Date: December 3, 2009
Grade Level:
College level lesson, adapted from a high school textbook (Meadows or Malls?)
Teacher Names:
Jordan Ballagh, Carolyn Bien, Rachel Coulter, John Farrell, and Nathan Noble
Content: 
College Level Mathematics

Title: Matrices with the TI-Nspire

Matrix-TINspire

Overview:  This lesson is targeted at college students in MATH4625.  They have learned about matrices in linear algebra but may have forgotten how to do some of the simple calculations along with matrix multiplication, and inverses.  The lesson expands on high school level introduction to matrices, introducing 3x3 matrices, Gauss-Jordan Elimination, inverses, graphical connections, and more.

Goals: To expand students’ knowledge about solving linear systems of equations with three unknowns using the method of matrices. We will also apply different problem solving strategies such as matrix inverses, augmenting matrices, and the TI-Nspire calculator applications.  Convince students that proper knowledge of matrix operations is a very useful tool when solving for 3+ equations and 3+ unknowns and is much more time efficient than previous strategies, then we will help the students discover the geometrical connections and connections between Gaussian elimination and inverses.

Standards: 

Virginia Standards of Learning

DM.6.  The student will solve linear programming problems. Appropriate technology will be used to facilitate the use of matrices, graphing techniques, and the Simplex method of determining solutions.

MA.11.  The student will perform operations with vectors in the coordinate plane and solve real-world problems, using vectors. This will include the following topics: operations of addition, subtraction, scalar multiplication, and inner (dot) product; norm of a vector; unit vector; graphing; properties; simple proofs; complex numbers (as vectors); and perpendicular components.

MA.14.  The student will use matrices to organize data and will add and subtract matrices, multiply matrices, multiply matrices by a scalar, and use matrices to solve systems of equations

NCTM Standards

Number and Operations Standards:

Represent and analyze mathematical situations and structures using algebraic symbols:
         Write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency—mentally or with paper and pencil in simple cases and using technology in all cases
         Use symbolic algebra to represent and explain mathematical relationships

Use mathematical models to represent and understand quantitative relationships:
         Identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships

Process Standards:

Problem Solving: After learning various ways to solve a problem involving matrices and vectors, students should decide which approach works best for the final word problem.
Connections: Students will make new connections or strengthen their previous understanding of matrices and vectors when solving real world problems.  Students will also make technological connections to the TI-Nspire.
Communication: The think-pair-share group activities will require positive communication between both peers and teachers in order for everyone in the group to obtain a solid understanding of the material covered.
Representation: Students will learn and understand what is happening graphically during Gauss-Jordan elimination, and will learn to visually represent how a matrix transforms a vector.

Materials and Resources:

Procedure: Roughly 40-45 minutes is needed for this lesson.
x + y = 3
3x + 2y + z = 7
-x + 4y = 2

Solution: (2, 1, -1)
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