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?

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

Is extendable

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

Promotes discussion, originality and invention

Encourages collaboration

Is challenging

Uses technology appropriately

Links with the personal lives of students

Uses mathematical modelling

Involves an historical, social or cultural component

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.

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

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

Ideas introduced on 6 September 2014 workshop

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.

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?

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.

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

NRICH Agile Algebra

E for Excellence!!

Activity for literacy!!

Thank you for coming to the workshop!! Ext