Zachary Okolowitcz
Theory/Technology Integration
Fall 2014
Lesson Plan 3: Web Resources
Lesson 3: Solving Quadratics Using the Quadratic Formula
Standards:
HSA-CED.A.1: Create equations in one variable and use them to solve problems.
HSA-REI.B.4a: Use the method of completing the square to derive the quadratic formula.
HSA-REI.B.4b: Solve quadratic equations…by the quadratic formula.
Objectives:
Students will be able to:
A: Solve quadratic equations using the quadratic formula.
B: Describe the process to derive the quadratic formula.
C: Interpret the discriminant of a quadratic equation.
Materials:
Classroom Materials: Chromebooks
Challenge Activity Handout
Exit Slip Handout
Homework Worksheet
Starter/Motivational Activity:
Students will have Chromebooks that are available within our math department throughout
this lesson. Try to complete the challenge problem independently. If you are unable to do so, use the
internet to find out how the quadratic formula is derived. If you are using the internet, please explain
what you have found and the process to taking a quadratic in standard form and manipulating it to
become the quadratic formula!
CHALLENGE!! CHALLENGE!! CHALLENGE!!
Can YOU solve the arbitrary formula for a quadratic ax2+bx+c=0, by first completing
the square, and then solving for x!!
Lesson Procedure:
Students will be working with 12 Short videos that walk through different types of problems
that can be solved using the quadratic formula. These include basic computation problems, more
challenging computation problems, discussion of the discriminant, and word problem applications.
After completing the Challenge problem and discussing the derivation of the quadratic
formula, students will watch and take notes on the following problems within the given links. They
are to pause and make comments within their notes and also get the problems into their notes. I will
be circulating the room as this is being completed so students can ask me further questions if need be.
Student Links will be available on my classroom website under the Lesson Plan 3 link within the
quadratics unit.
Go over Challenge Problem:
Discussion of the importance of properly putting a quadratic in standard form and
identifying a, b, and c.
Practice of this and plugging into the quadratic formula and simplifying to reveal
roots/solutions.
Students will have a hard copy of the following guided notes and practice examples done which will
also include the links to the practice problems they are to complete on their own and take notes on.
Students will go to my website to be able to click on and go to the links of each individual video.
Name:________________________________
Date:__________
Solving Quadratics Using the Quadratic Formula
Example 1:
Student Links to completing practice problems 1-4:
1:
http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05
_mp1/HSCC_Alg%201_09_05_mp1.html
2:
http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05
_mp2/HSCC_Alg%201_09_05_mp2.html
3:
http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05
_mp3/HSCC_Alg%201_09_05_mp3.html
4:
http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05
_mp4/HSCC_Alg%201_09_05_mp4.html
Example 2: Modeling
Students will now complete practice problems 5 & 6:
5:
http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05
_mp5/HSCC_Alg%201_09_05_mp5.html
6:
http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05
_mp6/HSCC_Alg%201_09_05_mp6.html
Example 3:
Student Links to 7-9:
7:
http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05
_mp7/HSCC_Alg%201_09_05_mp7.html
8:
http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05
_mp8/HSCC_Alg%201_09_05_mp8.html
9:
http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05
_mp9/HSCC_Alg%201_09_05_mp9.html
Example 4:
Student Links to practice problems 10-12:
10:
http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05
_mp10/HSCC_Alg%201_09_05_mp10.html
11:
http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05
_mp11/HSCC_Alg%201_09_05_mp11.html
12:
http://static.bigideasmath.com/protected/content/hs_tut/alg1/c09/05/HSCC_Alg%201_09_05
_mp12/HSCC_Alg%201_09_05_mp12.html
Closure/Lesson Assessment:
Closure/Exit Slip: Students will be asked to complete the following:
Explain the process to use the discriminant along with the quadratic formula to find the
solutions to a quadratic equation:
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
Rubric to Grade Exit Slip:
Rating:
1
2
3
Description:
Minimal effort in
Student identifies the
Student correctly
describing the use of
importance of
identifies the use and
the quadratic formula
determining what a, b,
application of the
and the discriminant to
and c equal and
quadratic formula and
solve a quadratic
discusses the use of the
the discriminant.
equation
discriminant with flaws
in explanation
HW: Select Problems from the following Assignment:
In Exercises 1–3, write the equation in standard form. Then identify the
values of a, b, and c that you would use to solve the equation using the
Quadratic Formula.
1. x2  5x
2. x2  3x  10
3. 5x2  2  7x
In Exercises 4–11, solve the equation using the Quadratic Formula. Round
your solutions to the nearest tenth, if necessary.
4.
x2  6 x  9  0
5. x 2  5 x  14  0
6. x 2  9 x  10  0
7. 3 x 2  2 x  1  0
8. 3 x 2  5 x  4  0
9. 4 x 2  4 x  1  0
10. 6x2  5x  6
11. 5x2  9x  3
12. Your friend competes in a high-jump competition at a track meet. The
2
function h   16t  18t models the height h (in feet) of your friend after t
seconds.
a. After how many seconds is your friend at a height of 4 feet?
b. After how many seconds does your friend land on the ground?
In Exercises 13–15, determine the number of real solutions of the equation.
13.
x2  2x  1  0
14.
x2  4 x  7  0
15. 3x2  2x  6
In Exercises 16–18, find the number of x-intercepts of the graph of the
function.
16. y  x2  3x  5
17. y  3x2  7x  8
18. y  5x2  10x  1
Select at least one web-based application or tool that will add value to your unit of study (or a
specific lesson). Incorporate one or more Web resources (tools or applications) into Lesson Plan 3.
This resource and a sample of how it is incorporated into the unit will be linked to your ePortfolio
(website). Examples include: blog, wiki, interactive, new media tool application.
Deliverables:
1. Lesson Plan
2. Sample Product (as if a student created or completed it)'
3. Assessment (how student work will be assessed; i.e. rubric, checklist, peer feedback)
4. Incorporated into ePortfolio / website