LESSON PLAN Date

Name: / Date: / Length: 90 minutes / Source:
School: / Grade: 9-12 / #students:
Subject: Algebra I/Algebra I Part 2 / Topic: Quadratic Functions – The Discriminant / #IEP:
Action –
Objectives- Clearly state broad goals and specific objectives for learning (e.g., concepts, procedures, skills, etc., you want students to learn).
To use the discriminant to find the number of roots of the equation ax2 + bx + c = 0 and the number of x-intercepts of the graph of the related equation y = ax2 + bx + c.
Connections- Explain how objectives relate to Kentucky Learner Goals and standards for learning content established by professional organizations. (Do not simply list the related goals, expectations, and or standards.)
KY Core Content:
4.2.5 Students will determine domain and range of a function, the slope and intercepts of a linear function, and the maximum/minimum and intercepts of a quadratic function
4.2.6 Students will determine approximate solutions to quadratic equations
Context-Clearly describe how objectives and lesson relate to broad goals for teaching about the topic. Explain what has been done previously as it relates to this lesson.
To this point in the unit, students have examined 3 different ways of solving quadratic equations (by taking square roots, by completing the square, and by using the Quadratic Formula). The students are now ready to compare solutions they’ve found algebraically to the graphs of these functions, as well as to examine x-intercepts of these functions.
Materials/Technology-List materials and technology which will be used during the lesson. Attach print material to be used with students.
Graphing Calculator
Virtual TI
Smart Board
Projector
Computer
TI Navigator system
Procedures-Describe strategies and activities to be used to involve students and accomplish objectives including how to trigger prior knowledge and adapt strategies to meet individual student needs and the diversity in your classroom.
**See attached sheet.
Student Assessment- Clearly state how you will assess student progress including performance criteria. Attach written assessment measures used in relation to the lesson
Students will be quizzed using the TI Navigator and TI Learning Check program. This will give immediate feedback in class with regards to the concepts discussed. Students will also be given a homework assignment that will be graded for accuracy next class period.

Class Opener:

On the overhead projector:

“Using the Quadratic Formula, find all solutions for the following equations:

(1) x2 + 4x + 1 = 0

(2) x2 – 2x – 3 = 0

(3) x2 + 2x + 1 = 0

(4) 25x2 + 20x + 4 = 0

(5) x2 – 4x + 7 = 0

(6) x2 – 3x + 4 = 0”

Lesson:

Discussion to of class opener:

First have students check their answers. Allow volunteers to put problems on the board for any that the class requests to see.

Note to class that some of the equations produced one answer, some produced two answers, and some had no answer at all.

Have students take out graphing calculators and graph each equation. (The teacher may do so simultaneously on the Virtual TI and Smart Board so students may verify their work.) First have students identify what type of curve represents a quadratic function (parabola) and name specific parts of that curve (vertex and axis of symmetry). Then ask students to compare what they see on the graph to the number of solutions they have for each equation and to write down any observations they make regarding the number of solutions and the graphs.

Ask for student input/observations. Talk about how the number of solutions from the equations matches the number of times the graph intercepts/crosses the x-axis. Discuss concept of x-intercept. What coordinate do we know is the same for all x-intercepts? How is this reflected in the original equations from our opener?

Now have students write down the numerators from each opener equation after the values of a, b, and c had been substituted into the Quadratic Formula and simplified. Ask students to compare the radicand of each numerator to the corresponding number of solutions in that equation.

Make a table:

If radicand is positive, then there are 2 real solutions and therefore 2 x-intercepts.

If radicand is zero, then there is 1 real solution and therefore 1 x-intercept.

If radicand is negative, then there are 0 real solutions and therefore 0 x-intercepts.

Vocabulary discussion … The radicand (b2 – 4ac) from the Quadratic Formula has a special name. It is called the DISCRIMINANT.

Examples:

Have students determine the number of real solutions for each quadratic equation using the discriminant:

(ex) x2 + 4x – 5 = 0(ex) 4x2 – 3x – 6 = 0(ex) x2 – 5x + 7 = 0(ex) 2x2 – 2x + 8

2 real roots2 real roots0 real roots1 real root

Discuss any problems the students may have had.

Lastly, have students change their 6 opener equations so that each one has a negative leading coefficient. Ask them what effect that had on the parabola. Talk about the value of the discriminant. Did it change when we made a negative? Also – discuss where the vertices were located. Have them look at the number of real solutions as well as the leading coefficient.

Assessment:

Have students log on to TI Navigator. Send to them the DISCRIMINANT Learning Check assignment.

Give them about 10 or 15 minutes to work through the problems.

Collect their results and examine them in TI Class Analysis. Discuss results and any problems as they arise and allow volunteers to come to the board and explain problems that several students missed.

(The teacher can run a report after class to see the results of individual students. The class results will be seen immediately during the analysis.)

Follow Up Assessment (Homework):

Discriminant Worksheet

Impact - Reflection/Analysis of Teaching and Learning-
Discuss student progress in relation to the stated objectives (i.e., what they learned with indicators of achievement). Discuss success of instruction as it relates to assessment of student progress
Refinement - Lesson Extension/Follow-up -

Document created by Joy Lynn Cox Buckingham July, 1999