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What is a Carroll Diagram? - Definition & Examples

Instructor: Danielle Wilson

Danielle is a certified elementary, middle school math, and special education teacher. She has a master's degree in elementary education and special education.

Have you ever sorted blocks or toys by color or size? In math, sorting things like numbers or shapes helps us to see the relationships between them and to better understand them. In this lesson, we will learn about a really popular way to sort in math.

What Is the Carroll Diagram?

Math is the study of numbers, quantity, and shapes. The best way to understand them is by looking at how they relate to one another. When we can identify the similarities and differences, it becomes easier to work with them. The purpose of the Carroll diagram is to help organize how we sort different math concepts on a visual graph. A Carroll diagram is an easy way to sort objects, numbers, or concepts by two different categories using yes/no situations.

Example of a Carroll Diagram
Carroll Diagram

Carroll Diagram History

Did you know that the man who created the Carroll diagram also wrote Alice In Wonderland? It's true! Lewis Carroll was not only a writer but he was a really smart mathematician. The Carroll diagram was originally known as the 'Lewis' Squares'. Lewis Carroll liked to organize information and create logic games. He used the diagrams to organize information so it was easier to categorize.

Lewis Carroll
Lewis Carroll

How Does It Work?

The easiest way to understand a Carroll diagram is to first use it with something you're familiar with. Let's use a Carroll diagram to sort fruits and vegetables. There are several different ways we could choose to sort our fruits and vegetables; color, size, has seeds, etc. For this Carroll diagram, we are going to sort by color; more specifically, by the color red.

We will sort our objects that are red and separate them from objects that are blue, yellow, or any other color. We are also going to sort the objects by if they are a vegetable or not. So, we can sort a group of objects into the following groups:

1. Red, Is A Vegetable

2. Red, Not A Vegetable

3. Not Red, Is A Vegetable

4. Not Red, Not A Vegetable

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