High school: algebra ii

! !Teacher: !Materials:

Objectives

----------------------------------------- high school: algebra ii

Date: Lesson 1 Board, Standard to Vertex Form Worksheet, projector, and calculators

Period(s): 2

!Content Standard(s)

CC.9-12.F.IF.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, symmetry of the graph, and interpret these in terms of a context.

!

Academic Language Considerations

Content Objective(s)

Language Objective

By the end of class, SWBAT

By the end of class, SWBAT

? Convert a quadratic in standard form

? Explain how to use completing the

to vertex form through the means of

square as a way to convert quadratics

completing the square.

from standard form to vertex form.

? Find the roots, vertex, and a graphical ? Explain how to find the roots of a

representation of the quadratic

quadratic through completing the

As evidenced by:

square

? Completing the, "Quadratics: writing

in vertex form," worksheet

Vocabulary & Concepts

Language of Instruction

Language of Production

? Complete the Square ? Standard Form ? Vertex Form ? Vertex ? Roots ? X-intercepts

? Recall the two forms quadratics are expressed in; Standard Form and Vertex Form

? Today we are converting quadratics in standard form to vertex form by completing the square.

? To complete the square we must first set the equation equal to zero, and bring over the, "cvalue" from standard form.

? We will take our b-value from standard form, divide it by 2, and square it. Here we are completing the square on the left hand side and

? We can use the process of completing the square to make a conversion of a quadratic expressed in standard form to vertex form.

? We first set the equation to zero, because like before when we were solving quadratics by completing the square we set the equation equal to zero.

? Then, we will complete the square where we bring the c-value over to the other side of the equal sign and perform the (b/2)

? we will add it to both sides to balance out the step, where b is the coefficient of the second term in

equations

standard form.

? From last week, we noticed that to express what ? Next we will minimize our left hand side by making it

is on the left as a binomial squared it took the

a binomial squared that takes this form (x+b/2)

form (x+b/2)

? After we will bring back our c-term from the

? Instead of solving for x (the roots of the

beginning and we are left with an equation in vertex

quadratic), we are going to bring back the new form.

c-value on the other side of the equal sign.

? Also, instead of rearranging the terms, we can solve

Which is now the k in vertex form.

for x by square rooting both sides, and then isolating

? We now have an equation of a quadratic that is x.

in vertex form, where (h,k) represents the vertex ? This x represents the roots of the quadratic

of the quadratic

? To graph the quadratic we use the vertex that we can

? To find the roots, we will go back to the step

easily find in vertex form and denotes the roots on the

where we completed the square and solved for x-axis.

x.

? We will also use the y-intercept from the quadratic in

? In doing this, we must perform an inverse

standard since they both represent the same quadratic

operation of a square, which is square rooting

just expressed in different forms.

both sides.

? Solve for x, and this represents the roots of the

quadratic.

? To graph the quadratic, we will start with the

vertex that we found using vertex form. The

(h,k).

? We will then mark the roots on the x-axis

(estimations may be found using a calculator).

? We will find the y-intercept by using the

equation in standard form. Why can we do this?

? The different forms represent the same

quadratic. Thus, they have the same vertex,

roots, y-intercept, and overall graph.

! ! ! ! ! ! !

!

Overview of Lesson

Time Interval Teacher Actions

10 minutes

Warm-up

!Solve the quadratic for x. !x2 - 8x - 25=-16 !Tell students to think about previous lessons covered.

Students will come in and work on the warm-up. I will walk around to make sure students are working on it correctly. When a students is done, they may be chosen by me to go up to the board and show their work to the whole class. Once the student is done, I will explain what the student did on the the board.

3 minutes

Go over announcements for the Quiz. Remind students it is 50% of their grade. Also make an announcement about retaking quizzes and how they must write a reflection before retaking a quiz. Have students copy down the reflection homework for that day.

Student Actions(W, I, P Monitoring Learning

Students will walk in and get started on copying the essential question and topic of the day to start off their notes. Students will proceed to answer the warm-up. Student will ask questions to their neighbor if they don't know how to begin then ask the teacher if both students are stuck

!Think about what we did last week? !What does it mean to solve a quadratic? !!Are we solving for x?

Would it be better to add 25 to both sides or

!add 16 to both sides? Why?

Students will ask questions regarding the quiz or retaking

!the quiz.

-How can you improve your grade for

!quizzes?

What must you do before retaking a quiz?

10 Minutes

Will proceed with answering example 1. *no new

Students take notes

Why do we set the equation equal to

! definitions*

zero?

! Will start by setting the equation equal to zero because since Will ask questions if they did

we are finding the roots, that is when the quadratic crosses not understand a specific How did we find the roots of a

! the x-axis.

step.

Will start off with previous methods on finding the roots of

!quadratic before? Can we factor?

the quadratic until we ultimately lead into completing the square.

! Will respond to questions How do we complete the square?

being asked by the teacher.

Will show the steps needed to complete the square and will

Can we simplify this square root? What

elaborate on how to perform inverse operations to isolate x. Will come across a number that is not a perfect square and

!multiples can we break it down to?

will question students if we can simplify that square root

What does our x represent in terms of

Will distribute calculators to students to determine an

the graph of the quadratic?

estimate of what roots are.

7 minutes

15 minutes 2 Minutes

Will go back to the binomial square step and show instead of solving for x, we can rearrange terms to attain the vertex form. Will recall how we can find the vertex of the quadratic by looking at the equation and find (h,k). Will begin graphing the roots, the vertex, and use the yintercept from standard form since both equation represent the same quadratic. Explain that conceptually even though the equations look differently, they represent the same quadratic. Will compare our sketch done in vertex form to a visual of the same quadratic inputted in standard form.

!Students take notes

!What form do we end up in?

! Will ask questions if they did How did we find the y-intercept?

not understand a specific

!step.

Are both these equations the same graph?

Will respond to questions

being asked by the teacher.

Allot students time to work on the handout that has practice problems on the material from the notes Pass out the handout and tell students how much time they have available to work on the handout Walk around the classroom and monitor IEP student first and help with specific steps that he may have trouble with. After, I will check in with every student one-on-one and ask questions regarding the steps they have performed to ensure they know what he or she is doing.

In pairs, students are to work on the handout. Each student is responsible to turn in a worksheet of their own.

!Where does this term come from?

When you solved for x, what does

!that give us?

Closure Explain to your partner what solving for x represents in terms of the graph of a quadratic. Use the appropriate language." I will be listening to students explaining to each other.

Students will work on the closure and when they are finished, they will leave the classroom.

We set the equation equal to zero and solved for x, so this point on a graph

!will be on...?

What is the accurate term for this?

Differentiation Additional Scaffolds for Specific Students' Needs

Extension Problems/Activities for Accelerated Learners

? Give on-on-one attention to the student. ? Provide a repetition of both the academic and simplified terms ? Color coordinate the different parts of the graph. ? Will ask simplified questions to distinguish which step the student

has the most difficulty. ? Have buddy-talk/ partner interaction during classwork time and

orally for the closure

? Have students explain the different approaches in using completing the square to solve for roots and converting from standard to vertex form

? Have the students assist students that may be struggling.

!

!

----------------------------------------- high school: algebra ii

!Teacher:

Date: Lesson 2

Period(s): 2

!Materials: Board, Standard to Vertex Form Worksheet Pt. 2, projector, guided notes, and calculators

Objectives

Content Standard(s)

!

CC.9-12.F.IF.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, symmetry of the graph, and interpret these in terms of a context.

!

Academic Language Considerations

Content Objective(s)

Language Objective

By the end of class, SWBAT

By the end of class, SWBAT

? Convert a quadratic in standard form

? Explain how to use completing the

to vertex form through the means of

square as a way to convert from

completing the square where there is

standard form to vertex form when

an "a-term" other than 1.

there is an "a" other than 1.

? Find the roots, vertex, and a graphical ? Explain how to find the roots of a

representation of the quadratic

quadratic through completing the

As evidenced by:

square with appropriate academic

? Completing the, "Quadratics: writing

language

in vertex form pt.2" worksheet

Vocabulary & Concepts

Language of Instruction

Language of Production

? Complete the Square ? Coefficient ? Standard Form ? Vertex Form ? Vertex ? Roots ? X-intercepts

? Today we are converting quadratics in standard form to vertex form by completing the square but there is an "a" that is no longer 1.

? We must recognize that we cannot complete the square just yet because we have an a-term.

? We will set the equation equal to zero, bring the c-term over to the right, then factor the a-term from the first two terms in standard form.

? When we add our term from completing the square multiply it by the a-value and add to both sides of the equal sign

? We can use the process of completing the square to make a conversion of a quadratic expressed in standard form to vertex form.

? We first set the equation to zero, because like before when we were solving quadratics by completing the square we set the equation equal to zero.

? Then, we will complete the square where we bring the c-value over to the other side of the equal sign and perform the (b/2)

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download