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Room Doubling

Age 7 to 11
Challenge Level Yellow starYellow star
  • Problem
  • Student Solutions
  • Teachers' Resources

Why do this problem?

This is an excellent investigation because it is suitable for learners of all ages (including adults!). It is similar to some ideas that have come from using Cuisenaire rods, in particular the red block [2].

Possible approach

Perhaps you could relate to any experiences that the pupils have had with alterations like these in their own homes. It is valuable to let most pupils have access to doing it practically as well as just on squared paper as people think in so many different ways. Encourage all kinds of recording - some pupils may get into using symbols to represent the rooms.

Key questions

Tell me how you have thought about the way you can get answers.

Possible extension

Children could search for patterns by going to much larger houses with $10$ to $15$ rooms across while still two wide. They could have a look at thoes houses which are symmetric and/or those that are a reflection in design to others. Try here for more!

Possible support

Give pupils copies of the pictures and maybe make some models out of Lego.


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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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