Key skills/concepts needed What key skills, understanding and knowledge do students need to acquire in relation to money?

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Simple

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Here are the concepts developed in this book.

The student: • shows awareness that money is used to buy things • is aware that coins and notes are worth differing amounts • realises that if you don’t have enough money you can’t buy things • realises that you should receive change if you hand over more money than the cost of an item • uses and understands language associated with money concepts (Note: Students will use more sophisticated words as they progress.)

• recognises the value of coins and notes • is able to count money: – in multiples of the same coin; e.g. multiples of 5c, 10c ...

– when coins are mixed • is able to exchange coins (and later notes) for equivalent amounts • is able to mentally calculate change (may need to physically calculate change first with the use of coins and/or money frames): – from purchases of $2 or less (i.e. coins only) – $5 or less (i.e. coins only) – larger amounts (i.e. coins and notes) • performs simple mental calculations involving money, including estimating • demonstrates basic awareness of financial literacy: – earning money – the need to save – spending money – the need to budget – shopping – comparing prices – looking for best buys.

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Complex

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Finding out what students know How can we find out what students already know?

Teacher tip The use of concept or mind maps is a powerful way of finding out what students know.

Remember, just because a student uses a particular word or term it does not mean that he/she knows what it means.

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The authors use a ‘before and after’ assessment technique that is often associated with weight loss advertisements, to determine what and how much a student has learned as a result of participating in a unit of work. At the start of the unit of work, ask the students to jot down all they know about the topic. Make sure the student’s name and date appear on the sheet of paper.

At the completion of the unit of work repeat the same exercise and compare the two with the addition of a few annotated comments. This ‘before and after’ sample can be a powerful indicator to parents of what their children are learning.

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It is important to find out what students know about a topic before launching into a unit of work, otherwise you might pitch the work at an inappropriate level—either too easy or too hard. One method the authors have found useful involves providing students with a blank sheet of paper and asking them to write or draw what they already know about the topic; in this case, money. The use of mind maps or concept maps helps to establish the students’ knowledge base.

Simple questions can then be asked to clarify what they know about a particular topic.

What are useful ways to monitor student achievement in relation to money?

The topic of money lends itself to the use of checklists as a means of monitoring students’ achievement. A checklist helps to focus teacher observation on specific behaviours such as counting money. Students can be observed as they carry out activities such as giving change when role-playing in the class shop.

Practical tests such as counting how much money is in a moneybox or money bag can be given. The level of accuracy displayed when counting the money, along with any strategies used, may be noted.

Specific suggestions for assessing particular aspects of money have been given throughout this book, along with sample checklists that may be used to keep a record of what individual students can do.

Coin recognition checklist

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Name

Recognises coins

Matches coins

Sorts coins

Comments

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Names coins

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Parents as partners

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• count coins in a money box. Discuss strategies for counting money such as separating the coins, then placing in piles with a value of one dollar or fifty cents

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Be aware that money can be a sensitive issue. Some parents are reluctant to discuss money matters with their children. Sensitive information such as how much a parent earns is not an appropriate topic for a classroom discussion. While children can learn a great deal from discussing money matters with parents or caregivers, it may be problematic.

If parents ask about supporting their child’s understanding of money then encouragement can be given to highlight any transactions when shopping. For example, they can:

• let the children see that if you hand over more than the required amount in a shop you should expect to receive change • discuss the features of a till ticket (date, cashier number, GST)

• show children an example of an electricity or water bill so they can see that utilities such as power are not free. Discuss ways to save power or water. It is good for the environment and saves money!

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• show children a credit or debit card and explain how they work.

Sometimes children do not understand how an ATM works.

Pocket money can be a sensitive issue. Children will receive varying amounts of pocket money from nil to large amounts. Some parents simply buy what a child wants but do not give any pocket money.

Others prefer their children learn to manage money and therefore provide a set allowance each week. Still others expect children to perform chores or jobs around the house in order to earn pocket money. Some children may boast about how much pocket money they receive, but the child’s allowance may include lunch money for the week. Some children who receive little or no pocket money may feel sensitive about the issue so it is better not to highlight pocket money as a topic for in-depth discussion. Parents will have different opinions when it comes to pocket money.

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Pocket money

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A letter to parents discussing the topic and the role they can play in supporting their child’s understanding of money is provided on page 8.

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Dear

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Teac he r

This term we will be focusing on the topic of money. While studying money the children will be learning some fundamental money concepts such as being able to recognise different coins and notes and to accurately count money. It would greatly assist your child if you can provide opportunities to count real money.

• If your child has a moneybox encourage him or her to count the money in the moneybox on a regular basis.

• Perhaps you keep some loose change in bowl that can be counted. To help, you might suggest strategies such as separating the coins into their various denominations and then stacking them into piles of 50c or $1. Feel free to check the accuracy of the count.

As well as learning some fundamental money concepts, your child will be encouraged to explore or research other aspects of money such as the animals that are featured on some coins or the people who are represented on the notes. Don’t be surprised if your children ask you to show them a $20 note so they can look at the picture of the Reverend John Flynn. You might also note the picture of the aeroplane.

Flynn was the person who began the Royal Flying Doctor Service. Encourage your child to share the many things he or she is learning with you.

We will also be dealing with issues of financial literacy: • Let your child see that if you hand over more than the required amount in a shop you should expect to receive change.

• Discuss the features of a till ticket (date, cashier number, GST).

• Show your child an example of an electricity or water bill so he/she can see that utilities such as power are not free. Discuss ways to save power or water. It is good for the environment and saves money!

• Show your child a credit or debit card and explain how they work. Sometimes children do not understand how an ATM works.

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o c . c e h r ore shop I would welcome your input on the topic of Should you work in a bank o t r s s rof your knowledge and e money. Maybe you could visit the classu andp share some experience with the children.

Yours sincerely

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Issues to consider Of interest The last one-cent coins were dated 1990 and the last twocent coins were dated 1989.

They were progressively removed from circulation starting in 1992.

Some teachers overcome this issue by starting the use of money with $1 and $2 coins. If teachers want to start by using cents as their currency, the lowest denomination coin is 5c. If students can count by 5s and 10s, there seems to be little problem.

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The $1 coin was introduced in 1984 and the $2 coin in 1988.

The Mint produces coins only.

Notes are produced by Note Printing Australia in Melbourne. <http://www.ramint.gov.au> Coins have been used as a medium of exchange since the 7th century BCE (before common era).

We do not have $1 or $2 notes; notes start at $5.

This means that if teachers decide to use $1 and $2 coins as their starting point, they are likely to need to switch to notes once the value of $5 is reached.

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1c and 2c coins are still Australian legal tender, but they are not considered ‘currency’ (money that is officially released for circulation). This means that you can take old 1c and 2c coins to the bank and exchange them for currency totalling the same face value.

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We no longer have 1c and 2c coins; therefore we cannot start with counting by 1s in cents.

Children need to be able to count in 1s, 2s, 5s, 10s, 20s and 50s to handle money successfully.

As mentioned before, to make sense of our money, it helps if students are able to skip count in the above values.

The size of coins: in Australia, the $1 coin is physically larger than the $2 coin.

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The size of coins and notes is not physically proportional.

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According to the book Making money: The story of the Australian Mint, ‘The words money and mint are derived from the name of the Roman goddess Juno Moneta, whose temple the Romans used as a workshop for making coins’.

Some currencies have the equivalent of our $1 and $2 coins in reverse sizes; i.e. the $2 is physically bigger than the $1 coin, which is more intuitive. If young children were given the choice of a 50c coin, $1 coin or $2 coin, they would often choose the 50c coin because it is the largest; or a $1 coin rather than a $2 coin.

The 10c coin is not twice as big or twice as heavy as a 5c coin.

Similarly, two 20c coins and one 10c coin bear no physical resemblance to a 50c coin.

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The number of coins versus the value of the coins (e.g. is it better to have 4 x 10c or 1 x 50c coin?)

This is an important issue with younger children, where intuition overrules reality.

The value of coins does not increase at regular intervals.

We have 5c, 10c, 20c, 50c, $1 then $2 coins. Similarly, with notes we have $5, $10, $20, $50 and $100.

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Of interest The collecting of coins is called numismatics. To find out more, a useful website is: <www.ramint.gov.au> The study of paper money or banknotes is called notaphily.

Symbols for money

For example, two dollars is worth more than 50 cents, yet the number 50 is greater than 2. The mixture of dollars and cents can be confusing for children; and if they do not have a clear idea of 50c as being half of one dollar, this issue can be difficult to deal with.

The different way that amounts less than one dollar can be written

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For example, we can have 5c, five cents, 5 cents or $0.05.(but not $0.05c) Children don’t always get to spend cash (e.g. pocket money) at a corner shop due to issues of safety and lack of corner shops

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The symbol for cents in Australia is a lower case ‘c’. For example, 75c.

The symbol for Australian dollars is an upper case ‘S’, with a single vertical line ($). The US dollar is an upper case ‘S’, with two vertical lines. To help distinguish between two currencies three block letters are shown before the amount. For example, AUD$10.00 indicates ten Australian dollars, whereas USDS20.00 indicates twenty United States dollars.

The symbols ($ and c) should not be used together. The following are both wrong: $5.75c or $0.75c.

A mixture of dollars and cents when looking at the value of coins

In today’s society, many children are not able to go to a corner shop on their own and make decisions about spending their valuable cash. Even at a school canteen, many young students simply hand over a fistful of coins and let the canteen worker figure out what coins are needed, and what, if any, change is required.

Rounding rules

Value of items

The rounding rules for shops is that a total ending in 1c or 2c is rounded down to the 10c value; a total ending in 3c or 4c is rounded up to 5c; a total ending in 6c or 7c is rounded down to 5c; and a total ending in 8c or 9c is rounded up to the next 10c.

When setting up a realistic context in which to teach money concepts— e.g. a shop—realistic prices can rarely be used. So a box of cereal, for example, may be priced in the class shop at 50c, whereas it would cost many times more than that in a real shop.

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The Currency Act stipulates that there is a limit to the amount of coins that can be handed over in a shop.

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5c, 10c, 20c, 50c

Maximum of $5

$1, $2, $5, $10

Not exceeding ten times the face value, inclusive; i.e. a maximum of $100 for $10 notes (10 x $10)

Others

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It is only on credit cards that exact amounts such as the above can be made. So if paying in cash, children need to be familiar with the concept of rounding and when a system rounds up or down. For example, if paying in cash for a purchase worth $3.98, cash registers will round this to $4; however, if the amount is $3.97 (only one cent less), the payment required is $3.95 (5 cents less than the $4).

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The use of ‘impossible’ values in advertising; e.g $3.99.

Exact amounts can not be made with coins.

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Till (cash register) operators in shops rarely count back change, or do numerical calculations.

Shop tills do the calculations for them and indicate how much change is needed. Often change is not counted back to the customer.

Being able to get a trolley full of shopping, hand over a card to pay and even get cash in hand!

Children see adults using cards to pay for goods and often getting extra cash as well as the purchase. No wonder they get confused about money!

To any value

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The original 50c coins were circular, but were changed to a dodecagon because the size was too similar to the 20c coin, and therefore easily confused.

The issue of truncation when using a calculator If entering an amount such as $4.50 into a calculator, the display will initially show it as entered. However, once a calculation has been entered, the final zero after the decimal point will be truncated or cut off; e.g. with $2.50 + $1, the solution will show as 4.5, not 4.50.

Children will need to be taught to read and interpret the display as four dollars and fifty cents. Note the obvious confusion with four dollars and five cents.

r o e t s Bo r e p ok u S Changing design of 50c and $1 coins

The Australian Mint sometimes changes the shape and design of the 50c and $1 coins to commemorate special occasions.

The rims of 5c, 10c, 20c and 50c coins have regular lines around them.

The rim of the $1 coin has groups of 10 lines with spaces between them.

The rim of the $2 coin has groups of 5 lines with spaces between them.

This makes it easier for visually impaired people to tell the coins apart.

Online shopping

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The milling on the rims of some coins is different

This is another example of children seeing purchases being made with no apparent exchange of money.

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If using real money, one idea is to give parents a list of requirements at the start of the year; e.g.

5 x 5c, 5 x 10c, 5 x 20c, 2 x 50c etc. and your preferred means of storage; e.g. a plastic soap container or zip-lock bag. These can then be handed out at the start of a session, counted by the students to check it’s all there, then counted out again at the end of the session when returning the bags of money to the teacher, who stores them all securely.

Classroom management

1. Use of real or ‘play’ money Some teachers like to allow students the opportunity to handle real money, at least when dealing with coins, whereas others are happy to use plastic play sets—or it may vary depending on the situation.

2. Counting out and back ‘money’ used in class This is a good habit to get students into, whether using real or ‘play’ money.

3. Storage of money If using real money, it needs to be stored somewhere safe. If using ‘play’ money, this issue is not as important.

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The use of credit, debit and EFTPOS cards to buy goods

Credit cards: Enable the use of a ‘line of credit’ from which the holder can borrow or use as a cash advance.

This is issued by banks, credit societies and even shops.

Holders aim to pay off their balance, but incur interest on any overdue amounts.

In reality, children may not see adults using cash very often.

Debit cards: Enable existing funds to be withdrawn to the value of money in the account. This can be in the form of cash withdrawals, or the funds can be used to pay for purchases electronically or using EFTPOS (Electronic Funds Transfer at the Point of Sale).

Simply put, credit cards are used for money that doesn’t belong to you; debit cards for money that does belong to you.

If plastic ‘bank’ bags are used to take coins to the bank, they may be emptied onto a balance and weighed by the teller to ascertain if they contain the correct amount. The bags are designed to hold $5 of 5c coins; $10 of 10c, 20c or 50c coins; $20 of $1 coins or $50 of $2 coins, with the instruction, ‘Do not mix denominations up’.

The hole in the wall (Automatic Teller Machine—ATM) that dispenses a seemingly endless supply of cash.

Children may not understand that you need to have money in an account, or money to be paid into an account, in order to take cash out.

Weighing of coins when banking large amount of coins

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Weight of coins: 5c 2.83 grams 10c 5.65 grams 20c 11.3 grams 50c 15.55 grams $1 9 grams $2 6.6 grams

Children may expect shops to have an unending supply of money, as they do not get to see the shopkeepers doing their banking.

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Of interest

The idea of the shopkeeper needing a float of money, or delivering takings to the bank, is rarely discussed.

The need for both exact and approximate calculations

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Dispensing machines; e.g. soft drink or snack food This is one situation where children may occasionally see coins used, although some mobile phones and credit cards can now be used to debit a bank account for purchases.

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Note 1: The $1 and $2 coins each weigh less than the 20c or 50c coin.

Note 2: The 10c and $1 coins are very close in mass and size (10c has a diameter of 23.6 mm and the $1 is 25 mm).

Sometimes an estimate is good enough; for example, if you need to know if $20 is enough to buy a basket of goods, then an overestimate will help. An exact calculation would be needed if working out how much of each denomination coin was being deposited in the bank.

People rarely get paid in cash. Money is deposited straight into bank accounts.

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Again, children are not as likely to be exposed to the counting of money as in years gone by.

The prevalence of gift vouchers

Most large stores and shopping centres have their own gift vouchers that can be exchanged for goods to an agreed value.

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Bartering

You may have heard the expression ‘as safe as Fort Knox’. It refers to a large vault situated on a military base called Fort Knox. The United States Treasury maintains a gold bullion depository there, which holds over 4000 tonnes of gold and other precious items. It was featured in the James Bond film, Goldfinger, where the villain planned to set off a nuclear bomb, thus making all the gold radioactive, thereby ruining the United States economy. At the time the movie was made, currencies had to be backed by gold; that is, an amount of gold equivalent to the currency in circulation had to be keep in storage at places like Fort Knox.

This is no longer the case.

It should be noted that there now is a larger gold bullion depository in New York (over 5000 tonnes) than at Fort Knox.

Once the main form of getting what was required, bartering is still often used informally in our community; for example, a lawn is mowed in return for babysitting for one evening. It is now possible to obtain a Barter Card where points accrue. (See section on Bartering on pages 14 and 15.)

GST and 10% At some stage, students need to be exposed to the idea of a government Goods and Services Tax. It would be useful for older students to be able to calculate 10% of a value mentally. Also, discounts are usually given as percentages.

r o e t s Bo r e p ok u S The value of money

The value of money was once locked to the value of gold, but this is no longer the case.

School banking is rarely provided

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Of interest

Many years ago, representatives from particular banks would attend a school once a week to collect small amounts of cash from students and deposit it in the children’s bank accounts. Students kept a bank book in which all their transactions were recorded.

Post offices use an object’s mass, volume and area when working out the cost of postage

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If a realistic context is to be used, it may be interesting to investigate the criteria used to work out the cost of sending a package or large envelope through the mail locally, nationally and internationally.

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The barter system Before money was developed as a measure of value, the process of ‘buying’ something was quite complicated.

Firstly, two or more people had to have some excess goods to trade.

Secondly, the two people had to meet. One had to want the item or goods that the other person had, and vice versa.

Do you want to swap some carrots for your potatoes?

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No, I want two carrots for every potato I give you.

I will give you one carrot for one potato.

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Once the two agreed to trade, then both people had to agree on the exchange rate.

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Exchanging one item for another sometimes became even more difficult if one person did not want what the other person had to swap.

I’ll swap you some of my carrots for some of your potatoes.

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I don’t want any carrots.

In this case, a third and sometimes a fourth and fifth person needed to be involved and a number of trades made in order to complete a simple transaction.

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I’ll swap some of my carrots for some apples, then I’ll swap some apples for some potatoes.

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I am happy to swap some apples for my potatoes.

I’ll swap some apples for your carrots.

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Bartering Purpose

• To establish the need for money to act as a ‘gobetween’ when buying an item and • to ‘see’ and experience how prices are set according to supply and demand (‘medium of exchange’).

Activity • Role-play the barter process using items such as pencils, pens, rulers, pencil sharpeners and erasers.

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• Focus on the issues of establishing an exchange rate (bartering).

• What happens if one person does not want what the other person has to swap?

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• What happens if one person has a service that the other person wants, rather than goods? For example, how would students work out the value of having their desk tidied in return for a certain number of felt-tipped pens?

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Students who have travelled to countries where it is common to ‘barter’ for lower prices for goods, will have a slightly different understanding of the term ‘bartering’ or ‘haggling’.

They may see it purely as a means to get a better price. However, it can in fact still be seen as coming to an agreed value for an item.

• Once students have had a chance to explore the idea of bartering, scenarios could be set to have them experience reaching a compromise.

Sample scenarios:

– Trying to exchange a pencil for a whole packet of felt-tipped pens.

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– Trying to exchange a pencil for an eraser, where the person with the eraser only wants a ruler owned by a third student who doesn’t want either a pencil or an eraser, but would like to have all of his/her coloured pencils sharpened. What compromises can be made to satisfy all participants?

Swap cards

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Discussion could take place about swap cards, and the notion of swapping. Questions could be asked, such as: How many of each card are there?

Which cards are there fewer/more of, and why?

How many of this card are worth one of that card?

What would be a fair swap?

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Note: Page 14 could be distributed among students to assist in explaining the barter system.

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Language associated with money What mathematical language do students need to understand and use in relation to money?

1. Brainstorm words associated with money

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As the students volunteer money-related words, try to separate them into meaningful groups. For example, the words money, cash, coins and notes all refer to currency. In fact, the word ‘cash’ refers to money in the form of coins or notes. It is a good idea to use a dictionary to define words, because sometimes we might assume the meaning is clear.

The words interest, deposit, balance, statement and withdrawal are associated with banking and bank accounts.

2. Acronyms

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Note: Just because a student uses a word, it does not mean he or she knows what it means.

Brainstorming the words associated with a new topic is an excellent way of informally assessing what students know about a topic. It also helps to ‘tune them in’ as they will be hearing these words throughout the unit of work.

Students may suggest various acronyms such as EFTPOS (Electronic Funds Transfer at Point Of Sale), ATM (Automatic Teller Machine), GST (Goods and Services Tax), BPay (Bill Pay), EFT (Electronic Funds Transfer) and PIN (Personal Identification Number). Some further explanation may be required. Note that some of these terms relate to internet banking so it is highly unlikely that the students will have direct experience with them. However, they may have heard their parents or older siblings using these terms.

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Below is a list (not exhaustive) of words associated with the topic of money.

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There is quite a difference between a credit card and a debit card. Credit cards are essentially small loans that need to be repaid with interest. Debit cards basically involve drawing money out of an account that has money deposited in it. You cannot withdraw more money than you have in the account. There are many store cards that are essentially credit cards.

ATM, balance, bank, bank account, bank statement, barter, budget, balance, bargain, cash, cash register, cashier, change, cheap, checkout, cheque, credit, credit card, coins, currency, dear, debit, debit card, debt, deposit, earn, EFTPOS, expensive, inflation, interest, invoice, lay-by, money, money box, notes, pay, purse, receipt, shop, spend, transaction, wallet, withdrawal …

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Charts or lists could be made of different types of shops.

Baker, bank, boutique, butcher, cafe, delicatessen, department store, general store, greengrocer, jewellers, newsagency, post office, restaurant, shoe shop, supermarket, toyshop …

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5. Money-related phrases

Of interest There are many phrases related to our previous non-decimal currency. While pennies are no longer used in Australia, students may have heard some phrases relating to pennies. They could ask their grandparents what these phrases mean.

Penny pinching

Discuss the meaning of phrases such as: • Money doesn’t grow on trees.

• I’m not made of money.

• A fool and his money are soon parted.

• Put your money where your mouth is.

r o e t s Bo r e p ok u S • In mint condition (uncirculated coins are said to be in mint condition).

In for a penny, in for a pound.

Spend a penny.

A penny for your thoughts.

Take care of your pennies and the pounds will take care of themselves.

• Deep (long) pockets, short arms

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• Money talks.

• Saving for a rainy day.

Penny-farthing bicycle

• Cost of living

The penny dropped.

• Money can’t buy happiness.

A pretty penny Penny whistle

• Money burns a hole in your pocket.

Consider the phrase ‘Two cents’ worth’.

• Time is money.

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Pennywise and pound foolish.

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6. Language-related issues

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We often say a ‘smaller’ coin meaning one with lesser value, and ‘larger’ coin meaning one with greater value.

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In many other aspects of mathematics, the terms ‘smaller’ and ‘larger’ are not confusing and may be used in connection with length or area, or in relation to the size of a number; e.g. 6 is larger than 5. But in this case, the smaller-sized coin may be $1 and the larger-sized one 50c, so the physically larger coin has the smaller value.

The use of the word ‘change’, changes.

Same word, different contexts and meanings. It can be about changing money; e.g. 5 x 20c for $1.00; the amount of money you get back if you spend 50c and hand over $1; and the amount of money in a purse or pocket; i.e. ‘loose change’. Also, it can be about an exchange rate when changing money to a different currency.

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Money recognition

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Coin recognition – activities Purpose Students will be able to: • recognise coins • sort coins • match coins and • name coins.

The following activities are designed to help students develop coin recognition.

r o e t s Bo r e p ok u S 1. Examining coins

Students will need a magnifying glass.

Ask the students to examine a twenty cent coin.

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Discuss features of the coin: • colour • size • shape • animal that is featured • other markings such as the date.

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From a collection of coins, students could be asked to find all the 20 cent coins (or other nominated coin).

Some students may have taken their moneybox to the bank to deposit money into their bank account. They may have noticed that the teller has to sort the money into special zip-lock bags, with writing on the outside. The teller may weigh the bag to determine how much money is in the bag. Ask the students why they think various amounts are written on the side of the bag. Hopefully, a student will explain that this means the teller doesn’t have to count the money in the bag.

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Symbols for money

The symbol for cents in Australia is a lower case ‘c’.

The symbol for Australian dollars is an upper case ‘S’, with a single vertical line ($).

Note: When writing amounts of money there is no space between the number and the cents symbol ‘c’; i.e. 50c not 50 c.

2. Coin sort Hand out zip-lock bags containing a variety of coins. Ask the students to sort the coins. Once the coins have been sorted, ask individual students to explain HOW they have sorted the coins. They may use criteria such as size, colour, shape, design, denomination ....

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$5 of 5c coins $10 of 10c/20c/50c coins $20 of $1 coins $50 of $2 coins

Now get the students to examine the other coins in the same way.

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Later, students can be asked to sort the coins according to particular criteria such as date or type of animal.

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3. Rubbing coins Place a coin under a sheet of white paper and colour over it with the side of a lead pencil.

Teacher tip We found that using a softer lead pencil and rubbing with a lighter pressure produced better results.

r o e t s Bo r e p ok u S 4. Rubbing coins game

Materials

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A game for two players

Coin dice or coin spinner (see page 39), two copies of the coin reference sheet (see page 25), two lead pencils and one of each type of coin.

Rules

Players take turns to roll the dice or flick the spinner.

If 50c turns up, then one side of the fifty cent coin is rubbed with the lead pencil.

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Play continues until one player has rubbed both sides of each coin.

The winner will have at least both sides of all six coins rubbed.

Note: Players may have more than twelve rubbings as some coins will come up several times.

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cup salt 1 cup flour 1 tablespoon cream of tartar 1 tablespoon oil 1 cup of water food colouring Method: Combine the ingredients in a saucepan. Heat gently, stirring all the time. When the dough has a good consistency, take it off the heat and allow to cool.

5. Coin prints

Make some play-dough. Flatten the play-dough with a rolling pin.

Press coins into the play-dough. Ask the students to match the coins to the impressions.

6. Coin collections Hand out zip-lock bags containing a variety of coins. Ask the students to separate all: • • •

the twenty cent pieces the silver coins the gold coins.

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Most students will recognise that all coins except the 50c piece are circular. The 50c piece has twelve sides. The mathematical name for a twelve-sided shape is dodecagon, which means twelve sides and twelve angles.

The 50c is a regular dodecagon, as all sides are the same length, and all angles are equal.

Play a guessing game where the students are given clues as to the identity of a coin. For example: • I am a silver coin. (Eliminates $1 and $2) • I am round. (Eliminates 50c piece) • You need to write ‘zero’ when writing down my value (Eliminates 5c piece) • I have a picture of a platypus on one side. (Answer: 20c)

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Some students will experience trouble cutting around the circumference of the coins, especially the 5c piece. A box can be drawn around the coins and the students cut out this square making the task easier.

For example:

• I am worth more than a 5c piece but less than a $2 coin.

• I have at least one kangaroo on me.

• I am round. (Answer $1)

• • • •

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Note: The outlines shown on the ‘coin cut-outs’ templates (see pages 26–27) have been made slightly larger than the actual coin size. This makes it easier for students to place real coins over them. When students trace around coins, the outline will be slightly larger than the actual coin. If plastic coins are used then the outlines will be larger than real money.

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7. What coin am I?

I am a round coin.

I am a silver coin.

The animal that is featured on me is a mammal.

Two of me can make one of another coin. (5c)

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• • • • •

One side of me features an animal.

The animal does NOT live in the water.

I am a silver coin.

The number shown on me is made up of two digits.

Ten of me make up a gold coin. (10c)

• • • •

I am a silver coin.

The number shown on me is made up of two digits.

I feature an animal that has feathers.

I am NOT round. (50c)

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When tracing around the coins, some students will notice that the rim or circumference of the coin is raised. This helps to protect the coin. The edge is also milled. This is designed to stop people filing or trimming pieces off the edge of the coin. When coins were made of precious metals such as gold, filing a little bit off many coins could mean that a lot of precious metal could be collected. Note: The $1 coin has a distinct milled pattern, made up of groups of ten. The $2 coin has a milled pattern made up of groups of 5.

• I am NOT a dodecagon shape.

• I am NOT silver.

• I am the more valuable of the two coins left. ($2)

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Ask the students to write their own ‘What am I?’ puzzles.

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8. Tracing around coins

50c

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$1

9. Feely bag

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20c

Using coins as templates, ask the students to draw around the edge of various coins to make outlines. The order in which the tracing takes place doesn’t matter as the coins will be ordered later.

Discuss issues such as the largest coin (50c) is not worth as much as some small coins ($2).

Cut out and order: • according to size • according to value.

Compare coins.

Match actual coins to the outlines.

Students can make two sets of outlines and then make rubbings of the coins so they have a reference set.

The $1 and 10c are almost identical in size so encourage the students to list as many differences as they can. Likewise the $2 and 5c are of a similar size so encourage the students to look for differences between the two coins.

Place a coin in a ‘feely bag’ (a drawstring bag) and ask students to place their hand in the bag, feel the coin and then try to identify it.

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10. Lucky dip

A game for two players

Materials • ‘Feely bag’ containing a mixed collection of coins • Two game boards (see coin reference sheet on page 25.)

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• Players take turns to reach into the ‘feely bag’ and take out a coin.

• The coin is placed on the game board in either the head or tail position.

• The winner is the first player to cover all of his/her game board.

11. Coin patterns

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Rules

Use coin stamps or cut out the coin cut-out templates on pages 26–27 to create pattern cards. Encourage the students to use coins to copy the pattern and extend it. Once the students have grasped the concept ask them to make pattern cards for other students to try.

Examples of pattern cards

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Coin reference sheet (game board)

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20c head

5c tail

10c head

20c tail

50c head

$1 tail

$2 head

10c tail

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$1 head

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50c tail

$2 tail

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Coin cut-outs

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Coin match game Purpose Students will be able to: • recognise coins.

A game for two players

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• Two game boards (see page 25) • One coin dice or coin spinner (see pages 39–41) • Container with four each of:

– 5c coins

– 10c coins

– 20c coins

– 50c coins

– $1 coins

– $2 coins

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Materials

Rules

• The first player throws the coin dice, or spins the spinner.

• This player then picks up the appropriate coin from the coin container.

• The first player places the coin on the game board.

• The first time a coin is placed on the board it is done so heads up. The second time, it goes heads down.

• If both the heads up and heads down for a particular coin are covered, then the player misses a turn.

• Players take turns to throw the coin dice or spin the spinner.

• Play continues until one player covers the last coin place on the game board.

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Coin reference sheet (game board)

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5c tail

10c tail

20c head

20c tail

50c head

50c tail

$1 head

$1 tail

$2 head

$2 tail

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10c head

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Money bags A game for two to four players

r o e t s Bo r e p ok u S Materials

• Empty labelled plastic zip-lock bags. One set of six bags per player, labelled 5c, 10c, 20c, 50c, $1 and $2. Older students will simply require 6 bags each.

• One coin dice or coin spinner (see pages 39–41) • Container with mixed coins Rules

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Purpose Students will be able to: • sort coins • count coins and • appreciate the need to keep records; e.g. bank statements.

• The first player throws the coin dice or spins the spinner.

• The player then picks up the appropriate coin from the coin container and places it into the appropriate bag.

• The second player does the same.

• Play continues for a set amount of time; e.g. ten minutes. At the end of the playing time, each player counts how much money he or she has accumulated.

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• As students gain experience, they can keep a record by using money stamps, coin cut-outs or written ‘bank statements’.

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Fill my board game A game for two players Materials

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2 copies of the game board on page 31 A ‘feely bag’ with 4 of each of the following: – 5c coins – 10c coins – 20c coins – 50c coins – $1 coins – $2 coins

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Purpose Students will be able to: • practise matching coins with pictures and written symbols.

Rules

• Each player takes turns to reach into the feely bag and take out one coin.

• The player places his or her coin on the game board. It needs to match with either the symbol or the picture of the coin.

• If a player picks out a coin that cannot be used, the coin gets put back in the bag, and the player misses that turn.

• The winner is the first to cover all of his or her game board.

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Note: The game board shows two places for each coin; one is the symbol and the other is the animal. The board is designed to be used with actual coins and may be enlarged for use with plastic coins.

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(Fill my board) game board

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Money concentration game Purpose Students will be able to: • practise matching coins with pictures and written symbols.

Materials • You will need a set of 24 laminated money cards (see pages 33–34). It is suggested that the pages are enlarged to A3 before photocopying onto card and laminating.

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• Place all of the money cards face down on the table.

• Player 1 turns over two cards. If the two cards match—i.e. the same amount is represented (five cents and 5c)—the player keeps both cards and has another turn. If they do not match, the player turns them back over and the next player has a turn.

• When all the cards have been matched, the person with the most cards is the winner.

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For a simpler game, the cards showing $0.05, $0.10, $0.20 etc. can be removed. In this case, two sets of cards will be need to be copied to ensure there are pairs of cards. For a longer game, make two sets of cards so that 48 cards are laid out.

Alternatively, ‘Snap’ can be played for a set period of time.

At the end of the time, the player holding the most cards is deemed the winner.

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Snap Two sets (48) of the same cards can be used to play ‘Snap’. The money cards are shuffled and dealt out equally. Players take turns to turn up a card and place it onto a central pile. If the new card matches the current one on the pile, then the first player to cover the cards with his or her hand keeps the whole pile. Play continues until one player has won all the cards.

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Note: You may wish to enlarge these before photocopying onto card and laminating.

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fifty cents

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Note: You may wish to enlarge these before photocopying onto card and laminating.

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Money dominoes Purpose Students will be able to: • recognise and match coins and • recognise and match coin amounts when written in different forms; e.g. 5c, 5 cents, five cents, $0.05.

Materials

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There are many variations to the traditional dominoes game. If your students know a different set of rules for dominoes, you may want to let them continue with these rules.

A set of coin dominoes (see page 36) or mixed dominoes (page 37) Rules

• Dominoes are placed face down on the table and 7 are given to each player. Each player looks at his or her dominoes and the person with the highest denomination double places that domino on the table, face up. If no player has a double, the player with the highest total starts the play.

• Players take turns playing one domino at a time, by matching one of their pieces with either end of the string of dominoes.

Doubles are usually placed at right angles to the other pieces.

New pieces can only be placed at either end of the string of dominoes. The string of dominoes can be turned to fit onto the playing surface, but the line essentially can only be built on at the two ends.

• When a player cannot match one of the ends of the line, he or she takes another domino from those face down on the table.

This becomes the end of his or her move. If there are no pieces left, the player misses that turn.

• Play ends when a player has no dominoes left, or when no further moves can be made.

• The winner is the player with no dominoes left, or in the case where no further moves can be made, the one with the least total amount of money shown on his/her remaining dominoes.

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‘Money dominoes’ are played in the same way as normal dominoes. If students play the ‘Money dominoes’ game, they need to be able to recognise all coins from 5c to $2.

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A game for 2–4 players

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The dominoes in the centre of the table are sometimes known as the ‘bone-yard’, taken from the original dominoes that were made from pieces of bone.

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Variations

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For the ‘Mixed money dominoes’ variation, students need to be familiar with the different ways the amounts on coins can be written.

• When a double is played, other dominoes of that denomination can be played off in the new directions.

• Scoring can take place where the remaining dominoes are totalled, and the winner scores the amount of his or her opponent’s total minus the total of his or her own.

For example, if Player 1 had a total of $1.50 and Player 2 $2.25, Player 1 scores 75c and Player 2 scores 0; or if Player 1 has no pieces left and Player 2 has $1.05, Player 1 scores $1.05 and Player 2 scores 0. The aim, therefore, is to keep the total value of the pieces in your hand as low as possible, rather than the number of dominoes.

• Game variation 1: Use the mixed money dominoes.

• Game variation 2: Use ‘Money dominoes’ (coins) and ‘Money dominoes’ (mixed) together.

• Game variation 3: Students make sets of dominoes using the template on page 38.

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Money dominoes (coins)

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Money dominoes (mixed) Two dollars Money matters

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Money dominoes (blank)

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Note: You may wish to enlarge these before labelling, photocopying onto card and laminating.

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Coin spinners

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If spinner arrows are not available, then a basic spinner can be created using a paper clip and pen or pencil, as shown.

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Spinner arrows and bases can be used to create professional-looking spinners. A hollow punch can be used to cut holes in the spinner template. The template will need to be photocopied onto card and laminated first.

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Coin spinners

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An alternative way to create a spinner involves placing a cocktail stick or pencil through the centre of the spinner. The top of the cocktail stick is spun between the thumb and the first two fingers of the hand. The spinner will land on a particular side, which indicates which coin is chosen.

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Notes on coins

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The following background provides a brief overview of each coin.

Coins have two sides, sometimes referred to as heads or tails.

However, the correct terminology is obverse (heads) side and reverse (tails) side. The obverse side of all Australian coins shows a picture of the monarch who is reigning at the time. The year the coin was minted is shown on the obverse side. Most Australian coins, except the two dollar coin, feature Australian animals. At times, special coins are minted to commemorate special events or famous people.

Even though the five, ten, twenty and fifty cent coins are often referred to as ‘silver coins’ they are actually made up of a mix of 75% copper and 25% nickel. The so called ‘gold coins’ don’t contain any gold. The one and two dollar coins are made up of copper (92%), aluminium (6%) and nickel (2%).

Five cents

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Purpose Teachers may wish to photocopy the following pages on notes and coins and give them to students as a note-taking exercise.

The five cent piece depicts the echidna. The echidna is one of only two mammals in the world that lay eggs; the second is depicted on the twenty cent coin. These two animals are monotremes. Once hatched, the babies feed on their mothers’ milk.

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A lyrebird is depicted on the ten cent coin. The lyrebird is unique to Australia. The lyrebird was named after an ancient musical instrument called a lyre, which the tail feathers resemble.

The platypus is the other mammal that lays egg and suckles its young with milk.

o c . che e r o t r s super Fifty cents

The fifty cent coin is the only coin that is not round. It is twelve-sided.

The mathematical name for that shape is dodecagon. The fifty cent piece depicts the Australian Coat of Arms. Close examination of the central shield shows the six state badges. On either side of the shield are the kangaroo and the emu, which are the animal emblems of Australia. In the background is the golden wattle—Australia’s national flower.

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One dollar The kangaroo appears on two coins—the fifty cent piece and one dollar. The kangaroo is a mammal, like the echidna and platypus, but it does not lay eggs. It is a special type of mammal, known as a marsupial. The one dollar coin shows five kangaroos.

Two dollars An Aboriginal tribal elder is depicted on the two dollar coin. The Southern Cross is shown in the background. A grass tree may be seen to the right of the number 2.

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Fifty cent, one dollar and twenty cent coins are, at times, used to commemorate events or famous Australians. Some of the famous people featured on commemorative coins include: – Captain Cook

The rarest Australian coin is the 1930 penny. A 1930 penny was sold for $225 000 in 1998.

The edges of coins are often milled. Originally this was done to check whether some of the precious metal had been filed from the edge. Circulating coins are no longer made from precious metals. Today, milled edges are used to help visually impaired people distinguish between different coins.

– ‘Weary’ Dunlop – Sir Henry Parkes – Sir Charles Kingford Smith – Bass and Flinders.

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Commemorative coins

Television was even featured on one commemorative coin!

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Students can research some of the following: • animals found on coins • people featured on coins and notes • Australian coat of arms, national emblem, States and territories coat of arms.

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To feature on a note or coin, one criterion is that the person must be deceased. The current Monarch is the exception.

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Notes on notes Australia adopted a decimal currency system in 1966. As the name implies, ‘decimal’ means there are 100 cents in the base unit—the dollar.

However, cents were phased out in 1992.

Useful website: The Royal Australian Mint: <www.ramint.gov.au>

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Australian coins show the date on which they were minted.

Australian bank notes do not show the date the note was printed. However, the serial number may be used to determine when the note was released. The current serial number system was adopted in 1993. From 1993 onward the last two digits of the serial number indicate the year in which the note was printed and circulated. For example, if the last two digits were 98 it would indicate the note was printed in 1998, whereas if the last two digits were 09 it would indicate the note was printed in 2009.

The $5 note

The five dollar note is the only note that features the Queen. Parliament House is featured on the other side. Both the old and new Parliament House are illustrated on the note.

The $5 note includes eucalyptus leaves on the side showing the Queen’s head. Geometric shapes are shown on the Parliament House side.

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Australia uses polymer (a type of plastic) notes and was the first country to use polymer for all its notes. Polymer notes were developed in Australia and are now used in many other countries, including New Zealand and Singapore. The main benefits of polymer notes are that they last a lot longer than paper notes and they are much more difficult to counterfeit. Australia is at the forefront of note-printing technology.

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Two poets are featured on the $10 note; A.B. ‘Banjo’ Paterson (1864 – 1941) and Dame Mary Gilmore (1865 – 1962).

If you look closely at the Banjo Paterson side you will see a picture of a horseman and some horses. This was included on the note to represent elements of Banjo Paterson’s famous poem, The man from Snowy River.

Directly beneath the 10 you will find the words Waltzing Matilda, a famous song that Banjo Paterson wrote. Most Australians would know at least the chorus if not all the words to this song. Near Banjo Paterson’s collar you will find some writing. The writing is part of the manuscript for The man from Snowy River. Several techniques are used to stop the counterfeiting on our notes. One such feature is microprinting. As the name suggests, very small type is used to print some words on the note.

You will need a strong magnifying glass to see the microprinting. In the case of the $10 note, microprinting surrounds the portrait of Banjo Paterson. All the words to The man from Snowy River are microprinted on the note.

The microprinting on the other side of the ten dollar note is from Dame Gilmore’s poem No foe shall gather our harvest. Two different pictures of Dame Mary Gilmore are depicted on the ten dollar note. One is based on a portrait, the other on a photograph. Photographs were not commonplace in the 1880s. A bullock team carrying wool can be seen on the lower left of the note.

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The $20 note

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Mary Reibey (1777 – 1855) is depicted on the other side. Mary arrived in Australia in 1792 as a convict and went on to become a wealthy businesswoman. If you look closely at the $20 note you will see a ship (schooner) and a building owned by Mary. If you also look closely at the clear window of the note you will notice a picture of a compass is featured.

The $50 note

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The Reverend John Flynn (1880 – 1951), the founder of the Royal Flying Doctor Service, is featured on one side of the note. The plane that can be seen on the note was called Victory and was the first plane used to pick up patients. A pedal generator is shown beneath the aeroplane. The significance of this is that the pedal generator was used to power the radio sets used to call the Flying Doctor. The numbers and letters shown on the body were used to communicate to the doctor where on the body the pain or injury had occurred. What may seem odd is the picture of the camel. Camels were used to carry people and supplies to the various bush hospitals that he helped to set up.

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Two people are featured on the $50 note; David Unaipon (1872 – 1967) and Edith Cowan (1861 – 1932). David Unaipon is best known for his inventing, writing and campaigning for Aboriginal rights. He was the first Aboriginal writer to be published. The handwriting featured on the $50 note is taken from his manuscript for Aboriginal legends. Unaipon is sometimes referred to as Australia’s Leonardo DaVinci, because he developed many inventions. One of his better known inventions was a handpiece for shearing sheep. You can see some of the drawings associated with this invention on the $50 note.

Edith Cowan is probably best known as Australia’s first female member of parliament. She was instrumental in many reforms associated with women and children’s health. For example, she campaigned for the introduction of what are today known as childcare centres. She was one of the first female justices of the peace.

She received an OBE for her work with the Red Cross and other organisations throughout WWI. She was elected to the Legislative Assembly in WA in 1921. The original front of the Western Australian Parliament House is depicted on the note. Her work for mothers and children is recognised by the picture of a foster mother and child.

The Edith Cowan University in Perth is named in her honour.

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$100 Note

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Sir John Monash began his working life as an engineer, having played a part in the building of the Princess Bridge in Melbourne. He is probably best remembered for his leadership roles in the First World War. He rose to the rank of Lieutenant-General. After the war he helped returning soldiers fit back into civilian life. He went on to take on administrative roles, heading the State Electricity Commission of Victoria and becoming Vice-Chancellor of the Melbourne University.

His links to the military are depicted on the $100 note. These include representations of a rising sun badge, cavalry, soldiers and artillery and the famous Simpson and his donkey.

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Dame Nellie Melba (1861 – 1931) and Sir John Monash (1865 – 1931) are featured on the $100 note. Nellie Melba was a worldrenowned soprano. Nellie Melba is not her real name but rather a stage name. Her real name was Helen Porter Mitchell. ‘Melba’ is actually a contraction of Melbourne, her home town. She sang in many operas. She was recognised for her work raising money for the war effort. Her Majesty’s Theatre, Sydney, is depicted on the $100 note. Her signature is shown and a lyrebird is printed on the clear window. The lyrebird is known as a songbird and features on the 10c coin as well as the $100 note.

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Project research ideas

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Students could be encouraged to design their own $200 note, based on observing key features of our notes. This will require them to research all aspects of notes.

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Coin recognition checklist Recognises coins

Names coins

Matches coins

Sorts coins

Comments

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Strategies for counting coins – activities Purpose Students will be able to: • count coins of the same denomination and • count coins of different denominations.

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What to look for when students are counting coins: Do they touch each coin as they count?

Do they realise that the last coin they touch/count indicates the total amount of coins counted? (For example, students say, ‘Ten, twenty, thirty cents’ when counting three 10c coins and recognises that this totals 30c.)

Start with coins of the same denomination, counting within the level of the student. For example: • Count by 5c to 50c.

• Count by 10c to $1.

• Count by 20c to $2.

• Count by 50c to $5.

• Count by $1 to $10.

• Count by $2 to $20.

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In order to count coins of the same denomination, students need to be able to count by 5s, 10s and 20s; and by 1s and 2s for the dollar coins.

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1. Students need to be encouraged in the counting of coins, both in sets of the same coins (e.g. a set of five 20c coins to make $1); or in mixed sets of coins (e.g.

20c, 10c, 10c, 5c and 5c to make 50c).

Ask students which coins they find easiest to count, and why.

Students can be asked to make informal comparisons by posing questions such as, ‘Who do you think has the most money?’ ‘Who has the most coins?’ ‘Is it always the person with the most coins who has the most money?’ ‘Count and find out who has the most money’.

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Do they start at the largest value coin (or group of coins) and count on from there?

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Do they put logical groups of coins into piles?

In the ‘Issues to consider’ section on page 11 is a ‘Teacher tip’ about using real money. Experience has shown that, at most schools, if the parents have provided the set of coins at the start of the year, students are very careful about ensuring that the full set is returned to the teacher each time it is used.

• counting from the largest denomination coins to the smallest • grouping coins of the same denomination together and counting each group • exchanging groups of coins for equivalent coins of higher denominations; e.g. five 20c coins for one $1 coin.

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Do they count to ‘milestones’; e.g. 50c, or $1?

2. For some students, counting a mixed set of coins can be difficult. They may need to be shown further strategies to make the task easier. These may include:

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3. One very real reason for counting coins in the classroom is the distribution of money (real or plastic) for any purpose.

If each set of coins is the same, and equals, for example, $5.00, then have students check that their set contains the correct amount.

Again, at the end of a session where the coins have been used, have students count the coins to make sure that none have gone missing.

See pages 102–104 for setting up a classroom shop.

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4. Try to find different contexts for students to count money in the classroom.

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One definition of the word ‘denomination’ is ‘the face value of a banknote, coin, postage stamp, etc.’ (Oxford English Dictionary) The word is from the Latin ‘nomen’ (name).

• Check the till in a classroom shop.

• Set up a Lucky Dip, where each child (or the teacher) chooses one or two zip-lock bags of coins and counts to find out how much is in his or her bags. (This could also be used as an assessment task; see page 65–69.)

• Have coins in opaque jars where students are given instructions as to what they may take; e.g. ‘Take 2 coins from the first jar, and 3 coins from the second jar’.

• Drop coins into an opaque jar that already contains a known amount of money. Count on from that amount; e.g. $4.30.

• Have a large container of coins. The student takes as many coins in one handful as he or she can, and counts to find out how much there is.

• Tip a container of coins onto a desk and ask students to estimate and then work out how much was in it.

• When fundraising, have the students sort the coins into piles or groups and count the takings. Too often it is the teacher or another adult who tallies it. Because accuracy will be required, different groups of students can do the counting, recording their totals on sheets of paper and comparing their results. If several groups obtain the same total, it is likely to be the correct one.

• Collections of money for class excursions and incursions could be totalled in the same way.

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5. Discuss the ways that banks count large amounts of coins.

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Older students can be asked to bring along currency from other countries and look at the various denominations of coins. These can then be counted.

Each coin may be counted, in which case the teller sorts the coins as they are counted, counting like coins together; or if the coins are in plastic ‘bank’ bags, they may be weighed by the teller to ascertain if they contain the amount stated on the bag. If plastic ‘bank’ bags are used, they will be placed onto a balance, and weighed by the teller to ascertain if they contain the correct amount. The bags are designed to hold $5 of 5c coins; $10 of 10c, 20c or 50c coins; $20 of $1 coins or $50 of $2 coins, with the instruction, ‘Do not mix denominations up’.

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Interesting to find out

How much does a $10 bag of 10c coins weigh?

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6. Challenges

Purpose This section leads to understanding of equivalence of coins.

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There are 13 combinations for 50c: 50c 20c 10c 1 0 0 0 2 1 0 2 0 0 1 3 0 1 2 0 1 1 0 1 0 0 0 5 0 0 4 0 0 3 0 0 2 0 0 1 0 0 0

5c 0 0 2 0 2 4 6 0 2 4 6 8 10

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• How many different ways can you make 20c?

• See how many ways you can make 30c using more than two coins.

• Find 4 coins that total 50c.

• Make up twenty cents and forty cents using the same number of coins for each amount.

• We can make 40c with 6 coins. How many different amounts can we make with only 6 coins? What is the smallest amount? What is the greatest amount?

• Show a set of coins; e.g. 20c, 20c and 10c. What different amounts can be made using all or some of these coins? What amounts less than 50c can not be made using only these coins?’

• Make a chart to show all the different ways you can make 50c. (You may want the students to use the cut-out coins from the blackline on pages 26 and 27.) How many different combinations are there? How will you know when you have found them all? (Students will need to be systematic in their search for all the combinations.)

• How many combinations do you think there would be for $1?

How can you check?

Note: In the section on money frames on pages 85–87, only three of the combinations for 50c are used: – 20c, 20c, 10 – 20c, 20c, 5c, 5c – 20c, 10c, 10c, 5c, 5c.

These are the only ones needed when working out the best way to give change when an item costs less than 50c and a 50c coin is tendered.

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(Refer to coin equivalence section on pages 75–79.)

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Note: In the section on money frames on pages 85–87, only three of the combinations for 50c are used: • 20c, 20c, 10 • 20c, 20c, 5c, 5c • 20c, 10c, 10c, 5c, 5c.

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Counting and weighing coins – activities Purpose Students investigate the mass of coins.

It takes a lot of time to count coins, so bank tellers often weigh the coins to determine how much is there.

How could you determine the mass of one coin?

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Most scales found in schools are not sensitive or accurate enough to weigh a single coin, so the mass needs to be found using an indirect approach. For example, you could weigh ten 20c coins and then divide by ten to calculate the mass of a single 20c coin.

The weight of each coin is: 5c 2.83 grams 10c 5.65 grams 20c 11.3 grams 50c 15.55 grams $1 9 grams $2 6.6 grams

Note 1: The 20c coin is the same weight as two 10c coins, and four times the weight of a 5c coin.

When a large number of coins is deposited at a bank, the tellers separate the coins into like groups, and weigh them. They then place them in specially marked zip-lock bags. The outside of the bag looks like this:

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Note 3: The 10c and $1 coins are very close in mass and size (10c has a diameter of 23.6 mm and the $1 is 25 mm).

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$10 of 10c/20c/50c coin or $20 of $1 coin or $50 of $2 coin

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Note 2: The $1 and $2 coins each weigh less than the 20c or 50c coin.

Reusable bag - please return to bank

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Students could find out more about coins by accessing the Australian Mint Website <http://www.ramint.gov.au>

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Do not mix denominations

Make up a bag of $2 worth of 5c coins.

• How much does it weigh?

• How many coins are used?

• How much does each 5c coin weigh?

• How does this compare to the actual mass according to the Australian Mint? (2.83 grams)

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Count coins game

Teacher tip

A game for 2–4 players, one of whom is the Banker.

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Note how the students count their coin collections. For example, do they group the coins before counting them?

Materials

A different coloured counter for each player A six-sided dice A collection of coins. The coins are to be kept in a box known as ‘The Bank’.

Some zip-lock bags Game board (see page 55) (You may wish to enlarge it).

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Purpose Students will be able to: • practise counting coins of different denominations and • practise counting coins of different denominations written in different forms; e.g. 5c, five cents, $0.05, 5 cents.

Rules

Players take turns to roll the dice and move their counter the number of places indicated.

If the player lands on a space containing a picture of a coin, then the Banker gives that player the appropriate coin.

Players keep their coins in their wallet, purse, pencil case or ziplock bag.

Once all players reach the Finish line, they total up their coin collection.

The winner could be the player with: • The highest total • The lowest total • The total nearest to …

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Track 1: Shows pictures of coins Track 2: Shows values written as 5c, five cents, and 5 cents.

Track 3: Shows values written in all different forms; e.g. $0.05, 5 cents, five cents and 5c, and actual pictures of coins.

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Another variation would be to throw the dice and make that many rotations of the track. For example, if they throw a 3, they all need to go around the board (track) three times.

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Count coins game board Track 1 (Pictures of coins)

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Count coins game board Track 2 (Coin values)

FINIS

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fifty cents

5c

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two dollars

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one dollar

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twenty cents

five cents

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Count coins game board Track 3 (Mixed)

two dollars

$1.00

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$0.20

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Money star game Game 1: A game for 2–4 players Materials

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A bank of coins or tokens A dice marked 1, 1, 2, 2, 3, 3 A counter for each player Money star game board (see page 59) Sets 1 or 2 of cards (Can be enlarged before photocopying onto card and laminating – see pages 60–63)

Rules

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Purpose Students will be able to: • practise counting coins of different denominations and • practise counting coins of different denominations written in different forms; e.g. 5c, five cents, $0.05, 5 cents.

Each player starts off with two 50c coins.

Players place their counter on Start.

Take turns to throw the dice, and move forward that number of places on the track.

When you land on a Star, take a card from the top of the pack and do as it says.

When you pay, you put the money in the bank.

Money you win comes from the bank.

At the end of the allocated time, the player with the most money is the winner.

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You may wish to add in your own final 4 cards – or ask the students to write them.

Use Set 2 cards, which are more difficult.

You will need 5 copies of these cards for each pair of players.

The winner could be the player with: • the highest total at the end of the allocated time • the person who ends up with the closest to his/her starting amount ($1).

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Money star game board

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ST AR T

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Money star game cards – Set 1

Happy birthday!

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Run an errand and get 30c

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Take 20c

Big sister gives you 50c

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Mum ©Buy R .

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Give the player on your right

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Give 20c to a charity

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Red Cross

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Note: You may wish to enlarge these before photocopying onto card and laminating.

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Money star game cards – Set 1

Gran gives you

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Buy a 40c banana

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Buy a drink for 45c

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Win a 50c prize in maths

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Pay 10c for a comic

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P b l i c a t i o n s down Pay 30c for a Do the dishes helping carry for swap card the back of •70c f orr e vi ew pur p ose sonl ya• the shopping chair

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o c . ch e Sell your r e o Get 75c for Pay a 10c t r s supe r pear helping your fine to a friend for 30c

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aunt

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for shouting

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Note: You may wish to enlarge these before photocopying onto card and laminating.

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Money star game cards – Set 2

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Buy a newspaper for $1.30

Donate $1.30 to a charity

Win $2.30 in a maths competition

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Get $1.50 for helping your gran

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Pay $1.75 for a muffin

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You find a $2 coin

You get a $5 reward for finding a missing cat

Get $ 0.55 for washing the dog

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o c . c e Ah friend Buy a $ 4 r e o Get $2.20 r s gives you supDVD att a er for helping $3.40 for

your notes

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secondhand shop

wash the car

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Note: You may wish to enlarge these before photocopying onto card and laminating.

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Money star game cards – Set 2

Win $2.50 in a lucky dip

Pay a $1.50 fine for a messy desk

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Pay the bank $4.10

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Find $2.35 in change down the back of the chair

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Your uncle gives you $2.70 for walking his dog

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Get $0.90 for helping wash up

Give $3.20 to your friend for lunch

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Note: You may wish to enlarge these before photocopying onto card and laminating.

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Coins match – Games 1 & 2 Purpose Students will be able to: • practise counting coins of different denominations and compare totals.

Game 1: A game for 2 players

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• Coin cards (see page 65). Five copies for each pair.

Shuffle the cards and divide equally between the 2 players, face down.

Each player turns over his or her top card. The person who has the largest amount keeps both cards. If the coin shown on both cards is the same, both players turn over their next card and the winner of that round takes all cards.

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Rules

The winner could be the player with: • the most cards when all of the cards have been played • the highest total when all of the cards have been played.

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• A set of coin cards (see page 65). Five copies fo each pair.

Shuffle the cards and divide equally between the 2 players, face down.

Each player turns over his or her top two cards, and works out the value of his or her cards. The person who has the largest amount keeps all four cards. If the totals of both sets of cards are the same, both players turn over their next card and the player with the highest amount takes all cards.

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The winner could be the player with: • the most cards when all of the cards have been played • the highest total when all of the cards have been played.

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‘Go for broke’ game

Teacher tip

A game for 2–4 players, one of whom is the Banker

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While the game is being played, check how the students are exchanging coins when necessary; e.g. if they have to pay 75c to the Bank, and do not have the necessary coins to enable them to pay directly, do they know to change a $1 coin for one 50c coin, two 20c coins and two 5c coins?

Materials

A counter for each player A collection of coins. The coins are to be kept in a box known as ‘The Bank’.

The game board (see page 67) – one 6-sided dice – one spinner (see pages 39–41)

Rules

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Purpose Students will be able to: • practise counting coins of different denominations, and exchange coins for equivalent amounts.

Each player starts with $5.00 (1 x $2, 1 x $1, 2 x 50c, 3 x 20c, 3 x 10c and 2 x 5c).

Players place their counter on Start.

Take turns to throw the dice and spin the spinner. The dice shows how many places to move forward, and the second spinner shows how much money to give or take.

Play continues for as long as the teacher determines—e.g. 10 minutes—or until the first player arrives back at the Start/Finish.

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Note how the students count their coin collections. For example, do they group the coins together before counting them? During the game, do they group the new coins they receive with their existing ones, or wait until the game has been completed?

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You may wish to use the money frames when working out change. See pages 86–98.

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The winner could be the player with: • The highest total at the end of the allocated time • The person who ends up with the closest to their starting amount ($5)

Variations

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Alternatively, if students are competent at handling money, they could pay in their $1 coin and take the 25c change as one 20c and one 5c coin.

Students must exchange coins; e.g. two 10c coins for one 20c coin; keeping the least number of coins. (They would therefore start off with one $5 note, not the suggested coins in the rules.)

Track 1: Single coin amounts on the money spinner; e.g. 20c, 50c, using pictures of the coins.

Track 2: Single coin amounts on the money spinner; e.g. 20c, 50c, using digits not pictures.

Track 3: More complicated amounts on the money spinner; e.g.

70c, $1.35.

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‘Toss to $10’ game A game for 2–4 players Materials A set of coins or tokens. The coins are to be kept in a box known as ‘The Bank’.

A coin dice or spinner A six-sided dice (1–6)

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Players take turns to throw the six-sided dice, and spin the spinner or throw the coin dice. He or she collects multiples of the amounts shown in coins or tokens; e.g. 4 on one dice and 20c on the other, so the player gets four 20c coins; i.e. 80c.

As the coins are collected, smaller coins are exchanged for ones of larger denominations; e.g. one 10c and two 20c coins would be exchanged for one 50c coin.

The winner is the first player to reach $10.

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Purpose Students will be able to: • practise counting coins of different denominations and exchanging coins for equivalent amounts.

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When students can make money calculations without needing the physical coins, they can play the game using pencil and paper to record their results.

By having only the money dice or spinner, and varying the amounts shown on the dice or the spinner, the game can become: • toss to $2 • toss to $5.

By having the six-sided dice and the money dice or spinner, and varying the amounts shown on the dice or the spinner, the game can become: • toss to $20.

By having the six-sided dice and two dice or spinners, one with cent amounts and one with dollar amounts on the dice or the spinner, the game becomes: • toss to $50 • toss to $100.

A 10-sided dice (0–9) could be used instead of the six-sided dice.

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Assessment 1: Coin count Purpose Students will be able to: • accurately count an amount of money.

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Some groups may choose to count a certain portion each and then attempt to add the portions to calculate the total amount. Some groups may assign various denominations to members of the group. For example; Chris counts the 5c pieces while Ian counts the 10c pieces, and so on.

Bring in a moneybox (or jar) of mixed coins. Try to include some foreign coins, buttons etc. Counting a set of mixed coins can be quite challenging for some students. Discuss various strategies such as placing coins into piles; e.g. ten 10c coins, five 20c coins, in stacks of $1.

Pour the contents of the moneybox onto a table, or show the jar to the group. Ask the students to guess how much money they think is there. If the students make wild guesses, ask questions to encourage considered guesses.

Explain that the money needs to be counted and set the task of counting the money to the students. Once the counting is complete, ask how the total might be checked to ensure the counting is correct.

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The amount of money in the moneybox or jar can be varied according to the ability of the group or individual.

The following activity can be completed as a group activity and then at a later time (with a change to the contents of the moneybox) repeated with an individual student as an assessment.

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Name

Counts accurately

Calculates totals correctly

Comments

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The discovery of foreign coins can raise informal discussions regarding where the coins come from. Some students who have travelled to other countries may bring up the need to change money from the home currency to the destination currency.

Students may then find the countries where the coins come from.

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Assessment 2: Counting coins Purpose To assess students’ ability to count coins; initially of one or two different denominations, but later extending to more denominations.

For younger students, use only 50c, 20c, 10 and 5c coins, with only one or two different denominations in each bag:

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If students can work out the correct amounts in two of the bags, we can assume they could have success with the others.

However, if they struggle with the counting, watching them as they count would be useful.

Bag 1 15 x 10c

Bag 2 15 x 5c

Bag 3 9 x 20c

($1.50)

($0.75)

($1.80)

Bag 4 4 x 20c 6 x 10c

Bag 5 1 x 50c 5 x 10c

Bag 6 2 x 50c 5 x 20c

($1.40)

($1.00) Bag 7 4 x 50c 7 x 10c

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Groups of students can be asked to count some of the bags of money and record their totals.

The results can be noted on a checklist (See page 72).

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Make up bags of money with varying amounts of coins. Some will have the same total amount, but made up in different ways.

($2.00)

Bag 8 5 x 50c 4 x 20c

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Points to look for:

• Do the students sort the money into like piles or groups?

( 3.30)

With older students, the following mixed denominations of coins can be used: Bag 2 1 x $1 2 x 10c 5 x 5c

• Do they start counting with the largest coins, or is there no logic in their order of counting?

($1.20)

($1.45)

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• Do they need to record amounts on the way to getting their totals?

Bag 3 1 x 50c 2 x 20c 4 x 10c 3 x 5c

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• Do they make each pile or group of piles into amounts equalling one dollar, or some other logical amount, or is it haphazard?

($1.45)

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Bag 5 3 x 50c 1 x 20c 4 x 10c 2 x 5c

Bag 4 1 x $1 5 x 10c 3 x 5c

($1.65)

($2.20)

Bag 6 2 x 50c 3 x 20c 7 x 10c 2 x 5c

Bag 7 5 x 50c 4 x 20c 6 x 10c 3 x 5c

Bag 8 2 x $1 1 x 50c 12 x 20c 1 x 10c

($2.40)

($4.05)

($5.00)

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Counting coins checklist Sorts ‘like’ coins

Calculates totals correctly

Comments

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Assessment 3: Counting coins 1. Write under each piggy bank how much money it has inside.

20c

20c

20c 5c

50c

10c

10c

5c

50c

Total:

20c

20c 20c

10c

$1

10c 5c

5c

5c

10c

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5c

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5c

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10c

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20c

20c

$1

50c

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2. Show how you would make the following amounts using the least number of coins.

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$ 4.85

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Individual assessment: Counting coins Record date when student has demonstrated concept. Each concept may be assessed on more than one occasion, sometimes with a different task for the same concept.

Student name:

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Sorts ‘like’ coins

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Calculates totals correctly

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Coin equivalence

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Changing and exchanging coins – activities

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How many ways can we make up 20c?

Watch for the systematic recording of all the different ways. Students may keep track using money stamps, coin cut-outs or symbols to show the various ways to make a particular amount. In this case the ways to make 20c are: 5c, 5c, 5c, 5c 5c, 5c, 10c (Discuss whether this is the same as 10c, 5c, 5c or 5c, 10c, 5c.)

10c 10c 20c Discuss the reasons why you may wish to have various combinations to make a particular amount. For example, rather than carry around a lot of loose change you may prefer to exchange a lot of coins for a single coin or note. However, if you need to share out some money then you will need to exchange a coin or note of higher value for the equivalent amount of coins or notes of a lesser value. For example, if twenty cents was to be shared between two people then you will need to exchange a single 20c coin for two 10c coins. If it was to be shared among four people then exchanging the 20c coin for four 5c coins would make sense. The discussion will lead to the need for different coin configurations.

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Make sure the students realise that despite the fact there are different numbers of coins they may still represent the same amount; e.g. 5c, 5c, 5c, 5c, has the same value as 10c, 10c and as 20c.

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1. Initially, students can be given open questions such as:

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Some students experience difficulty understanding the concept that a single coin represents a store of value. For others the lack of proportion between the coins causes difficulty. The fact that a onedollar coin is larger than a two-dollar coin in size is quite difficult to understand, let alone that the fifty-cent piece is the largest coin and yet the one- and two-dollar coins are worth more.

In the following activities, students will be swapping or exchanging coins for equivalent amounts. For example, two 20c pieces and one 10c piece may be exchanged for a single 50c coin. Students need to be able to exchange a number of lesser value coins for a single coin or note of greater value. They also need to be able to exchange a coin or note of a high value for the equivalent amount of coins of a lesser value. For example, a person may wish to exchange a $5 note for two $2 coins and $1 so that the coins may be used in a vending machine.

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Purpose Students will be able to: • exchange equivalent amounts of coins and • develop an understanding of equivalent coin values, which is an important prerequisite to the ability to exchange coins with ease.

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2. From the bank

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For example, I want 50 cents worth of 5 cent pieces please.

The banker then needs to count out 5, 10, 15, 20 ...

Initially begin with simple equivalences. For example: • 50c worth of 10c pieces • $1 worth of 10c pieces • $1 worth of 20c pieces • $2 worth of 50c pieces • $2 worth of 10c pieces • $2 worth of 20c pieces.

3. Exchanging coins Materials

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Ask the students where shops get their change. Explain that takings for the day are deposited at the bank. When the shopkeeper goes to the bank he or she exchanges some money for particular coins. The shopkeeper must decide what coins are required to give change.

Ask students to work in pairs to role-play going to the bank to get change. One player takes on the role of the shopkeeper, the other the banker. Begin with simple exchanges. Encourage the students to state: I want ___ cents worth of ___ cent pieces please.

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A collection of mixed coins from 5c to $2 per group of 2 – 4 students.

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How many possibilities are there? and How will I know when I have found them all?

This will encourage students to work mathematically by keeping a systematic record.

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Pose the two questions:

Set challenges for the students such as: • make $1.00 with two coins • make $1.00 with five coins • how many ways can you make $1.00 using all the same coins (e.g. five x 20c coins)?

• make $1.50 with three coins • make $1.50 with as many coins as you can • make $1.50 with the least number of coins that you can.

• make $2.00 with

2 coins

4 coins

10 coins • make $2.60 with the least number of coins you can • make $3.50 with seven coins

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Set further challenges such as: • I have two coins in my pocket. How much money might I have?

• I have three coins in my pocket. At least one is a gold coin. How much might I have?

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Race to $2 Purpose Students will be able to: • exchange equivalent amounts of coins and • develop an understanding of equivalent coin values, which is an important prerequisite to the ability to exchange coins with ease.

A game for 2–4 players

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You will need dice and containers of 5c pieces and another container or money tray containing the other coins.

Players take turns to roll a 1 – 6 dice and pick up that many 5c pieces from a central container. Coins must be exchanged for coins of higher value wherever possible. For example, if a player rolls a three, he or she picks up three 5c coins. Then two of the 5c pieces are exchanged for a 10c piece and the 15c (one 10c and one 5c) left in front of that player. This amount is added to on subsequent rounds.

For example, on the second round this player might throw a five and pick up five 5c pieces. The 15c and the 25c (in five 5c pieces), need to be exchanged for two 20c pieces. After each turn, the player should have the least number of coins in front of him or her.

Play continues until one player reaches $2.

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Students who require extra support may find the coin exchange on page 79 helpful.

The grid aids in scaffolding the exchanging of coins for the least number of coins. An example is illustrated on the right.

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• Provide students with an equivalence grid to support them when first playing the game.

• Change the coin that is collected in each turn from 5c to 10c.

Note: The target amount will need to change to $5 and $2 coins will need to be added to the money tray.

• Play with two different coloured dice. One represents 5c pieces and the other 10c pieces.

• Change the coin that is collected in each turn to 20c or 50c.

Note: As above (but to $10 or $20) • Throw several dice of different colours each turn, with each colour representing a different coin. Adjust the target total amount accordingly.

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Coin exchange grid 5

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Exchange one 50c, two 20c and two 5c for one $1.

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‘Pay the person’ game A game for 4 players

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Some zip-lock bags or pencil cases containing a set amount of money (the amount will vary according to the version of the game that is played) dot dice coin dice You will also need a set of coins in a container in the middle of the group that can be used as an exchange bank.

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Purpose Students will be able to: • count money and decide when they have made a profit (more money than they started with) or a loss (less money than they started with) • count money and • exchange coins for equivalent amounts.

Each player starts with a bag (wallet or purse) containing $2, made up of ten 5c pieces, six 10c pieces, two 20c pieces and one 50c piece.

Players sit in a group of four. It is simpler if the students sit in a circle.

The first player rolls a dice and the player to the left of that player must pay that many 5c coins, or the equivalent amount, to the roller.

For example, if the first player rolled a 4, then the player to the left could pay the roller 4 x 5c; 1 x 10 and 2 x 5c; 2 x 10c, or 1 x 20c.

Play continues in a clockwise direction.

If a player does not have the appropriate coins to pay the debt, then he or she will need to exchange coins for an equivalent amount. For example, a player who runs out of five cent coins could exchange a 20c coin for four 5c coins.

Play continues for a set number of rounds (e.g. three) or until one player runs out of money altogether. At this point, players count the money in their bags and work out whether they have made a profit (have more money than they started with) or a loss (less money than they started with).

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Change the pay-out amount, for example, from 5c to 10c coins. If the pay-out amount is changed, then the amount of money placed in the bags will need to change. In the above example, the pay-out amount is doubled so $4.00 instead of $2.00 would need to be placed in the bag.

A coin dice or spinner can be used instead of a normal dice.

Note: A coin dice or coin spinner shows all the coins from 5c to $2, so players will need to start with $10 (See pages 39–41).

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Vending machines Purpose Students will be able to: exchange equivalent amounts of coins.

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It wasn’t until the late 1800s that modern vending machines started to come into their own.

The first machines were used to dispense items like chewing gum. Since then vending machines have been used to dispense a wide variety of items.

Today, the principle behind vending machines has been applied to ticketing machines, game machines and even toilets. Students may be interested to know that the phrase ‘to spend a penny’ refers to paying to go to the toilet.

Some students may have experienced the frustration of losing their money to a malfunctioning vending machine. You may wish to warn them of the consequences of shaking or rocking the machine. There have been at least three recorded deaths of people crushed as a result of the machine falling on them.

There are many more incidents of people suffering injury as a result of machines toppling on top of them.

Vending machines provide an ideal context where coins and notes need to be exchanged for particular coins. The questions on page 82 involve the ‘machine context’ as a reason for exchanging money for equivalent amounts. Encourage pairs of students to act out the changing of money. You may wish to copy these situations onto card and distribute them to pairs of students.

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It appears that the first vending machine was created in the 1st century CE (Common Era). It operated on a simple principle.

A coin was dropped into the machine and struck a lever, causing a valve to open. The vending machine was used to dispense holy water.

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Some vending machines and parking meters will only accept certain coins. For example, some vending machines will not not accept 50c pieces or 5c cent pieces.

Some students may have bought snack food or drinks from vending machines. Others may have been to game arcades where the various machines—pinball, racing car machines, air hockey and pool tables—require the insertion of coins or tokens. Newer vending machines accept notes, credit and debit cards. There are even cashless vending machines where you phone a number on your mobile phone, and an amount is added to your mobile phone bill and the item is released from the machine.

This machine takes only 5c, 10c, 20c, $1 coins.

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of loose change but there is only one $1 coin. List which coins you will use in the machine.

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C.Pu bl i ctoabuy t i o s You wish ann item worth $2.65.

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Vending machine problems ❶ The snack machine

❷ A vending machine

does not accept 5c, 10c or 50c coins. You have a five dollar note and wish to buy an item for $2.60. Explain what coins you would like to be exchanged for your $5 note. How much money would you expect to be left after you put your money in the machine?

This machine does not take 5c, 10c, or 50c coins.

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accepts only $1, 20c and 10c coins. You have two $2 coins and wish to buy an item for $3.50.

Explain one way you can exchange your coins so you have $3.50 to put in the machine.

This machine takes only $1, 20c and 10c coins.

No change given

No change given

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drink. The drink machine is an old machine and accepts only 20c and 50c pieces. All you have is one $2 coin. You wish to buy a drink that costs $1.70. Work out the coins that you require in exchange for your $2.

This machine takes only 20c and 50c pieces.

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accepts only gold coins but will give change.

You have a pocketful of change—eight 5c pieces, four 20c pieces, six 10c cent pieces and three 50c pieces. You wish to buy an item for $3.

Describe how you will perform the exchange.

This machine takes only gold coins.

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Coin equivalence checklist Changes two 10c for a 20c

Changes 50c to 2 x 20c & 1 x 10c

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Money frames

Note: Some students may not need the support contained on the following pages. If they can already handle money competently and give change, then do not force them to apply this method.

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Money frames Purpose Students will be able to: • scaffold understanding of coin equivalences and give change.

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Twenty-cent Frame 1

Twenty-cent Frame 2

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Note: Full-sized money frames are on pages 88, 90, 91 and 93–98.

Money frames develop naturally out of coin equivalence.

Some particular combinations are very useful when giving change. The situations occur in shopping when: • the exact money may be tendered, possibly involving counting, but requiring no change; e.g. using either a 50c coin or two 20c and one 10c coins to pay for a purchase of 50c. Note: There are other alternatives.

• the nearest amount over and above the total is given; e.g. a purchase of 35c, paid with two 20c coins, receiving 5c change.

• a single coin over and above the total is given; e.g. a purchase of 35c, paid with one 50c coin, receiving 15c change.

• the most convenient amount is given; e.g. buying an item for $1.20 and, if no $1 coin is available, paying with $2.20 receiving a $1 coin as change.

• paying close to the amount with a mix of coins, often done when wishing to reduce the number of coins in a pocket or purse.

To start with, at least, bullet point 3 above can be acted out using money frames.

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The use of money frames can be a means of scaffolding students from using real (or plastic) coins to working out money problems mentally. The circles in the money frames are slightly larger than the actual coins (or plastic coins), so that the money and the ‘border’ can both be seen when a coin is placed in the correct spot. You will find separate money frames for real and plastic coins on the accompanying blacklines. The coin amounts can be written into the circles if desired.

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When students are ready to start working out change, especially if a class shop has been set up (see pages 102–104), they may need to be shown how to use the frames to help them work out the correct change.

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Once the students have been using the money frames for a while, and appear confident with their use, they could gradually try doing the calculations without them.

Note: Separate money frames for real coins and for plastic coins are provided, as the plastic coins are bigger.

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Money frames: twenty cents The price is 10 cents. Use Twenty-cent Frame 1 (see p. 88).

Step 1. Cover all the circles.

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Twenty-cent Frame 1

1. If the price is 10 cents and 20c is given, the Twenty-cent Frame 1 would be used (page 88). The student hands over his or her 20c piece, and the shop assistant exchanges the 20c for two 10c coins. These are used to cover all of the circles on the money frame. The cost of the item is then removed (10c), and the coins in the remaining circles make up the correct change; i.e. one 10c coin (see column on left).

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Using money frames for working out change from twenty cents.

Step 2.Remove the cost (10c).

The change is 10c.

Twenty-cent Frame 1 10c

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The price is 5 cents. Use Twenty-cent Frame 2 (see p. 88).

Step 1. Cover all the circles.

2. If the price is 5 cents and 20c is given, the Twenty-cent Frame 2 would be used (page 88). The child hands over his/ her 20c piece, and the shop worker exchanges the 20c for one 10c and two 5c coins. These are used to cover all of the circles on the money frame. The cost of the item is then removed (5c), and the coins in the remaining circles make up the correct change; i.e. one 10c coins and one 5c coin (15c) (see column on left).

3. If the price is 15 cents and 20c is given, the Twenty-cent Frame 2 would be used (page 88). The student hands over his or her 20c piece, and the shop assistant exchanges the 20c for one 10c and two 5c coins. These are used to cover all of the circles on the money frame. The cost of the item is then removed (15c), and the coin in the remaining circle makes up the correct change; i.e. one 5c coin.

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Step 2. Remove the cost (5c).

The change is 15c.

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Note: There is no need for a 10c money frame, as the only possibilities when tendering a 10c coin are: if a purchase of 5c is made, requiring 5c change; or if a purchase of 10c is made, requiring no change.

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Twenty-cent money frames: real or plastic coins (Only provide the frame that matches the coins being used.)

Twenty-cent Frame 1 Use with real money for prices involving multiples of ten.

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Use with real money for prices involving multiples of ten and five.

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Twenty-cent Frame 1 Use with plastic money for prices involving multiples of ten.

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Money frames: fifty cents The price is 5 cents. Use Fifty-cent Frame 2.

Step 1. Cover all the circles.

1. If the price is 5 cents and 50c is given, the Fifty-cent Frame 2 would be used (because it includes 5c) (pages 90–91). The child hands over his or her 50c piece, and the shop assistant exchanges the 50c for two 20c and two 5c coins. These are used to cover all of the circles on the money frame. The cost of the item is then removed (5c), and the coins in the remaining circles make up the correct change; i.e. two 20c coins and one 5c coin (45c).

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2. If the price is 10 cents and 50c is given, the Fifty-cent Frame 1 would be used (pages 90–91). The student hands over his or her 50c piece, and the shop assistant exchanges the 50c for two 20c and one 10c coins. These are used to cover all of the circles on the money frame. The cost of the item is then removed (10c), and the coins in the remaining circles make up the correct change; i.e. two 20c coins (40c) (See bottom left).

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Step 2. Remove the cost (5c).

The change is 45c.

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Using money frames for working out change from fifty cents.

3. If the price is 15 cents and 50c is given, the Fifty-cent Frame 3 would be used (pages 90–91). The student hands over his/her 50c piece, and the shop assistant exchanges the 50c for one 20c, two 10c and two 5c coins. These are used to cover all of the circles on the money frame. The cost of the item is then removed (one 10c and one 5c). The coins in the remaining circles make up the correct change; i.e. one 20c coin, one 10c coin and one 5c coin (35c).

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The price is 10 cents. Use the Fifty-cent Frame 1.

Step 1. Cover all the circles.

Fifty-cent Frame 1

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Step 2. Remove the cost (10c).

The change is 40c.

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For 5c, use the Fifty-cent Frame 2.

For 10c, use the Fifty-cent Frame 1.

For 15c, use the Fifty-cent Frame 3.

For 20c, use the Fifty-cent Frame 1.

For 25c, use the Fifty-cent Frame 2.

For 30c, use the Fifty-cent Frame 1.

For 35c, use the Fifty-cent Frame 3.

For 40c, use the Fifty-cecnt Frame 1.

For 45c, use the Fifty-cent Frame 2.

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Teaching point Money frames can be used when students purchase a total of less than 50c, and pay with a 50c coin. They need to know that they would probably only do this if they did not have the required number of 20c, 10c or 5c coins.

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Fifty-cent money frames: real coins Fifty-cent Frame 1

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Fifty-cent money frames: plastic coins Fifty-cent Frame 1

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Money frames: one dollar

The price is 45 cents. Use the One-dollar Frame 1.

Step 1. Cover all five 20c circles.

In a shopping situation, when a $1 coin is handed over, there are a number of different situations that can apply, but a similar process to the 20c and 50c money frames could be used.

One-dollar Frame 1

If no fifty-cent coins are needed, use the One-dollar Frame 1 (pages 93–94).

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Step 2. Exchange one of the 20c coins for one 10c and two 5c coins.

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The student hands over his or her $1 coin and the shop assistant covers all of the 20c circles on the money frame (using five 20c coins). Depending on the amount being spent, one of the 20c coins is then swapped for one 10c and two 5c coins. The cost of the item is then removed—e.g.45c—and the coins in the remaining circles make up the correct change; i.e. two 20c, one 10c and one 5c coins (55c).

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If a fifty-cent and no 5c coins are needed, use the Onedollar Frame 2 (pages 95–96).

The student hands over his or her $1 coin and the shop assistant covers the two 50c circles on the money frame. One of the 50c coins is then swapped for two 20c and one 10c coins. The cost of the item is then removed (e.g. 40c) and the coins in the remaining circles make up the correct change; i.e. one 50c and one 10c coins (60c).

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Step 3. The cost of the item is then removed (45c), and the coins in the remaining cirles make up the correct change; i.e. two 20c coins, one 10c coin and one 5c coin (55c).

If a fifty-cent and 5c coins are needed, use the Onedollar Frame 3 (pages 97–98).

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The student hands over his or her $1 coin, and the shop assistant covers the two 50c circles on the money frame. One of the 50c coins is then swapped for one 20c and two 10c and two 5c coins. The cost of the item is then removed (e.g. 35c), and the coins in the remaining circles make up the correct change; i.e. one 50c, one 10c and one 5c coins (65c).

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Teacher tip Once the students have been using the money frames for a while and appear confident with their use, they could gradually start doing the calculations without them.

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One-dollar money Frame 1: real coins, no 50c One-dollar Frame 1

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One-dollar money Frame 1: plastic coins, no 50c One-dollar Frame 1

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One-dollar money Frame 2: plastic coins, using a 50c coin, but no 5c coins

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One-dollar money Frame 3: plastic coins, using a 50c coin, and 5c coins

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One-dollar Frame 3

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Integration and shopping Write jingles for products.

Investigate fast foods.

Write and read labels.

Make graphs of popular items in shop.

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Make signs for shop – including specials.

Weigh items in shop.

Role-play shopping.

Measure containers to decide where to place them in shop.

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Arrange containers in order.

Write a shopping list.

Sort and stack items.

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Calculate change.

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Count coins.

Write a report on a shopping trip.

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Cost meals.

Literature: Alexander, who used to be rich last Sunday by Judith Viorst; The shopping basket by John Birningham

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Fill containers for sale.

Make containers for small items for sale.

Healthy food pyramid

Read and follow recipes.

Make a shopping list of a healthy (or multicultural) meal.

Make tables of ways of getting, for example, $1.

Make nets for boxes of produce to be sold in shop.

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Weighing

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Other ideas for integration

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When planning a shopping theme, consider the mathematics the students might learn apart from the money concepts. Counting is part of shopping. Early volume and capacity ideas may be developed by filling shopping bags, containers etc. Arranging cans and packets on shelves requires estimation. Serving drinks and food involves capacity.

Shopping also involves concepts of geometry. The students will be manipulating 3-D shapes in the process of the arrangement of goods and in wrapping parcels (also surface area). These activities also incorporate many measurement concepts such as length and area.

Arranging furniture so there is a pathway to the shelves and past the ‘checkout’ is part of geometry.

Measurement also can occur in shopping activities. If students are measuring out amounts of goods to be sold—flour to bake a cake— they will be using scales and needing to know about accurate measuring of mass. Students could be asked to buy and sell items, such as ribbon, that require them to measure length.

• Sorting: arrange the stock, classify the coins • Labelling: give each set the value of the coin or coins • Counting: stocktaking, (skip) counting coins in 1s, 2s, 5s, 10s, 20s, 50s Language/Vocabulary

A sample of words students may encounter in a shopping environment.

ATM baker bankcard boutique butcher cash register change cheap chemist cheques coffee shop coins credit credit card customer dear debit debit card deli department store EFTPOS exchange florist food hall gift store greengrocer grocer jewellery store lay-by newsagent notes price restaurant shoe shop shop assistant shopkeeper stock stocktaking supermarket till trade transaction valuable value withdrawal

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Setting up a class shop Purpose Students will be able to: • know that money is used to buy things and • recognise the value of coins.

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1. You may like to consider the different ways you can label the items in a shop; e.g. 15c, fifteen cents, 15 cents or $0.15.

2. You could use Post-It® notes for students to write the prices on.

3. If students are working in pairs, having them alternate as shopkeeper and purchaser gives them practice in both roles.

4. It may be useful to have money stamps as another way to make money for the classroom.

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Setting up a class shop provides the opportunity to put into practice many of the concepts that students have been building up, in a meaningful situation. The teacher may start with the shop as a wholeclass activity, and later have small groups or pairs use it. Students enjoy the aspect of play-acting as a customer or shopkeeper. The students will practise: • recognition of coins • relationships between coin values • counting coins • coin equivalence • simple operations with money • giving change • repeated addition • complementary addition (shopkeepers’ method of giving change).

Relating number facts and equivalent values of coins helps students see the relationship between the two, and offers the opportunity to reinforce them in a meaningful context.

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A corner with a table Play (or real) money or tokens for money A box for the money (or a till, or money sorting tray) Calculator (depending on the levels of calculations required) Stock; e.g. collections of cartons, boxes, tins; or more specialised items such as balls, dolls and other toys for a toyshop.

Labels, stickers or Post-It® Notes to identify prices (Note: Labels or Post-It® Notes may be better than stickers if you intend to change the prices at a later date.)

Shopping basket or bags Purses or wallets (could also use pencil cases or zip-lock bags) You may also want a ‘uniform’ such as an apron, cap or a badge

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What you will need to set up a shop:

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It is a good idea to have 2–3 students run the shop for a day/week.

The set up of the shop will depend on the activities the students have already experienced. They can be made more or less demanding according to the prices of the items for sale, the number of items to be purchased or whether change is to be given. As part of the shopping experience, students could be involved in determining the price of goods and writing the price labels.

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Shop rules

Teacher tip Students are generally not bothered by having the price of a particular item set as, for example, 5c one week and 25c a few weeks later.

• • • • •

Always be polite.

Wait your turn.

Only one customer to be served at a time.

Money must be given directly to the shopkeeper.

Both the shopkeeper and the customer must check at the beginning and end of each transaction.

• The shopkeeper must count back any change.

• Wash your hands before handling any real food items.

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Depending on the level of the students, your ‘shop rules’ may change; for example: • Start with only buying one item, and all items priced the same; e.g. 20c.

• Have all items priced less than 20c with change to be given (using the 20-cent money frame).

• This would be similar for the other money frames; e.g. 50c to spend, or all items priced at 50c.

• Have a $1 shop, where all items are exactly $1.

• Students can buy 2 or more items of the same price, with no change; i.e. exact money.

• Students can buy 2 or more items of different prices, with no change.

• Refer to the two bullet points above but with change given (you may wish to use the appropriate money frames).

• Use of items priced at more than 20c, starting with values up to 50c, then $1, and so on.

• Prices above $1 in multiples of 10c or 20c at first, followed by 5c intervals.

• The use of money frames is phased out.

• Students given a maximum amount to spend and decide what they can buy with; e.g. $2.50.

Note: Handling money can be a source of germs. Consider loose change held in a pocket with a tissue.

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Students could compare: • ‘Half price’ • ‘2 for the price of 1’ • ‘Buy one, get one free’ • ‘50% off’

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– Why do people handling fresh foods wear gloves?

Students may be familiar with sales promotions in shops. A similar situation could be made in your classroom shop, where for one week all items are on sale at half price. For younger students, this can simply mean they can get two items for $1, whereas older students can work with items now costing 50c each. Discussion can arise about the concept of shop sales and why they have them.

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Types of shops The types of shops that can be set up will vary depending on the resources, themes and interests of the teacher and students. These could include: • toyshop • food shop • supermarket • greengrocer • pet shop (with soft toys for pets) • stationery shop • school canteen • general store (very flexible) • $1, $2 or $5 shop.

Although it would be good to have a stack of $1 coins available for students to use in the ‘shop’, it is impractical. Give students the opportunity to handle a real $1 coin, and then explain that plastic $1 coins or tokens will be used instead.

Our $1 (or $2 or $5) shop

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With younger students a $1 shop may be the first option. Set up a $1 shop in the Shop Corner. Students know that this is a special shop where everything costs exactly the same, $1. Some shopping centres have a similar shop, though usually with a base price greater than $1, where no prices are more than a set amount; but in this shop, everything is $1.

Each student gets a set number of $1 coins or tokens to spend in the shop; e.g. 5 coins ($5). These can be placed in a wallet, purse or ziplock bag. They are now ready to go shopping.

• How many items can you buy with your money?

• How do you know how much to give to the shopkeeper?

• Will you get any change?

• Have you got enough money to buy anything else?

• How many more things can you buy?

• What will the shop worker do with the money you spend?

Once the students are familiar with the $1 shop, the same can be done with a $2 or $5 shop. If a $5 shop is set up, the issue of the use of notes or coins arises. This may be a good time to introduce students to the range of Australian bank notes.

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Counting by 2s or 5s should not be too difficult, even for younger students. They should be encouraged to count the value of their coins or tokens when they receive them.

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Transactions Money frames

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Some students may find difficulty when counting on to give change.

When first starting to work with the notion of giving change, the use of money frames can scaffold students until they are ready to work out problems mentally (see pages 86–98).

When buying one or more item, or when giving change, students will need to recognise that the total cost of the purchase and the change given should always equal the coin or coins tendered.

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• Students checking by counting when giving out and collecting back the coins or tokens for the shop • Students verbalising their transactions • Students keeping a record of their spending; e.g. a ‘bankbook’.

Encourage students to practise the shopkeepers method of giving change; e.g. when giving change for a 20c item paid with a 50c coin, the student would say, ‘twenty cents, forty cents, fifty cents; that’s thirty cents change’ as he/she hands over the coins.

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You may like to consider having the students make their own ‘Ready Reckoners’ using Excel® or a similar computer program.

You could encourage the use of ‘Ready reckoners’ when selling multiples of the same item. For example, if juice drinks are being sold at a school fete for 60c each, the Reckoner could look like:

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Students could practise using the Reckoners prior to the event (a school fete) with such questions as, ‘How much would it cost to buy 2 drinks? What about 4 drinks?’ They may get to see the number patterns produced with the Reckoners.

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Transactions Purpose Students will be able to: • calculate prices of items from advertised lists.

Collect advertisements from newspapers or shopping catalogues.

These provide many activities related to money. To begin with, you will probably need to adjust the advertised prices to suit the level of the students; e.g. changing the price of a box of cereal advertised as $3.49 to 30c. Questions can then be posed, such as: • What is the cost of a box of cereal and a carton of milk?

• How much would it cost to buy two cans of dog food?

• What is the total cost of a drink for 40c and a banana for 30c?

• What two things could you buy for less than $1?

• How many bananas could you buy for $1.50?

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Shopping catalogues are a ready source of current prices and interesting options. Many shops and supermarkets now have their catalogues available online.

Some schools have a different canteen menu for each day of the week. Comparisons can then be made between a lunch purchased, for example, on Tuesday, compared to a similar one purchased on Thursday.

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Advertised prices

Later, more realistic prices can be used. Discussion could take place about the types of numbers used in advertisements; e.g. $2.99 and $1.49.

Canteen menu

If the school has a canteen, students can be asked questions related to the prices: • How much does a chicken sandwich cost?

• What is the total cost of a salad roll, a drink and an apple?

• What is the cheapest lunch, including a drink, that you can buy at the canteen?

• How much change would you get if you had $10 and bought a cheese sandwich, a bottle of water and an orange?

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The choice of menus can be linked to such things as food from different countries or a multicultural day.

Cooking activities

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For older students, recipes can be used to generate a shopping list.

For example, if they wanted to bake some Anzac biscuits, they would need to price the required ingredients and add them. Later still, they could make a menu for a meal; e.g. spaghetti bolognaise followed by a fruit salad, and estimate the cost of the ingredients, and then calculate the cost of the meal. Ask questions such as: • How could we work out the cost of 250g of mince beef? What do we need to know first?

• If you need 100g of meat for each person, how much will you need for 6 people?

• How many different items do you need for the fruit salad? Which fruits are the best buy?

• Was your estimate of the cost of the meal close?

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Catalogue shopping Purpose

Students select items that add up to $30.00 from a food catalogue.

Ask them to make a table to record the items they selected, the costs and ask them to round each cost to the nearest dollar. By mentally keeping a running total of the amounts in the dollar column, they can estimate when they are getting close to $30.00. Students can then total their ‘purchases’ on a calculator and compare it to their estimated total cost.

Students will be able to: • use estimation to solve shopping problems in context, and make sensible use of calculators.

Teacher tip

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To get a closer estimate, some students may see the value in overestimating, rounding the amounts up to the nearest 50c; e.g. $3.49 to $3.50 rather than $3.00. They may realise they get closer estimates when rounding prices with 99c or 95c. This should be an enjoyable activity, with students helping each other and talking about their results.

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When working on this problem, some students may go over the prescribed amount, and have to either deduct one or more items from their list, or substitute a cheaper item; and then make adjustments to their totals.

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chocolate chips x 2 bisc Tim Tam™ x 2 Kit Kats™ choc bars soft drink chips multipack Twisties™ x 2 Natural snakes™ Total Change

$3.29 $3.98 $3.29 $1.79 $3.29 $0.99 $2.99 $3.99 $0.99 $1.99 $29.59 $0.41

$3.00 $4.00 $3.00 $2.00 $3.00 $1.00 $5.00 $4.00 $1.00 $2.00 $30.00 $0.40

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Maths - Money It worked out for me. I got an under estimate. I wouldn’t need any more change. If I added another 99c, it would be $30.37. The rounding technique is very useful because it is easier to add and was only $1.38 off the real total.

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I got an Bring a underestimate spare $1.00 You sometimes might need to round to the closest 50c. (get a closer estimate).

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I thought rounding was a good strategy to use.

Fizz Lemonade

(Age 10)

Using this method made it easier to work out about how much money I need to pay for all the food. For some of the items, it would have been easier to round them to 50c. I got an over estimate but I would have had enough mo ney to pay for the items.

(Age 9)

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Sharing money Purpose Students will be able to: • share amounts of money using 5c, 10c, 20c, 50c, $1 and $2 coins and • share mixed sets of coins.

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1. Students should be familiar with sharing several of one type of coin before sharing a selection of mixed coins.

2. When sharing a mixed set of coins, initial activities need not require exchange. The idea of exchange should be developed after many experiences of equivalent coin values.

3. Be aware of the two different aspects of division: sharing and grouping.

Sharing question: Share $1 among five people.

Grouping question: Put these twenty 5c coins into bags so that each bag has 20c in it. How many bags will you need?

1. Given one coin, share among several students. One student acts as Banker, as coins will need to be exchanged; e.g. given a 50c coin to share among two, given a 20c coin to share between four, given a $1 coin to share among four. Later, give two or more coins; e.g. one 50c and two 20c to share among three people.

2. Set problems where equal shares need to be made. Ask questions such as: Do the coins share evenly?

How much money does each person get?

Do they have the same number of coins?

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During shopping and other activities, students will have had experience in adding and subtracting amounts of money. Sharing money is another transaction that can take place, and may vary in complexity depending on the Year level of the students.

Problems:

• Share 60c among three people. How much will each person get?

What coin(s) would be best?

• Find out how many people can have 20c each if I have $1.20.

• Share the $3 among four people. How much money will each person have to spend at the shop? What coins can I use to make this amount?

• Share $10 among eight people. (Note: The $10 can start as one note, or five $2 coins. In either case, exchanges will need to take place.)

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3. Using fewer coins Have a bag with ten 50c, ten 20c, ten 10c and ten 5c coins. Groups of six students take turns to share out the ten coins of each type.

Later, the bag can contain twenty or thirty of each coin.

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Each student takes one pile at a time—e.g. ten 20c coins—and shows the same value for the pile using fewer coins.

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Financial literacy Financial Literacy: Financial literacy is the ability to make informed judgments and to make effective decisions regarding the use and mangement of money.

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Australian Securities and Investment Commission

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Financial literacy Purpose Students will be able to: • compare prices of items from different sources.

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1. Find the best price Provide students with a list of items to be ‘purchased’, or they can generate their own list. These lists can be random, or have a purpose such as buying items for a class party, making a recipe or buying items for the start of a school year. Using a catalogue, or the internet, one group of students finds the cost of each item from one source—e.g. a supermarket—and calculates the total.

A second group prices the same list of items, but with the prices coming from a second source; e.g. a different supermarket. The groups then get together and compare the costs of each individual item and the total amounts. Ask questions such as: • Could you find different prices for the same sized item by looking at different brands?

• How much difference was there between the cost of the lowest and highest priced brands?

• Why are some brands cheaper than others?

• Was one shop cheaper for each item or did it vary with different items?

• Which shop was cheaper overall?

Challenges can be put to the students when deciding on the items to be priced. They could be given a specific number of items to be purchased; e.g. four different items; a total cost to aim for; e.g. close to, but no greater than $10; or both; e.g. four different items with a maximum total of $10.

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Mr Micawber is a character in the novel David Copperfield by Charles Dickens. This quote sums up the idea that if you spend more than you earn you will end up in financial difficulties.

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With financial literacy, students come to realise: • that needs and wants can be prioritised • that most people have a limited amount of money • the need for a budget.

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Asking students to order items according to price is another way of getting them thinking about money and making sensible comparisons. They can be asked to estimate the order of prices first, and then see how close their estimates were.

Comparison chart Source Shop 1 Product

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‘Annual income twenty pounds, annual expenditure nineteen pounds, nineteen and six, result happiness.

Annual income twenty pounds, annual expenditure twenty pounds, nought and six, result misery’.

Shop 2

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$3.65 Brand X

$3.85 Brand Y

Shop 3

$4.15 Brand Z

Note: Comparisons may be made between one brand at different shops; different brands of a similar product at different shops; or different brands of a similar product at the one shop.

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2. Value for money There is often an assumption that a large container of an item will be cheaper than a number of smaller containers of the same item to the same weight. For example, Is buying four 500g packets of biscuits at $1.65 each more expensive than buying one 2kg box of the same biscuit for $6.00? In order to work out which is the better buy, students need to be able to calculate the total cost of the four packets, and then compare the prices.

Some instances are more difficult to calculate. For example, Which is the better buy, 375g of coffee for $3.90 or 500g of the same brand coffee for $4.50? To calculate this, students need to be able to find a common unit—e.g. 25g—and work out the cost of 25g of each option and then compare the results.

This introduces the idea of shopping around and comparing prices to get the best result.

Purpose Students will be able to: • compare prices of different sizes of the same item.

The coffee problem:

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There are 20 x 25 grams in 500g, so $4.50 ÷ 20 = 30c (for each 25 grams).

So the 375g jar is the better buy.

(See also page 115 for unit pricing.)

Students can investigate: • impulse buying • bargain and sales signs • buying when hungry • buying when choices are limited; e.g. at a sporting event, where drinks and snacks may be priced higher.

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There are 15 x 25 grams in 375g, so $3.90 ÷ 15 = 26c (for each 25 grams).

Note: Although bulk buying may save money, it may not be the best option. For example, a person living alone may end up with bulk purchases perishing, or a pensioner may not have enough money to buy more than needed for any particular pension period.

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Some teachers find it useful to have students work with Thinkboards for these types of problems.

For example, create a table that shows: • the cost of the item; e.g. $3.55 • the amount tendered; e.g. $5.00 • the change given in increments and total change; e.g. 5c, 20c, 20c, $1, which is $1.45 • a calculation check; e.g. $5.00 – $3.55 = $1.45 or $1.45 + $3.55 = $5.00 and $5.00 – $1.45 = $3.55.

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Number story Example: I bought a magazine for $3.55 and handed over a $5 note. How much change should I get?

Number sentence $5.00 – $3.55 = $1.45

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What does the change look like?

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Note: In the ‘Calculation check’ column they record possible calculations to check the result (inverse operations of + and –).

$1

Estimation It should be close to $1.50

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5c

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Calculation check $3.55 + $1.45 = $5.00

See page 112 for a blackline master template.

This may also be used for assessment purposes.

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Recording proforma Number story

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Calculation check

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3. Food shopping for the family Purpose Students will be able to: • use mental strategies to estimate and solve problems in context.

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Many shopping catalogues provide sample recipes. Work out the price for a family of four.

4. Estimating when shopping

Ask students to estimate the cost of items in two trolleys and decide whether there is enough money to cover the purchase.

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Children often believe that if a shop owner has been paid sums of money, this represents the profit. At some stage, they need to realise that some of the money from purchases goes towards paying the shop rental, wages, the purchase of more stock, utility bills etc.

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There is likely to be a range of ways the children’s parents or carers organise their food shopping. Discussion can take place about how people know what they need to buy when they go shopping for food.

Some people keep a list of items to be filled in when they run out, others make shopping lists from specials in store catalogues, some make a list of their meals for the week and work out what they will need for them, others buy on impulse. Also, some people shop on a daily basis, and others on a weekly, fortnightly or monthly basis.

Obviously, more planning is needed when visits to shops are less frequent.

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5. Shop receipts

Purpose Students will be able to: • make decisions about money.

Have a collection of recepts from different shops. These could include long supermarket dockets, smaller receipts with only one or two items purchased, and handwritten ones from smaller stores, though it is quite hard to find examples of the latter nowadays. Students can choose three or four of the receipts and place them in order from the smallest total to the largest.

6. Budgeting

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Discussion can take place about how people keep track of what they spend. Do they keep a budget and record all of their spending? Do they pay by by credit card and check their statements every month?

Do they pay by EFTPOS, and again check their statements as they come in? Do they keep no records at all?

1. Students can be given one section of a shop receipt with the total removed. Ask them to estimate the total amount.

2. The longest docket or till ticket is not necessarily the largest amount.

3. Things cost different amounts of money. Students need to decide whether something is ‘worth it’. You can only spend your money once, so students need to compare prices and make sensible decisions.

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Using unit pricing is way of comparing like products that come in different sizes. Many shops now put unit prices on their advertised prices for easy comparison.

For example; if rice is priced as 250g for $2.79, 350g for $2.95, 750g for $5.68 and 1kg for $7.78, it is not obvious which is the best buy. But if the labels also include the price per 50g, it is a simple matter to work out the cheapest.

Price

Money is used in everyday situations, and students need to be comfortable working out realistic money problems. Also there are many activities, investigations, projects and challenges that would be interesting for them to pursue.

• What two things in the shop will cost the most to buy?

The least?

• What two things can you buy that come to exactly $1?

What two things could you buy and still get change from $1?

• Three of you have been given 75c each. How much is that altogether, and how can you exchange it for the least number of coins?

• Compare prices of the same item from different sources; e.g. a packet of peanuts from a snack machine, corner shop, service station, supermarket and a fete or show.

• If a box of 15 pencils costs $2.50, how much does one pencil cost? Is this better than buying one pencil for 20c?

• Investigate the unit prices of different foods.

• Keep a table of items the class spends at the school canteen in a week and graph the results.

• Plan a class excursion and work out the cost; maybe factoring in lunch for everyone.

• Look at advertisements for large items—e.g. plasma TV—and compare the prices. Which one is the most expensive? The cheapest?

• Investigate pre-decimal currency in Australia. How many different coins and notes were there? What were the equivalences (e.g. 12 pennies = 1 shilling)?

• Investigate the currency in different countries. Are they based on a decimal system? What are the base units? What denominations do the coins and notes come in?

• Discuss exchange rates. Why is the Australian dollar sometimes quoted as worth only 70c (US)?

• Investigate purchasing from a mail order catalogue or from the internet. What additional costs are incurred? What are the risks?

• Plan a holiday for a family of four to a nearby city, or an overseas resort. Make an estimate of the total cost. Then list all the items that need to be priced, and calculate a total package cost.

• Plan how to spend a $1000 inheritance.

• Make a collection of books or other items to be sent to an overseas charity. Check out the price of sending packages through the post, considering the ways that parcels are costed for postage. Investigate any other issues that may have an impact on getting the goods there.

• Draw up a spreadsheet for comparing the cost of keeping particular types of pets for a year. How much more is the upkeep of a large dog—e.g. a golden retriever—than a small dog such as a Jack Russell?

• Although the book Would you rather … (1978) by John Burningham is not strictly a ‘mathematics’ storybook, it can be used to stimulate situations about money.

– Would you rather a one-metre line of $1 coins or a one-litre milk carton of 20c pieces?

– Would you rather a kilogram of $1 coins or a square metre of 5c pieces?

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250g

$2.79

55.8c

350g

$2.95

42.1c

750g

$5.68

37.8c

1kg

$7.78

38.9c

So the 750g packet of rice is the most economical to buy.

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Size

7. Further investigations and challenges

Symbols for money

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1. A single vertical stroke through the upper case S is the only acceptable symbol for the Australian dollar ($).

2. The symbol for cents is a lower case ‘c’ with no full stop and no line through it.

3. Either the dollar sign or the cents sign must be used, but not both at once.

4. If there are no dollars and the decimal point is to be used, it must be preceded by a zero.

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Class monetary system

Purpose

One way of helping students acquire financial literacy is to create a class monetary system. This can be operated in teams or individually.

Students are able to earn income or bonuses by doing particular jobs, good work or behaving well. Cash (probably plastic) can be used.

Cheques can be issued for special items. Students are also charged for certain expenses such as rent of their desk, or extra computer time.

Fines for late homework, overdue library books etc. can be paid at an amount negotiated by the class.

Students can earn weekly income by: • Doing a class job ($2) • Doing an extra job (20c–50c) • Good work (50c–$1) • Improved work ($2) • Attendance ($4).

A bank is set up, and students take turns being the banker on a weekly basis. The teacher may need to double-check most transactions.

Students keep a bankbook in which to record their activities. Once they have a certain amount of money, they are encouraged to donate some of their money to (fictional) charities. They may also get windfalls by various means, such as a tax refund, or by drawing a card similar to the Community Chest cards from Monopoly™.

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Students will be able to: • make decisions about money.

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1. Students earn and spend money all day, and are encouraged to exchange coins for higher denominations so they have the least number of coins for their total. Once they get over a prescribed total, they deposit money in the class bank.

2. Auctions can also be arranged, so students spend some of their savings, with small items donated by parents. The students can determine the values of the products.

No homework Calling out Chair out Incomplete work Littering

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Transaction Amount Total

Deposit Debit Deposit Deposit Deposit Deposit Debit

$10.00 $2 $5 $2 $1 $1 $3

Date

Transaction

Amount

Date

$10.00 $8 $13 $15 $16 $17 $14

The use of deposit slips, withdrawal slips, cheques, balance sheets and bank statements allows students to become familiar with some of the protocols of banking (see pages 117 to 121).

An auction can be a way of spending their earnings. Parents can be asked to contribute items (to a set value) that children then bid for in the Class Auction. The process of bidding for items at an auction sets the value. This is a good example of supply and demand.

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Cheques Bank of

Pay

Date:

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Sign: Money matters: A teachers handbook for developing money concepts

117

Deposit slips

DEPOSIT

Bank of Acc. Number 123:45678

Acc. Name

Branch

Date:

$

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Cash

Cheques

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DEPOSIT

Bank of

Acc. Name

Acc. Number 123:45678

Date:

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DEPOSIT

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Withdrawal slips

WITHDRAWAL

Bank of Acc. Name

Acc. Number 123:45678

Date: Amount required:

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$ $ $

WITHDRAWAL

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Number © RAcc. .

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Notes Coins

Signature

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$ $ $

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How much do I have?

Deposits Date

Withdrawals

Balance

Total Cheques

Cash

Cheques

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Note: Use a new line for each transaction.

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Keeping track of your money Bank Statement

Bank

Name and address

Account No.

Account name

Statement date

Transactions

Balance Brought Forward

(total at end of previous statement)

Date

Description

Credits

Debits

Balance

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Total debits:

Total:

At the end of each month, the bank usually sends a statement.

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GST Students may have heard the term GST (Goods and Services Tax.) This is a broad-based Federal government tax that is added to the cost of many goods, services and other items sold or consumed in Australia. It is similar to the Value Added Tax (VAT) used in many other countries.

Of interest

Supermarkets must display the GST-inclusive price of items on their shelves; i.e. the amount the purchaser has to pay in total. However, when examining till dockets, the GST is shown.

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GST is set at 10%. Explain that ‘per cent’ (%) means ‘per hundred’. In this case, 10% means ten per every hundred. A way to visualise this is to show that an MAB flat is made up of 100 squares. Coverting ten of these squares represents 10% of the flat.

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GST was first introduced by the Australian Federal government in 1999 and took effect in July 2000. This tax replaced the Wholesales Sales Tax (WST) that was paid on the wholesale price of goods. There were no real equivalent taxes on services, other than payroll taxes. Also, different goods attracted WST at different rates. The GST was designed to simplify the tax system and also to earn the government revenue from service providers.

It is generally levied at a flat rate of 10%, although there are some GST-exempt items such as fresh food, and most education and health services. Also, there are some exceptions such as imported luxury items, where taxes may be higher than 10%.

Not all businesses charge GST. A large business must be registered with the Australian Tax Office (ATO), although businesses with a total revenue of less than $75 000 per annum do not have to register.

In this case, they cannot charge their customers any GST. Goods and services providers who charge GST are required to pay the collected amount to the ATO on a regular basis, using a Business Activity Statement (BAS).

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Students may be taught how to estimate 10% of simple amounts of money. The GST may be thought of as 10c for every $1.

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To calculate 10% of $4, a student might think ‘10% of $1 is 10, so 10% of $4 would be 4 x 10c or 40c’.

For slightly more difficult question such as ‘Calculate the GST on $6.50’, a student might think ‘10% of $1 is 10c, so 10% of $6 is 6 x 10c or 60c. 50c is half of a dollar and 5c is half of 10c. So the GST would be 65c’.

• What is the purpose of taxation? What does the government use the taxes for? (building schools, roads, etc.)

• What is the difference between ‘goods’ and ‘services’?

• Some items such as fresh food do not attract GST. Discuss why this is the case.

• For GST-inclusive purchases, the full price shown can be multiplied by 1/11 to calculate the amount of GST paid. Alternatively, the amount can be divided by 11. Discuss why this figure is 11 and not 10.

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