A 40 tonne weight is dropped and it breaks into 4 pieces. Luckily it can still weigh all the weights...
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Transcript of A 40 tonne weight is dropped and it breaks into 4 pieces. Luckily it can still weigh all the weights...
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?
• Involves students in speculating, forming conjectures, explaining, justifying, refuting and interpreting
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
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 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.
Thank you for coming to the workshop!!
• 09 623 8899 Ext. 48663