Pocket money

The Problem

Sally and David have agreed to work for their Mum over the holidays. The pay they get will vary though. Sally will get $10 for the first day she works and two more dollars for every day she works after that. David, on the other hand, 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

1. Read the problem to the class. Give them time to think about the problem by themselves.
2. Ask them to highlight the important pieces of information. Encourage them to explain why they consider them important.
3. Brainstorm for ways to solve the problem. Remind them that it is important to plan ways to keep track of their working.
4. If the students are beginning problem solvers you may work out the first couple of days together. Once more encourage the students to plan ways to keep track of the totals.
5. Let the students work on the problem 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.
6. Sharing of solutions.

Extension to the problem

After how many days will David’s Mum run out of money?

Solution

This problem actually doesn’t have a definite answer. Nowhere in the problem does it say how many days the two students work. If they work for less than 6 days then Sally will earn most money. If they work for more than 6 days, then David will get the most.

Extension to the problem

Here again 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 mothers won’t be able to afford that!