Venn Diagram Puzzles – Algebra

I recently added some Venn Diagram puzzles I’ve made with some teachers this year for Geometry in this post. I wanted to add some Algebra ones here! Though most were created with certain answers in mind, we welcome creative ideas from students. So there may be more than one answer!

Some are good for vocab.

Some involve solving for x first.

Or looking at graphs.

Some are focused on what process you might prefer to use…

We made some “challenging” ones that may not always have answers for every question mark.

I’d love to hear what you think or how it goes if you try one with your students. Feel free to share any you make!

Venn Diagram Puzzles – Geometry

Back in 2020, I wrote about some Venn Diagram debate questions that I had made for student discussion. I’ve finally had the time and space this year to play with this more and make more!

I’ve been fortunate to work with many teachers across the US (and Canada) in consulting role, and sometimes I’ve worked with teachers who wanted to create some Venn Diagram questions. Below are a few of the ones we came up with for Geometry topics.

Some of these are open-ended, with more than one possible answer. Some might only have one. They were great to use as a warm-up thinking problem (maybe have students discuss with a partner) at the start of class. They were also great as part of a problem set (for class or homework), to give students a challenge to think more deeply about vocabulary and categories…and to be creative!

The task is usually to “fill in the blank” where you see a big red question mark.

Sometimes we had more than one red question mark.

Some were much more open to interpretation, which led to rich discussions.

A Fraction Riddle

If you know me, you know I LOVE puzzles and riddles. I’m a big escape room enthusiast. So I was delighted to find the following riddle in a book I was reading, which the author attributes the the mathematician Tartaglia! See if you can solve it! I left a hint…and then the solution.

THE RIDDLE: A man dies, leaving 17 camels to be divided among his three heirs, in the proportions 1/2, 1/3 and 1/9. How can this be done?

I had a lot of fun with this, trying to think of creative solutions. Just to be clear: we are not hurting any camels. That is, none of them are being cut up into fractional pieces.

---

As a HINT:

*SPOILER ALERT*

Something I noticed after playing around was that the sum of the fractions was almost, but not quite, equal to one whole. That is, 1/2 + 1/3 + 1/9 can be thought of as 9/18 + 6/18 + 2/18, which is equal to 17/18…not quite 1.

---

THE SOLUTION:

*SPOILER ALERT*

Are you sure you want to know it?

I’ll start from the hint…You may have noticed the fractions added up to 17 out of 18, and we have 17 camels…so imagine we borrow a camel for a moment. We now have 18 camels. We can then give away 1/2 (9 camels), 1/3 (6 camels), and 1/9 (2 camels) to the heirs. That’s a total of 17 camels. Every heir got their fraction, and we still have the borrowed camel that we can now return.