Playing with Money (From the New Zealand Point of View)

The above screen, maybe with different numbers, appears every night on TV One’s news. What does it all mean? You can find it on http://www.tvnz.co.nz/view/news_sub_cat_skin/news_business_index_group. Click on ‘Markets’.

We will use the information here to begin a unit on proportion.

Starting at the top this screen is about exchange rates, that is, the rates at which currency is exchanged. More specifically, the table tells us how much in given overseas currencies one New Zealand dollar is worth. So we can see that one New Zealand dollar is worth

0.7825 United States dollars
0.8373 Australian dollars
0.3945 British pounds
0.5013 Euros
81.68 Japanese yens

The burgundy triangles (pointing down) indicate that the New Zealand dollar has gone down against the given currencies since the last news; the ‘NC’ means that there has been no change.

You should start thinking about this unit well before you give it. The students should be given two of the Copymasters to get two week’s worth of exchange rates. (If you miss the programme you can find the table on the TV One’s web site.) This data will be used in Session 5.

In session 3, the students will produce currency converters for each of the currencies here to give a quick method of converting from $NZ 1 to $NZ 10.90 into the other five currencies. This can be done in several ways. You might like to let them think about how this might be done but we give four ways here. Once you have decided what it is that you want to get out of this exercise, then you can point them in the appropriate direction.

Method 1: A table. You can set up a table like the one below. In the table you put the exchange value of the currency you are converting to. For instance, in the position marked XXX you will put the foreign equivalent of $2.20.

Make sure that the students find quick ways to fill in the table. You won’t expect them to use the exchange rate for each one. For instance, the $4.40 cell can be filled by simply doubling the entry in the $2.20 cell. Encourage them to use as many short cuts as they can think of.

Method 2:A similar table can be completed more quickly (and maybe more accurately) by using an Excel spreadsheet. Once a column has been started the rest can be filled in by ‘dragging down’.

Method 3: Let them discover an algebraic equation for the conversion so that when they put in the New Zealand value for x, say, they get out the foreign value, y.

Method 4:They could write a program for a computer or graphics calculator.

Session 4 deals with approximations. What values you use to approximate will depend on the accuracy you want to get. But you might use 0.8 for the US dollars; 0.4 for sterling; 0.5 for Euros; and 80 for yens.

But what is a good approximation? Presumably it will be good if it is reasonably accurate and if it can be calculated in the head. Are there other criteria?

Some background to this unit can be found in the Staff Stuff ‘Dinner in London’. This might be particularly useful towards the end of Session 5.

There are various web sites that you might find useful for your students to use to find out more about the different currencies. Here are some suggestions:

http://www.24carat.co.uk/britishorenglishcoinsframe.html (British coins)
http://www.amphi.com/~psteffen/fmf/currency.html (Japanese currency)

There are many web sites that talk abut US or Australian notes and coins but many of them are for currency dealers or numismatists. However, you can find interesting things about these currencies from these sites.

Teaching Sequence

Session 1

In this session, we look at exchange rates.

1. Show the class a copy of the TV One News exchange rate table. (If possible, use one that you have got from the web from the night before.) Leave it where they can see it. Ask:
   What is this? What does it tell us?
   What denominations are there in the (i) United States currency (dollars and cents); (ii) Australian currency (dollars and cents); (iii) British currency (pounds and new pence); (iv) Euros (euros and cents); and (v) Japanese currency (yens)?
   What is another name for the British currency? (Sterling)
   The symbol for dollars is S with a line through. What is the symbol for pounds? What is the symbol for new pence? (They may need to look this up.)
   Which countries use the Euro? (There are many here. Perhaps you could start a list on a notice board and add to it when someone in the class finds another European country that uses the Euro. The complete list is Belgium, Germany, Greece, Spain, France, Ireland, Italy, Luxembourg, The Netherlands, Austria, Portugal, Slovenia and Finland.) The symbol for dollars is S with a line through. What is the symbol for Euros? (They may need to look this up.)
   What is the symbol for yens?
   What do the burgundy triangles tell us?
   What was the value of the New Zealand dollar yesterday in (i) United States currency (70.48 cents) (ii) Australian currency (91.83 cents) (iii) British currency (38.99 pence); (iv) Euros (57.07 cents ); Japanese currency (77.71 yens there is no smaller currency unit)?
   Does anyone have any questions about this table?
   You should feel free to add any questions that you think might be interesting or fit into work in other subjects. For instance you might like to ask students to point out on a map where the various countries are. You might like to ask what the capitals of those countries are.
2. Now get into some harder calculations. Spread the following question around the class (not just to the first person who puts up their hand.) You might ask more than one student to answer the same question. If there is a difference of opinion this can lead to a worthwhile discussion. Make sure that the students use the correct units. Ask:
   What is $NZ 100 worth in US dollars and cents? ($70.48) How did you work that out?
   What is $NZ 100 worth in Australian dollars and cents? ($91.83) How did you work that out?
   What is $NZ 200 worth in British currency? (£77 and 98 pence) How did you work that out?
   What is $NZ 200 worth in Euros? (€114.48) How did you work that out?
   What is $NZ 300 worth in yen? (¥233.13) How did you work that out?
3. Let the students go off in groups of 4 to make up questions like the ones you have just asked. They should work out the answers to their questions. Possibly they should produce at least 2 questions for each currency. Everyone in each group should be sure that the answers are correct. Encourage them to ask for New Zealand dollar amounts that are not just multiples of 100. Ensure that the students use the correct symbols and unit names.
4. Collect up all of the questions and answers.
5. If there are any questions that needed to be researched, get the students to do that before the next session.

Session 2

In this session, a quiz is held using the questions the groups made up yesterday as well as the items that needed to be researched.

1. Ask the class what the last session was about and let them recall the way New Zealand dollar amounts in foreign currency were calculated. You will need to decide whether or not calculators are to be allowed.
2. Put them in group of two and, one at a time, ask the questions that they invented in the last session along with other questions that you asked yesterday and the pieces of information that they had to find out. Include non-mathematical questions such as who is the President of the United States.
3. Check their answers every 5 questions and keep a record of the scores.
4. Declare a winning group (perhaps even the top five groups) and then go over the hard questions in a class discussion.

Session 3

In this session, the students will produce currency converters for each currency.

1. Let the class recall what you have been doing over the last two sessions. Get them to see that it would be easier if they had a device to calculate the value of New Zealand amounts in the other currencies. Discuss how this currency conversion might be done.
2. Let them work in groups to produce currency converters for all five currencies. As this could be a fairly time consuming task, you might want to get each group to do only one currency converter.
3. Get groups who worked on the same currency to check the entries in their currency converters.
4. Photocopy enough currency converters so that all students can have a copy of each currency converter.
5. Get them to use their currency converters to calculate 10 or so of the questions from the last session. Many of these will be outside the range of the converters so additional arithmetic will be needed.

Session 4

In case there are no calculating devices handy, it’s often useful to make approximations. Here the students calculate approximate cross currency values.

1. Talk about the fact that calculating devices will not always be handy.
   So how will you know if a shopkeeper has charged you about the right amount?
   Talk about the use of approximations. Discuss what would be ‘good’ approximations for each currency.
2. Discuss roughly how much of each currency you would get for $NZ 100.
3. Practice finding approximate amounts for values from the quiz. This can be done in groups or in a class discussion.
4. Make sure that the students know about rounding.
5. You may have used the approximations suggested in the Teachers’ Notes.
   But how accurate are the approximations? Are they good enough? Would it make any difference if you were buying a car or a cake?
6. Use some actual values to highlight the points above.
7. Get the class to compare actual values against approximate values.
   What is the error in the approximation (as a percentage)? Is there a better approximation?

Session 5

Here we see that currencies change value from day to day.

1. Here you will use the data on currencies that you have collected over the last two weeks.
2. Get the groups to produce a graph showing the movement of each of the five currencies over the last fortnight. Let the students use their imagination here but they could do each currency in a different colour on the same graph. How could they keep yens on the same page as the rest though?
3. Give them the following set of questions.
   When was the best day to buy (i) US dollars; (ii) Australian dollars; (iii) Pounds sterling; (iv) Euros; (v) Yens? (In other words when would you get the most of the other currency for your New Zealand dollar?)
   When was the worst day to buy (i) US dollars; (ii) Australian dollars; (iii) Pounds sterling; (iv) Euros; (v) Yens?
   In each of these currencies, what was the difference between the two extremes?
   By how much did each of these currencies change over the two week period?
   If you bought one New Zealand dollars’ worth of each currency two weeks ago and you sold those currencies now, how much would you have lost or gained?
4. The last question is a difficult one. You might want to have a class discussion about it after they have struggled with it for a while.
5. You might then ask them to work out how much various items in these other countries (you specify the price) will cost in New Zealand dollars. (Use the exchange rates at the end of the two week period.)