Grade 10-11: Transformations


The student is given a diagram in which a transformation T (from graphs 1 to 4) is “factored” as a composition of “basic” transformations (these are the “primes” of the system, rotations, dilations and shears). The objective is to calculate the parameters θ, a, b and h. In phase 1 we use geometric reasoning, simple Euclidean geometry and triangle trig.

Phase 2, comes towards the end of week 1. Here we tell the students how to find the 2×2 matrix of a transformation and that composition of transformation corresponds to multiplication of matrices. That striking “isomorphism” allows them to solve the problem algebraically.

For the remaining examples, we often let each of them choose the method to use and it’s interesting to see their preference. On the whole, the majority seem to prefer the algebra because it’s more algorithmic––even though it involves the solution of four non-linear equations in the four unknowns!

Teacher manual
Student workbook
Example 1 Example 2 Example 3 Example 4
Example 5 Example 6 Example 7 Example 8