the particular sums are intentionally presented out of sequence

students might decide/wish to re-order them

in order to generalise

a purpose for this task is to use algebraic simplification to show why you obtain the (particularly easy to spot) result

in a similar vein, students might create their own families of questions

## Friday, 12 February 2016

## Thursday, 11 February 2016

### from powers of 3 to Sierpinski

how many squares at each stage?

thanks to John Mason

[O.U. project mathematics, expressing generality (PM751) page 29, available as a pdf]

thanks to John Mason

[O.U. project mathematics, expressing generality (PM751) page 29, available as a pdf]

## Tuesday, 9 February 2016

## Monday, 8 February 2016

### decimal addition

another attempt to suggest a lesson with sections involving

they can speed up....

maybe for homework or extra work

- teaching or reviewing a skill
- practice of that skill in tasks that involve generalisation and possibly proof

they can speed up....

maybe for homework or extra work

## Saturday, 6 February 2016

### cancelling fractions

this is an example of a lesson split into two sections:

sometimes, as in question (7), you only part-cancel a fraction in order to find the nth term rule

sometimes, for other fraction sequences, there is a stray fraction that cancels - not part of the general cancelling rule

some features of an overall generalisation are relatively easy to discern

and others aren't (for me anyway)

- teaching or reviewing a skill
- practice of that skill in tasks that involve generalisation (in this case an nth term rule) and possibly proof

sometimes, as in question (7), you only part-cancel a fraction in order to find the nth term rule

sometimes, for other fraction sequences, there is a stray fraction that cancels - not part of the general cancelling rule

some features of an overall generalisation are relatively easy to discern

and others aren't (for me anyway)

## Friday, 5 February 2016

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