You may also like

problem icon

Rectangles with Dominoes

Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?

problem icon

Chain of Changes

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

problem icon

Sorting Shapes

This activity challenges you to make collections of shapes. Can you give your collection a name?

Making Shapes

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Why do this problem?

This problem links shape with factors and multiples, and is a great way to introduce children to the idea of visualising numbers - in this case as rectangles.

Possible approach

You might like to use the interactivity on an interactive whiteboard or with a projector initially and ask for a volunteer to make one rectangle to begin with. Once the group has grasped the idea of where counters can be placed, they can explore in pairs. Allowing them time to investigate in this way is very valuable, but you might like to bring the whole class together at various stages in order to discuss what they have found so far.
 
Opportunities for use of language associated with shape and space are plentiful, and children will find it necessary to talk about the properties of rectangles. They can be encouraged to think about whether a square is a rectangle or not and will begin to mathematically justify opinions. The problem allows children to explore factors and multiples in a tactile way, and you can encourage them to talk about whether $2\times3$ is the same as $3\times2$.
 
Counters on a grid are equally useful for investigating this problem if you are not using the interactivity.

Key questions

How about starting with a small number of counters and working up?
How will you know that you haven't missed any out?

Possible extension

Introduce more counters for children to continue the investigation.

Possible support

Using $2$cm squared paper and counters will help children to access this task.

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.
Copyright © 1997 - 2012. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.