Students will learn how to draw points, line segments, and polygons rotated about the origin. Specifically, clockwise and counterclockwise rotations which are multiples of \(90^\circ.\) Here's an example. Students will also learn the relation between clockwise and counterclockwise rotations. Students should be shown that any combination of rigid transformations can be done solely by reflection, as shown in this video. As an interesting aside, demonstrate how an affine transformation can be used to divide an oval pizza equally amongst any number of people, as seen here.
Next, give your students these challenges:
- Fitted by NRICH
- A Patchwork Piece by NRICH
2017 AMC 10B Problems/Problem 18 by AoPS: My solution is based upon Solution 1. Denote corner as C and side as S. I started by thinking about all the ways I could place the 3 blues. There is 1 way for CCC, 2 for CCS, 2 for CSS, and 1 for SSS. Here's how I drew the 1 CCC and 2 CCS:
If you're very careful, you can also solve this problem by placing the 1 green first, as seen here. My way is a bit nicer, because after placing the blues you can figure out all possible positions for the green in your head. That is, you will end up drawing the 6 arrangements for the blues instead of all 12 arrangements for the blues and greens.
Conclude by leading this investigation:
Round Tower – (drill and kill multiplication)
by MathPickle