# The Money Maze

Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?

Go through the maze, collecting and losing your money as you go. You may not go through any cell more than once, and can only go into a cell through a gap, for example, you may not go from $5$ to $6$, or from $7$ to $3$.

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Which route gives you the highest return? How much is it?

Which route gives you the lowest return? How much is it?

There are only two ways to go from the first square - it might be a good idea to look at each way in turn.

How will you record which routes you have taken?

We received several well reasoned solutions to The Money Maze. Lucy and Hayley from Thomas Reade Primary School and Ben from St Michael's C of E Primary School sent particularly clear solutions where they showed each step in turn. Here is Lucy and Hayley's contribution:

The highest integer:1. $100 (-10)=$

2. $90 (+150)=$

3. $240 (-50)=$

4. $190 (+120)=$

8. $310 (-20)=$

7. $290 (+145(+50$%$))=$

6. $435 (-50)=$

10. $385 (\times2)=$

11. $770 (-10)=$

15. $760 (+30)=$

16. $790$!!!

Lowest integer:

1. $100 (-50)=$

5. $50 (+10)=$

9. $60 (-50)=$

10. $10 (+5(+50$%$))=$

6. $15 (-20)=$

7. $-5 (\times2)=$

11. $-10 (-10)=$

15. $-20 (+30)=$

16. $10$!!!

I like the way you have presented this, girls, it makes it easy to follow the operations.

A teacher from St Luke's Church of England Primary School Westbeams Road, Sway, Hampshire, sent in the following email.

One of my students, Jasper has this morning completed this challenge and found a different answer to the second part of the problem to the one published.

Before looking at the solution, he came up with the answer as £40, following this route:

Cell 1. Start with £100;

Cell 5. Lose £50,

Cell 9. Add £10,

Cell 10. £50 less,

Cell 11. Double your money,

Cell 15. £10 less

Cell 16. £30 more

Then he explored the published solution and thought that his answer was 'more correct' because you can't minus £20 from the £15 you end up with in Cell 6, otherwise you'd end up with a negative amount of money, which he says is impossible!

When exploring number challenges and investigating all the possibilities the idea of negatives often depends on the pupils' thoughts. Some will allow them, others will not and some do not understand negativity. When it's money then those who consider negatives to be acceptable will often call them "being in debt".

Thank you Jasper for your thoughts wnd work.

### Why do this problem?

This problem gives learners the opportunity to practice addition, subtraction, multiplication and division of money, while it includes calculating with percentage. It is also a good context for developing a recording system and a systematic approach.

### Possible approach

Pupils will need to develop their own recording system to show which routes they have tried. Encourage them to discuss how they know they have tried the different options so that they begin to see the need for a systematic approach.

This sheet has two copies of the maze on it.

### Key questions

Have you thought of a way of recording the routes you have found?

How do you know that you have tried all the different ways through the maze?

How many ways are there to go from the first square?

Which one will you try first?

Are you sure there is a gap to go through between those two squares?