don steward
mathematics teaching 10 ~ 16

Tuesday, 24 November 2015


the last three questions could involve trial, thinking, improvement


the quadratic formula

Monday, 23 November 2015

area and perimeter of rectangles

this task could be initiated by asking students to draw several rectangles on squared paper
they find the perimeter ('P' number) and area number ('A' number) (using the size of square provided as a unit)

then invite one of them out to let the class know the P and A numbers for one of their rectangles
the class try to work out the dimensions

discussions might focus on the two sizes of rectangles (including squares) for which P = A
and then for which A = 2P

finding examples that fit various relationships
 linking P with A for various widths
 continuing a pattern
 providing reasons why rules work

plotting the rules for particular fixed widths

what are the intersection points?

forming and solving simultaneous equations in P and A
various hard questions....

sum and difference of two cubes

approaching this numerically is slow...
students will need to be able to form a quadratic general rule after a factor has been extracted for their results
with, probably, a few other examples

it may be advisable to move on to a understanding a geometric interpretation and then return to generalisations for the forms of these questions later

cube number problems

an intention is that some students might list the cube numbers
and see which work

others might become involved with cubing a binomial expression
and a method that Diophantus seems to have promoted

Monday, 16 November 2015

amount of blood

the following tables are from the Welsh government numeracy sample materials (2013)

assume a linear sequence (constant difference)

early arithmetic test

without a calculator or, apparently, paper work out:

'a difficult assignment' 1895
an interesting question

Nikolay Bogdanov-Belsky

population UK

how could you investigate the extent of population growth in the UK?

what might you look at to see how many secondary school places are likely to be needed in, say, 10 years time?

the Google graph has data from the World Bank
(with graphs for other countries as well)

a version of the UK population pyramid

Department for education data (just for England)
SFR 17/2015
England population is (recently) 83.9% of the UK

Wednesday, 11 November 2015

polyhedron wreaths

a coffee store chain has polyhedron wreaths this year (in the UK anyway)
(not too many of the polyhedra are Platonic)
you might want to demonstrate an understanding of why there are only five Platonic solids - with all faces the same

geometric solids: Illuminations (NCTM) is helpful for showing the nets and the solids
and the solids can be rotated