### Percentage Unchanged

If the base of a rectangle is increased by 10% and the area is unchanged, by what percentage (exactly) is the width decreased by ?

### CD Heaven

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at each price?

### A Change in Code

There are two sets of numbers. The second is the result of the first after an increase by a constant percentage. How can you find that percentage if one set of numbers is in code?

# The Legacy

##### Stage: 4 Challenge Level:

This is an opportunity for pupils to set up their own models using a spreadsheet and investigate what happens when they change variables such as interest, inflation rates and how much is spent each year. Investigating how a small change in interest rates can affect the total income over different time periods can be enlightening. Investigating the impact of spending large amounts of money up-front can also provide valuable insights.

Some models are suggested on the model cards which have varying levels of complexity. Some suggestions about how a series of sessions working on this problem might run are given briefly below.

After spending some time "making sense" of the problem and what is meant by a model, discuss ideas for making good use of the legacy:
• What types of things should the money be spent on?
• Why would the ex-pupil want the money to have a long term impact?
• What is the importance of inflation in any model we try?
• Why would you invest the money?
Students could work in groups to think about the models they might like to investigate then choose two models to compare. Think about:
• Total expenditure for each model,
• Benefits and limitations of each model,
• Comparisons between models,
• How a change in inflation might change the recommendations,
• How a change in the time-scale for using the money might affect any recommendation.
A plenary might include a discussion of the elegance or realism of some of the models and what the use of a spreadsheet had to offer to the task.