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Age 7 to 11
Challenge Level
Amy's Dominoes
You may like to have a look at Domino Sets before trying this problem.
Amy has a box containing ordinary domino pieces but she does not think it is a complete set.
She has 24 dominoes in her box and there are 125 spots on them altogether.
Which of her domino pieces are missing? How do you know?
If you do not have any dominoes, you might find our interactive Dominoes Environment useful.
Why do this problem?
This problem requires learners to understand the numbering system on dominoes and use this to solve a problem. Learners will need to use addition, subtraction and multiplication as well as logical reasoning.
Possible approach
If you have an interactive whiteboard, you may find our Dominoes Environment useful for this problem.
You could start by giving the whole group sets of dominoes to sort out in pairs or alternatively, if the children are already familiar with dominoes ask questions such as "How many domino pieces have four spots on them altogether?" and "How many domino pieces have five spots on them?"
Children could then work in pairs on the actual problem with a real set of dominoes or use the dominoes on this sheet which will need to be cut up.
In a plenary, children could discuss not only the solution, but what information they needed to have to work it out and what calculations they had to do along the way. There will be several different approaches which will not only help other children but will also inform you about their thinking.
Key questions
How many dominoes are there in a complete set? So how many are missing in Amy's set?
How many lots of six spots are there in a set of dominoes? How many spots is that altogether?
How many spots are there altogether in a complete set of dominoes?
Possible support
Children could explore the structure of a set of dominoes first, which is encouraged in the task Domino Sets.
Possible extension
You could ask some follow-up questions, such as: If Amy had not 104, but 140 spots could you have found a solution? Is there just one possible answer or more? What was the fewest number of spots that could have been on the dominoes if four of them were missing? What could have been the greatest number of spots on a set that was missing four pieces?
NRICH is part of the family of activities in the Millennium Mathematics Project.