don steward
mathematics teaching 10 ~ 16

Saturday, 26 August 2017

rounding to different amounts

usually rounding to a finer amount (5p or 5c) will provide a more accurate estimate to the true cost than rounding to e.g. the nearest 10p or 10c
but not always...

for three addends:
rounding to the nearest 5p is more accurate in 123 cases
rounding to the nearest 10p is more accurate in 28 cases
and for the remaining 69 cases, both methods of rounding are equally accurate

for four addends:
nearest 5p = 417 cases
nearest 10p = 105 cases
equally accurate = 193 cases

for five addends:
nearest 5p = 1210 cases
nearest 10p = 321 cases
equally accurate = 471 cases

[thanks to the National Mathematics Project team (published in the UK in 1989, Eon Harper et al) for these solutions and the suggestion for this task]

Tuesday, 22 August 2017

multiplication of big numbers

no calculators
coping with the noughts

thanks to Jana for pointing out that there aren't enough zeroes in the question

there should be four more...

Thursday, 17 August 2017

quadrilaterals on a 6 by 6 dotty grid

quadrilaterals on a 3 by 3 dotty grid

almost an antique
part of the South Nottinghamshire Project ('Journey into Maths')
by Alan Bell, David Rooke and Alan Wigley
published by Blackie in 1978
the teacher's guide (1) claims there are a total of 94 different positions
counting translations, reflections or rotations

an intention might be that students don't count transformations of each shape (initially anyway)

quadrilaterals on a 5 by 5 dotty grid

Wednesday, 16 August 2017

power sums

a reworked resource:

 a development of an idea suggested by Martin Wilson, Harrogate
 (replacement - the original had errors in Q1 and Q6 - my apologies)

Sunday, 6 August 2017

shape fitting

the intention of this task is that students progressively fit shapes together
to form a rectangle at each stage

a while ago, Edward de Bono devised similar shape puzzles to encourage a view that when problem solving, sometimes you need to dismantle what you have done already and start again

there is a powerpoint that reveals the shapes, one at a time

alternatively two students could work together, revealing each new shape (in a column) one at a time (after the first two)
holding another piece of paper over the rest

as this task is/was envisaged, it is important that the shapes are encountered one at a time

students will need some kind of squared paper