median
don steward
mathematics teaching 10 ~ 16

Friday, 24 February 2017

same volume and surface area, different cuboids

it's likely to be a bit of a surprise that you can have two different cuboids (rectangular prisms) with the same volume and surface area

but these are quite rare creatures
[thanks to www.mathspad.co.uk for the two that both have integer dimensions]




Wednesday, 22 February 2017

volume doubling

this is a problem posed by James Tanton
to find solutions, students use trial and improvement with maybe some thinking about factors







area doubling

students use trial and improvement to try to find values
should all be integer L,
exploring the function




new £1 coin

a new £1 coin is due to be introduced on 28th March 2017
it's a dodecagon
the powerpoint is here
thanks for the insights of Birmingham University ITT students (21st Feb 2017)






thanks to David Wells, 'curious and interesting geometry'

also thanks to David Wells




see chapter 22 of Pierre van Hiele's 'structure and insight'

Saturday, 18 February 2017

45 degree angles

a companion to isometric angles

a restricted set of angles form the interior angles of polygons

to practice multiples of 45 degrees angles:

tap on the end points
students call out the angles
(chanting in unison...)

decide what each interior angle is, then sum them

Friday, 17 February 2017

two similar shapes




some of the enlargements involve surd scale factors

but can usually (?) be established as being similar by dissecting the shape





see also the fine work of Michael Reid at mathpuzzle

these two are amongst his collection

Thursday, 16 February 2017

drawing similar triangles

an intention is that students use a 'vectorial' approach to completing the similar triangles

for the first side, the angles of the triangles can be calculated from this information:





Monday, 13 February 2017

recurring decimals

this idea is due to Martin Wilson in Harrogate
I have slightly adapted his questions, to give answers that are easily marked

Sunday, 12 February 2017

getting the same number

extending 'making a positive whole number' to a quadratic expression

could be a start to factorising a quadratic equation






Saturday, 11 February 2017

another blog

median practice makes perfect blog
[not to be confused with median practice and quiz questions]

I've tried to collect together some questions for arithmetical (and other) practice to include some longer questions and some questions that can involve exploration

I introduced some aspects of these questions/tasks in this presentation to Somerset Schools on Friday 10th February 2017. Thanks to Polly Checkley and Jenny for this invitation  and a well-organised day.

these could be presented as two sides of a sheet
e.g. as a resource for subtraction:



















I've tried to choose questions that might have some interest:
why do questions 1) and 2) have the same solution?
what has happened to the digits?
questions 3) and 4) are for those particular students who tend to like taking smaller numbers from larger ones
questions 5) and 6) reverse the digits - what other examples can be found for subtracting 396, and more generally?

questions 7) and 8) involve all the digits 1 to 8
questions 9) and 10) involve the digits 1 to 9 and questions 11) and 12) involve 0 to 9
are there other examples of these?

in question 14) there is a common feature to the solutions, why is this?

relationships

a powerpoint from a talk (Tuesday 7th Feb 2017)

Ulverston Victoria High School - an impressive school, in many ways, situated with grand views of Cumbria. Many thanks to Sheila Hirst and departmental staff at the school for hosting the session so admirably well (scones and jam) and to Alison Scott and NNW mathshub for their support.

My intention for the session was to suggest some ways that students could be involved in tasks where variables do actually vary. This follows a view, expressed by Professor Anne Watson in particular, that we maybe don't do enough to explore functions/relations with students.

Friday, 27 January 2017

parallel line angle relationships and proofs

reworked to (i) angles on parallel lines questions and (ii) relationships and proofs

the powerpoint is here