Venn and Carroll diagrams

Hello, and welcome to Myriora Maths! How can we sort numbers into groups, when some fit in two groups at once? Venn diagrams and Carroll diagrams can help. Let's see!

A Venn diagram has overlapping circles. One circle is for even numbers. The other is for numbers bigger than ten.

Four is even, but not bigger than ten: it goes in the even circle only. Fifteen is bigger than ten, but not even. Twelve is both, so it goes in the overlap, in both circles at once. And seven is neither, so it goes outside both circles.

A Carroll diagram uses a grid instead. The columns are even and not even. The rows are bigger than ten, and not bigger than ten. Each number goes in exactly one box.

Both diagrams sort the same numbers. The overlap in the Venn diagram is the same as the even, bigger than ten box in the Carroll diagram.

Let's try one together. Where does eighteen go in the Venn diagram? Say it out loud!

Eighteen is even, and bigger than ten. So it goes in the overlap!

Here's a question that catches lots of people. Where does seven go in this Venn diagram? Some people leave it out, because it isn't in either group. But every number goes somewhere! Seven goes outside the circles, inside the box.

Your turn! In the Carroll diagram, which box does nine go in? Pick the right card. You've got twenty seconds, or pause the video. Go!

Time's up! Nine is not even, and not bigger than ten. So it's the not even, not bigger than ten box!

Quick review. A Venn diagram sorts with overlapping circles: things that fit both go in the overlap. Things that fit neither go outside. A Carroll diagram sorts with a grid: every thing goes in exactly one box. See you next time!