lesson+plan


 * __Lesson Plan__**

Topic: Factoring quadratic equations

Class: Algebra I

Title: Fear Factor

Time allotted: 75 minutes


 * __Rationale for Selecting Learning Outcomes:__** Common Core Standard A-SSE.3a. Factor a quadratic expression to reveal the zeros of the function it defines.


 * __Organization__**: Whole Group/Small Group.


 * __Objectives:__**

At the end of this lesson, students will:

-Identify a quadratic equation.

-Produce an equivalent form of an equation by factoring.

-Explain the properties of the equivalent form of the equation.

-List the zeros of the quadratic equation.


 * __Teaching Mode:__** Direct


 * __Prerequisites:__**

-The student should be able to interpret parts of an expression such as its terms, factors, and coefficients.

-The student should know the FOIL method with multiplying polynomials.

-Know how to factor the GCF from polynomials.

-Students should be familiar with prime factorization and factor trees of numbers.

-Overhead projector -Graphing calculator
 * __Materials__**

__ Lesson Activities __


 * __ Rules __**__ : __ Class, be sure to respect your fellow classmates in this lesson because I will be asking questions, and every answer and question is important so lets all be respectful. Also, please do not answer unless called upon.

**#1. Anticipatory Set:** (3 minute)

How can we use the quadratic equation? Write down the quadratic equation ax2+bx+c=0 on the

board as well as the equation 2x+4=0 and compare. Briefly explain that the polynomial 2x+4=0 tells

us that x has a zero or root at x=-2. )

**#2. Overview of learning outcomes to pupils:** (1 minute)

By the end of class, you will be able to produce an equivalent form of an equation by multiplying

polynomials and explain the properties of this equivalent form. In other words class, you be able to

take a quadratic equation, and put it in a more simpler form that will allow you to easily graph the

equation.

**#3. Lecture:** (10 minutes)

Explain that there are four types of equations that can be factored and write each on the board using

the formula: ax2+bx+c=0, ax2+bx-c=0, ax2-bx+c=0, and ax2-bx-c=0. Class, this is important because

you can have the same values for a,b, and c in these equations, but their solutions or factors are

different. Express this idea on the overhead by graphing each equation using the graphing

calculator and pointing out that they are indeed different.

When we have an equation in the form ax2+bx+c=0 and a=1 we look at the variables c and b

when factoring it. So basically what we are doing class is taking all the factors of c and choosing

those factors who’s sum equals b.

**#4. Modeling/Examples:** (25 minutes)

Give an example using the equation x2+7x+12=0. Start off by first looking at the term 12 and making

its factor tree on the board: 12=6*2=3*2*2. By looking at the factor tree we can see that 12 can be

expressed as 4*3 too. We must choose a combination whose sum is equal to 7. Explain that 4 and 3

are the correct terms to use since 4*3=c and 4+3=7. So we will write this as (x+4)(x+3), which is

equivalent to x2+7x+12=0. Explain that x=-4 or x=-3 since (x+4)(x+3)=0.

So likewise if my equation was x2-10x+16=0 what are the factors of 16? (Do this problem on the over head using bubbl.us)

Since are factors are 2, 4, 8 then we need to multiply two of them who’s sum is -10. Remind them that

other factors are also -2, -4, and -8. We need to use -2 and -8 since -2*-8=16 and -2+-8=-10. Our

equation is factored out as (x-2)(x-8)= x2-10x+16=0. Make sure you multiply back out using FOIL

to check you work. So, x=2 or x=8 is our zeros since when either one are plugged into the

equation you will get zero.


 * #5. Checking for Understanding: ** (5 minutes)

So class if we had the equation x2+11x-24=0 what would we do first? They should tell you to find the

factors of 24 first so write them out on the board: -2,2,-4,4, -8, 8, -12, 12. Make sure they include

the negative factors too. The should come to realize that in order to get a sum of 11 the factors that

must be used should be 8+3. However, point out that 8*3=24 not -24 so the equation cannot be

factored.


 * #6. Guided Practice: ** (20 minutes)

Split students into groups of three and hand out the “fear factor” work sheet that has a list of ten

quadratic equations on it and tell them to factor them together as a group. They will have ten minutes

to complete as many problems as they can. Explain that you will

choose two groups at random to show their problem on the board and each member will have

to participate in the explanation.

**#7. Independent Practice/ Closure:** (about 10 minutes)

Have them complete the rest of the sheet that was passed out independently and explain that you will

be walking around the room if they have any questions. Tell them that this assignment will also be

taken up at the end of class. Address any frequent questions that are asked by a student so that the

whole class may understand better too.