Unit Plan Template

Unit Plan that Incorporates the Use of Thinking Tools

Author
First and Last Name=	Ja= mes Carnes
School Name	= Herington High School
School District	USD 487
= School City, State	Herington, Ka= nsas
Classroom Informati= on
Subject Area
Ma= thematics
Grade Level(s)<= /p>
9-= 12
Unit Ov= erview
Unit Title
Qu= adratic Equations
Unit Summary
In this unit, students will learn graphing of quadratic equations, factors that affect the graph of the quadratic equat= ions, what the graphical representation of the solutions of quadratic equations look like and how to solve a quadratic equation by Quadratic Formula, completing the square, factoring and graphing. We will graph quadratic equations using paper and pencil and graphing calculators/computers to look at mult= iple graphs for comparison while changing various factors affecting the graph = of the equation. Students will= use the Visual Ranking Tool to rank equations according to given attributes of their graphs. Students will= use the Seeing Reason Tool to flow chart their thinking process in determining how and when to solve for a solution.&nb= sp; Students will use the Showing Evidence Tool to discover a continuum of need for problem solving by researching t= he importance of math in a chosen field or career.
Building the Founda= tion
Habits of Learning Taxonomy <= /span>
<= font size=3D2 face=3DArial>Knowledge, Comprehension, Application, Analysis, Synthesis, Evaluation Po= sitive attitudes and perceptions about learning, Acquisition and Integration of Knowledge, Extension and Refinement of Knowledge Pe= rsisting, Managing Impulsivity, Listening to Others with Understanding and Empathy, Thinking Flexibility, Thinking about our Thinking, Applying Past Knowledg= e to New Situations, Thinking and Communicating with Clarity and Precision.
Standards
2.= 4.K1d b 2.= 4.K1a, d-f 2.= 4.A1c-e 2.= 4.K1f 2.= 4.A1g 2.= 4.A1e
Learning Objectives
St= udent will be able to: In= terpret the graph of a quadratic equation. De= termine if a solution needs to be found by analyzing the attributes of a given eq= uation. De= termine best method for finding solutions So= lve a quadratic equation by graphing, factoring, completing the square or by quadratic formula. Ex= plain the meaning and rationale for accepting a solution and reason for rejecti= ng extraneous solutions.
Curriculum-Framing Questions	Essential Question
Wh= y do you need to become a problem solver?
Unit Questions
Yo= u are to jump out of an airplane and need 20 seconds of freefall. At what altitude must you jump i= f you must open your chute at 4000 feet? You are selling a product. What= is the maximum price for the maximum profit?
Content Questions
How does changing the sign and/or coefficient of the leading term change the graph of the equation? How does adding a linear term and/or constant change the graph of the equatio= n? How are x-intercepts related to the solution of the equation? Wh= at does the determinant tell us about the solutions? Wh= at does the vertex tell us about the equation? What are reasons you would reject a solution? What is the formula for finding the vertex? What is the line of symmetry? How do you factor a quadratic equation? How do you complete the square? What is the quadratic formula? Where is the max or min of a quadratic equation? What is the determinant in the quadratic formula? How many solutions does a quadratic equation have? What is an extraneous solution?

= Student Assessment Plan

Assessment Summary

Assessments will be by writt= en test after Factoring, Graphing, Completing the square, and solving by Quadratic Formula

Assessment Timeline


Before Project Work Begins	While Students Work on Projects=	After Project Work Ends

= · = Factoring will be covered. = · = Completing the square will be cove= red. = · = Quadratic Formula will be covered.= = · = Graphing techniques will be covere= d. = · = Vertex, max, min, determinant, lin= e of symmetry, x and y intercepts will be defined.	<= font size=3D1 face=3DSymbol>· = Grades for the completion= of each unit/tool.	·= Comprehensive problems requiring the use of all problems solving techniques.=

=	=	=

Visual Ranking Elements (Complete this section if this tool will be used in the unit)<= /font>

Visual Ranking Project Name (For the Visu= al Ranking workspace)<= /font>

Fi= nding Zeros of Quadratic Equations

Project Description (For the Visu= al Ranking workspace)

In this project, you will solve a number of equations = to find their zeros. You will = then rank them according to number and type of zeros. Many problems, such as problems = in economics, can be modeled using quadratic equations. Example: The manager of a Rock group has = found the predicted income from one of the group’s concerts can be modele= d by the function I(X)=3D-5X^2+400X-750, X is the price per ticket.=

Prompt (For the Visu= al Ranking workspace)<= /font>

Rank the following quadratic equations with two real zeros at the top followed by equations with doubl= e zeros and ending with imaginary zeros at the bottom. In each group, list equations wi= th maximums first and then equations with minimums.=

Sorting List (For the Visu= al Ranking workspace)<= /font>

I(x)=3D -5x^2 +400x -750

f(x)=3D x^2 -4x +9

f(x)=3D 2x^2 -4x +1

g(x)=3D x^2 -4x +4

h(x)=3D x^2 +8x +16

f(x)=3D -3x^2 -1

f(x)=3D x^2 -9x +18

g(x)=3D x^2 -12x +36

Practice Ranking (For your future quick reference)<= /font>

Te= acher ID: carnes

Practice Team ID 1:Team01

Practice Team ID 2:

Pa= ssword:

Pa= ssword: Team01

Pa= ssword:

Seeing Reason Elements (Complete this section if this tool will be used in the unit)
Seeing Reason Project Name (For the Seei= ng Reason workspace)<= /font>
A problem in economics or how to make the most money.
Project Description (For the Seei= ng Reason workspace)
Ma= ny problems have multiple answers depending on the scenario and what we want= to find out about the problem. In this exercise you will use the seeing reason tool to show which parts of a problem are needed and need to be solved for or found to lead us to a particular answer.
Research Question (For the Seei= ng Reason workspace)<= /font>
What do we need to know to decide how much to charge for a concert ticket?<= /p>
Practice Map (For your future quick reference)<= /font>
Practice Team ID: team08	Pa= ssword: team08
<= ![endif]>
Showing Evidence Elements (Complete this section if this too= l will be used in the unit)
Showing Evidence Project Name (For the Show= ing Evidence workspace)<= /font>
Wh= at does your future hold?
Project Description (For the Show= ing Evidence workspace)
In this activity, you will find historical examples from your chosen profess= ion or field of study of how math has increased or decreased in importance. Using this information you will formulate a claim as to whether it will continue to increase or decrease = and then use the examples to support your claim.
Prompt (For the Show= ing Evidence workspace)<= /font>
In the future, will the importance of math in your planned career continue to increase? Find evidence in the library= or on the internet to support your claim.&n= bsp; You should find evidence on the importance of math starting in 1900 and each 25 years up to the present.
Practice Case (For your future quick reference)<= /font>
Practice Team ID: Re= viewing Team ID:	Pa= ssword: Pa= ssword:
Claims
In the future, will the importance of math in your planned career increase?
Evidence <= /span>

= Unit Details

Approximate Time Ne= eded

In= troduction to lesson 1 class period of 1.5 hours, 2 weeks for research, 1-2 class periods for presentation and summary.

Prerequisite Skills=

Ca= reer goal, be able to use computer and internet, be able to use resources in library

Procedures <= /font>

This unit has the curriculum framing question, “Why do you need to become a problem solver? “. In this unit stude= nts will be introduced to several situations related to several fields in whi= ch solving problems is necessary. They will do research to discover how or if math will be as import= ant in their chosen field in the future as it has been in the past.

Introduction of Factoring. 1 class period=

Introduction of Completing t= he Square. 1 class period

Quiz 10 to 15 questions.

Introduction of Quadratic Formula. 1 class period