Matrices and Vectors
I’ve been asked by some curriculum writers to offer my thoughts on how I might introduced MATRICES and VECTORS to high-school students in response to the Common Core State Standards N-VM. In response I have done two things:
i) Written a 69-page chapter on introducing these concepts (TOC below.)
ii) Quickly put together some very rough overview videos of my approach.
Here’s the pdf document for download: Pamphlet_ Vectors and Matrices
Here is the series of rough overview videos:
Matrices_Idea 1 Part 1
Matrices_Idea 1 Part 2
Matrices_Idea 2 Part 1
Matrices_Idea 2 Part 2
Matrices_Idea 3
What is a Vector?
And here is the ToC of what you are in for if you want to look at my sequence of thoughts and suggestions (Feel free to write to me to comment on what you think of all this!)
The Common Core State Standards ……………………………… 2
PART I: MATRICES
Preliminary Meta-Comments ……………………………… 5
Theme 1: Networks ……………………………… 6
Theme 2: Systems of Linear Equations ……………………………… 13
Theme 3: Complex Numbers and Transformations……………………………… 26
Collecting Thoughts and an Epiphany ……………………………… 28
The Confused Role of Technology ……………………………… 33
Do Inverse Matrices Exist? ……………………………… 34
Required Extra Material
Is Every Transformation of the Plane given by a Matrix? ………… 38
The Geometric Interpretation of Determinant……………………………… 40
The “Arithmetic” of Square Matrices ……………………………… 43
Additional Exercises ……………………………… 44
PART II: VECTORS
What is a vector ? ……………………………… 48
Vectors between points ……………………………… 51
Optional Additional Ideas
Vectors and Geometry ……………………………… 54
The Equation of a Line ……………………………… 58
Fun Applications ……………………………… 60
Additional Exercises ……………………………… 63
