Wag worms
Problem
When intergalactic Wag Worms are born they look just like a cube.
Each year they grow another cube in any direction (except on their faces of course). So a Wag Worm in its second year might look like any of these.
The next year it grows another cube onto its second cube (not its face cube). So one shape a Worm in its third year can be is this:
Find all the shapes that a Wag Worm in its third year can be.
Getting Started
Do you have a system or way of getting more solutions?
How will you know you have found them all?
How would it help to start with the two-year-old wag worms?
Student Solutions
Many people produced good results and it was interesting to see the different ways the problem was interpreted.
Did you decide that you can add another cube onto one that you have already added to or not? So, in the following, can the latest blue cube go in the places pictured in the 2nd and 3rd diagrams?
S Cowper, a teacher, sent in the following:
My year 6 class from Laygate Community school have spent all morning trying figure out the solution to 'Wag Worms'
Here are the pictures showing their work:
Thank you these pictures showing your excellent work and thinking of doing a check for duplicates.
Teachers' Resources
Wag Worms
When intergalactic Wag Worms are born they look just like a cube.
Each year they grow another cube in any direction (except on their faces of course). So a Wag Worm in its second year might look like any of these.
The next year it grows another cube onto its second cube (not its face cube). So one shape a Worm in its third year can be is this:
Find all the shapes that a Wag Worm in its third year can be.
Why do this problem?
Possible approach
Key questions
Possible extension
