don steward
mathematics teaching 10 ~ 16

Monday, 2 May 2016

length, area and volume factors

it's probably helpful if students appreciate what happens to the overall size of a shape if you double in two or three directions*

see also big sprouts and Frodo Baggins
and wombats and diprotodons 

*an estimate of the adult height of a male is double their height when they are 2 years old
for a female it is double their height at 18 months

Sunday, 24 April 2016

combined enlargements

what happens (in general) if you do one enlargement scale factor 2 from one centre and then enlarge the resultant shape from another centre, also scale factor 2?

the ppt is here
it needs to be downloaded for the animations to work

enlarge the brown triangle, scale factor 2, to obtain the blue triangle

then enlarge the blue triangle from a different centre, to obtain the red triangle

the two enlargements, one after the other

students could either do their own or use these resources

the third triangle can also be obtained from the first via an enlargement

what will the scale factor be and where will the centre of enlargement be?

it seems as if the three centres have some relationship

check this with the ones drawn above

what happens with different scale factors?

the proof of the relationship can be done using vectors

this was done by James Pearce, of Mathspad fame

many thanks for the very neat vector proof, which he did generalise

Thursday, 21 April 2016


this is a copy of my LIME presentation after school today in Oldham (21/04/2016)
please download it to get the animations

many thanks to Lindsey Bennett and the Radclyffe School for organising this
it's great that such clustering events happen

Wednesday, 20 April 2016

barn roof angles

involving angles in polygons
creating a generalisation

Tuesday, 19 April 2016

randomly generated numbers

numbers generated using Excel 2007 (=randbetween(1,6))
concerns have been expressed about this random number generator passing standard tests for randomness but it is deemed to be good enough for illustrative purposes
and is so much quieter than dice rolling

Sunday, 17 April 2016

scatter graphs with algebra

using the fact that the line of best fit passes through
the mean of the x and the y numbers
find an added point from the old and new line of best fit equations 

involving straight line graph rules as a possible extension to work on scattergraphs

averaging expressions

extending finding the mean of numbers to this average of expressions
simplification and substitution, involving subtracting negatives

students could be asked to create their own sets of expressions

eating olives

thanks to professor smudge (@ProfSmudge) for featuring and providing this context for a % question by John Mason (RME 17.2) where he used the third question on the classroom resource as an example of mathematical unexpectedness

they can be solved in a variety of ways

 a mixture of olives
 a simpler view