Students will learn how to identify symmetric figures and count lines of symmetry and rotational symmetries. Conclude by giving this challenge to your students. 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:
X X X
O O X O O X
X O X X O O X O O ...
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.
Concude by giving your students this challenge:
How Many Triangles Do You See? Challenging Puzzle by MindYourDecisions: When providing the solution, give both the solution found in the video, and my more elegant solution, which is as follows: Draw the lines of symmetry, a horizontal line and a vertical line. Consider one quadrant, whichever one you like. There are 4 triangles that occur entirely in that quadrant. These 4 triangles will occur 4 times, because there are 4 quadrants. There are 2 triangles which are cut by the vertical line of symmetry, but not the horizontal. These 2 triangles will occur 2 times, because there are 2 halves. There are 6 triangles that are cut by both lines of symmetry, and thus occur only once. Hence, the total number of triangles is
$$4 \cdot 4 + 2 \cdot 2 + 6 = 26$$