When teaching, I try (with mixed results) to keep my students interested in the topic at hand.  Sometimes I motivate them by giving them a project where they discover a mathematical relationship with minimal help and minimal direct instruction from me.  Or a project that demonstrates a deep connection between the real world and the mathematics we use to describe it!

However, sometimes the topic is not all that inherently interesting, or students just need a great deal of practice to really hone a skill.  For example, the skill of solving quadratic equations.  At this point in the course, I’ve already taught them how to solve quadratic equations by factoring, by working backwards, and by the quadratic formula.  To liven things up a bit, I’ll next challenge my students to complete this quadratic equations puzzle (partly pictured at right).

The way it works:

1. Cut up the triangles (in the picture and linked document, they are already mixed, not in their correct final locations).
2. Give each student (or pair of students) a batch of puzzle pieces.
3. Students match each quadratic equation edge to another edge that contains its zeros.  They can tape them together as they go.
4. When complete, it makes a large hexagon, like this:

For extra fun, do the puzzle yourself first, then write a secret message on the backs of the pieces.  Cut it back up into its component pieces, and make double-sided copies so each tile has a letter on its back.  Only students who complete the puzzle correctly will be able to read your secret message!

For example, I have written [one letter to a puzzle piece]:  “BRINGTHISTOMRYFORACOOKIE” (Bring this to Mr. Y. for a cookie!), and then I had cookies available for the students as they finished.  When the first student finishes, brings it up and gets a cookie, the other students sit up and start working harder!

Here’s another puzzle I designed as review of Algebra1-style equations (for my engineering students, to gauge their math strengths and weaknesses in the first week of class).  It could also be used to wrap up an Algebra 1 course, or to refresh students’ memories during the first weeks of Algebra 2.

These puzzles are made with Formulator Tarsia software, which is available for free download.  Developing these puzzles is a bit labor-intensive, in that it takes a good 1.5 – 3 hours to create a good puzzle, including the secret message.

Puzzles (and food) create a nice change of pace in the classroom, every now and then.  I encourage you, gentle reader, to use either of the two I have created, and to download the software to create more yourself!  Happy puzzling!

Filed under math, teaching

### 12 responses to “Puzzling Out Some Quadratics”

1. What a great idea! I have been looking for ways to make vocabulary games for art class that go beyond the standard crossword and word find puzzles. You’ve got my tumblers turning now….

2. nyates314

Note: edited to remove a non-working link to the software, then again to place an updated working link once Hermitech / Formulator was back up and running.

3. Roy

Any chance of your posting (or e-mailing) a larger version of the solution image? Thanks!

• nyates314

I seem to have lost the solution page to the quadratics puzzle (each year I need to build the puzzle myself to check). But I do have the solution to the linear equations hexagonal puzzle, which I’ve just emailed you.

4. Misty

This looks great. Can you give me an estimate of how long a student might take with this(your average student)? Do you find working in pairs is better? Can you email me a solution to the quadratic and the Alg I puzzle you refer to?
thanks

• nyates314

Students do take varying amounts of time with this. I’d say on average they take (and I give them) two ninety-minute class periods, minus time for warm-up activities, etc. So about 150 minutes. Some go quicker, and I have some extra credit options available to them when they finish. Others work very slowly and need to take it home and finish for homework.

One way to save time is cutting up the pieces beforehand. While I usually let students do this sort of thing, I have found that some students can take forever just cutting out the pieces, before they get to any of the real math involved.

I don’t have them work in pairs, because I want each student to solve every quadratic equation and get the volume of practice with the q. formula that requires. With pairs, my concern would be one student who works very slowly and the other who works very quickly; the first student would get very little practice while the second student completed most of the puzzle. But, if you have students you know would work well in partners, of relatively matched pace, it might help to have partners who can check each others’ work (it’s easy to make an arithmetic error while doing the q formula, and get a totally wrong answer).

I’ve emailed a solution to the Alg I puzzle (mostly linear equations, with a few nonlinears thrown in). The quadratics puzzle I seem to have lost the solution file. But, we’re working on that one right now in Algebra II, so when a student finishes I’ll try to remember to take a picture and send that along.

5. Shane Friedman

Hello can you post the solution to the quadratic equation puzzle?

• nyates314

Sorry, see previous comments. If you create a solution, I’d be happy to post it here!

6. IGUANA LEFTWICH

Could you email me the solutions for the Algebra I style equations?