Trigonometry is probably my favourite thing to teach because of how hands-on the subject is. The students are more able to see the mathematics in action, plus it gives them a chance to get up and move around.

This lesson is primarily focused on the tangent ratio. In the past I have taught it as an introductory lesson to the tangent ratio, which split up the monotony of the top-down instruction, and made it more of a discovery activity. By this point students have already learned how to measure angles, a little bit about the three ratios ‘sin, cosine and tangent’, as well as how to type them into the calculator, but not yet as far as they apply to triangles.

Here is a general layout of how I conducted the lesson, you are welcome to add and change anything you want. I am also attaching both a PDF and a WORD document for you to use as you like.

Prep:

Items:

Yarn (about a ruler’s length for each student)

Tape or Glue

Stapler & Staples

Copies of the assignment (1 per pair) Clinometer Activity General (PDF) or Clinometer Activity General (DOC)

Copies of the Clinometer Resource Sheet (4 per page) Clinometer Resource Page to Print

Cardstock paper cut into size 4″ by 6″

Washers (or something with a bit of weight that can easily be tied), I had the students bring their own from home

Class set of yard sticks or tape measures

Setup: I had all of the supplies laid out in an assembly line at the front of the room. The students chose their partners and one person from each group came up and grabbed the necessary supplies.

Total Class Time: ~ 90 minutes

Introduction:

This will entirely depend on how well your students figure things out on their own. I have in the past simply handed them the assignment and the supplies and told them to “have at ‘er” up until the actual calculations (as we haven’t yet learned them yet). Some groups struggled with this and needed more guidance, but some quickly got through the instructions on the page, built their clinometers correctly, and ventured off into the school looking for something to measure.

Regardless of how autonomous you want them to be, here are a few helpful things to mention to get them started:

Do not measure the height of the object that you have selected (this will defeat the purpose) Measure the horizontal distance from yourself to the object you have selected Measure the vertical distance from the floor to your eyes Make sure you record the number displayed on your clinometer somewhere on your page (Optional) Sometimes it helps to do a sample drawing with them, showing them where to write the measurements and how to draw the triangle.

Process:

Before sending the students out to roam, be sure to give them a time to return by so that the calculations can be completed. The majority of the class is spent roaming freely in the school grounds looking for objects or items ot measure. I like to walk around and check that everyone is on task, but for the most part the students are engaged, sometimes working together in larger groups, and are sparking curiousity from other classes.

Conclusion:

Once all of the students have returned, I open a discussion about what had just happened. I use promts such as:

What was the number on the clinometer and what do you think it represents?

What was the purpose of measuring your eye-height?

What kind of triangle does your diagram have?

Finally, and depending on time, I will create a similar diagram to theirs on the board where I solve for the height using the tangent ratio.

To ensure the students have done correct calculations I will have them share with other groups that have measured the same objects, and compare their numbers. If the numbers do not match, they will have to go through their calculations together.

At the end of all of my tasks I like to use a Reflections sheet (sort of as an exit slip) that the students fill out. I will go into more depth about the importance of using reflections in a mathematics classroom in a future post. The reflection here allows you (as a teacher) to improve upon the lesson for future use, as well as check in with the students to see how well they’ve grasped the concept, and whether or not you will need to revisit it at a later time.

Issues:

Here is a list of some issues I have run into the past and how to avoid/remedy them:

Students are not measuring correctly In this case I will either instruct the entire class on how to do all of the measurements before the task begins, or as I am walking around, I will correct the individual groups as needed

Students are disruptive to other classes Because this is a social activity, it is possible that other classes will get distracted and curious. Depending on the situation, I have previously invited other classes to join the activity (teacher permitted, of course). However, it may be a better idea to simply send the students outside instead.

In some groups it is very clear that one student is doing ALL of the work After guaging my classes, I have in the past made all of the students accountable for their own sheet and their own calculations (meaning I had every single student hand in the assignment, even though it was a group activity). This is also where the reflection comes in handy, because the students who were focused on the activity and DID the work are the ones with a more thorough reflection on their learning.



Credit where credit is due:

Becuase I taught this lesson in my busiest time as a teacher, I OF COURSE scoured the internet for some inspiration and resources. I stumbled upon this teacher’s website and found her resource here. You will notice that our resources seem similar. I just changed it slightly to fit my teaching style and decluttered some of the wording so as not to overwhelm my students (the more words, the less likely they are to read the instructions).

I hope this lesson helps you out in any way. If you do end up using it, please leave a comment and let me know how it goes.