ODD ONE OUT
23 20 15 25
Which number is the odd one out?
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Most people’s immediate response to ‘Odd one out’ is that 20 is ‘odd’ because it is ‘even’ (pun intended!). A moment’s reflection can open up a seemingly closed problem like this to some creative thinking.
Can we find a reason for each of these numbers being singled out as the odd one?
And how many different reasons for each number?
Here are some starters for 25. It is the only number in the set that:
is a perfect square number
is a factor of 125
has an odd number of factors
has digits that add to seven
Thinking creatively can engage learners in mathematical reasoning with the different reasons given acting as springboards for further inquiry:
Can you find some other numbers with exactly three factors?
How many numbers under 100 have digits that add to 7?
Creativity as a key to deeper learning?
One popular argument for encouraging creativity is that we live in times of rapid change and being creative helps learners cope with such changes. Over and above this the work of the psychologist Ellen Langer suggests that creativity can have other payoffs.
Langer has extensively researched what she calls the conditionality of knowledge: that what we hold to be ‘true’ relies on certain conditions (in this case 20 is the odd one out under the conditions of odd and even numbers).
Langer’s research on Mindful Learning shows that treating knowledge as ‘conditional’ rather than ‘absolute’ not only leads to creativity but also to deeper learning of the knowledge being explored. In other words, justifying a range of answers may help kids become mathematically smarter.
I discuss these ideas more fully in my new book ‘Transforming Primary Mathematics’