Two By One
An activity making various patterns with 2 x 1 rectangular tiles.
Age
7 to 11
Challenge level
Problem
In Tom's house there are tiles on the floor. Each tile is twice as long as it is wide so they each look like this:
Image
How do you think they fit together to cover the floor? Use squared paper to help you to draw your pattern.
Can you find any other patterns?
How many different patterns can you find?
Getting Started
You may find dominoes and/or squared papers useful.
Are you sure your patterns are different?
What shapes will you need at the edges of the floor?
Have you chosen a particular size floor?
Are you sure your patterns are different?
What shapes will you need at the edges of the floor?
Have you chosen a particular size floor?
Student Solutions
There are lots of answers to this question, depending on what patterns you look for, and how big you think the room is.
Have a try for yourself, and if you discover anything interesting, let us know by emailing primary.nrich@maths.org.
Please don't worry that your solution is not "complete" - we'd like to hear about anything you have tried.
Teachers - you might like to send in a summary of your children's work.
Teachers' Resources
Two by One
In Tom's house there are tiles on the floor. Each tile is twice as long as it is wide so they each look like this:
Image
How do you think they fit together to cover the floor? Use squared paper to help you to draw your pattern.
Can you find any other patterns?
How many different patterns can you find?
Why do this problem?
This open-ended activity may well appeal to those children who find number work difficult. It will allow all children to work at their own level and encourage creativity, and this can be a good assessment opportunity for you. Squared paper will be useful.Key questions
Are you sure your patterns are different?
What shapes will you need at the edges of the floor?
Have you chosen a particular size floor?