In Durban the average salary is R160,000 and in Cape Town it is R180,000. Mdu moved from Cape Town to Durban.
Mdu has made both cities richer because the average salary has gone up in both due to his move. Can you explain how that could happen?
Describe what is needed for one person moving to:
a) increase the average income in both cities
b) decrease the average income in both cities or
c) increase one whilst decreasing the other.
In what circumstances could Mdu, moving from one place to another, reduce the average income in one place and double the average income in the other?
Click here to download the FOR RICHER FOR POORER Notes for Teachers
Click here to download the FOR RICHER FOR POORER worksheet
This activity is adapted from the NRICH task For Richer for Poorer with permission of the University of Cambridge. All rights reserved.
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A good problem solving technique is to try a simple case first. You might like to download the Notes for Teachers which suggests a simple case with a small group of people.
You might also like to give your learners just part (a) of the problem and tell them you are going to do it in class the following week. Challenge them to find an explanation. It requires no calculations, just an understanding of the concept of the mean and clear thinking.
My grade 4 learners know nothing about averages. I just gave them the problem. What some of them said amazed me because they said that if you are staying in a big city you get more money so that you can use it for traveling to work which is far form where you stay, pay the rates, school fees for your children, send money home, buy food and buy electricity. I ask them if it will be better to stay where you get less money or move to where your salary will be increased. One of them said that there’s nothing better because her mum is working in Cape Town and earning a big salary but is always complaining about not having enough money. One of them said that the cities are rich because of their parent’s moneys. They answered from their level of development and their frustrations about their parents who are getting bigger salaries but could not meet their children’s needs.