# 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.

Sincerely

Aunt Lucy

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

Investigations Home

The Maths Class Of 9p, The Teacher Miss Whitaker

Wednesday, November 30, 2011

"I think the second one."

Miss Hopson, Little School For Stars

Thursday, February 16, 2012

"We like the first one."

Tina, 8c

Wednesday, September 19, 2012

"The second one."

Tom And George, The Grammar School

Wednesday, November 28, 2012

"We think it is the forth one."

Tom And George, HGS

Friday, November 30, 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."

5EH WHCS, Aylesbury

Tuesday, December 11, 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!"

Year 5 Set 1, William Harding School

Monday, December 16, 2013

"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.
5EH."

Ryan, APA

Tuesday, March 4, 2014

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

Tishya, Garden International School

Tuesday, April 29, 2014

"I think it is the second one."

Kyle, Oxted School

Tuesday, July 11, 2017

"I think that No.1 is the most profitable if she lives longer however if she lives shorter No.1 I the best choice."

Romain B, LIS - 3MS

Wednesday, September 6, 2017

"I think it is the fourth one. If she still lives 10 years, it is the one that brings the most money."

Leonard.s, LIS 3MK

Saturday, September 9, 2017

"I think it is the 4 one because if Aunt Lucy gets to be 84 (which is the average) I would get 16.383"

Yasmin, 3MK LIS

Sunday, September 10, 2017

"I think the option 3 is the best if she lives for 10 years."

Tracy, Nexus International School Malaysia

Wednesday, December 6, 2017

"I think it's option 4. Even though Aunt Lucy lives until 90 year old or older, the sum of option 4 is still more than all the others options."

Meriel, LIS 3AMT

Sunday, September 23, 2018

"If she lives 5 more year`s then option 1 is the best. I don´t think option 2 is a good option because it goes up so slowly. Option 3 would be good if she lives 10 more years. But I am going to go for number 4 because if she gets higher then 10 then I get loads of money!"

Cameron, Sir John Talbot's School, Shropshire

Saturday, March 23, 2019

"I don't think No.1 is a good option becaif she lives longer than 10 years, the amounts become negative, which subtracts from your money, not adds to it! No.4 grows exponentially each year (so does No.3, but No.4 grows quicker) which, in effect, is better than No.2, which only grows by only £10 each year. So, I think No.4 is the best option."

Cool Person, My Home

Friday, April 5, 2019

"I choose option 4 as it is the most profitable after 9 years. However, if Lucy dies 5 years later I would choose option 1. If Lucy dies 9 years later I would choose option 3 as the total profit is bigger than option 1 (9 years later). Option 2 is the worst becait starts at 10 dollars and it increases very slowly."

5 Galileo, Parramatta Public School

Monday, November 11, 2019

"If she lives a year or 10, then option one is the most suitable and profitable. However, if she lives for 10 or more years, option two and four are the best."

Hi, Pps

Monday, November 11, 2019

"I think its option 3 as you are multiplyng the numeral by 1 and a half which gives you more than the other options ( I and 2 are equivelant )."

Qasim Elemam, 5 Galalieo

Monday, November 11, 2019

"Number 1 for me is the best option if she was just about to die.Number 2 if she had a 100-90 % of living becashe would be building up by ten.Number 3 if we needed money becait gets times ed by two.Number 4 if you wanted to be nice and get cheap."

Lily Hughes, Claremont

Wednesday, April 29, 2020

"I’d say number 1. It secures more money and we don’t know how long the aunt will live. If she would to die, then they would stop receiving money. If she died a year later you would only make a smaller amount."

Year 7's Of 2020, OneSchool Global, Swan Hill Campus

Thursday, August 20, 2020

"We think the first one, especially because Aunt Lucy is likely to die soon. After all, it's better safe than sorry!"

Mansur, Bedfont Primary School

Friday, January 29, 2021

"I will choose the third one because you get smaller at the first but then go more higher and higher with each one."

Irina, Maryland

Tuesday, February 23, 2021

"The second one if she lives 20-30 years
the first one if she lives <=10 years."

Mathsclub1, Herts

Thursday, February 25, 2021

"We like Schemes 2 and 4 as you will probably have the most money based on the average life expectancy!"

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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