Mathematical Investigations

Aunt Lucy's Legacy

Dear Lindsay

Now that I am getting on (I turn 70 today) I want to give you some of my money. I shall give you a sum each year, starting now. You can choose which of the following schemes you would like to use.

1. £100 now, £90 next year, £80 the year after, and so on.
2. £10 now, £20 next year, £30 the year after that, and so on.
3. £10 now, one and a half as much next year, one and a half as much again the year after, and so on.
4. £1 now, £2 next year, £4 the year after, £8 the year after that, and so on.

Of course, the scheme can only operate while I am alive. I look forward to hearing which scheme you choose, and why.


Aunt Lucy

This investigation comes from the 1989 Hertfordshire Information Technology Across the Curriculum (Mathematics and Data Handling) project document.


Schemes Spreadsheet

Investigations Home

"I think the second one."

The Maths Class Of 9p, The Teacher Miss Whitaker
Wednesday, November 30, 2011


"We like the first one."

Miss Hopson, Little School For Stars
Thursday, February 16, 2012


"The second one."

Tina, 8c
Wednesday, September 19, 2012


"We think it is the forth one."

Tom And George, The Grammar School
Wednesday, November 28, 2012


"We Think that it is the third one, because life expectancy means she will say she lives ten years and 3 gives you the most money."

Tom And George, HGS
Friday, November 30, 2012


"As a class, we agree that option 4 is the best solution because after 10 years, it's the most lucrative. Assuming she lives an average life expectancy!"

5EH WHCS, Aylesbury
Tuesday, December 11, 2012


"We think that option 4 is the best because over a long period of time, you would receive £32,767.
Option 1 is the least profitable if she lives longer. However, this is the best option in the first 5 years.

Year 5 Set 1, William Harding School
Monday, December 16, 2013


"I like the third one because you get a high amount getting slowly more."

Ryan, APA
Tuesday, March 4, 2014


"I think it is the second one."

Tishya, Garden International School
Tuesday, April 29, 2014


Do you have any starting points for mathematical investigations or comments about the investigations we have presented here?
Click here to enter your ideas.

A mathematical investigation is quite different to other mathematical activities. The best investigations are open ended and allow students to choose the way they work and how they record their findings. It is one of the few occasions when 'going off on a tangent' is not only acceptable but actively encouraged (within reason).

Students may ask for 'the answers' but this supposes that the activity is closed. Investigations can always be extended by varying the initial instructions or asking the question 'what if...?'. Sometimes students point out that the instructions are ambiguous and can be interpreted in different ways. This is fine and the students are encouraged to explain how they interpreted the instructions in their report.

Some students may benefit from a writing frame when producing the reports of their investigations. Teachers may suggest sections or headings such as Introduction, Interpretation, Research, Working and Conclusion or something similar.


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