Topic 4 Schedule - Matrices - HL Math, Year 1
(A) List of Topics and Content to be Taught
point to consider ==> present in the context of familiar concept ==> linear systems and their intersection. Then get into modelling math setting up some word problems involving linear systems ==> connection to make is that matrices have two general purposes => (i) solve linear systems and (ii) store info related to linear systems. We can extend our linear systems to lines in 3-space as well to set a context for 3x3 matrices
| Objective | Topic | Content | Teaching Emphasis |
| Objective 4.0 | Introduction to Matrices | - solve linear systems
- model linear systems => matrices store info |
demo solutions using GDC and introduce row operations |
| Objective 4.1 | Matrix Concepts and Contexts | Definition | use GDC as much as possible, but emphasis is also placed on algebraic solutions |
| Elements | |||
| Row | |||
| Column | |||
| Order | |||
| Objective 4.2 | Algebra of Matrices | Equality | use GDC as much as possible, but emphasis is also placed on algebraic solutions |
| Addition | |||
| Subtraction | |||
| Multiply by Scalar | |||
| Matrix Multiplication | |||
| Identity and Zero Matrices | |||
| Objective 4.3 | Determinants and Inverses of Matrices | 2x2 determinants | use GDC as much as possible, but emphasis is also placed on algebraic solutions |
| 3x3 determinants | |||
| Inverse of 2x2 and 3x3 matrices | |||
| Conditions for existence | |||
| Objective 4.4 | Solving Linear Systems using Inverse Matrices
Conditions for existence of a unique solution, no solution and an infinity of solutions |
Solving 2x2 and 3x3 matrices
these cases can be investigated using RREF unique solutions with inverses |
use GDC as much as possible, but emphasis is also placed on algebraic solutions |
(B) Timing/Pacing
From our list of required content, we can now set up a tentative schedule for Topic 4. Note the recommended time frame is 12 hours (or 9 classes of 1.3333 hours - 80 minutes)
(C) Sequence of Topics
The relevant sections in the textbook are as follows:
Chapter 14 - Matrices
(A) Introduction
(B) Addition and Subtraction of Matrices
(C) Multiples of Matrices
(D) Matrix Algebra for Addition
(E) Matrix Multiplication
(F) Using Technology
(G) Some Properties of Matrix Multiplication
(H) The Inverse of a 2x2 Matrix
(I) Solving a Pair of Linear Equations
(J) The 3x3 Determinant
(K) The Inverse of a 3x3 Matrix
(L) 3x3 Systems with Unique Solutions
(M) Solving Using Row Operations
Outline
| 4.1 - Introduction to Matrix Concepts (Terms, Applications, etc) | 14A | 1 period |
| 4.2 - Algebra of Matrices | 14B (add, subtract)
14C (scalar multiples, zero matrix and negative matrix) 14D (Matrix Algebra for Addition) |
1 period |
| 14E Matrix Multiplication
14G Properties of Matrix Multiplication |
1 period | |
| 4.3 - Determinants and Inverses | 14H - Inverses and Determinants of 2x2 Matrices | 1 period |
| 14I - Solving a Pair of Linear Equations (using Inverses) | 1 period | |
| 14J - The 3x3 Determinant
14K - The Inverse of a 3x3 Matrix 14L - 3x3 Systems with Unique Solutions |
2 periods | |
| 4.4 - Applications | 14L - 3x3 Systems with Unique Solutions
14F - Using Technology 14M - Solving Using Row Operations |
2 periods |
So this sets up 9 periods plus another period for a Unit 4 Exam - time may be amended depending on student mastery of material.
(D) Schedule and Calender