2017-03-28 On The Spot Ahhhaaaa

Although I have many blog posts on the tarmac ready for lift off, this entry takes special priority as I had a powerful Ahhhha moment that lasted two full periods.

Quick background, I have been teaching about trig functions in IM3 and coordinate geometry in 8th-grade math.

My IM3 students look similar to Fry from Futurama….(see below)….when I begin discussing trigonometric functions and their relationship to a right triangle and the unit circle.


Yesterday, I thought I would slow the progress down and focus on right triangle trig relationships, then move back up to unit circle and beyond. Before I even began today, the students’ lips were moistening with anticipation of the drool onset….So I changed directions, had handed out a sheet of paper to every student, and we began folding.

I didn’t know where I was going with this, but I was on an inspirational kick and was going for it. After students folded their papers, I checked each stage, I’d ask a question and have them label their own triangle, the students would confirm with their partner, and stand up when they agreed.


The 3 step process was extremely helpful in uncovering areas of stuckedness and bringing their understanding to light. My next step was to have them write each of the trig functions according to their triangle they had created.


Time quickly ran out for the students when were at this point, so tomorrow, they’ll finish the trig functions relationships. Students literally gasped when the bell ring, they were so into the lesson they couldn’t believe the period was over.

Then my 8th-grade party began, immediately after IM3, and I’m working on giving the students plenty of repetitions on problem varieties to allow them to be successful. Yesterday, the progressions began with a problem having them plot three ordered pairs, which form the vertices of a right triangle.

The students would plot the three points, then find the distance between each of the ordered pairs. Students should find that the two of the lengths are easy, just counting the distance between points, the third combination would require the use of the Pythagorean theorem. The third stage in this progression asked students to determine the slope between points forming the hypotenuse, with the hint that if stage 2 was done well, there shouldn’t be any additional requirements for calculations. The final stage asked for an explanation of how students know that the triangle formed in stage 1 was a right triangle.

Well students shared they were having a hard time with the concept of slope, so fresh of the triangle fame of IM3, I gave the same concept a try in 8th-grade.


Since this was near the end of the period, I performed a think aloud to indicate my learning. Tomorrow I’m expecting that this will be part of their work, creating the ordered pairs on a triangle, perhaps on centimeter grid paper, and do it exactly. Anyway, I felt the explanation landed with the students, several heads were nodding with that smug look of understanding….


Which showed I was on to something that may uncover more of their thinking as we explore and shed light on that which was previously in the dark.

My excitement for this simple idea and the reason for posting this moment is tied to my developing understanding of students learning and being back in the classroom for a couple of periods. Addressing students understanding in visual ways, with a manipulative and a slow pace were all pieces that helped gain students attention to make it truly impactful.

I always love these inspirational teaching moments that shed light on understanding for students, and the fact it worked in 8th through 12th yields potential for my favorite kind of tools that go K12.

What were some experience you’ve had that are similar or different? What about those experiences made them turn out the way they did?

Published by mathkaveli

I'm a math geek.

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