Carroll Diagram

Two questions at once, four boxes, and everything lands in exactly one of them. It is usually met in maths, but a Carroll diagram is at its sharpest sorting characters - because the awkward item that will not fit is always the most interesting one in the book.

Your own headings. Type any two questions across the top and down the side, not just odd and even.

The empty box is a finding. A box nobody can fill tells you something about the story.

Prints your headings and cards. The cards as a word bank to sort, or blank for the class to invent their own.

Fill it in on the whiteboard · printing a blank grid is free to try

The sheet it prints

The printable Carroll diagram - a blank two-by-two grid with room to write your own headings across the top and down the side.

What is a Carroll diagram?

A Carroll diagram is a grid that sorts things by two yes-or-no questions at the same time. One question runs across the top, the other down the side, and every item goes in exactly one of the four boxes. Nothing overlaps and nothing is left out, which is what makes it different from a Venn diagram.

They are named after Lewis Carroll - the pen name of Charles Lutwidge Dodgson, an Oxford mathematician who used diagrams like these in his work on logic, and who also wrote Alice's Adventures in Wonderland. Children reliably enjoy that fact, and it is a useful reminder that the diagram came out of logic rather than out of maths lessons.

What is the difference between a Carroll and a Venn diagram?

A Carroll diagram sorts by two yes/no questions and everything lands in exactly one of four boxes. A Venn diagram sorts by membership, so an item can sit in both circles at once. Carroll shows how a whole cast splits; Venn shows what two characters share.

	Carroll diagram	Venn diagram
Sorts by	Two yes/no questions	Membership of sets
Where things go	Exactly one box	One circle, both, or neither
Shows overlap?	No - the grid replaces it	Yes, that is the point
Best for	Clean either/or criteria	Comparisons with genuine common ground

So: if you want to know what two characters share, use a Venn diagram. If you want to know how a whole cast splits along two lines, use a Carroll. Asking a class which one a question needs is itself a good five minutes.

How do you use a Carroll diagram in reading?

Most children only ever meet them sorting numbers, which is a shame, because the interesting version is sorting a book. Pairs of questions that work:

Knows the secret / is in danger - brilliant for any mystery, and the box with one lonely name in it is usually the plot.
Changes during the book / is likeable - produces arguments immediately.
Appears in more than one chapter / speaks - good for younger classes, and quietly teaches what a minor character is.
Indoors / safe for settings - a neat way into how a writer uses place.
Fact / stated in the text for non-fiction - the box that is opinion-but-presented-as-fact is where bias lives.

From the classroom

The best thing that ever happened in one of these lessons was an empty box. We were sorting characters by tells the truth and gets what they want, and nobody could fill the honest-and-successful box. A child said "so being honest doesn't work in this book" - which is a thematic reading of a novel, arrived at from a sorting grid. Now I choose my two questions hoping for an empty box, and I never tell them it might happen.

What makes a good pair of headings?

Both headings have to be answerable yes or no, they have to be independent of each other, and at least one should be arguable. Write them before you look at the items, or children reverse-engineer questions that make the sorting easy. Four tests:

Both must be answerable yes or no. "How brave is he?" is not a Carroll question. "Is he ever brave?" is.
The two questions must be independent. If knowing one answer tells you the other, two of your boxes will be empty for a boring reason rather than an interesting one.
At least one should be arguable. A grid where every placement is obvious is a filing exercise.
Write the headings before you look at the items. Otherwise children reverse-engineer questions that make the sorting easy.

How do you make it harder or easier?

Start by supplying both headings and keeping the items concrete, so the only job is sorting. Once that is secure, give one heading and let them invent the second. The hardest version is choosing both themselves, which is much harder than it looks and is where the real thinking is - a class that can pose two good questions about a book has understood it. The shape itself is already familiar to most children from data handling in maths.

Try it now

Sort the characters in your class book by two questions - knows the secret against is in danger, say. The character who ends up somewhere surprising is your next lesson.