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The Money Maze

Stage: 2 Challenge Level: Challenge Level:1

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.