Missing Middles
Problem
Missing Middles printable sheet
Here are eight sets of dominoes. Each set should have three dominoes that make a sequence.
Which domino would go in the middle of each set to complete the sequence?
How do you know?
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Getting Started
What numbers are at the top of the dominoes?
What number could come between them? Why?
What numbers are at the bottom of the three dominoes?
What number could come between them? Why?
Student Solutions
Well done to everybody who had a go at this activity.
Kevin and Aurelius from Kingswood College School in Australia sent in this picture and explanation:
A We chose 4/4 because the numbers are the 2x table.
B We chose 2/3 because the top number 2 comes between 1 and 3 and 3 comes between 2 and 4.
C We chose 3 up the top because it comes between 2 and 4. We chose 5 down the bottom because it comes between 6 and 4.
D We chose 1 because all the top numbers are the same and chose 4 because the bottom numbers are the 2 x table.
E The top numbers are the 1x table going down so we chose 2. The bottom numbers are adding 1 each time.
F The top numbers are going down in 1s. The bottom numbers are going down in 1s.
G We chose 3 because it comes between the 4 and the 2. We chose 5 because it comes between 6 and 4. The numbers are going down in 1s.
H We chose 2 because the top numbers are going down in 1s and we chose 4 because it the bottom numbers are going down by 2s.
Well done to both of you for sending in these very clear explanations!
I wonder if there are any other possible solutions? If you've found anything different, please let us know by emailing us with your ideas.
Teachers' Resources
Why do this problem?
This problem uses the idea of number sequences in a very tangible form. Children will be challenged to recognise odd and even numbers, as well as to count fluently both backwards and forwards. They will also have opportunities to justify their answers.
Possible approach
Key questions
What numbers are at the top/bottom?
What number might come between these two? How do you know?
Possible support
The activities Next Domino and Domino Sequences would be good precursors to this task as they invite learners to extend sequences as opposed to completing the middle of a sequence. Having a set of real dominoes that can be manipulated makes the problem less abstract. You could encourage learners to start with just the 'tops' of the dominoes, then look at the 'bottoms'. Children will benefit from saying the numbers in the sequence out loud to reinforce the familiar counting patterns.
Possible extension
Children could work in pairs inventing domino sequences of their own. A set of 9spot dominoes would be very useful so that longer and more complicated sequences can be made. Always expect the children to be able to justify the dominoes they have chosen. A set of 9spot dominoes can be found on our printable resources page.