Algebra 1 Lesson Plan – Linear Equations with Graphing Calculators
Nolan Tang
Context:This lesson is designed for an algebra class at Queens Lake Middle School. This class includes 26 students, none of which have learning disabilities. There are gifted students in this class. The students in this class have learned how to graph linear equations and find slope, intercepts, and zeroes of a function. They also have learned about slope- intercept form of a function.
Objective:Students will be able to graph a linear function and determine the slope, intercepts, and zeroes of a linear function using a graphing calculator.
SOL:SOL A.6a: The student will graph linear equations and linear inequalities in two variables, including determining the slope of a line when given the equation of the line, the graph of the line, or two points on the line. Slope will be described as a rate of change and will be positive, negative, zero or undefined.
SOL A.7: The student will investigate and analyze (linear) function families and their characteristics both algebraically and graphically, including determining whether a relation is a function, domain and range, zeroes of a function, x- and y- intercepts, finding the values of a function for elements in its domain, and making connections between and among multiple representations of functions including concrete, verbal, numeric, and algebraic.
Materials: TI-83 or equivalent calculators (26)
Worksheets
TI-83 PC Emulator
Document Camera
Time:80 minutes
Content and Instructional Strategies:
- Do Drill and Practice: Review graphing and finding slope, intercepts, and zeroes of a function by hand as a warm-up.
Use the function: y = 2x + 1.
Use the points: (-4, -2) and (8, 1). (y = (1/4)x - 1)
Go over the warm-up problems with the class (10/80)
- Attend to a Demonstration: Start with the lecture notes. Go over how to graph warm-up problems using the TI-83 PC Emulator on the computer, or the graphing calculator and document camera if the technology does not work. (15/80)
- Recognize a Pattern: Students use what was done to fill out notes and figure out the example problems using a graphing calculator. (25/80)
- Discuss: After students fill out the notes, students will answer questions concerning linear functions (slope, intercepts, zeroes) using their past knowledge. Review how to use the calculator to find the slope, intercepts, and zeroes and the example problems so that everyone has the correct notes and examples (35/80)
- Do Drill and Practice: Each student will work on worksheets using a graphing calculator. (60/80)
- Describe an Object Mathematically: The class will reconvene and go over the worksheets. The teacher will call on students to answer the questions. (70/80)
- Discuss: Sample summary questions: How do you find the slope of a line using a graphing calculator? The y-intercept? The x-intercept? The zeroes? (75/80)
- Recognize a Pattern: Students can use remaining time to find out the effects that changing slope and y-intercept have on the graph using the graphing calculator. (80/80)
Evaluation: Check the students' answers to the above questions, and the worksheets. After class, homework is assigned, which is also graded based on correctness.
Differentiation and Adaption: Students can work in pairs if one is a special education student. If needed, the teacher can pair up with the student and work together on graphing and/or reduce the amount of work for the student. If students finish work early, they can get started on homework. For gifted students, there is an extension activity regarding using linear regression with the calculator.
Linear Equations using a Graphing Calculator Notes
To graph a function on the calculator:
Turn on the graphing calculator.
Press the ______button.
Enter the function in ______form to the right of the equals sign.
Make sure that there is a black box around the equals sign.
Press the ______button.
If you cannot see the graph:
Press the ZOOM button.
Use the 0:ZoomFit function.
If that does not work:
Press the WINDOW button.
Change Xmin and Xmax to the minimum and maximum x-coordinates you want to see.
Repeat with Y.
(Change Xscl and Yscl to how far apart you want the tick marks)
To find the slope of the function (only works with linear functions!!!):
Press the ______button, then the ______button. (This is the ______function.)
Take the value of ______at ______and subtract the value of ______at ______.
To find the y-intercept of the function:
Press the ______button, then the ______button. (This is the ______function.)
Use the 1:value function.
Enter X=______and press ENTER.
**Make sure that the correct function is at the top of the screen when the result is shown**
To fine the x-intercept(s) (______) of the function:
Press the ______button, then the ______button. (This is the ______function.)
Use the 2:zero function.
Make sure that you are on the correct function.
Move the cursor to the ______of the zero when it asks for Left Bound and press ENTER.
Move the cursor to the ______of the zero when it asks for Right Bound and press ENTER.
Move the cursor to the best guess when it asks for Guess and press ENTER.
Examples:
Graph the following functions and find the slope, y-intercept, and zero(es) of the functions.
y = 2x + 3
(-1, 4) and (2, -5)
Classwork
Graph the functions below and solve for the slopes, y-intercepts, and zeroes. If need be, find the function in slope-intercept form first.
- y = x + 2
Slope = y-intercept =
Zero =
- y = (-1/2)x – 1
Slope = y-intercept =
Zero =
- y = 2x + 2
Slope = y-intercept =
Zero =
- y = (1/4)x + 2
Slope = y-intercept =
Zero =
- (-1, -3) and (2, 3)
Slope = y-intercept =
Zero =
- BONUS: Nathan started out with 5 hot dogs at his stand. After 2 hours, he only had one left.
Slope = y-intercept =
Zero =