median
don steward
maths teaching 10 ~ 16

Sunday, 23 November 2014

percentage deals

Jordan Sloan posted a fine idea on the TES during the World Cup 2014
(I found it thanks to the very welcome help of Craig Barton on his site)

here is a version of Jordon's task, intentionally not giving any original price





Saturday, 22 November 2014

takes and adders generalisations


an intention for this task is to
  • work on patterns in various sums
  • reach a conjecture about how the patterns can be generalised 
  • prove this using (a) diagrams (b) algebra
thanks to the teachers in Derbyshire for their insights





















which questions are these?
what do the diagrams show?

Wednesday, 19 November 2014

expression pyramids




establish that the outer two bottom expressions must sum to a multiple of 8

students can be asked to form their own, similar, addition pyramid i.e. with a multiple of 'p' at the top

more expressions magic squares





find the gaps



going somewhere


meaned triangular numbers


Saturday, 8 November 2014

mobile moments

the diagrams are sketches, the numbers on the bars show the ratios/proportions along the bars




















Erich Friedman's weight puzzles are great...



place weights 1 to 5 so that this mobile balnces
place weights 1 to 5 so that this mobile balances



place weights 1 to 6 so that this balances





place weights 1 to 7 so that this balances



Wednesday, 5 November 2014

Tuesday, 4 November 2014

mobile inequalities




















the idea for this task came from Ian Sugarman who now works with Melvyn Rust on NumberGym software

see also Paul Salomon's fine (logic) work on imbalancing on Lost in Recursion

Saturday, 1 November 2014

mobiles































in good mathematical fashion you say that the weights of the bars and the string are negligible compared with the hanging weights...

(moments are ignored by having the bars suspended at their mid-points)
good practice in doubling and halving to start with:






















then an introduction of some algebraic expressions:





Sunday, 19 October 2014

equations and equivalent fractions


problem number 8 of book 1 of Diophantus' Arithmetica (~ 200 CE) asks which number must be added to 100 and to 20 (the same number) so that the sums are in the ratio 3 : 1    these questions are in the same vein