1. A 40 tonne weight is dropped and it breaks into 4 pieces. Luckily it can still weigh all the weights from 1 to 40. What are the weights of each of the four pieces?

2. A Rich Mathematical Activity is one which…. Is accessible to everyone at the start

3. Is extendable

4. Involves students in speculating, forming conjectures, explaining, justifying, refuting and interpreting

5. Promotes discussion, originality and invention

6. Encourages collaboration

7. Is challenging

8. Uses technology appropriately

9. Links with the personal lives of students

10. Uses mathematical modelling

11. Involves an historical, social or cultural component

12. Assumptions Four pieces add to 40 therefore once three pieces chosen the fourth is a given Can not all be even numbers because then no odd numbers would result There are a huge number of combinations which fit, therefore the numbers are special.

13. Trials Find 4 numbers that add to 40. Check their variety. Is one amongst them? Must it be? Try to falsify this group Use the information gained to try again

14. On-going Investigation? Try, try, try again Build in resilience Build up strategies

15. Ideas introduced on 6 September 2014 workshop

16. Open-Top Box This activity is about investigating the maximum volume of an open-top box that can be made by removing squares from the corners of an A4 piece of card. This leads to trianglulation from different methods, trial and improve, through to differentiation and algebraic thinking.

17. Maximum Volume of a cone This activity leads on from the open-top box to the idea of maximum volume of a cone made from a very large round filter paper from the science labs in your school. Cut to the centre, and watch as the height, circumference, material used, all change, what is the variable?

18. Circles within circles Problem In the diagram below, the circles are all touching and have a common horizontal tangent. If the radii of the circles A, B and C are a, b and c respectively, find c in terms of a and b.

19. Circles within Circles comes from : Lighting Mathematical Fires Derek Holton and Charles Lovitt ISBN 1-86366-389-4 This is a brilliant book – you may have it in your resources area as it was given out to maths teachers in 1998.

20. NRICH http://nrich.maths.org/7074 Agile Algebra

21. E for Excellence!!

22. Activity for literacy!!

23. Thank you for coming to the workshop!! g.frankcom@auckland.ac.nz 09 623 8899 Ext. 48663