Venn diagrams are not taught well anywhere.

With little effort, these diagrams can be brought to life with beauty and by going beyond that little 3 circle Venn diagram. At the very least a teacher should end a lesson on the three circle Venn diagram with a question: "I wonder if this is possible with four circles?"

But we can go much, much further... and the puzzle sheets created below are designed to get you there 😉

"Venn for Polygons" is a highly engaging puzzle that gives students ages 8+ practice with properties of polygons. All edges are the same length unless they are obviously different lengths. Thanks to student Calvin Chan for finding a shape that was a little wonky 😉

"Mishap at Venn Zoo" is a full presentation of a polyomino variant that includes rotational symmetry.  This is good for students as young as 8 or 9.

"ToothPick Polygons" has got a tough second question, but the first part is as easy as "Mishap at Venn Zoo."

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Mishap at Venn Zoo

Find where all the animals go based on identifying the presence or absence of mirror and rotational symmetry, height, and size. Unfortunately the zookeeper might have made a mistake!

Download pdf here.

This is our zoo. There are 31 cages… 32 if you include the outside region. It is made up of five shapes in different colors. These colors will be linked to 5 questions we are going to ask about each animal.
These are the 32 animals that the zookeeper has mail-ordered to fill the cages. The expectation is that one animal will fit in each cage.
Let’s look at this Liopleurodon. Where does it go? The first question is about how many holes it has.
No – Liopleurodon does not have exactly one hole.
Does it have rotational symmetry?
Yes – it could be rotated 180 degrees around its centre and would look the same.
Has it got mirror symmetry. Not this way, but we need to check all the options…
Has it got mirror symmetry. Not this way, but we need to check all the options…
Has it got mirror symmetry. Not this way, but we need to check all the options…
No – Liopleurodon does not have mirror symmetry.

Is its size exactly 12 squares?

No – it is much bigger than 12 squares.

Is it taller than it is wide?

Yes – it is 9 squares high and only 7 squares wide.

We have all the information to figure out which is Liopleurodon’s cage…

Yes – it is 9 squares high and only 7 squares wide.

We have all the information to figure out which is Liopleurodon’s cage…

So does it go in the middle?

No, this would be the cage for an animal that we answered “yes” to all the questions.

Does it go here?

This does not look better. We answered “no” to the red question: “Has exactly one hole.”

That means the cage for our creature must be outside the red loop.

Does it go here?
It is outside the red loop. Good.
It is inside the purple loop. Good.
It is outside the blue loop. Good.
It is outside the green loop. Good.
It is inside the tan loop. Good.

Looks like we’ve found the right place.

Now find out where all the animals go. You can download the puzzle-sheet above. It is the second one listed.

Steve Heller made a beautiful online adaptation of Venn Dice! Play it here. Thank you, Steve!