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Trig Ratios Puzzle

I’m here today to share a trig ratios puzzle with you.

I’m currently using part of my summer to create some activities for my Pre-Calculus classes for this upcoming year. Last year, I felt like I definitely spent more of my time creating things for my Algebra 2 classes than my Pre-Calc classes. This was probably because I had 4 sections of Algebra 2 and only 2 sections of Pre-Calc. This next year is looking like it will bring 3 sections of each. This has me super excited, and I’m especially looking forward to teaching Pre-Calc to classes of which most had me for Algebra 2!

Last year, I started Pre-Calc with a review of Algebra 2. This was necessary because the teacher I replaced had retired early the year before, and many of my students did not get a full year of Algebra 2 as a result. This review was necessary, but we kinda ended up getting bogged down in reviewing concepts that they should have already known.  (I must admit that my Algebra 2 students this past year didn’t end up getting a full year of algebra instruction either as I ended up going on maternity leave at the beginning of May.)

For this upcoming year, I’ve decided to skip the review and jump straight into our units on trigonometry. So, I’ve been on the lookout for some great trig tasks to use with my students.

As soon as I saw this Open Middle task from Bryan Anderson, I know I needed to recreate it with moveable pieces. You could also use this for a geometry class as well!

First, I set out to recreate the table in Microsoft Publisher. I went through four or five iterations of how to label which way the table should be increasing before I found a way that was visually pleasing enough for me.

Trig Ratio Puzzle Open Middle Style Puzzle by Bryan Anderson

Next, I typed up the eight trig ratios to be printed out and placed on the template. 

Trig Ratio Puzzle Open Middle Style Puzzle by Bryan Anderson

Once I got everything typed up and printed out, I set out to solve the trig ratios puzzle by myself without a calculator or anything to write with. I’ve struggled since high school with doing trig in my head, so this was definitely a challenge for me.

I can do trig problems just fine if I draw out the triangles and label the sides, but picturing the triangles in my head and working out the answers without a pen or pencil in my hand is a real stretch for me. But, I persevered and was able to figure it out myself.

Trig Ratio Puzzle Open Middle Style Puzzle by Bryan Anderson

I did arrive at a different answer than the solution provided on Open Middle. So, do be aware that this trig ratios puzzle has multiple solutions.

Trig Ratio Puzzle Open Middle Style Puzzle by Bryan Anderson

I look forward to watching my students tackle this trig ratios puzzle. They, of course, won’t be restricted from using a calculator or writing utensil. I’ve already got a copy printed, laminated, and cut for each group so they are ready to go when school starts back!


drawing of laminator machine with text "laminating recommendations"

A laminator is a MUST-HAVE for me as a math teacher! I spent my first six years as a teacher at a school with a broken laminator, so I had to find a way to laminate things myself.

I’ve had several laminators over the years. I currently use a Scotch laminator at home and a Swingline laminator at school.

I highly recommend splurging a bit on the actual laminator and buying the cheapest laminating pouches you can find!

Puzzle Solutions

I intentionally do not make answers to the printable math puzzles I share on my blog available online because I strive to provide learning experiences for my students that are non-google-able. I would like other teachers to be able to use these puzzles in their classrooms as well without the solutions being easily found on the Internet.

However, I do recognize that us teachers are busy people and sometimes need to quickly reference an answer key to see if a student has solved a puzzle correctly or to see if they have interpreted the instructions properly.

If you are a teacher who is using these puzzles in your classroom, please send me an email at with information about what you teach and where you teach. I will be happy to forward an answer key to you.

More Activities for Teaching Trig Functions


Sunday 23rd of June 2019

Congratulations on becoming a mother! Thank you for all of your activities over the years. You got me started on ISNs years ago! I don't remember who I got this idea from, but a calculus teacher would do a series of "Algebra Bootcamp" lessons at the beginning of each unit to review just the algebra that was needed in that unit. Thought that might work in your pre-calc class as you think about how to use your time most effectively.

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