Grade 10 (MPM2D) Trigonometry

The Crystal of Royal Ontario Museum

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Challenge:

Mr. Anusic is surprised to see how much dust has collected on the surface of the ROM crystal since his last visit and spots a bucket of soapy water and squeegee that one of the ROM’s cleaning staff has conveniently left behind. If Mr. Anusic can wash one square metre of the surface of the crystal every 15 seconds, how long will it take him to wash a chosen section of the ROM crystal?
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Student Assignment:

Students (in group of 2 or 3) will select a polygon on the ROM crystal, that is fully visible from the ground, and use the available tools to solve their challenge.
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Assessment:

Students will be evaluated based on the following Achievement Chart.
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Sample Student Response 1:

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Student Response 2:

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ROM Crystal
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3-Part Lesson Plan:

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Rationale:

We chose this activity because we thought it would be fun and interesting for students to visit this site, while at the same time give them opportunities to apply math skills (in particular, trigonometry of right and acute triangles) learned in a new way. Most teenagers I know love going downtown!


We thought that the site would provide many different opportunities for students of varying grades to consolidate and demonstrate their learning and we considered a number of them using not only the ROM but the surrounding area. We thought the busy intersection would lend itself to a statistical analysis of travel patterns; the rate of people entering and leaving the museum; and budgeting for the trip could be an activity in itself, akin to the trip to the Eaton’s Centre you mentioned. We then got to thinking about the interesting geometry in the interface between new and old buildings at that intersection and finally arrived at considering just The Crystal. We briefly thought we could incorporate all of these elements into one activity but for the scope of this assignment decided to focus just on practicing the application of trigonometry, area, and upon observing a window cleaner, the extension to the time it might take to clean windows on The Crystal! And thereby settled on this being a summative activity for a grade 10 academic class. We left the activity open ending enough to allow students many opportunities for collaborative decision making and problem solving.


As all three of us attended UofT as undergrads, we thought a great way to end the trip would be to take students on a guided reality tour through the university sharing with them our experiences and inspiring them to think about their post secondary destinations – this has actually been done upon visits to Queen’s Park with civics/careers students and it’s great!