Rectangles with dominoes
Can you make a rectangle with just 2 dominoes? What about 3, 4, 5,
6, 7...?
Age
5 to 7
Challenge level
Problem
Can you make a rectangle with just 2 dominoes?
What about 3, 4, 5, 6, 7 ...?
Here's a rectangle made with 6 dominoes to get you
started:
Image
Getting Started
If you don't have any dominoes to have a go with, you might like to
use our interactive
Domino Environment.
Student Solutions
Sam, Ben from Matthew Arnold School, and Rohaan from Long Bay Primary School in New Zealand all noticed that you can make a rectangle using any number of dominoes. Here is what Ben said:
It is possible to make a rectangle with any number of dominoes. You simply lay them end to end so that the resulting rectangle gets longer and longer.
Of course, there are lots of more interesting ways to make rectangles; why not try to find some?
Teachers' Resources
Why do this problem?
This activity is good for introducing pupils to the exploration
of spatial mathematics. It allows the pupils some degree of freedom
as to how they approach it and record their findings.
Possible approach
Using something bigger than dominoes like giant lego (or just
large dominoes) and initially introducing the challenge altogether
will help learners 'get into' the problem. Pupils can then be left
to find other rectangles, perhaps in pairs.
If you have an interactive whiteboard, you may find our
Dominoes Environment useful for this problem.
Key questions
Tell me about the differences between this one and that one.
(Having chosen two that have the same outline.)
Are there any other ways you could put those dominoes together
to make a rectangle?
Possible extension
Allow the pupils to ask "I wonder what would happen if we
...?". For example they could place a domino on its edge.
Possible support
Having access to dominoes, or as many congruent cuboids as
possible, will help.