Domino pick
Problem
They pick a domino in turn.
Erik can only choose dominoes which have an odd number of spots in total.
Sanjay chooses the dominoes which have an even number of spots.
Now they change the rules. They lay out the dominoes again.
Erik can only choose dominoes where the total number of dots is a multiple of $3$.
Sanjay chooses the dominoes where the total number of dots is not a multiple of $3$.
Who is able to pick up the most dominoes now? Is this fair? Explain your answer.
Getting Started
How many dominoes would they have each if the game was fair?
Student Solutions
Well done Annie (who didn't give her school) and Rukmini from Dowanhill Primary who sent well explained solutions. Rukmini says:
The totals which were odd were: 1, 3, 3, and 5. There were 4 odd-total dominoes. Erik can only choose these 4 dominoes.In the next game Erik can only choose a multiple of 3, which are: 6, 3 and 3. So Erik can choose 3 dominoes.
Children from WHS pointed out that it cannot be fair because there are only 9 dominoes and this does not divide equally by two. A very good point, well done.
Teachers' Resources
Domino Pick
Erik can only choose dominoes which have an odd number of spots in total.
Sanjay chooses the dominoes which have an even number of spots.
Now they change the rules. They lay out the dominoes again.
Erik can only choose dominoes where the total number of dots is a multiple of $3$.
Sanjay chooses the dominoes where the total number of dots is not a multiple of $3$.
Who is able to pick up the most dominoes now? Is this fair? Explain your answer.
Why do this problem?
Possible approach
You could introduce this problem by setting up a similar activity with you 'against' the class, using large dominoes or dominoes on the interactive whiteboard. Set criteria that are deliberately biased towards you, such as you can collect all the dominoes which have a total of four or less, the class can choose those which have totals of five or more. If you play a second time, will the class be able to win? Why or why not?
Children could work in pairs on the first part of the problem, recording their ideas on mini-whiteboards, for example. Then it would be useful to bring the whole group together, perhaps on the carpet with some large dominoes, to talk about how they approached the task. Invite a pair to explain what they did, using the large dominoes. Draw attention to those learners who give sound reasons for the fairness of the activity, based on whether or not they each have the same number of dominoes. When children try the second part of the problem, encourage them to articulate their explanations in a similar way.