Copyright © University of Cambridge. All rights reserved.
'Largest Even' printed from http://nrich.maths.org/
Why do this problem?
The idea of this problem
is to encourage children to work together to develop a method of finding a solution which will always work and perhaps one that is the most efficient or quickest. This challenge will also help to reinforce understanding of odd and even numbers.
You could introduce the challenge by inviting one child to choose a card from the digit cards $1$ to $9$, perhaps without looking so it is a random choice. You could then ask another child to choose a card, again without looking. What is the largest two-digit even number that can be made from the two cards? You could try this a few times so that the children have a chance
to explain when it is impossible to make an even number.
Then tweak the task. This time, the second person to choose can decide which digit they would like in order to make the largest possible two-digit number. You could suggest that in fact a pair of children chooses the card so that they have a chance to talk to each other about the best choice. You could invite others to comment on their choice. (You could use the
interactivity at this point instead.)
Ask pairs to have a go at the challenge for themselves with a set of digit cards per pair. Explain that you'd like them to come up with a method that will always work so they can identify the best card to choose as quickly as possible.
After a suitable length of time, bring the whole group together and share their strategies. You could test out a few of them and perhaps a consensus can be reached about the 'best' method to use. (This may not be possible but having the discussion is valuable. In this case 'best' might be quickest but perhaps the children may want to clarify that for themselves.)
How would they change their method if the task was to make the highest two-digit odd number?
What do you know about even numbers?
What do you know about the units digit of even numbers?
Where could the digit on that first card go - in the units or tens? Why?
How can we make a large number?
How do we know that's the biggest even number we can make?
Challenge children to extend the strategy for three-digit numbers. They could pick two numbers out of the pack of digit cards at random, then try to make the largest possible three-digit even number by selecting one of the remaining cards as well. Another possibility would be to aim for multiples of $5$ rather than even numbers. Some learners might want to investigate what
happens if $0$ is included as well.
Some children might benefit from having equipment to help them check whether a number is even, for example multilink cubes or counters that can be put in pairs.