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Fencing

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

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Two by One

An activity making various patterns with 2 x 1 rectangular tiles.

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Hallway Borders

A hallway floor is tiled and each tile is one foot square. Given that the number of tiles around the perimeter is EXACTLY half the total number of tiles, find the possible dimensions of the hallway.

Pebbles

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2
You could use cubes or counters for pebbles, with squared paper.
Can you make a rectangle with just one more pebble? Two more? Three more ...?
Have you checked that each rectangle is double the size of the last one?
How are you recording what you have done?
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. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.