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# Carroll Diagram

## What is a Carroll diagram?

A Carroll diagram looks like a table and is a way to sort data, such as a group of shapes, objects or numbers, based on given properties or traits in a yes/no manner. Carroll diagrams are named after the famous mathematician and authour Lewis Carroll, who wrote 'Alice in Wonderland'.

A Carroll diagram looks like a table and can, in its simplest form, allow people to sort data by just one attribute. For example:

However, the most familiar form of Carroll diagram allows data to be sorted by two attributes as shown below.

## How does a Carroll diagram work?

Let's have a look at an example. In the example below, the number 9 has to go in the top left box as it is both in the 3 times table and is also odd. The number 13 has to go in the top right as, although it is odd like 9, it is not in the 3 times table. If we look at the bottom row, the number 6 has to go in the bottom left box as it is both an even number and is in the 3 times table. The number 10 goes in the bottom right box as it is an even number and is not in the 3 times table.

## Ideas for using Carroll diagrams

Carroll diagrams should not just be used when looking at data handling. They are an effective vehicle for helping children understand aspects of both geometry and number.

If children, for example, are learning the 7 times table, asking them to sort a collection of numbers into a Carroll diagram, such as the one below, will help develop children's understanding of patterns within the table. Children's learning could be deepened by asking them to explain how they know particular numbers go where on the Carroll diagram. Furthermore, they could be asked to suggest other numbers that could be positioned within each part of the Carroll diagram. They could be asked to spot patterns in all the numbers within one of the sections of the Carroll diagram.

An activity like this could be put up on the classroom board as a morning task to get children thinking. Alternatively, it could be used as a Maths starter activity or within the lesson itself. A Carroll diagram could also be used as an assessment tool in the plenary.

Another useful activity is to provide a completed Carroll diagram with deliberate mistakes. Children could be asked to study the Carroll diagram and then explain which numbers, objects or shapes are in the wrong place and why. This would be a great way to develop children's reasonong skills. For example, in Science, the Carroll diagram below (with deliberate mistakes) would be a good way to deepen children's understanding of material properites.

In the example above, children could be asked to identify which objects are in the wrong place on the Carroll diagram (the table and the blocks) and then explain how they know they are incorrectly placed. They could then be required to justify where they should go instead.

## Carroll diagram KS1

In Years 1 and 2, Carroll diagrams will be used to support children in their learning of geometry. Through sorting shapes into a Carroll diagram, children's understanding of shape properties can be developed. Initially, the teacher will provide the attributes the children need to sort the shapes by.

However, as children's confidence and understanding grows, they can start to develop their own.

## Carroll diagram KS2

As children progress through KS2, they will move on to use Carroll diagrams to sort numbers. They will be asked to look for patterns within numbers. This is especially useful when learning their times tables, learning about odd and even numbers or when learning about prime numbers. Carroll diagrams will continue to be used to support the geometry parts of the National Curriculum.

A Carroll diagram can also be a useful tool when sorting sets in Science, such as the classification of animals.