median
don steward
mathematics teaching 10 ~ 16

Friday, 12 February 2016

nth term sums

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

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]






Monday, 8 February 2016

decimal addition

another attempt to suggest a lesson with sections involving
  • teaching or reviewing a skill
  • practice of that skill in tasks that involve generalisation and possibly proof
students can be taught to make the first digits up to 9 and then the last one to 10 (unless it's zero)

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:
  • teaching or reviewing a skill
  • practice of that skill in tasks that involve generalisation (in this case an nth term rule) and possibly proof
the investigative equivalent fraction task was introduced to me by Ken Garner






















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)

largest product from 10

this task was introduced to me by Mike Ollerton



number line

varying the gap