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Unit Plan: Quadratic Functions

Scott Tiefenthal

Algebra II

Student Teaching

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Table of Contents:Content Page

Introduction 3Goals 3

Standards 3Introductory Lesson 4

Lesson 2: Vertex Form 6Lesson 3: Standard Form 9

Lesson 4: Modeling Quadratic Functions 12Lesson 5: Factoring Quadratic Expressions 14

Lesson 6: Quadratic Equations 17Lesson 7: Quadratic Formula 19

Lesson 8: Modeling Quadratic Functions 21Aerospace Camp Activity 23

Lesson 9: Final Assessment 28Unit Evaluation/Reflection 29

Student Feedback Form 30Unit Plan Organizer 31

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Introduction

Welcome to a unit on quadratic functions. Throughout this unit, students will learn the characteristics of a quadratic function, as well as the characteristics of the graphs of quadratic functions. Throughout the unit we will use different types of learning, such as discovery and hands on learning, to lecture and modeling, to small group and class discussions. We will begin with an introductory lesson where we explore the quadratic function and its graph and end with a nice activity titled “Aerospace Camp” and final assessment.

Unit Goals

By the end of this unit, students will be able to find the vertex of any quadratic function.

By the end of this unit, students will be able to solve quadratic functions (aka find the zeros of a quadratic equation).

By the end of this unit, students will be able to graph and identify different characteristics of a quadratic function graph and analyze what the information means given real-world context.

Standards

HSF-LE.A.4- Construct and compare linear, and quadratic models.

HSF-IF.C.7- Graph functions expressed symbolically and show key features of the graph.a. Graph linear and quadratic equations and show intercepts, maxima and minima.

HSF-IF.C.9- Compare properties of two functions each represented in a different way.

HSF-BF.B.3- Identify the effect on the graph by replacing f (x) by f ( x )=k, kf (x), f (kx ), and f (x+k ) for specific values of k .

HSF-IF.C.8-a: using the process of factoring in a quadratic function to show zeros, extreme values, and symmetry of the graph and interpret these in a form of context.

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Lesson 1: Introduction to Quadratic Functions

Standards: HSF-LE.A.4- Construct and compare linear, and quadratic models.


HSF-IF.C.9- Compare properties of two functions each represented in a different way.

ObjectiveBy the end of the lesson, the students will be able to identify a quadratic equation and its graph 8 out of ten times.

Lesson Management: Focus and OrganizationThis class will just be an exploratory lesson for students to be introduced and gain a basic understanding of what a quadratic function is, what its graph looks like, and how we can transform these graphs and equations.

IntroductionAs the students walk in, they will have their daily warm up question posted. The warm up question will be a question to get students thinking about quadratic functions and will have them compare and contrast a graph of a linear equation y=x to the graph of a quadratic function y=x2.

Input Task Analysis

For this lesson, students will be investigating quadratic functions and their respective graphs, transformations of those functions, and some of the characteristics of a quadratic function.

After the warm up, students will be instructed to take out their notes. Since this is an introductory lesson, we will get a bulk of the vocabulary for the unit out of the way. We will define the following terms:

Vertex Form Standard Form Vertex Parabola Axis of Symmetry Maximum/Minimum Domain and Range

We will then pass out a Chromebook to each student. We will then use the Desmos graphing calculator to explore what happens to these graph characteristics. Students are welcome to work by themselves or in groups up to three students to make observations about the quadratic functions.

Thinking Levels (Blooms)

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1- Knowledge: Students will be able to define some of the terms we will be using in our unit with quadratic functions. Students will also be able to describe some of the characteristics of the translations of quadratic functions.

4-Analysis: Students will be examining and experimenting what happens to quadratic function graphs as a result of manipulating some of the values within the function.

Methods, Materials, and TechnologyThis lesson requires paper and pencil, as well as access to Chromebooks (or a similar technology) that allows students to access the Desmos online graphing calculator. The teacher may also find it helpful to have a computer-projector to model to students how to use the Desmos online graphing calculator.

Modeling Once students all have access to a Chromebook, the teacher will model how to use Desmos, and how to input the desired function with sliders to manipulate some of the values within the function.

Checking for UnderstandingWhile the students are working on their assignment, the teacher will walk around asking the students questions about their work as a means of formative assessment.

Guided PracticeAs a class, we will discuss and work through problems that require us to interpret the resulting graphs after manipulating values within the functions.

Collaborative or Independent PracticeStudents will work collaboratively or independently (based on their preference) with a computer program that will allow them to make conjectures and have them explain their findings.

ClosureAt the end of class, the students will be asked to turn in their Chromebooks back to the Chromebook cart. Students will also be asked to write down 3 conjectures or observations that came up while working with the Desmos graphing calculator.

AssessmentBy having students turn in their observations and conjectures, it allows the teacher to see what types of things that the students observed when manipulating the graphs and allows to plan for further lessons with their conjectures that could possibly be proven later in the lesson.

ReflectionAfter the lesson, I will reflect and make changes to the lesson as needed for future reference or for future use. I will also identify areas in the lesson that may need more or less emphasis, depending on how the students reacted to the lesson.

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Lesson 2: The Vertex Form of a Quadratic Equation




ObjectiveBy the end of this lesson, students will be able to accurate identify the following transformations of a quadratic equation in vertex form: horizontal translation, vertical translation, vertical stretch, and vertical compression, 8 out of 10 times on the given homework assignment.

Lesson Management: Focus and OrganizationThis class will be discussion based. It will begin with students sharing their observations from the exploratory activity to introduce the quadratic functions from the previous lesson. We will determine what causes the transformations of the graphs and how we can see them by graphing the function and without graphing the function.

IntroductionAs the students walk in, they will have their daily warm up question posted. The warm up question will ask the students to recall some of their observations and conjectures from the previous day in order to be prepared for the upcoming discussion.

Input Task Analysis

After the warm up question, the class will discuss some of their finding from the previous day and what may be the cause of these transformations. We will then begin breaking down the vertex form of a quadratic function, which looks like this:

f ( x )= y=a ( x−h )2+kwhere

a is the vertical stretch/compression factor. If a>1, the graph will be stretched vertically. If a<1, the graph will be compressed vertically.

h is a horizontal translation. k is a vertical translation.

We will then define the vertex of a parabola to be at point (h , k ), which can be found explicitly in the vertex form of a quadratic equation.

We will then determine how to find the axis of symmetry, which is a vertical line that runs through the parabola. This line will always be at x=h.

We will then determine whether the quadratic function will have a minimum or maximum. This can be determined by our a value. If a is positive, the graph will have a minimum and if a is negative, we will have a maximum. The minimum or maximum will be at our k value.

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We will then determine how to find our domain (which will be all real numbers for all quadratic functions) and the range. The range is the potential outputs of the function. Depending on whether the parabola opens up or down (whether a is positive or negative) will determine if our range will be ≤ or ≥ k .


3- Application: Students will use their observations from the previous day to find out how to manipulate a quadratic function to get a desired translation.

5- Synthesis: Students will be able to create quadratic functions in vertex form that will get them a desired vertex, or with desired transformations.

Methods, Materials, and TechnologyThis lesson will require a computer-projector for modeling. This can also be done with students using Chromebooks as well as determining how to find the characteristics of quadratic functions in vertex form.

Modeling Modeling will be done mostly on the projector and board to show students some of the relationships between the graphs and the equations that the graphs represent.


Guided PracticeAs a class, we will discuss and work through problems that require us to interpret the resulting graphs after manipulating values within the functions. We will determine how to write equations of quadratic functions with certain stipulations, such as:

Translated 3 units to the left and 5 units up with a compression of 12

Collaborative or Independent PracticeStudents will work collaboratively or independently (based on their preference) on the given assignment to check for students understanding of quadratic functions in vertex form.

ClosureAt the end of class, the students will be asked to turn in their in-class assignment. We will end with a short discussion and journal jot about what advantages the vertex form of a quadratic function may have as well as what makes the vertex form easy to use.

AssessmentFor this lesson, the student’s in-class assignment will be used as a formative assessment. I will select 3 problems to check for correctness (the three most challenging problems) and use this information to determine whether or not there are any misconceptions or if the students have mastered the material.

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ReflectionAfter the lesson, I will reflect and make changes to the lesson as needed for future reference or for future use. I will also identify areas in the lesson that may need more or less emphasis, depending on how the students reacted to the lesson. Students will also be given an opportunity to reflect in their journals about how vertex form can be beneficial when working with quadratic functions.

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Lesson 3: The Standard Form of a Quadratic Equation




ObjectiveBy the end of this lesson, students will be able to accurate identify the vertex of a quadratic equation that is expressed in standard form.

Lesson Management: Focus and OrganizationThis class will be discussion based, but will be based around the idea of deriving a formula that can represent the coefficients b and c when we have a quadratic function in standard form. The end result of this derivation is to find a way to determine the vertex of a quadratic function expressed in standard form.

IntroductionAs the students walk in, they will have their daily warm up question posted. The warm up question will ask the students to determine if they can find the vertex of a quadratic function written in standard form and a picture of its graph without graphing it themselves (by only using the function itself). They will soon see that they do not know how to find the vertex, which is what we will be learning in this lesson.

Input Task Analysis

After the warm up question, we will introduce the standard form of a quadratic equation, or f ( x )= y=a x2+bx+c

where a ,b , and c are real-number coefficients.

We will then discuss what is similar and what is different between the standard form and the vertex

form of a quadratic equation. The big points here are that both share a, and that standard form does not have a h or k value, but does have b and c values.

We will use this observation and begin with the vertex form of a quadratic equation, and derive a way to find the vertex.

f ( x )=¿ a ( x−h )2+k (1)Expanding the squared term: a ( x−h ) ( x−h )+k (2)

Multiplying the binomials (FOIL): a (x2−2hx+h2 )+k (3)Distributing the a: a x2−2ahx+ah2+k (4)

THINK PAIR SHARE: What do you think happens next? Students will be asked to think for a minute, share their thoughts about the derivation so far and what may come next, and then share their thoughts

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with that class to gain a better understanding of who is following along and where students are having trouble with the content.

Since −2ah is a coefficient for our x term, we can say that b=−2ah

And since ah2+k is what is left, we can say that c=ah2+k

Here, I will remind the students that the vertex is (h , k ). We can now use b=−2ah and solve for h, giving us

h=−b2a .

We can then find our k value by evaluating the function for x=−b2a .

Voila! We have found a way to determine our vertex when given a function in standard form. Now that we have found our vertex, we can determine our axis of symmetry, maximum or minimum value, domain and range. We can also just substitute our values of a, h and k into a vertex form equation to make our standard form equation into a vertex form equation.


5- Synthesis: Students will construct a method for finding the vertex (and other characteristics) of a quadratic equation in standard form. They will do this by deriving the vertex form and finding what b is equal to.

Methods, Materials, and TechnologyThis lesson will incorporate deriving meaning of different coefficients from two different representations of a quadratic function. Most of the work will be done on the board and in the students notes. We may use Desmos just to show that a vertex form function and a standard form function represent the same function, but just look different.

Modeling The modeling for this lesson will be done on the whiteboard. It will depict a story in a way. We will make our way from the left side of the board to the right side, showing work and making connections as we go in an effort to determine how to find our vertex when given a standard form quadratic function.

Checking for UnderstandingWhile the students are working on their assignment, the teacher will walk around asking the students questions about their work as a means of formative assessment. Since this lesson can be quite lengthy because of discussions as we proceed through the lesson, I will ask students to complete a 2-3 question exit slip that has them find the vertex of a standard form quadratic equation and also determine the various characteristics of that function once they have found the vertex.

Guided PracticeAs a class, we will discuss and work through problems that require us to find the vertex of a standard form quadratic equation.

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Collaborative or Independent PracticeStudents will work collaboratively or independently (based on their preference) on the exit slip to be completed by the end of the class period.

ClosureAt the end of class, the students will be asked to turn in their exit-slips. We will also have a short wrap up discussion on what benefits the standard form equation has over the vertex form.

AssessmentFor this lesson, the student’s exit slip will be a formative assessment for this lesson. It will be short and easy for me to determine what misconceptions, if any, students are having with the ideas covered in class.


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Lesson 4: Modeling Quadratic Equations



ObjectiveBy the end of this lesson, students will be able to construct a quadratic equation from a given set of data using a quadratic regression 4 out of 5 times on the in-class assignment, and analyze quadratic data and quadratic models to solve problems 2 times on the in-class assignment.

Lesson Management: Focus and OrganizationThis class will be discussion based with the opportunity for students to work together on a hypothetical problem that will allow them to use what they know about quadratic functions to determine the heights of two rockets.

IntroductionAs the students walk in, they will have their daily warm up question posted. The warm up question will ask the students to determine if they can find the vertex of a quadratic function written in standard form. It will also ask the students to find the maximum or minimum of that function.

Input Task AnalysisAfter the warm up question, we will begin our lesson by looking back at linear regressions. We will

use a similar method to do a quadratic regression, or find a quadratic equation that best represents a set of data that has a parabolic shape when graphed. We will look at data represented as ordered pairs, and data represented in function notation. This should be familiar to the students, as the process is very similar to doing a linear regression.

We will then move into an in-class group activity. The premise is that the students are at an aerospace camp. We have two rockets that we are testing and want to determine which rocket can reach a higher altitude. The rockets will have a parabolic flight path. The rockets have the following flight paths:

Rocket 1: h=−16 t2+150 t+1Rocket 2: h=−16 t2+145 t+10

There are also a few rough sketches of what their flight paths look like. I will then separate the class into two groups, each given the task to find the maximum height of one of the rockets, which will be assigned to each group. The students will be given 5 minutes (approximately the length of the song “Rocket Man” by Elton John) to come up with their solution.

Once both groups have a solution, we will explain their work and determine which rocket actually reaches the higher altitude, and what some of their information that they found actually means

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in context to the problem at hand. Students will then be assigned and in-class assignment to complete with the time remaining in class.


4- Analysis: Students will develop quadratic equations that represent a given set of data. Students will also examine what they know about the characteristics of quadratic functions and parabolas and use that information to solve word problems with different contexts.

Methods, Materials, and TechnologyThis lesson will incorporate cooperative learning, discussion, and a small bit of lecture to guide students to build a better understanding of how to model information using quadratic equations and parabolas. Students will need access to a graphing calculator to perform a quadratic regression, and may also want the calculator to graph some of the information on the assignments. Access to Desmos graphing calculator may also help with this lesson, but is not necessary.

Modeling The modeling for this lesson will be done on the whiteboard and using a document camera to show how to use that calculator to perform a quadratic regression. We will conduct the cooperative group activity on the white board as well.

Checking for UnderstandingWhile the students are working on their assignment, the teacher will walk around asking the students questions about their work as a means of formative assessment. The assignment will be relatively short in terms of number of problems, but I anticipate students will have questions about some of the story problems. I will encourage the students to first ask a neighbor or a friend before asking me for help.

Guided PracticeAs a class, we will complete a cooperative learning activity, during which students will determine how to find the maximum height of a rocket as Aerospace Camp. Students will also gain a better understanding about some of the characteristics of parabolas and quadratic equations.

Collaborative or Independent PracticeStudents will work collaboratively or independently (based on their preference) on the in-class assignment.

ClosureAt the end of class, the students will be asked to return their graphing calculators and asked if there are any last minute questions about the lesson before it is time to leave.

AssessmentFor this lesson, the student’s homework will be the assessment for the lesson. It will be short, and easy to check for understanding with just a few problems.

Reflection

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After the lesson, I will reflect and make changes to the lesson as needed for future reference or for future use. I will also identify areas in the lesson that may need more or less emphasis, depending on how the students reacted to the lesson.

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Lesson 5: Factoring Quadratic Functions



ObjectiveBy the end of this lesson, students will be able to factor 4 out of 5 quadratic expressions on their exit slip.

Lesson Management: Focus and OrganizationThis class will be discussion and modeling based. Students will learn about factoring a quadratic expression and what we can use this strategy to do. We will work through examples and find a strategy to check our work.

IntroductionAs the students walk in, they will have their daily warm up question posted. The warm up question will ask the students to recall what a greatest common factor (GCF) of a list of numbers is. This will be used later in our lesson.

Input Task Analysis

We will start out by multiplying two binomials together (also known as FOIL). Then I will ask the students how we can do this process of FOILing in reverse. That is, how can we take one quadratic function and make it into two binomials? There are a few cases that we need to consider. What might they be?

1) If a=1This is the easiest case. To factor a quadratic expression with a=1, we need to find two factors

of c that also have a sum equal to b.We will do this example as a class:

f ( x )=x2+9 x+20I will then ask how we can check our answer.

I will then have students work on a problem on their own. That problem is:f ( x )=x2+10 x−75

2) If a=−1, we have to factor out the negative and then continue to factor the positive quadratic expression.For example:

f ( x )=−x2−13x+12f ( x )=−(x2+13 x−12 )f ( x )=−(x−12)(x−1)

3) If |a|≠1

We first look to see if the GCF of a ,b ,and c is a. If it is, we just factor out a and factor as if a=1.

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f ( x )=4 x2+20 x−56f ( x )=4 (x2+5 x−14 )f ( x )=4 ( x−2 )(x+7)

If a is not the GCF of a ,b ,and c, we have to factor by grouping. We first must multiply a by c and find factors of ac that have a sum of b. Then, split b into two terms and factor each half of the expression by the same binomial:

f ( x )=2x2+11 x+12f ( x )=2x2+3x+8 x+12f ( x )=x (2x+3 )+4 (2x+3)f ( x )=(2 x+3)(x+4)


2- Comprehension- Students will be able to rewrite quadratic equations as a product of its factors.

Methods, Materials, and TechnologyThis lesson will be mostly modeling and allowing students to work on problems and practice their factoring skills.

Modeling Modeling will be done mostly on the board to show students how to factor quadratic expressions and how to think about solving them.


Guided PracticeAs a class, we will discuss and work through problems that require us to factor quadratic expressions and discuss what to think about when factoring quadratic expressions.

Collaborative or Independent PracticeStudents will work collaboratively or independently (based on their preference) on the given assignment to check for students understanding of factoring quadratic expressions.

ClosureAt the end of class, the students will be asked to turn in their in-class assignment. We will end with a short discussion of what we will be using this factoring strategy for in the next couple of lessons.


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Lesson 6: Quadratic Equations



ObjectiveBy the end of this lesson, students will be able to solve 4 out of 5 quadratic equations on their in class assignment.

Lesson Management: Focus and OrganizationThis class will be inquiry based. We will be determining how to solve quadratic equations by solving for zeros. These zeros are points on a graph where the parabola crosses the x-axis.

IntroductionAs the students walk in, they will have their daily warm up question posted. This question will have the student factor a quadratic expression. We will use this strategy later in the lesson.

Input Task Analysis

We will begin the lesson by defining what a zero is (a value for x such that f ( x )=0).We will then introduce the Zero Product Property:

If ab=0 thena=0 or b=0.Solve x2−5 x+6=0 by factoring.

x2−5 x+6=0( x−2 ) ( x−3 )=0

So, from the Zero Product Propertyx−2=0x=2

Orx−3=0x=3.

This tells us that our quadratic equation is equal to 0 when x=2, or x=3. We can check our answer by solving f (2) and f (3):

f (2 )=(2 )2−5 (2 )+6=0f (3 )=(3 )2−5 (3 )+6=0.

Students may also use a graphing calculator to determine where the parabola crosses the x-axis.

Have students complete the problemx2−7 x=−12

On their own. We will go over it as a class and ask if any more examples are needed or if there are any more questions.

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3- Application: Students will use what they know about factoring quadratic expressions to solve quadratic equations that are ¿0.

Methods, Materials, and TechnologyThis lesson will be mostly modeling and inquiry and will allow students to determine the zeros of quadratic equations by factoring and by graphing.

Modeling Modeling will be done mostly on the board to show students how to factor quadratic expressions and how to take the factoring a step further in order to solve the functions for f ( x )=0.


Guided PracticeAs a class, we will discuss and work through problems that require us to factor quadratic expressions and discuss what to think about when factoring quadratic expressions and finding the zeros of a quadratic equation.

Collaborative or Independent PracticeStudents will work collaboratively or independently (based on their preference) on the given assignment to check for students understanding of factoring and solving quadratic expressions.

ClosureAt the end of class, the students will be asked to turn in their in-class assignment. We will end with a short discussion of what happens when we have a quadratic equation that is not factorable? Are we limited to only graphing to determine the zeros or can we find them algebraically?



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Lesson 7: The Quadratic Formula



HAS-CED.A.1- Create equations in one variable and use them to solve problems.

ObjectiveBy the end of this lesson, students will be able use the quadratic formula to solve quadratic equations 4 out of 5 times on the in class assignment.

Lesson Management: Focus and OrganizationThis class will be inquiry based. We will be determining how to solve quadratic equations by solving for zeros. These zeros are points on a graph where the parabola crosses the x-axis.

IntroductionAs the students walk in, they will have their daily warm up question posted. This question will have the student find the zeros of an unfactorable quadratic equation by graphing. Then asking how we can find these algebraically.

Input Task Analysis

We will begin by reviewing the warm-up question and how we found the zeros of the equation even though we could not factor the equation. We will then introduce the quadratic equation:

−b±√b2−4 ac2a

It is very important to explicitly state that the quadratic formula works for any quadratic equation that can be solved. It is also important to note that if the discriminant (√b2−4ac) is negative, then we will have no real solutions (you cannot find a real solution to the square root of a negative). If the discriminant is 0, we will have one solution, and if the discriminant is greater than 0, we will have two real solutions.


4- Analysis: Students are developing a method to solve quadratic equations. Students are also distinguishing where we can solve by factoring or where we would need to use the quadratic formula.

Methods, Materials, and TechnologyThis lesson will be mostly modeling and inquiry and will allow students to determine the zeros of quadratic equations by using the quadratic formula.

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Modeling Modeling will be done mostly on the board to show students how to solve quadratic equations using the quadratic formula.


Guided PracticeAs a class, we will discuss and work through problems that require us to use the quadratic formula to find the zeros of a quadratic equation.

Collaborative or Independent PracticeStudents will work collaboratively or independently (based on their preference) on the given assignment to check for students understanding of solving quadratic equations using the quadratic formula.

ClosureAt the end of class, the students will be asked to turn in their in-class assignment. We will end with a short discussion of when it would be appropriate to use factoring to solve and when it would be appropriate to use the quadratic formula.



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Lesson 8: Rocket Applications of Quadratics



ObjectiveBy the end of this lesson, students will complete the Aerospace Camp activity and be able to determine maximum height and hangtime of a rocket that has parabolic flight path.

Lesson Management: Focus and OrganizationThis class will be exclusively focused on cooperative learning and little assistance will be given from the teacher.

IntroductionAs the students walk in, they will have their daily warm up question posted. The warm up question will ask the students to solve a quadratic equation using the quadratic formula.

Input Task AnalysisFor this lesson, students will complete the Aerospace Camp activity.


4- Analysis: Students will develop quadratic equations that represent a given set of data. Students will also examine what they know about the characteristics of quadratic functions and parabolas and use that information to solve word problems with different contexts.

Methods, Materials, and TechnologyThis lesson will incorporate cooperative learning and discussion to guide students to build a better understanding of how to model information using quadratic equations and parabolas. Students will need access to a graphing calculator to perform a quadratic regression, and may also want the calculator to graph some of the information on the assignments. Access to Desmos graphing calculator may also help with this lesson, but is not necessary. Students will have the opportunity to have some hands-on learning and real life application of parabolas.

Modeling The modeling for this lesson will be done on the whiteboard and using a document camera to show how to use that calculator to perform a quadratic regression. We will conduct the cooperative group activity on the white board as well.

Checking for Understanding

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While the students are working on their activity, the teacher will walk around asking the students questions about their work as a means of formative assessment.

Guided PracticeAs a class, we will complete a cooperative learning activity, during which students will determine how to find the maximum height of a rocket as Aerospace Camp. Students will also gain a better understanding about some of the characteristics of parabolas and quadratic equations.

Collaborative or Independent PracticeStudents will work collaboratively on the in-class activity.

ClosureAt the end of class, the students will be asked to return their graphing calculators and asked if there are any last minute questions about the lesson before it is time to leave. We will also have a discussion about whether the rockets achieved their goals or not.

AssessmentFor this lesson, the student’s activity sheet will be the assessment for the lesson. It will be short, and easy to check for understanding with just a few problems.


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AEROSPACE CAMP

You have been recruited by NASA to work with your group to do testing on a new fleet of rockets that they have been developing. NASA has provided you with some supplies to your group, which are:

Graph Paper Graphing Calculator Chromebook with Internet Access Groupmembers A briefing from NASA

As your project coordinator, NASA has asked that I give you no assistance in determining the characteristics of your rocket, but I will tell you to use information you know about parabolic flight. I will check in periodically. Best of luck.

- Mr. T

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TOP-SECRET ROCKET #1:_____________________________________________________

*IN ORDER TO KEEP THE ROCKET A SECRET, YOU MUST FIRST COME UP WITH A CODE NAME SO THAT THE ROCKETS IDENTITY WILL NOT BE COMPROMISED. WRITE THAT IN THE SPACE PROVIDED ABOVE.

BRIEFING:

THIS ROCKET THAT YOU WILL BE ANALYZED IS TASKED TO BE ABLE TO REACH AN ALTITUDE OF 500 FEET ABOVE SEA LEVEL. THE REASON WHY IS CONFIDENTIAL. WE HAVE ASSEMBLED THE BEST AND BRIGHTEST THAT MR. T’S ALGEBRA II CLASS HAS TO OFFER TO DETERMINE WHETHER OR NOT THIS ROCKET WILL BE ABLE TO COMPLETE ITS INTENDED MISSION. WE HAVE ALSO PROVIDED YOU WITH ALL MATERIALS YOU MAYU NEED TO COMPLETE YOUR MISSION. YOUR WORK HERE IS IMPARATIVE TO OUR OPERATION. YOU MUST SHOW SUFFICIENT ALGEBRAIC EVIDENCE OF YOUR FINDINGS. THE FATE OF THE WORLD AS WE KNOW IT MAY DEPEND ON YOU.

NAME SIGNATURE

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TOP SECRET ROCKET #1 (TSR1)

THE FOLLOWING IS WHAT LITTLE INFORMATION WE HAVE COMPILED REGARDING TSR1:

TIME (SECONDS) HEIGHT (FEET)1 1393 3015 3357 241

IT HAS ALSO BEEN CONFIRMED THE TSR1 FOLLOWS A PARABOLIC FLIGHT PATH.

WE NEED YOU TO DETERMINE WHAT THAT FLIGHT PATH IS AND STATE HOW YOU DETERMINED IT:

AT WHAT HEIGHT DOES TSR1 LAUNGH FROM AND HOW DID YOU DETERMINE THIS?

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WE ALSO NEED TO KNOW WHETHER OR NOT TSR1 WILL REACH ITS INTENDED HEIGHT AS OUTLINED IN THE BRIEFING. WE MUST HAVE SUFFICIENT ALGEBRAIC EVIDENCE TO SUPPORT THIS:

IT IS IMPARATIVE THAT ONCE TSR1 HAS FLOWN A MISSION WE CAN RECOVER IT AS EFFICIENTLY AS POSSIBLE. WE MUST KNOW AT WHAT TIME THE ROCKET WILL BEGIN ITS DESCENT AND HOW LONG THE ROCKET WILL BE IN THE AIR AND HOW YOU DETERMINED THAT INFORMATION.

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Lesson 9: Final Assessment

ObjectiveBy the end of class, students will complete the final assessment for the unit with an 80% or higher.

Lesson Management: Focus and OrganizationThis class will be focused on assessment and giving students an opportunity to show what they have learned.

IntroductionWe will begin with a quick review of the main concepts of the lesson and answer any last minute questions the students might have.

Input Task AnalysisFor this lesson, students will be taking the final assessment.

Checking for UnderstandingThe assessment will be used to check for understanding.

ClosureAt the end of class a unit evaluation will be passed out for students to complete and return for feedback on the lesson.


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Unit Evaluation/Reflection

Throughout this unit I gained a great sense of confidence and accomplishment. Not only did most of my lessons go over extremely well with the students, it was great to introduce the students to learning mathematics in a way they had not been exposed to before. It was also very interesting to compare the reactions of lessons between my honors students and my regular Algebra II students. This is most definitely a unit I will always remember and something that I plan on using again in the future if I get the opportunity.

While observing the class for the first week or two of my placement, I got the sense that the way math was taught was fairly monotonous. It seemed to be the same routine day after day. A goal for myself was to never do the same thing two days in a row. If I had to lecture one day, I would make it a point to do some hands-on learning the following day, and get a good class discussion going the day after that. I wanted the students to get a better understanding of what mathematics really is, and not that it is simply memorizing and executing steps to answer a question. In these two areas, I feel that I really succeeded in giving the students something different and something that better represented math than just taking notes and following steps to solve a problem.

Unfortunately at my placement I was not able to make my own final assessment. My host school uses common assessments throughout the department for every unit. However, if I were to use have my own final assessment, it would be very similar to the Aerospace Camp Activity. I thought that that particular activity embodied everything that we covered in the unit and would have been a great problem solving activity as well. I feel that a final assessment like this could and would have taken away some of the stresses that students face when you force them to take something called an assessment.

I collaborated with my Cooperating Teacher when coming up with lessons and lesson plans for this unit, but most of the work was done by myself. I created the Aerospace Camp activity on my own as well. My CT helped me the most with sequencing and getting the unit to progress in a way that would best make sense for the students.

The students reacted very positively to my lessons. I feel that I brought more enthusiasm about mathematics than they were used to, but they responded well. I even got feedback such as, “This is boring, but I couldn’t imagine how boring it would be if you weren’t so excited about it,” and I often receive, “How can you be so excited about this?” While many comments may have been intended as sarcastic, it provides evidence that I really am bringing my best every day and am enthusiastic about math and teaching to the point that my students are starting to notice and even changing their own views on mathematics.

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Student Evaluation of Unit

Although the unit is not complete yet, I plan on giving this short feedback form to students after the final assessment:

1. How do you feel the unit went?

2. What went well for you (teaching strategies, assignments, problems, other)?

3. What did you struggle with the most?

4. How could I improve this lesson for future use?

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Documents

scotttiefenthal.weebly.comscotttiefenthal.weebly.com/.../26538909/unit_plan_quadr… · Web viewUnit Plan: Quadratic Functions. Scott Tiefenthal. Algebra II ... Table of Contents: