TV Antenna Problem #MFM2P #3ActMath

Tuesday’s MFM2P class was presented with this image:TVantenna (1)It is a problem out of a sample textbook I have, but I created my own image for it. Students were asked “What Mathematical questions could we ask about this scenario?”. Their ideas:CaptureSome good ones in there … we talked about the misconception that the wire is 15.4 feet long. Reflecting now I wish I’d taken off the bottom measurement before asking them for questions. I believe in Dan Meyer’s theory of stripping a question down in order to “be less helpful”. And I think I was a bit too helpful here. Although I like that it led to questions about converting between feet and metres as that’s part of our curriculum this year.

Students were then told the angle of elevation of the guy wire is 56º and to estimate: Capture

I then sent students to their boards (VNPS) to solve. I went to my desk & took attendance & checked homework. I listened to conversations trying to discern whether or not groups were too stuck. Up until today we learned about the trig ratios and could use the ratios and a trig table to solve for missing angles. We had not yet learned how to find missing sides at all (which is what this question requires). Most groups decided fairly early on to label the sides as opposite, adjacent, and hypotenuse; whether by themselves or by looking at another group’s board. But they weren’t sure what to do next. One group figured out they could use the trig ratios. Originally they had written down $latex sin\theta =\frac{opp}{adj}$. I questioned them about whether or not this matched their formula sheet, and then listened to them reason out whether they wanted the sin formula or the tan formula. They settled on tan & proceeded to solve:IMG_0231.JPG

Another group saw this group’s work and tried to do the same:IMG_0232.JPGThey used the top angle as their theta. But did not adjust their opposite & adjacent sides accordingly. This gave me a great teaching moment when we were done – you can see my writing in green & blue. I showed how their work would have been different & that also allowed me to show how to handle the scenario where the missing side winds up on the bottom of the proportion.

A note here: I try not to teach the “trick” of cross-multiplying. But I wonder if flipping the proportion is simply another trick I’m teaching them without them really understanding WHY we can do that. Something to think more about.

Here are the other groups’ work:IMG_0233.JPGThis group seems to have misread the trig table & gotten the wrong tan value.IMG_0234.JPGThis group is dividing angles and also writes the Pythagorean Theorem formula down.IMG_0235.JPGThis group is getting some ideas off the other boards but not too sure where to go with it.

I revealed the correct answer (which the group on the 1st board had) and did the “teaching” you saw written on the 2nd board.

I then gave them the period to work on these practice problems.

The entire folder of materials is here.

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)

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