Pocket money
This problem solving activity has a number focus.
Matiu and Ariana have agreed to work for their Mum over the holidays.
The pay they get will vary.
Ariana will get $10 for the first day she works and two more dollars for every day she works after that.
Matiu will get $1 for the first day he works, but for each day he works from then on, his pay will be doubled.
Who would you rather be and why?
- Add a series of two digit numbers.
- Double numbers.
- Systematically keep track of their calculations to compare numbers.
This problem poses a question that involves students comparing two rates. In one a fixed number is added, and in the other the total is continually doubled.
It is worth noting that, regardless of the whole numbers you begin with, doubling will eventually win.
- Play money
- Copymaster of the problem (English)
- Copymaster of the problem (Māori)
- Calendar
The Problem
Matiu and Ariana have agreed to work for their Mum over the holidays. The pay they get will vary. Ariana will get $10 for the first day she works and two more dollars for every day she works after that. Matiu will get $1 for the first day he works, but for each day he works from then on, his pay will be doubled.
Who would you rather be and why?
Teaching Sequence
- Read the problem to the class. Give them time to think about the problem by themselves.
- Have students restate the problem in their own words, identifying what it is asking them to find out. They should recognise the need to find out how much Matiu will earn, how much Ariana will earn, and the need to compare these amounts. They might also recognise that a definite number of days is not given.
- Ask how they might approach the problem and keep track of the totals.
- Have students work on the problem individually or in small groups.
- As they work ask questions that require them to compare the daily totals. Ask them to justify the number operations that they are using and to explain the steps they are taking to find the answers.
- Share and discuss solutions.
Extension
After how many days is Matiu’s Mum likely to run out of money?
Solution
This problem doesn’t have a definite answer as it does not state how many days the two students work. If they work for less than 6 days then Ariana will earn most money. If they work for more than 6 days, then Matiu will earn the most.
Solution to the Extension
There is no precise answer. However, the students should be able to see that doubling raises the number fairly quickly. After 20 days the amount exceeds one million dollars. Most people won’t be able to afford that amount in pocket money!