![]() ![]() The U of Chicago uses the letter r for reflection, but no letter for translation. Also, the New York lesson uses the letter R to denote a rotation, with two subscripts - the first being the center and the second being the magnitude (that is, the angle). But it also uses the abbreviation CW for clockwise. We observe that the New York lesson also uses positive angles to denote counterclockwise and negative angles to denote clockwise. ![]() Of course, nothing is stopping the teacher from having the students take a blank sheet of paper, draw a coordinate plane with a large F in the first quadrant, and then perform the reflections, possibly even by folding. Actually, yesterday's task of reflecting the letter F in the y-axis and then the x-axis would also make a good Opening Activity or Anticipatory Set - I considered posting a separate page to perform the reflections, but I want to conserve paper and avoid excessive visits to the Xerox machine. I don't do that - but of course, I did sort of hint that the folding tasks at the beginning of my reflection lessons would make good Opening Activities. Notice that unlike this blog, this New York lesson prescribes what questions are meant to be the Opening Activity, Exercises, Exit Ticket, and Problem Se, as well as how many minutes are to be devoted to each learning task. Our focus today will be on Lesson 13, on rotations. And Lesson 17 is essentially the Perpendicular Bisector Theorem, which we've already covered last week. But the giveaway that Topic C is based on Wu is Lesson 18 - which uses 180-degree rotations to construct parallel lines and ultimately prove the Alternate Interior Angles Theorem!Īs it turns out, Lesson 15 covers the relationship between a reflection and a rotation - so it's just yesterday's lesson. Reflections come next (Lesson 14) and then translations (Lesson 16). Rotations come first (Lesson 13) - just like Wu. We see that transformations are covered in Topic C, Lessons 12-21. I suspect that much of the Empire State's curriculum is based on Wu. Luckily, here's a link to the Common Core Geometry curriculum developed for New York State. But the Wu link that I gave yesterday doesn't give exercises or problem sets, since it mainly focuses on definitions and theorems. Recall that for Wu, rotations are of primary importance. Yet the U of Chicago text doesn't spend enough time on rotations do accomplish this. But ordinarily, when we think about rotations, we want to think about its center and magnitude - not the two reflections. So far, our work on rotations focuses the composite of two reflections in intersecting lines, for that's how the U of Chicago text defines them. ![]()
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