Algebra IIUnit of Study: Systems of Equations

Second Grading Period: Weeks 1- 3 (14 days) CURRICULUM OVERVIEWEnduring Understandings (Big Ideas) Unit Rationale

A wide array of methods and tools is available to solve systems of equations and inequalities including algebraic, graphical, tabular and technological.

Solutions to systems of linear equations and inequalities are in demand continuously in business and industry from finance to logistics. Linear algebra is a popular course at schools emphasizing business and economics.

Essential Questions Guiding Questions

Algebraically, is solving a linear equation much different than solving a system of linear equations?

How does a student recognize whether more than one equation is required to solve a problem situation?

√Compare and contrast formulating an equation for a linear situation requiring one equation with formulating two or more equations for a system of equations situation.

√What is the elimination method of solving a system of equations?

√What is the substitution method of solving a system of equations?

√What is the graphical method of solving a system of equations?

√What is the matrix method of solving a system of equations?

√What determines which method to use?

√Do all methods work in all problem situations?

TEKS (Standards) TEKS Specificity - Intended Outcome2A.2 Foundations for Functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills to simplify algebraic expressions and solve equations and inequalities in problem situations. The student is expected to:

2A.2A use tools including factoring and properties of exponents to simplify expressions and to transform and solve equations.

2A.3 Algebra and Geometry. The student formulates systems of equations and inequalities from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to:

2A.3A analyze situations and formulate systems of equations in two or more unknown or inequalities in two unknowns to solve problems;

2A.3B use algebraic methods, graphs, tables, or matrices, to solve systems of equations or inequalities; and

2A.3C interpret and determine the reasonableness of solutions to systems of equations or inequalities for given contexts.

” I CAN” statements highlighted in yellow should be displayed for students.I can :

use matrices with and without graphing calculators to solve systems of linear equations (2A.2A)

formulate systems of equations or inequalities from a word problem (2A.3A) use several types of methods to solve systems of equations or inequalities

(2A.3B) determine whether a solution to a systems problem makes sense (2A.3C)

SAISD © 2010-11 – Second Grading Period Algebra II Page 1 of 22

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.

ELPS Student Expectations ELPS Specificity – Intended OutcomeELPS 1c– use strategic learning techniques such as concept mapping, drawing, memorizing, comparing, contrasting, and reviewing to acquire basic and grade0level vocabularyELPS 2c – learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactionsELPS 2d – monitor understanding of spoken language during classroom instruction and interactions and seek clarification as neededELPS 3e – share information in cooperative learning interactionsELPS 4d – use prereading supports such as graphic organizers, illustrations, and pretaught topic-related vocabulary and other prereading activities to enhance comprehension of written text

Explore the meanings of the word matrix via discussion, brainstorming, graphic organizer and usage (1c, 2c, 4d)

Take advantage of student and teacher-led group discussions to hear content language used in context and ask for assistance in understanding if needed (2d, 3e)

College and Career Readiness Expectations College and Career Readiness – Intended OutcomeMathematics StandardsII-C1: Solution – recognize and use algebraic properties, concepts, procedures and algorithms to solve equations, inequalities, and systems of linear equations. II-D2: Representations – translate among multiple representations of equations and relationships.VII-C2: Functions – develop a function to model a situation.Cross-Disciplinary StandardsII-E4: Technology – use technology appropriately

Solve systems of linear equations and inequalities Translate between graphical, algebraic and verbal representations of systems

of equations and inequalities Formulate equations from word problem situations Use a graphing calculator to solve a system of linear equations with matrices

and point (s) of intersection

Evidence of Learning (Summative Assessment) On a formative mini-assessment (FMA), students will solve a system of linear equations by any method at least 80% of the time. On a unit assessment when given an appropriate word problem situation, students will formulate a system of equations or inequalities at least 80% of the

time. On a periodic quiz on solving systems of linear equations or inequalities, students will check their final answer for reasonableness at least 80% of the

time.

SAISD © 2010-11 – Second Grading Period Algebra II Page 2 of 22

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.

Algebra IISecond Grading Period CURRICULUM GUIDE

Essential Pre-requisite SkillsAlgebra 1

analyze situations and formulate systems of linear equations in two unknowns to solve problems (A.8A) solve systems of linear equations using concrete models, graphs, tables, and algebraic methods (A.8B) interpret and determine the reasonableness of solutions to systems of linear equations (A.8C)

Geometry select an appropriate representation (concrete, pictorial, graphical, verbal or symbolic) in order to solve problems (G.4) use numeric and geometric patterns to develop algebraic expressions representing geometric properties (G.5A) use properties of transformations and their compositions to make connections between mathematics and the real world, such as tessellations (G.5C)

The Teaching and Learning PlanInstructional Model & Teacher Directions

The teacher will…So students can demonstrate competency,

the students willEnsure a thorough review of “Show Professional Support” using the View selection at the top of the Agile Mind page: Advice for Instruction for Topics 4 and 16 Skim Prepare Instruction once before Day 1 Thoroughly read daily Deliver Instruction which delineates for each block

o Agile Mind materials needed

o Opening and framing questions for the lesson

o Lesson activities

o Suggested assignment

o Further questions

The Agile Mind lessons stress solutions of systems using the graphing calculator for intersections and tables. Added is a lesson on the use of matrices to solve systems. Wrapping up the unit are a few Agile Mind lessons on solving systems of inequalities.

Begin each class day with a 10-minute TAKS review.

Use the Promethean system to bring the lesson alive by getting students to the Promethean system to explore, study, assess and evaluate. Use the ActivExpressions and ActivView to solicit student input and grant some degree of control of the lesson progression.

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Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.

Agile Mind Topic 4 – Introduction to Systems7 Days

Day 1 Block 1 Formulating a linear system and solving by any method

Days 2-3 Block 2 Solving linear systems primarily by graphing and using tables Days 4-5 Block 3 Solving linear systems algebraically Day 6 Block 4 Solving nonlinear systems

Day 7 Block 5 Guided practice

Agile Mind Topic 4 – Introduction to Systems7 Days

Day 1 Block 1 Formulating a linear system and solving by any method (2A.2A, 2A.3A)

Days 2-3 Block 2 Solving linear systems primarily by graphing and using tables (2A.3B, 2A.3C) Days 4-5 Block 3 Solving linear systems algebraically (2A.3B, 2A.3C) Day 6 Block 4 Solving nonlinear systems (2A.3B, 2A.3C)

Day 7 Block 5 Guided practice (2A.3A, 2A.3B, 2A.3C)

Day 8 – Solving Systems using MatricesEngage/Explore

Have students in pairs discuss the word matrix and how it relates to algebra class. How is it used outside of math class? Is matrix on your graphing calculator?

Explain Distribute Systems of Equations using Matrices. Direct the students in pairs to learn the matrices method of solving

systems of linear equations – by one student working odd problems and one working the even problems. Explain their results to each other after about 10-15 minutes.

Monitor that students understand from the handout how to enter and use matrices on their graphing calculator.

Elaborate Direct all students individually to solve problem #1 on the handout by the

substitution method and then the elimination method. Does either of these methods resemble the matrix method?

Evaluate (time allowing) Consider the option of collecting the activity for either a grade or a

completion check. GRADABLE ACTIVITY

If time allows, have the students journal on how they like the matrix method compared to the other two algebraic methods and why.

Day 8 – Solving Systems using MatricesEngage/Explore

Discuss the word matrix with a partnerExplain

Read the handout how to use the matrix method of solving systems of equations. (2A.2A, 2A.3A, 2A.3B, 2A.3C)

Complete with a partner the problems on page 2 related to the matrix method of solving systems of linear equations. (2A.2A, 2A.3A, 2A.3B, 2A.3C)

Elaborate Solve the given problem with the substitution method, then the elimination method.

Does either method resemble the matrix method? (2A.2A, 2A.3A, 2A.3B, 2A.3C)Evaluate

Journal whether you prefer the matrix method to either the substitution method or the elimination method of solving systems of linear equations. (Marzano’s SimDiff) (2A.3B)

Agile Mind Topic 16 – Systems of Inequalities4 Days

Day 9 Block 1 Solutions methods for linear inequalities

Days 10-11 Block 2 Guided practice Day 12 Block 3 Linear programming

Agile Mind Topic 16 – Systems of Inequalities4 Days

Day 9 Block 1 Solutions methods for linear inequalities (2A.3B)

Days 10-11 Block 2 Guided practice (2A.3A, 2A.3B, 2A.3C) Day 12 Block 3 Linear programming (2A.3A, 2A.3B)

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Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.

Day 13 – Systems Review Engage

10-minute TAKS warmup Have the students discuss in groups of four the strengths and

weaknesses of group work. Explain

Distribute Solving Systems Review, one for each student. In groups have four, have the student groups decide on how to split the

problems between them, or even for each to do all. Encourage the students to ask for assistance if needed.

Day 14 – Unit Assessment Answer any student’s request for assistance. Distribute the tests which have been aligned with the TEKS verbs and

nouns.

Day 13 – Systems Review Engage

10-minute TAKS warmup Discuss the strengths and weaknesses of group work in your group. (Marzano’s

Cooperative Learning)Explain

Complete the systems review as the group decides. (2A.2A, 2A.3A, 2A.3B, 2A.3C) Ask questions if needed.

Day 14 – Unit Assessment Ask the teacher for any assistance required. Take the unit assessment. (2A.2A, 2A.3A, 2A.3B, 2A.3C)

Vocabulary: system of linear equations consistent inconsistent substitution method elimination method matrix

TAKS Vocabulary (verbs): understand manipulate solve simplify transform formulate analyze interpret determine

Resources: Algebra 2 Activities

Day 8 – Systems of Equations using Matrices Day 13 – Solving Systems Review

Agile Mind Algebra 2 Topics 4 and 16 4 Introduction to Systems 16 Systems of Inequalities

Promethean system

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Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.

Evidence of Learning (Summative Assessment)Formative Mini Assessments TAKS College-Readiness i.e.,

Anticipated Skills for SAT/ACT/AP/Career/LifeDuring one week of playing basketball, Manu Ginobili hit 30 shots from the floor and scored 68 points. Each shot was either a 2-point shot (x) or a 3-point shot (y). Which system of equations could be used to find the number of each type of “shot” that Manu made?

A. x + y = 68 2x + 3y = 30B. x – y = 68 2x – 3y = 30C. x – y = 30 2x – 3y = 68D. x + y = 30 2x + 3y = 68

2003 TAKS Exit Level Problem 46

SAT Prep

1. 3x + y = 19, and x + 3y = 1.Find the value of 2x + 2y.

A. 20

B. 18

C. 11

D. 10

E. 5

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Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.

2003 TAKS Exit Problem 3

2006 TAKS Exit Level Problem 32

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Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.

Algebra IIUnit of Study: Quadratic Functions

Second Grading Period: Weeks 4-9 (26days) CURRICULUM OVERVIEWEnduring Understandings (Big Ideas) Unit Rationale

In the polynomial progression, quadratic functions are the first to offer a unique point on the graph (vertex), an unambiguous visual representation of transformations, the property of real symmetry and the introduction of imaginary numbers to express solutions.

Ballistic motion, maximization or minimization of economic data, and architectural shapes are just a few of the situations modeled by quadratic functions. Students must understand the properties of quadratic functions to understand the implications of a horde of models of life around us.

Essential Questions Guiding Questions

How do quadratic functions vary from linear functions?

What is a unique point of the graph of any quadratic function?

Do all quadratic functions have a line of symmetry?

What are real-world applications that may be modeled by quadratic functions?

√What uniquely identifies an equation as quadratic?

√What is the characteristic shape of a graphed quadratic?

√What are the significant points found on the graph of most quadratics?

√What is the only solution method that always yields all the roots of a quadratic equation?

√How do you change a quadratic equation from the standard form to the vertex form?

√How does the discriminant predict the characteristics of the roots of a quadratic equation?

√What are complex numbers?

TEKS (Standards) TEKS Specificity - Intended Outcome2A.1 Foundations for Functions. The student uses properties and attributes of functions and applies function to problem situations. The student is expected to:

2A.1B collect and organize data, make and interpret scatterplots, fit the graph of a function to the data, interpret the results, and proceed to model, predict, and make decisions and critical judgments.

2A.2 Foundations for Functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills to simplify algebraic expressions and solve equations and inequalities in problem situations. The student is expected to:

2A.2A use tools including factoring and properties of exponents to simplify expressions and to transform and solve equations; and

2A.2B use complex numbers to describe the solutions of quadratic equations.

” I CAN” statements highlighted in yellow should be displayed for students.I can :

take data through a well-researched and time-tested process to produce a model for making predictions , decisions and judgments (2A.1B)

use factoring to transform and solve quadratic equations (2A.2A) use the properties of exponents to transform and solve quadratic equations

(2A.2A) use graphing calculators to transform and solve quadratic equations (2A.2A) use imaginary numbers as a form of solutions to quadratic equations (2A.2B)

SAISD © 2010-11 – Second Grading Period Algebra II Page 8 of 22

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.

2A.3 Foundations for Functions. The student formulates systems of equations and inequalities from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to:

2A.3A analyze situations and formulate systems of equations in two or more unknowns or inequalities in two unknowns to solve problems; and

2A.3B use algebraic methods, graphs, tables, or matrices, to solve systems of equations or inequalities.

2A.4 Algebra and Geometry. The student connects algebraic and geometric representations of functions. The student is expected to:

2A.4A identify and sketch graphs of parent functions, including linear (f(x) = x), quadratic (f(x) = x2 ), exponential (f(x) = ax ), and logarithmic (f(x) = loga x ) functions, absolute value of x (f(x) = ׀x׀ ), square root of x ) f(x) = ), and reciprocal of x f(x) = 1/x ); and

2A.4B extend parent functions with parameters such as a in f(x) = a/x and describe the effects of the parameter changes on the graph of parent functions.

2A.5 Algebra and Geometry. The student knows the relationship between the geometric and algebraic descriptions of conic sections. The student is expected to:

2A. 5E use the method of completing the square.

2A.6 Quadratic and square root functions. The student understands that quadratic functions can be represented in different ways and translates among their various representations. The student is expected to:

2A.6A determine the reasonable domain and range values of quadratic functions, as well as interpret and determine the reasonableness of solutions to quadratic equations and inequalities;

2A.6B relate representations of quadratic equations, such as algebraic, tabular, graphical, and verbal descriptions; and

2A.6C determine a quadratic function from its roots or a graph.

2A.7 Algebra and Geometry. The student interprets and describes the effects of changes in the parameters of quadratic functions in applied and mathematical situations. The student is expected to:

2A.7A use characteristics of the quadratic parent function to sketch the related graphs and connect between the y = ax2 + bx + c and y = a (x – h )2 + k symbolic representations of quadratic functions; and

2A.7B use the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of y = a (x – h)2 + k form of a function in applied and purely mathematical situations.

I can :

formulate equations or inequalities to solve a problem situation (2A.3A) use various methods including algebraic, graphical, tabular, and matrices to

solve systems of quadratic equations or inequalities (2A.3B) identify and sketch the graph of the quadratic parent function of y = x2 (2A.4A) describe the changes to the graph of a quadratic function when parameters

associated with the parent function such as a, b, and c in ax2 + bx + c are changed (2A.4B)

use the method called “completing the square” to switch various algebraic

versions of quadratic equations to point-specific forms (2A.5E) determine domain values of quadratic functions that reasonably fit the

situation (2A.6A) determine range values of quadratic functions that reasonably fit the situation

(2A.6A) interpret the solution to quadratic equations and inequalities (2A.6A) determine whether the solutions to quadratic equations and inequalities make

sense (2A.6A) easily move between the 4 common representations of quadratic functions –

equations, tables, graphs and verbal descriptions (2A.6B) write the equation of a quadratic function given its graph (2A.6C) write the equation of a quadratic function given its roots (2A.6C) go easily back and forth between the standard form and the vertex form of a

quadratic function and sketch the appropriate graph (2A.7A) predict the effects on the graph of a quadratic function when changes are

made to the parameters of its vertex form (2A.7B)

SAISD © 2010-11 – Second Grading Period Algebra II Page 9 of 22

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.

2A.8 Quadratic and square root functions. The student formulates equations and inequalities based on quadratic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to:

2A.8A analyze situations involving quadratic functions and formulate quadratic equations or inequalities to solve problems;

2A.8B analyze and interpret the solutions of quadratic equations using discriminants and solve quadratic equations using the quadratic formula;

2A.8C compare and translate between algebraic and graphical solutions of quadratic equations; and

2A.8D solve quadratic equations and inequalities using graphs, tables, and algebraic methods.

I can :

formulate quadratic equations and inequalities to solve problems for a given situation (2A.8A)

solve a quadratic equation using the quadratic formula (2A.8B) predict the characteristics of the solutions of quadratic equations by

determining the value of the discriminant (2A.8B) easily go back and forth between the algebraic and graphical solutions of

quadratic equations (2A.8C) compare the algebraic and graphical solutions of quadratic equations (2A.8C) use graphs to solve quadratic equations and inequalities (2A.8D) use tables to solve quadratic equations and inequalities (2A.8D) use algebraic methods to solve quadratic equations and inequalities (2A.8D)

ELPS Student Expectations ELPS Specificity – Intended OutcomeELPS 1c– use strategic learning techniques such as concept mapping, drawing, memorizing, comparing, contrasting, and reviewing to acquire basic and grade0level vocabularyELPS 2c – learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactionsELPS 2d – monitor understanding of spoken language during classroom instruction and interactions and seek clarification as neededELPS 3e – share information in cooperative learning interactionsELPS 4d – use prereading supports such as graphic organizers, illustrations, and pretaught topic-related vocabulary and other prereading activities to enhance comprehension of written text

Explore the meanings of the words linear and quadratic via discussion, brainstorming, graphic organizer and usage (1c, 2c, 4d)

Take advantage of student and teacher-led group discussions to hear content language used in context and ask for assistance in understanding if needed (2d, 3e)

College and Career Readiness Expectations College and Career Readiness – Intended OutcomeMathematics StandardsI-A1: Number Representations classify numbers as natural, whole, integers, rational, irrational, real, imaginary, and/or complex.I-A2: Complex Numbers – state the standard form used to represent complex numbers and describe their real and imaginary partsVII-C2: Solutions – explain the difference between the solution set of an equation and the solution set of an inequality.VII-C1: Functions – apply given quadratic models to solve problems (e.g., area, velocity, projectile motion)

When solving a quadratic equation with the quadratic formula, explain the meaning, usage and forms of complex numbers

Show the similarity and differences between the solutions of equations and the solutions of inequalities

Demonstrate how quadratic models are useful for problems in optimization and ballistic motion

Evidence of Learning (Summative Assessment) On a class project, students will take data through a well-researched and time-tested process to produce a model for making predictions , decisions and judgments at

least 80% of the time On a periodic quiz given mathematical expressions or quadratic equations, students will use tools including factoring and properties of exponents to

either simplify or transform them at least 80% of the time. On a unit assessment given quadratic equations, students will use complex numbers to describe their solutions at least 80% of the time. Given an appropriate word problem situation on an FMA, students will analyze the situation to formulate systems of equations or inequalities in two or

more variables at least 80% of the time.

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Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.

On a unit assessment given a system of equations, students will solve the system using algebraic methods, graphs, matrices or tables at least 80% of the time.

On a periodic quiz given the quadratic parent function , students will identify and sketch the graph of the function at least 80% of the time. On an FMA given the graph of the quadratic parent function, students will describe the effects of parameter changes on the graph at least 80% of the

time. On a unit assessment given the standard form of a quadratic equation, students will use the method of completing the square to switch to the vertex form

at least 80% of the time. On a periodic quiz when given a quadratic function, students will determine domain and range values to fit the situation at least 80% of the time. On a unit assessment after solving a quadratic equation or inequality, students will interpret and determine the reasonability of the solutions at least 80%

of the time. On a unit assessment given a quadratic function in any representation, students will show the connections between the four common representations of

a quadratic equation at least 80% of the time. On an FMA given either the graph or roots of a quadratic function, students will write the equation of the function at least 80% of the time. On a unit assessment given either form of a quadratic equations, students will sketch the graph and translate between the standard form and the vertex

form of a quadratic function at least 80% of the time. On a periodic quiz given a quadratic function expressed in the vertex form, students will predict and describe the effects on parameter changes at least

80% of the time. On a unit assessment given a quadratic equation to solve, students will analyze and interpret the solutions of a quadratic equation using the discriminant

and solve the equation using the quadratic formula at least 80% of the time.

SAISD © 2010-11 – Second Grading Period Algebra II Page 11 of 22

Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.

Algebra IISecond Grading Period CURRICULUM GUIDE

Essential Pre-requisite SkillsAlgebra 1

determine the domain and range for quadratic function in given situations (A.9A) investigate, describe, and predict the effects of changes in a on the graph y = ax2 + c (A.9B) investigate, describe, and predict the effects of changes in c on the graph y = ax2 + c (A.9C) analyze graphs of quadratic functions and draw conclusions (A.9D) solve quadratic equations using concrete models, tables, graphs, and algebraic methods (A.10A) make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the

function (A.10B)Geometry

select an appropriate representation (concrete, pictorial, graphical, verbal or symbolic) in order to solve problems (G.4) use numeric and geometric patterns to develop algebraic expressions representing geometric properties (G.5A) use properties of transformations and their compositions to make connections between mathematics and the real world, such as tessellations (G.5C)

The Teaching and Learning PlanInstructional Model & Teacher Directions

The teacher will…So students can demonstrate competency,

the students willDay 1 – Introduction to Quadratic Functions

Engage 10-minute TAKS warmup Review Systems Assessment

Explore Present the Introduction to Quadratics powerpoint as a review, an

activator of prior knowledge and a catalyst for questions. Proceed through it quickly as it is meant to only set the stage for this many week unit.

Distribute Quadratic Function Notes to each student to complete as a personal benchmark of where each student stands as far his/her knowledge of quadratics.

Explain/Evaluate Distribute Graphing Quadratic Functions: Vertex Form for students to

start in class as pairs and to finish up as homework. Students may use section 4.1 of the text as a reference.

Day 1 – Introduction to Quadratic FunctionsEngage

10-minute TAKS warmup Review your assessment of systems

Explore Watch and take notes (optional) (Marzano’s Notes) on the quadratics powerpoint

(2A.4A, 2A.4B, 2A.6B, 2A.8A) Complete the quadratics handout as your benchmark of what you currently know

about quadratics (2A.4A, 2A.4B, 2A.6B, 2A.8A)Explain/Evaluate

Start on the Vertex Form handout with a partner and finish up as homework. Use section 4.1 of text as a reference. (2A.4A, 2A.4B, 2A.6B, 2A.7B, 2A.8A)

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Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.

Day 2 – Graphing Quadratics in the Standard FormEngage/Explore

10-minute TAKS warmup Have students (volunteers or appointed) post on the overhead, board or

chart paper problems 4 and 9 from the homework (Quadratic Functions: Vertex Form)

Answer any other homework questionsExplain

Distribute Graphing Quadratics: Standard Form to each student. Have them work in pairs for each to complete a different half of the 12

problems – even or odd. Have student pairs discuss their completed problems prior to leaving class.

Have students complete the unfinished problems for homework. Use text section 4.2 for reference. GRADABLE ACTIVITY

Evaluate Monitor students by walking throughout the room and observing both

student progress and students working together.

Day 2 – Graphing Quadratics in the Standard FormEngage

10-minute TAKS warmup Post homework problems as desired or asked. (2A.4A, 2A.4B, 2A.6B, 2A.8A)

Explain/Evaluate Complete the standard form handout with a partner each doing half, even or odd.

(2A.4B, 2A.7A, 2A.7B, 2A.8A) Discuss results with your partner. (2A.4B, 2A.7A, 2A.7B, 2A.8A)

Finish the assignment for homework . Use text section 4.2 for reference. (2A.4B, 2A.7A, 2A.7B, 2A.8A)

Day 3 – Sections 4.1 and 4.2 on Graphing Quadratic FunctionsEngage

10-minute TAKS warmup Have students (volunteers or appointed) post on the overhead, board or

chart paper problems 14 and 15 from the homework (Graphing Quadratics: Standard Form)

Answer any other homework questionsExplain

Assign as guided practice for pairs to work together: pp 242/3 – problems 55-60 and pp 250/1 problems 51-55.

If required, assign completion for homework.

Day 3 – Sections 4.1 and 4.2 on Graphing Quadratic FunctionsEngage

10-minute TAKS warmup Post homework problems as desired or asked. (2A.4B, 2A.7A, 2A.7B, 2A.8A) Ask for homework assistance if needed.

Explain Complete guided practice problems on graphing quadratics with a partner (2A.4A,

2A.4B, 2A.6B, 2A.7A, 2A.7B, 2A.8A) If required, complete for homework .

Day 4 – Section 4.3 Solve x2 + bx + c = 0 by factoring Engage/Explore

10-minute TAKS warmup Ask your students to list all the paired factors of 20 and can any of the

pairs possibly add to 8 through any combinations of signs. Ask your students to list all the paired factors of 30 and can any of the

pairs possibly add to 7 through any combinations of signs.Explain

Follow up the above activity with example 1 and draw the parallels. What two factors of 20 with the same sign could add to -9? (-4 and -5) What two factors of -12 with opposite signs add to 3? (none).

Assign the 3 guided practice problems on page 252. Cover the two special cases – perfect square trinomial and difference of

two squares. Assign the 3 guided practice problems on page 253. Going from factors to roots, cover examples 3 and 4. Stress the zero

Day 4 – Section 4.3 Solve x2 + bx + c = 0 by factoring Engage/Explore

10-minute TAKS warmup Find the paired factors that meet the requirements given by the teacher.

Explain Take notes (Marzano’s Notes) on factoring and the two special cases – perfect

square trinomials and the difference of two squares. (2A.4A, 2A.4B, 2A.6B, 2A.7A, 2A.7B, 2A.8A)

Work the guided practice problems as assigned. Ask questions when appropriate. (2A.4A, 2A.4B, 2A.6B, 2A.7A, 2A.7B, 2A.8A)

Evaluate

Complete homework assignment on factoring and finding solutions (2A.2A, 2A.6A, 2A.8A, 2A.8D)

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product property which results in a change of sign – this always confuses students.

Assign the guided practice problems # 8 and # 9 on page 254.Evaluate

Assign for homework: 1, 2, 14, 17, 33, 39, 43

Day 5 – Connect FourEngage

10-minute TAKS warm-up Review questions from homework assignment

Explain Divide students into groups of 4 – 2 players, emcee (marks paper and

calls game) and judge (has answer sheet) – for Algebra Connect Four Announce rules and distribute 2 game cards and 2 sheets to each group. There will be two games:

1. Game 1 – as designed with players and others as designated with factors as answers

2. Game 2 – roots are answers and emcee and judge from Game 1 are players with the Game 1 players as emcee and judge (put new answers on answer sheet)

Day 5 – Connect FourEngage

10-minute TAKS warmup Ask any questions regarding homework assignment

Explain Play Connect Four in Game 1 in designated role (answers are factors) (2A.2A,

2A.6A, 2A.8A, 2A.8D) Play Connect Four in Game 1 in new designated role (answers are roots) (2A.2A,

2A.6A, 2A.8A, 2A.8D)

Day 6 – Quadratics Standard and Vertex FormsExplore/ Explain

10-minute TAKS warm-up Distribute Quadratics Standard and Vertex Form (four pages) to each

student Explain that this is an activity which covers all aspects of the quadratic

function covered thus far – graph, x-intercepts, both algebraic forms of the equation, vertex, axis of symmetry and minimum/maximum value

Have students work in pairs for each to complete a different half of the 12 rows – even or odd. Have student pairs discuss their completed work prior to leaving class.

Day 6 – Quadratics Standard and Vertex FormsExplore/Ex[plain

10-minute TAKS warm-up Complete with a partner the Quadratics Standard and Vertex Form activity. (2A.4A,

2A.4B, 2A.6B, 2A.7A, 2A.7B, 2A.8A)

Day 7 – Section 4.4 Solve ax2 + bx + c = 0 by factoring Engage/Explore

10-minute TAKS warm-up Ask students to multiply (5x – 2) times (x – 3). Then ask how would you

do it backwards to get your original two factors from 5x2 -17x + 6.

Explain Demonstrate via Examples 1 and 2 a formal method of performing this

task. Assign guided practice problems 5 and 6.

Tell students that if a and c are perfect squares, always be aware of a perfect square trinomial or the difference of two squares (Example 3)

Day 7 – Section 4.4 Solve ax2 + bx + c = 0 by factoring Engage/Explore

10-minute TAKS warm-up Perform given binomial multiplication and then do problem backwards to get the

original factors.Explain

Take notes (Marzano’s Notes) on factoring – look for perfect squares for a and c and always begin by factoring out common factors for each term. (2A.2A, 2A.6B, 2A.8A, 2A.8D)

Complete problems assigned as guided practice and ask questions if assistance is needed (2A.2A, 2A.6B, 2A.8A, 2A.8D)

Evaluate

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Always look for common factors in each term as a first step when a is not 1 (Example 4).

Assign guided practice problems 11, 12, 13, 18.Evaluate

Assign for homework problems 1, 2, 7, 10, 17, 21, 27, 29

Complete homework assignment (2A.2A, 2A.6B, 2A.8A, 2A.8D)

Day 8 – Section 4.4 Solve ax2 + bx + c = 0 by factoring cont’dEngage

10-minute TAKS warmup Have students (volunteers or appointed) post on the overhead, board or

chart paper problems 27 and 29 from the homework Explain

Now put together the factoring process with the solution process via Example 5.

Put the mathematical procedures together to work two applications problems – Example 6 (area) and Example 7 (maximization).

Assign guided practice problems 20, 21 and 22.Evaluate

Assign for homework 47, 49, 63, 67 GRADABLE ACTIVITY

Have students journal how comfortable they feel with working with quadratic functions.

Differentiate Instruction Struggling Learner –

Show student the following rules for factoring ax2+bx+c=0 into (kx+m)(lx+n) If c>0, then m and n are both positive If b>0, m and n are both positive If b<0, m and n are both negative If c<o, them m and n have different signs

Day 8 – Section 4.4 Solve ax2 + bx + c = 0 by factoring cont’dEngage

10-minute TAKS warmup Post homework problems if asked

Explain Take notes (Marzano’s Notes) on solving quadratic equations with a not equal to 1.

(2A.2A, 2A.6B, 2A.8A, 2A.8D) Complete assigned guided practice problems as a check for understanding. (2A.2A,

2A.6B, 2A.8A, 2A.8D)Evaluate

Complete homework assignment (2A.2A, 2A.6B, 2A.8A, 2A.8D)

Journal your comfort with working with quadratic functions.

Day 9 – Quadratic BingoEngage

10-minute TAKS warmup Have students (volunteers or appointed) post on the overhead, board or

chart paper problems 63 and 67 from the homework Explain

Let’s play Quadratic Bingo as a class! Distribute a bingo card and the direction page to each student. Give them time to set up their bingo card with their choice of zeros or

roots.

As the caller, you retain the Problems for Quadratic Bingo and the Questions Key.

Day 9 – Quadratic BingoEngage

10-minute TAKS warmup Post homework problems if asked

Explain Play Quadratic Bingo after preparing your card. (2A.2A, 2A.6B, 2A.8A, 2A.8D)

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When all is ready, start the game by calling the first problem chosen at random.

Repeat the game as time allows.Day 10 – Quiz over Quadratics

Explain Review any homework or general questions from students

Evaluate Administer quiz (yours or Quiz-Properties of Quadratics) ensuring

alignment with guiding TEKS nouns and verbs.

Day 10 – Quiz over QuadraticsExplain

Get any lingering concerns or questions answered (2A.2A, 2A.6B, 2A.8A, 2A.8D)Evaluate

Take quiz (2A.2A, 2A.6B, 2A.8A, 2A.8D)

Day 11 – Simplifying Radical ExpressionsEngage

10-minute TAKS warmup Review quiz results.

Explain Show 13-minute video Simplifying Radical Expressions Video Distribute Simplifying Radical Expressions activity Have students work in pairs for each to complete a different half of the

30 problems – even or odd. Have student pairs discuss their completed work prior to leaving class.

Elaborate If not completed, assign completion for homework.

Day 11 – Simplifying Radical ExpressionsEngage

10-minute TAKS warmup Review quiz results.

Explain Watch video on simplifying radical expressions. (2A.4A, 2A.4B) Complete radical expressions activity with a partner either in class or for homework.

(2A.4A, 2A.4B)

Day 12 – Section 4.5 Solve Quadratic Equations by Finding Square RootsEngage

10-minute TAKS warmup Review any homework or general questions from students

Explain If you showed the video during the last class period, start with Example

2, rationalizing the denominator. Cover box in upper right corner of page 267.

Put it all together to solve a quadratic equation in Examples 3 and 4 by simplifying and/or rationalizing as required.

Assign guided practice problems 9, 11, 13 and 15. Evaluate

Assign for homework problems 1, 2, 9, 12, 17, 27, 29, 33

Day 12 – Section 4.5 Solve Quadratic Equations by Finding Square RootsEngage

10-minute TAKS warmup Post homework problems if asked

Explain Take notes (Marzano’s Notes) on taking square roots and simplifying radical

expressions. (2A.6A, 2A.6B, 2A.8A, 2A.8D) Complete guided practice problems. (2A.6A, 2A.6B, 2A.8A, 2A.8D)

Evaluate

Complete homework assignment (2A.6A, 2A.6B, 2A.8A, 2A.8D)

Day 13 – Section 4.5 Solve Quadratic Equations by Finding Square Roots cont’d

Engage 10-minute TAKS warmup Review any homework or general questions from students

Explain Present modeling dropped objects beginning on page 268. h(t) = -16t2 + h0 for h in feet and t in seconds and h0 the initial height

On an h vs t graph, this yields half a parabola with (0, h0 ) at the maximum. Present Example 5 Assign for guided practice problems 38, 39 on page 270.

Day 13 – Section 4.5 Solve Quadratic Equations by Finding Square Roots cont’dEngage

10-minute TAKS warmup Ask any questions regarding homework assignment

Explain Take notes (Marzano’s Notes) on a quadratic equation governing free fall. (2A.6A,

2A.6B, 2A.8A, 2A.8D) Complete the problems assigned for guided practice on free fall. (2A.6A, 2A.6B,

2A.8A, 2A.8D)

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Day 14 – Solving Quadratics on the Graphing Calculator Engage/Explore

10-minute TAKS warmup Have students graph the equation from Example 5 ( y = -16t2 + 50 ) on

their graphing calculators and solve through any method.Explain

Present steps 1 through 4 on page 272 for solving with table. Present steps 1 through 3 on page 273 for solving with graphing zero

function. For guided practice, assign 1, 3, 5, 9

Day 14 – Solving Quadratics on the Graphing CalculatorEngage/Explore

10-minute TAKS warmup Graph y = -16x2 + 50 on your graphing calculator and solve through any method.

Explain Follow along on your graphing calculator as the teachers show how to solve your

equation above use the table function and the zero function. (2A.6A, 2A.6B, 2A.8A, 2A.8D)

Complete the problems assigned for guided practice. (2A.6A, 2A.6B, 2A.8A, 2A.8D)

Day 15 – Section 4.7 Complete the SquareEngage/Explore

10-minute TAKS warmup Square (x + y) ( x2 + 2xy + y2 or as rewritten x2 + x•2xy + y2) Compare to X2 + 6x + __ What number goes here to “complete the

square?”Explain

Present the Key Concept on page 284 term to complete square is (b/2)2 for x2 + bx Present example 2 Assign guided practice problems 4, 5 and 6 on page 285 Present examples 3 and 4 Assign guided practice problems 7, 9 and 11 on page 286.

Day 15 – Section 4.7 Complete the SquareEngage/Explore

10-minute TAKS warmup square x + y and compare to x2 + 6x + __ to find what number goes in the blank to

complete the squareExplain

take notes (Marzano’s Notes) on completing the square (2A.2B, 2A.5E, 2A.8A, 2A.8D)

complete the guided practice problems (2A.2B, 2A.5E, 2A.8A, 2A.8D)

Day 16 – Section 4.8 Use the Quadratic Formula and the DiscriminantEngage/Explore

10-minute TAKS warmup Ask the students to attempt the following using what they learned in

example 4 of section 4.7: Solve ax2 + bx + c = 0 for x by completing the square.

Explain Present the Key Concept on page 292 or present the solution to the

above Engage challenge. Show how to substitute for a, b, and c in the quadratic formula with

Examples 1-3: example 1 two different real solutions, example 2 two real solutions which are the same, example 3 two solutions involving imaginary numbers.

Present the Key Concept box on page 294, correcting the middle box to say Two real solutions which are identical.

Assign for guided practice on pages 293/4 problems 3, 5, 8

Day 16 – Section 4.8 Use the Quadratic Formula and the DiscriminantEngage/Explore

10-minute TAKS warmup Solve ax2 + bx + c = 0 for x by completing the square

Explain Take notes (Marzano’s Notes) on using the quadratic formula for solving quadratic

equations. (2A.8A, 2A.8B, 2A.8C, 2A.8D) Complete the guided practice problems to check for understanding. (2A.8A, 2A.8B,

2A.8C, 2A.8D)

Day 17 – Exploring the DiscriminantExplain

10-minute TAKS warmup Distribute Exploring the Discriminant to each student Have students work in pairs for each to complete a different half of the

10 problems – even or odd. Have student pairs discuss their completed work prior to leaving class.

Day 17 – Exploring the DiscriminantExplain

10-minute TAKS warmup Complete the discriminant activity with a partner by each of you doing half the

problem set. Discuss the results when you both complete your half. (2A.8A, 2A.8B, 2A.8C, 2A.8D)

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Day 18 – Quadratic Functions ReviewExplain

10-minute TAKS warmup Distribute Quadratic Functions Review to each student. Have students work in pairs for support and discussion, but to work each

problem individually. Encourage the students to ask questions when they need assistance.

Day 18 – Quadratic Functions ReviewExplain

10-minute TAKS warmup Complete the review individually but feel free to collaborate with your partner. Ask for assistance when needed. (2A.2B, 2A.5E, 2A.6A, 2A.6B, 2A.8A, 2A.8B,

2A.8C, 2A.8D)

Day 19 – QuizExplain

Review any homework or general questions from studentsEvaluate

Administer Quiz Finding roots of Quadratics ensuring alignment with guiding TEKS nouns and verbs.

Day 19 – QuizExplain

Get any lingering concerns or questions answeredEvaluate

Take quiz (2A.2B, 2A.5E, 2A.6A, 2A.6B, 2A.8A, 2A.8B, 2A.8C, 2A.8D)

Day 20 – Section 4.9 Graph & Solve Quadratic InequalitiesEngage

10-minute TAKS warmup Review Quiz

Explain Present Key Concept on page 300 and demo with Example 1 Show a system of quadratic inequalities via Example 3. Assign for guided practice 1, 2, 3, 4

Elaborate Have students compare KEY Concepts on pages 300 and 168.

Evaluate

Assign for homework problems 3, 4, 5, 9, 17, 18, 19, 21, 25 GRADABLE ACTIVITY

Differentiate Instruction Struggling Learner –

1. review graphs of linear inequalities, such as x>1 (number line)2. review Ex 7 on pg 3033. review graphs of linear inequalities in 2 variables y > x + 2

(coordinate plane)4. review Ex 1 pg 3005. review graph of system of linear inequalities in 2 variables6. y > x – 1 and y < 2x + 1 (coordinate plane)7. review Ex 3 pg 31

Advanced Learner - Investigate paraboloids and the creation of a “liquid mirror” with mercury (Algebra 2 Best Practices Toolkit pg 57 Lesson 4.9)

Day 20 – Section 4.9 Graph & Solve Quadratic InequalitiesEngage

10-minute TAKS warmup Review quiz

Explain Take notes (Marzano’s Notes) on graphing a quadratic inequality in two variables

(2A.3A, 2A.3B, 2A.8A, 2A.8D) Complete guided practice problems as a check for understanding (2A.3A, 2A.3B,

2A.8A, 2A.8D)Elaborate

Compare KEY Concepts on pages 300 and 168. (2A.3A, 2A.3B, 2A.8A, 2A.8D)Evaluate

Complete homework (Marzano’s homework (2A.3A, 2A.3B, 2A.8A, 2A.8D)

Day 21 – Section 4.9 Graph & Solve Quadratic Inequalities cont’dEngage

10-minute TAKS warmup

Day 21 – Section 4.9 Graph & Solve Quadratic Inequalities cont’dEngage

10-minute TAKS warmup

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Review homeworkExplain

Introduce 1-variable inequality solutions via Examples 4 (tablularly), 5 (graphically) and 6 (algebraically).

Present Example 6 as an application. Assign as guided practice on pages 302/3: 5, 6, 7

Evaluate

Assign as homework problems 1, 2, 27, 33, 39, 41, 51, 53, 71

Review homework (2A.3A, 2A.3B, 2A.8A, 2A.8D)Explain

Take notes (Marzano’s Notes) on 1-variable inequalities (2A.3A, 2A.3B, 2A.8A, 2A.8D)

Complete guided practice problems as a check for understanding (2A.3A, 2A.3B, 2A.8A, 2A.8D)

Evaluate

Complete assigned homework problems (2A.3A, 2A.3B, 2A.8A, 2A.8D)

Day 22 – Section 4.10 Write Quadratic Functions & ModelsEngage/Explore

10-minute TAKS warmup Homework review. Have the students find a water fountain and notice that the water follows

the path of a parabola. Measure the width (x-intercepts) and the height (maximum) using the water spigot as the “origin.” The equation will come later.

Explain Present Example 1 – graph with coordinates of vertex and one other

point to equation in vertex form Present Example 2 – graph with coordinates of x-intercepts and one

other point to equation in intercept form Present Example 3 – given three points to equation in standard form Have students solve the 3 simultaneous equations on their graphing

calculator with the matrix function Present Example 4 – data to scatterplot to quadratic equation via

quadratic regressionElaborate

Have students find their water fountain equation Assign the guided practice problems 1, 3, 5 and 7 on page 310.

Evaluate

Assign for homework problems 1, 2, 5, 17, 27, 45

Day 22 – Section 4.10 Write Quadratic Functions & ModelsEngage/Explore

10-minute TAKS warmup Homework review (2A.3A, 2A.3B, 2A.8A, 2A.8D) Make measurements of water path at a school water fountain

Explain Take notes (Marzano’s Notes) on writing quadratic equations for a given situation

(2A.1B, 2A.6B, 2A.6C, 2A.8A)Elaborate

Write quadratic equation of your water fountain. (2A.1B, 2A.6B, 2A.6C, 2A.8A) Complete assigned guided practice problems (2A.1B, 2A.6B, 2A.6C, 2A.8A)

Evaluate

Complete assigned homework problems (2A.1B, 2A.6B, 2A.6C, 2A.8A)

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Day 23– Quadratic JeopardyEngage

10-minute TAKS warmup Review homework.

Explore/Evaluate Divide class into two teams to play Quadratic Jeopardy Play Jeopardy

Day 23– Quadratic JeopardyEngage

10-minute TAKS warmup Review homework. (2A.1B, 2A.6B, 2A.6C, 2A.8A)

Explore/Evaluate Play Quadratic Jeopardy (2A.2B, 2A.5E, 2A.6A, 2A.6B, 2A.8A, 2A.8B, 2A.8C, 2A.8D)

Day 24 – Unit ReviewExplain

Use any of the following to generate student awareness of their need for clarification or depth of understanding:

Day 9 Quadratic Bingo Day 10 Quiz: Properties of Quadratics Day 18 Quadratic Functions Review Day 23 Quadratic Jeopardy Text Chapter Summary pages 317-322 Text – Chapter 4 Test page 323 Alternate resources for a Quadratics review is Agile Mind:

Topic 8 Quadratic Functions Summary Assessments – Guided assessments and self-test questions Testing – Multiple choice and constructed response

Day 24 – Unit ReviewExplain

Review using any of the following (2A.2B, 2A.5E, 2A.6A, 2A.6B, 2A.8A, 2A.8B, 2A.8C, 2A.8D):

Day 9 Quadratic Bingo Day 10 Quiz: Properties of Quadratics Day 18 Quadratic Functions Review Day 23 Quadratic Jeopardy Text Chapter Summary pages 317-322 Text – Chapter 4 Test page 323

Day 25 – Unit Assessment Answer any student’s request for assistance. Distribute the tests which have been aligned with the TEKS verbs and

nouns.

Day 25 – Unit Assessment Ask the teacher for any assistance required. Take the unit assessment. following (2A.2B, 2A.5E, 2A.6A, 2A.6B, 2A.8A, 2A.8B,

2A.8C, 2A.8D)Day 26 – Unit Assessment Review, Reteach, Reflect

Engage 10-minute TAKS warmup

return assessments to students give statistics associated with assessment scores

Explain assign students randomly in groups of 3 or 4 instruct them to together review the problems missed and see if they can

now solve them for any problems left over, show solutions to students

Elaborate

assign students to evaluate in their journals why they received the score that they got

Evaluate

assign as homework to turn in a fully corrected exam

Day 26 – Unit Assessment Review, Reteach, ReflectEngage

10-minute TAKS warmup receive individual assessment and class average

Explain in groups, work on solutions to problems missed

Elaborate

journal how he/she earned the grade receivedEvaluate

correct all problems missed

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Vocabulary: quadratic function standard form of quadratic

function vertex form of quadratic

function intercept form of quadratic

function parabola vertex axis of symmetry root of an equation zero of an equation radical radicand rationalization of

denominator conjugates imaginary unit, i complex number

absolute value completing the square quadratic formula discriminant best-fitting quadratic model minimum, maximum value

TAKS Vocabulary (verbs): collect organize interpret fit model predict understand manipulate solve simplify transform describe formulate

connect identify sketch extend translate determine relate investigate analyze compare

Resources:

McDougal Littell Algebra 2:Chapter 4 Quadratic Functions and Factoring

Algebra 2 Activities:Day 1 – Introduction to Quadratics (PowerPoint), Quadratic Function Notes, Graphing Quadratic Functions: Vertex FormDay 2 – Graphing Quadratics: Standard FormDay 5 – Algebra Connect FourDay 6 – Quadratics Standard and Vertex FormDay 9 – Quadratic BingoDay 10 – Quiz-Properties of QuadraticsDay 11 – Simplifying Radical Expressions Video , Simplifying Radical ExpressionsDay 17 – Exploring the DiscriminantDay 18 – Quadratic Functions Review Day 19 - Quiz Finding roots of QuadraticsDay 23 – Quadratic Jeopardy

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Evidence of Learning (Summative Assessment)Formative Mini Assessments TAKS College-Readiness i.e.,

Anticipated Skills for SAT/ACT/AP/Career/LifeThe equation gives the height , in feet, of a football as a function of time , in seconds, after it is kicked. What is the maximum height reached by the football?

2003 TAKS Exit Level Problem 47

2003 TAKS Exit Level Problem 49

2006 TAKS Exit Level Problem 18

SAT Prep

A B_ 2 5 3 10 4 17 5 26

4. Which of the following describes the relationship

between A and B as shown in the pairs of numbers in

the table above?

A. B = A + 4

B. B = 2A + 1

C. B = 3A - 1

D. B = A² + 1

E. B = A² - 1

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Power Standards represent the essential knowledge and skills students need for success in high school and beyond. Power Standards must be mastered to successfully pass the required assessments at each grade level. All TAKS eligible knowledge and skills are identified as Power Standards.