don steward
mathematics teaching 10 ~ 16

Saturday, 29 April 2017

dividing a fraction by a whole number

a powerpoint is here

four consecutive numbers

developing an idea from the Y6 'mastery' resources at the NCETM site

Simpson's paradox (iii)

some near realistic situations where it could be important to consider Simpson's 'paradox'

who is the better batter overall?
who was the better batter in each of the years being considered?

research seems to show that overall there is a better survival rate without a drug than with the drug

however, splitting the cohorts into those who began treatment in poorer health and those who began treatment in good health, a different view emerges

Simpson's paradox (ii)

playing around with equivalent fractions
seeing when they start to produce a 'Simpson' result

Simpson's paradox (i)

to appreciate the peculiarity of the result, students might need to look at some examples that show it is not generally true
results are usually as you might expect them to be...
but sometimes they are not....

a powerpoint

two reds unit fraction

combined events, without replacement

two consecutive numbers of red and white counters

two reds fair game

it might be interesting to try to devise other games where the probability of obtaining two red balls (in two picks, without replacement) is 1/2

how many red balls and how many yellow balls would you need?

there is one easy to obtain answer and then lots of difficult ones... that would be hard to find
students could be asked to show that the numbers below do provide for a fair game with P(R,R) = 1/2

two dice experiments

considering whether a 'game' is fair or not
using a sample space diagram

the powerpoint

theoretical outcomes

NRich have developed simulations for two of Geoff Giles' DIME material probability experiments (no longer available unfortunately)

trials can be simulated and then compared with a theoretical analysis

I think a theoretical consideration is difficult
a teacher could present an argument and then see if students can recreate it

the powerpoint