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.

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

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.

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.

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!