Zawodniak, M Course Project
Precalculus Unit 5 - Matrices
Overview:
Matrices are intended, as part of the common core, to be addressed in high school. Specifically, it is suggested to take place as unit 5 in a precalculus course. Below are 3 activities, intended to take place over 3-4 class periods, which can be used to teach students about matrices and engage students with the many properties of matrices. The first two activities use web applets, while the third activity uses Geometer's Sketchpad. No prior knowledge will be required to implement these technologies in the classroom.
Outline of Unit:
Day 1: Beetle Survey Scenario (Part 1)
Day 2: Beetle Survey Scenario (Part 2)
Day 3: Useful Inverses
Day 4: Transformation Matrices
Summative Assessment
Summative Assessment Solutions
Day 2: Beetle Survey Scenario (Part 2)
Day 3: Useful Inverses
Day 4: Transformation Matrices
Summative Assessment
Summative Assessment Solutions
Standards Covered By This Unit:
- MCC9-12.N.VM.6 - Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
- MCC9-12.N.VM.7 - Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
- MCC9-12.N.VM.8 - Add, subtract, and multiply matrices of appropriate dimensions.
- MCC9-12.N.VM.9 - Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
- MCC9-12.N.VM.10 - Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and onluy if the matrix has a multiplicative inverse.
- MCC9-12.N.VM.11 - Multiply a vector (one-column matrix) by a matrix of suitable dimensions to get another vector. Work with matrices as transformations of vectors.
- MCC9-12.N.VM.12 - Work with 2x2 matrices as transformations of the plane.
- MCC9-12.A.REI.8 - Represent a system of linera equations as a single matrix equation in a vector variable.
- MCC9-12.A.REI.9 - Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3x3 or greater).
Note: MCC9-12.N.VM.12 includes interpreting the absolute value of the determinant in terms of area. We believe that this part of the standard is best addressed during a unit on vectors, and thus it is not included here.