Enrichment in Mathematics – Handling Data
True, false or iffy?
Teachers notes
This task really lends itself to stimulating discussion and debate and is perfect for working
in pairs and groups.
The classification of statements being true, false or iffy is far from new, however the
justification of those choices based on these cards stimulates lively discussion,
disagreements and challenge as they cover commonly held misconceptions about
probability.
You might want to use this during the main body of the lesson rather than as a starter to
get the most out of the discussion opportunities. Perhaps introduce the task by using
mini-whiteboards, asking questions such as, ‘estimate the probability that you will be hit
by lightning this afternoon; get a 4 with the roll of a die; sleep tonight’ etc.
Give each pair a set of cards. Explain that these cards are intended to reveal some
common misconception about probability. Ask them to take each card in turn and decide
whether or not it is true, false or iffy and write down reasons to support their decision.
To pull the class into discussion, as pairs one at a time to hold up one card that they are
confident it true and ask them to reason why this is the case. The rest of the class is then
given the opportunity to ask questions of the pair if they disagree.
Key questions
Can you give me a different example where this might be the case?
Would this really be the case in the everyday world?
Give pupils equipment to trial is appropriate.
Solution
Card A – False.
Outcomes are equally likely.
Card B – True.
There are two ways of rolling a total of 3, but only one way of rolling a
total of 2.
Card C – False
Outcomes are equally likely.
Card D – False.
There are four equally likely outcomes, HH, HT, TH, TT.
Card E – False.
The probabilities will change depending on the quality of the opposition
the team are facing.
Card F – False.
This statement would be correct if we replaced the word ‘certain’ with
the words ‘most likely’. Probabilities do not say for certain what will happen, they only
give an indication of the likelihood.
Card G – False.
Otherwise known as ‘gamblers fallacy’! The statement indicates that
the coin has some sort of memory thus compensates from previous throws.
Card H – True.
There are more learners than there are days of the week.
Card I – False.
The bearing on one child has no impact on the gender of the next
child.
Card J – False.
Pupils will argue that if the probability of one head in two coin tosses is
one half then the probability of n heads in 2n coins is also one half. In reality the
probability of three out of six coin tosses being heads is 20/64 or just under 1/3.
Variations on a theme
Ask pupils to make up a similar set of cards for another class or topic area.
Copy the cards onto A4 card and look at them one at a time, asking pupils to stand in
true, false or iffy corners of the room to show their response.
Worcestershire Numeracy Team
Enrichment Activities
Enrichment in Mathematics – Handling Data
Card A
Card B
When you roll a fair six sided dice it is
harder to roll a six than an four
Scoring a total of thee with two dice is
twice as likely as scoring a total of two.
Card C
Card D
In a lottery the six numbers
3, 12, 26, 37, 44, 45 are more likely to
come up than the six numbers
1, 2, 3, 4, 5, 6.
When two coins are tossed there are
three possible outcomes:
Two heads, one head or no head.
The probability of two heads is
1 .
3
Card E
Card F
There are three outcomes in a football
match : win, lose or draw. The
probability of winning is therefore
In a ‘true or false?’ quiz with ten
questions, you are certain to get five
right if you just guess.
1
3
Card G
Card H
If you toss a fair coin five times and get
five heads in a row, the next time you
toss the coin it is more likely to show a
tail than a head.
In a group of ten learners, the
probability of two of the learners being
born on the same day of the week is 1.
Card I
Card J
If a family has already got four boys,
The probability of getting exactly three
then the next baby is more likely to be a heads in six coin tosses is 1
girl than a boy.
2
Worcestershire Numeracy Team
Enrichment Activities
Enrichment in Mathematics – Handling Data
Worcestershire Numeracy Team
Enrichment Activities