Chapter 2: Linear Equations Section 1: Using Graphs & Tables
Topics in Algebra 1 © 2001 Texas Instruments Teacher Notes 2-6
Linear Equations: Using Graphs & Tables Teacher Notes
Objectives
•
To illustrate how to locate the real number solution of a linear equation using tables.
•
To illustrate how to locate the real number solution of a linear equation using a graphical
method on a Cartesian (x-y) graph.
Math Highlights
In the table of values method, students see a table of values for the left and right side of the
equation. They see that the x value, which makes the two sides of the equation equal, is the
solution. They also see that they may need to refine the table of values to search for the solution.
In the x-y graphical method, students graph both sides of the equation and find the intersection
of the lines. If students have not graphed lines, they can first make a table of values and then plot
the points to graph the lines. The x coordinate of the intersection of the lines is the solution.
Common Student Errors
•
Using graphs and tables can mislead a student to think that they can always find the exact
solution using these methods. Although they often will find exact solutions using these
methods, using algebra will give exact answers for these equations. Have students try to
search for the solution to x +
À
2 =
À
7 . The exact answer is x =
À
7
N
À
2 = 1.2315377 . . .
•
At times, introducing the algebraic solution of equations gives students just the mechanics of
doing a problem. Algebraic methods alone usually do not invite the student to reason out the
solution using number sense. The graphs and tables method gives students the opportunity to
see the values of each side of the equation so they can see when the right side and left side of
the equation are equal.
Visual learners benefit by seeing the numbers and graphs first, and then by using these as the
tool to find the solution.
•
Some students are able to see the solution to an equation using their number sense and may
have difficulty taking the time to show their work. This may also be an issue in
Chapter 2: Linear Equations, Section 2: Using Algebra. Encourage the use of written
mathematics and drawing graphs and tables as a communication tool. Have students look in
newspapers for graphs and tables of information to show real examples for the need for this
communication skill.
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