Domino sequences
Find the next two dominoes in these sequences.
Problem
Domino Sequences printable sheet
What might the next two dominoes be in each of these sequences?
Can you explain why you chose those two dominoes?
Getting Started
Look at the tops and the bottoms of the dominoes separately.
Student Solutions
Well done to everybody who completed these sequences. We had an anonymous solution sent in from a child in Scotland, who said:
The first solution is 1/4, 1/5. I chose these numbers because the pattern is already 0, 1, 2, 3.
The solution for the second problem is 3/1, 2/0. I chose these numbers because the pattern is going down on the top and on the bottom of the dominoes.
The solution for the third problem is 4/3, 3/3. I chose these numbers because the pattern is going down on the bottom, then on the top.
The solution for the fourth problem is 4/3, 5/2. I chose these numbers because the top is going up, but the bottom is going down.
The solution for the fifth problem is 3/0, 3/5. I chose these numbers because the pattern goes right number, left number, both, left number, right number (up one) both.
Well done for those clear explanations!
David from Tithe Barn Primary School sent us some pictures of the dominoes which complete these sequences. Abigail and Rachel from Histon and Impington Infants School have explained the patterns for the last two:
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| You are counting backwards on the bottom and forwards on the top. You would need an extra domino set, because the same dominos are used twice. |
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| There are two patterns that bounce over each other: 0/5 1/5 2/5 3/5 and 1/0 2/0 3/0 |
Thank you all for sending in your ideas!
Teachers' Resources
Domino Sequences
Domino Sequences printable sheet
What might the next two dominoes be in each of these sequences?
Can you explain why you chose those two dominoes?
Why do this problem?
This problem introduces number sequences in a simple way using a familiar resource. The sequences become increasingly complex so that there is also a challenge for learners.
Possible approach
This problem featured in the NRICH Primary webinar in June 2022 alongside Missing Middles.
Ideally, children should be familiar with dominoes through free-play and domino games before attempting more formal tasks such as pattern building.
Look at the first sequence together, perhaps using giant dominoes on the floor, or some on the interactive whiteboard (you might find our Dominoes Environment useful). Ask children to talk in pairs about what they notice and then share ideas with the whole group. Then invite them to suggest how the pattern could be continued, focusing on their explanations and justifications.
Key questions
What do you notice about the numbers at the top of the dominoes? What will the next one be?
What do you notice about the numbers at the bottom of the dominoes? What will the next one be?
Can you explain the pattern?
Possible support
Having a number line or number square available to mark off numbers might help children identify a pattern. There are some more similar domino sequences in Next Domino.
Possible extension
Handouts for teachers are available here (Word document, pdf), with the problem on one side and the notes on the other.