## Saturday, 28 November 2015

## Tuesday, 24 November 2015

## 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

etc.

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....

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

etc.

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

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

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)

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

'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

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

SFR 17/2015

England population is (recently) 83.9% of the UK

## Sunday, 15 November 2015

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