Purpose

This unit is about making calculations in the real life situations of taxis, hire cars, and cell phones.

Specific Learning Outcomes
  • calculate the cost of hiring a taxi, hiring a car, and using a phone
  • compare the costs of different taxi companies, hire car companies, cell phone brands
  • find percentages and GST in these situations.
Description of Mathematics

The basic idea behind this unit is to understand the charges for hiring a cab, hiring a car, and using a cell phone and making comparisons between companies to see which offers the best deal. The majority of calculations are numerical and involve the costs of various scenarios. The calculations are mainly of the type 20 x 2 + .5 x 100. However it is necessary from time to time to calculate percentages and GST.

In comparing the prices of different firms it is necessary to solve algebraic equations. Clearly it is important to be able to apply mathematics to real situations.

Required Resource Materials
Calculators

Dice

Coins

Activity

Teachers’ Notes

Encourage your students as much as possible to calculate the answers by hand but let them use calculators to check their results.

In your discussions ask the class how they got the answers and what methods they used to do the calculations.

The Hire Car Game: Three pairs of students at a time run their own hire car company. (Try to give as many pairs a chance to do this as possible.) They have overall overheads of $20 a day per small car, $25 a day for a medium car, and $35 a day for a large car, whether the car is used or not. They have to set the cost of hiring small, medium or large cars to the rest of the class. Each company has 11 cars: 3 small, 5 medium and 3 large.

The customers decide which company they will hire their car from. They then roll two dice. If they get 2, 3 or 4 they hire a small car; 5, 6, 7, 8 or 9 they get a medium car; 10, 11 or 12 they get a large car.

The customers then flip a coin. If it is heads they get to hire their car from Sunday. If it is tails, they then roll a dice. 1 is for Monday, 2 is for Tuesday, and so on.

The company owners have to keep track of their receipts and which cars are out when. To do the latter they probably need to draw up a table.

If a company is out of cars for any reason, they can (i) give the customer a larger car at the cost of the original sized car; (ii) borrow a car from a competitor at an extra $5 cost; or (iii) pass the client on to another company.

Play the game for two weeks of game time.

The winner is the company that make the largest profit.

Teaching Sequence

Session 1

In this session, we look into the cost of hiring a taxi.

  1. Have a discussion about taxis.
    Who has ridden in a taxi recently? Why did you go in a taxi?
    How did the taxi driver calculate the fare?
    Why was there a dollar amount on the meter before you even started off?
  2. To simplify things slightly, taxis charge so much as soon as you get in the cab (the flag fall) and so much per kilometre. Suppose that Tricky Taxis charge $10 flag fall and $1.50 a kilometre. (Students can work in pairs for this exercise.)
    How much would it cost you to travel 25 kilometres in the cab?
    How much would it cost you to travel 32 kilometres in the cab?
    If you were given a 10% discount, how much would it cost to go 15 kilometres?
    How far could you go for $60?
    How far could you go for $75?

    Check the students work as you go round the class.
    Bring them back to discuss the answers they got as well as the methods that they used to get the answers.
  3. Tiki Taxis charges $20 flag fall and $1.25 a kilometre.
    How much would it cost you to travel 25 kilometres in the cab?
    How much would it cost you to travel 32 kilometres in the cab?
    If you were given a 10% discount, how much would it cost to go 15 kilometres?
    How far could you go for $60?
    How far could you go for $75?

    Check the students work as you go round the class.
    Bring them back to discuss the answers they got as well as the methods that they used to get the answers.
    For any group that finishes early they can make up their own problems.
  4. Which taxi company is cheaper for the different situations above?
    So which taxi company would you call and why? (The answer to this depends on how far you are going. So first they will need to find the distance when the two cabs charge the same amount.)
  5. There is one other charge that we omitted above. That is for standing time. When the cab is standing still the meter still ticks over. This explains why two otherwise identical trips may cost quite different amounts. Tricky Taxis charges 50c a minute for standing time while Tiki Taxis charges 40c.
    In your groups, think about how far it is from your school to the centre of town. What would you expect it to cost to take a Tricky Taxi or a Tiki Taxi cab from school to town?
    The students will need to make some estimates here of both standing time and distance.
    How much extra would it cost you to make the trip in peak hour compared with Sunday morning?
  6. As research, ask the class to find out the costs of two taxi companies. Ask them to say which cab they would take and why. Keep the data and their answers for discussion in Session 4. Remember that there is no right answer here so the students will need to justify their choice.

Session 2

In this session we look at hiring a car.

  1. Have a general discussion about hire cars.
    Has anyone’s family or friends ever hired a car?
    What company did they use?
    Where did they go?
    Why didn’t they use their own car?
    How many days did they hire the car for?
    How far did they travel?
    Do you know how much it might have cost?
    What different things do you have to pay for?
  2. Let’s start off simply. Suppose that Rent-A-Bomb charges $25 a day and 50c a kilometre.
    How much would it cost for a two day hire if you travelled 300 kilometres?
    If you used the car for three days and it cost $290 how far did you go?
    If you travelled 900 kilometres and it cost $650, how many days did you hire the car for?

    Let them work in pairs and discuss the answers when they have finished. Is there more than one way to do these problems?
    For any group that finishes early they can make up their own problems.
  3. On the other hand, Bomber-Rent charges $30 a day and 45c a kilometre.
    How much would it cost for a four day hire if you travelled 400 kilometres?
    If you used the car for two days and it cost $195 how far did you go?
    If you travelled 800 kilometres and it cost $450, how many days did you hire the car for?

    Let them work in pairs and discuss the answers when they have finished. Is there more than one way to do these problems?
  4. Suppose that you need to go from Dunedin to Christchurch a distance of 360 kilometres. You take one day travelling and one day coming back and you spend two days in Christchurch. You probably do 125 kilometres while you’re in Christchurch.
    Would you use Bomber-Rent or Rent-A-Bomb?
  5. In general, which company would you use?
    There is no unique answer to this. However you can work out the break-even cases. For instance, if you only needed the car for one day, both companies would cost the same if you travelled 100 km. For a larger distance than that you would be better with Bomber-Rent; for a smaller distance, go for Rent-A-Bomb.
    What if you needed the car for 2 days, 3 days, etc.?
    Is there a pattern here?
  6. Now tell the class that you forgot to include GST in your considerations. If you are calculating the cost of a trip you have to add in the GST.
    Redo the costings above using this new factor.
  7. But Avertz doesn’t charge you for each kilometre you go. They just charge you $65 a day.
    Which of the three companies would you prefer to hire a car from?
    Does it make any difference if you add the GST in or not?

    Again it all depends.
  8. Now ask them to plan a trip for seven days around the North Island.
    What do you estimate your costs would be? (You should add in the price of petrol too. What is your estimate for the number of kilometres that you get per litre?)
  9. As research, ask the class to find out the costs of two hire car companies. Ask them to say which company they would use and why. Keep the data and their answers for discussion in Session 4. Remember that there is no right answer here so the students will need to justify their choice.

Session 3

In this session, we look at phones, txts, and calls.

  1. Have a general discussion about phones.
    Who has their own phone? 
  2. What colour/brand is it? (What colour would you like to have?)
    How many times a week would you use it to phone a friend?
    How many text messages would you send in a day?
    Does the school have a policy on phones?
    What features are there in the most expensive phones?
    What do you think that they’ll put in the next generation of phones?
    How long do phones last?
    How long do you spend on your average phone call?
    What do phones cost?
    What do phone calls cost?
    What does it cost to text someone?
    Who pays for the calls?
  3. Let’s say that Phone X charges $1 a minute for local calls.
    If you speak on the phone for 2 hours a week, how much will that add to the phone bill?
    (It might be worth writing this on the board.)
  4. Give the class time to individually work that one out. Check their answers. Make any necessary corrections.
  5. Keep the same Phone X, we’re not advertising for anyone here, and the same cost for a phone call.
    How long would you have talked on the phone if the bill for the week came to $153?
  6. Suppose that the same phone charges 20c for a text message.
    What would it cost you to send 50 text messages a week?
    How many text messages would you be able to send for $153?

    Let them work by themselves to find the answers to these.
    Do you get more value out of text messages or phone calls?
  7. Let’s make a comparison with Phone Y who charges 75c for a local call and 20c for a text message. (Let the class work in pairs for this one.)
    What would it cost you to use the phone for 2 hours?
    How long could you speak on the phone for a total of $153?
    What would it cost you to send 50 text messages?
    How many text messages would you be able to send for $153?
  8. Make sure that most groups have finished before you go on.
    If you only had a choice of Phone X and Phone Y, which phone would you choose and why?
    The answer to this would probably depend on whether they prefer to text or phone. It’s important for them to understand that there is no absolute answer. Personal choice will come in here.
    What other factors would come in to your choice?
    Cost of phone; phone features; other?
  9. Alright let’s get down to the important things. You can get Phone X for $150 and Phone Y for $250. Suppose that you make 1.6 hours of phone calls and 50 text messages a week.
    Is it cheaper to use Phone X or Phone Y?
    If you didn’t text at all, how long could you phone for before the cost of Phone Y was more than the cost of Phone X?
    (Include the cost of the phone.)
    If you didn’t phone at all, how many text messages could you send before the cost of Phone Y was more than the cost of Phone X? (Include the cost of the phone.)
  10. You are setting up your own phone company in competition with Phone X and Phone Y. You can buy a phone for $50; call for 35c a minute; and text messages for 5c.
    What prices would you charge in order to beat the competition on 1.6 hours of phone calls and 50 text messages a week over a year? (Don’t forget you will have to include GST.)
    Can you do this and still make 50% return on your investment?
    Is there a bigger percentage return on calls or texts?
  11. Let them work on this in their groups. Then compare the answers of the groups. Who made the most money? Who made the least?
  12. If they are not familiar with GST and percentages you will need to explain them. Perhaps they can check another group’s answers.
  13. For the quicker students you can ask them what percentage profit Phone X and Phone Y make with the same numbers of calls and texts.
  14. As research, ask the class to find out the costs of two brands of phone. Ask them to say which brand they would buy and why. Keep the data and their answers for discussion in Session 4. Remember that there is no right answer here so the students will need to justify their choice.

Session 4

In this session we discuss the research undertaken at the end of each of the last three sessions.

  1. Give as many groups as possible a chance to report on what they have found. Let the class discuss the various findings.
  2. Ask each group to write up their report with full calculations.

Session 5

In this session we give the students a chance to operate a hire car company.

  1. Play the hire car game shown in the Teachers’ Notes.
  2. Get the class to report back at the end of the session.

Log in or register to create plans from your planning space that include this resource.