Day 12 started with a review of "opposite, adjacent, hypotenuse". They are improving but I think having a practice sheet just for naming sides might have been a good idea. We picked up where we left off yesterday with the table which we completed with a row of student data:

I think I will reorganize this table for next time... I like that the hypotenuse is in the middle but some students had a hard time understanding how to correctly complete it.

We then moved on to calculating ratios:

I asked them what they noticed and they said that some of the numbers repeated. They noticed a pattern - that they "switch". I'm not confident they understood the "why" here. To be reviewed. We also discussed why the first two columns of ratios are all numbers between 0 and 1, but that one of the ratios in the 3rd column is greater than 1.

On the back of their sheet are trig tables with the headings that match the ratios - no mention of "sine", "cosine" or "tangent". They noticed that their results matched the numbers in the table fairly closely. I talked about how we can use these tables to help us find unknown side lengths or angles in right triangles.

We worked through two examples together, starting with "compared to the marked angle, label the sides opposite, adjacent or hypotenuse" and moving forward from there.

I am fairly confident that they can at least label the sides correctly, but know that we will have to do quite a bit more work together to get solid on how to use trig. Then we will put it together with sum of squares and similar triangles.

We spent the last 25 minutes of today's class preparing for the OSSLT (Ontario Literacy Test) which I think was a welcome break from math for some!

Enjoying the progression of days mary. Last year, I began setting this up as a proportion. The .7071 over 1. Then students would guess/check on the first few...x has to be more than 14 bc 1 is more than .7071. Eventually, students began finding their own way to arrive at x (and some got much better at estimating the value). It was a student who asked, since it's a proportion can I rewrite as x/14 =1/.7071 and this eliminated the x in the denominator. Not necessarily a way to handle but just some things I recall from our class convo. Another figured sometimes they could use the other angle if it was tangent ratio to eliminate x in denominator.

ReplyDelete16 August 2014 07:39

I like this idea a lot. Thanks!

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