Overview

This lesson is intended to give students the opportunity to explore Systems of Equations graphically on Graphing Calculator and then using matrices on their calculator. Given a word problem the students will figure out the system of equations and use these to plot and make a matrix.

Objectives

The student will:

1. Read the word problem and figure out what the appropriate equations are that belong in the system.

2. Graph these equations in Graphing Calculator to get a visual representation of what a system of equations is.

3. Use the matrix application of their personal graphing calculators to figure out the solution to the system.

4. Using knowledge of what they know about systems and matrices compare and rationalize the solutions they got.

Standards Addressed

NCTM Principles and Standards

• interpret representations of functions of two variables

• 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 expressions, including iterative and recursive forms, to represent relationships arising from various contexts

• create and use representations to organize, record, and communicate mathematical ideas

• recognize and apply mathematics in contexts outside of mathematics

• Create and use representations to organize, record, and communicate mathematical ideas

• Students will make connections among mathematical ideas and to other disciplines

• Solve problems that arise in mathematics and in other contexts

• Use the language of mathematics to express mathematical ideas precisely

Audience

This lesson is intended for high school students in Algebra III or Advanced Algebra and Trigonometry.

Prerequisites

The students should be able to:

1. Enter matrices on the TI graphing calculators.

2. Know what a system of equations is and how to make a system (from a word problem).

3. Enter expression/equations into technology programs.

Materials Needed

Computers with Graphing Calculator already installed.

TI-83, TI-83 plus, or TI-84 plus graphing calculators.

paper and pencil

Procedure

Activity

Technology Connection: Students are using real life problems to make systems of equations from these they are putting the equations into Graphing Calculator to get a three dimensional representation of what the system really looks like. Being able to visually see what the system looks like graphically will give them a better understanding of why systems have one solution or many solutions.

Rationale

The activity should get the students thinking about what a system of equations actually is in the world. Having them use real world scenarios to pick out the system of equations gives them an opportunity to see when, why, and how we use these things. It gives them a look at a practical way of how systems can be found in the real world. Students need to realize that mathematics is all around us and see when it's used.

Students are working individually in order for the teacher to gage who has understanding of the prerequisite knowledge needed for the activity. Technology is important in the activity to get a visual representation of the idea of systems of equations. For those students who are visual learners, this activity should be able to give them a more clear representation of what systems are and how we solve them. Doing them in matrices is another example to show how they are solved. Some students should make the connection of how matrices are vectors in space which is what the graphs show.

Assessment

Students will be assessed on their work throughout the activity, the solutions to the problems, and the homework assignment that follows up the activity. The teacher will also look for particpation, involvement during class time, and being on task during the lesson.

Evaluation

Throughout the lesson the teacher will roam around the class checking student involvement/participation. The teacher will also look at the time management of the lesson, behavioral issues that may arise, and overall effectiveness of the lesson. As always lessons are continually modified so any modifications will be noted.

Return to Home