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GATEWAY REGIONAL HIGH SCHOOL

ALGEBRA II GRADE 10-12

PACING GUIDE

PURPOSE STATEMENT/PHILOSOPHY

The Algebra II curriculum is comprised of the following major concepts or ‘Big Ideas’:  (1) expressions, equations, and inequalities; (2) polynomial functions and graphs; (3) rational, irrational, and complex numbers; (4) quadratic equations and inequalities; (5) rational functions and graphs; (6) exponential and logarithmic functions; (7) sequences and series; (8) statistics and probability; and (9) matrices.  While knowledge of content is being developed, students are engaged in hands-on and cooperative activities that encourage mathematical reasoning, problem solving, communicating, and making connections.  Through these activities students utilize technology such as graphing calculators, computers, and calculator-based lab equipment.  In addition, they are encouraged to think more critically through activities that will involve investigations, explorations, and discovery.  Finally, evaluations appear in several formats:  pencil and paper tests, performance tasks, and long- and short-term projects.

PACING GUIDE

Month

# Days

Standards

Skills

Activities

Assessments

September

Analyzing Functions

30

MA.ALG2.3.1

MA.ALG2.4.2

MA.ALG2.4.3

Identify Functions

Evaluate Functions

Interval and Inequality Notation

Discrete Vs. Continuous

Domain and Range

 

Operation with Functions

Composite Functions

Graphic organizer 1.1 -identifying key terms and function relations

Graphic Organizer Function Notation 1.2- Identify function notation and evaluate functions

-Practice-Evaluating functions

Graphic Organizer 1.3-Graph inequalities on a number line using using inclusive and non-inclusive notation.  

-Practice-Interval Notation

Graphic Organizer 1.4-Identify if functions are discrete or continuous by analyzing graphs, functions, mapping, and tables.

Quiz Review-Intro to functions

Quiz Intro to functions

Graphic Organizer 1.5-state the domain and range of given data, graphs, and functions.

Graphic Organizer 1.6-Perform indicated operations with functions.  (adding, subtracting, multiplying, and dividing)

Practice function operations

Graphic Organizer 1.7- Evaluate Composite functions for the given values.

Secondary assessment

Quiz 1.1-1.4 Introduction to functions

Secondary Assessment

Quiz operations and evaluating functions.

Primary Assessment

Primary assessment on identifying functions and all function operations

October

Graphs of functions and Desmos Project

30 days

MA.ALG2.1.7

MA.ALG.3.1

MA.ALG2.3.4

MA.ALG2.4.2

Graphs of Functions

Increasing and Decreasing

Finding X and Y Intercepts

Exploring Polynomial Functions

Graphic Organizer- Identifying functions and the graphs that     correlate with them.

Graphic Organizer- Identify parts of graphs of functions. Identify the maximum and minimum of the graph.

Guided notes-  find the x and y intercepts of functions algebraically

Graphic Organizer-Determine the behaviors of functions (ex. Max,

min, translations, and end behaviors)

Test-Function Basics and their graphs

Performance Assessment-Desmos Graph Activity

  Secondary Assessment-Analyzing graphs of functions and behaviors

Primary Assessment

Function Basics and their graphs

Primary Assessment

Create a name using Desmos and the understanding of  graphs of functions.

November

Complex Numbers

Graphing Quadratic Functions

10 Days

15 days

MA.ALG2.1.1

MA.ALG2.1.2

MA.ALG2.1.2

MA.ALG2.1.6

MA.ALG2.1.7

Complex Numbers

Operations with Complex Numbers

Complex Numbers Unit Review

Quadratic Functions-terms and standard form

Characteristics of a quadratic function

Graphic Organizer-Define a complex number. Find the root of a negative number.

Graphic Organizer – Multiplying imaginary numbers and complex numbers.

Practice-Performing operations with complex numbers

Quiz Complex Numbers

Unit Review Packet-Overall review of finding roots and performing operations with complex numbers.

Test Complex Numbers

Graphic Organizer Intro To Quadratic Functions-Key terms for quadratic functions unit.  Standard form of a quadratic function.  

Graphic Organizer Characteristics of Quadratic functions-Understand how to determine the characteristics of a parabola given the equation.  Find domain and range. Practice problems built into Organizer

Secondary assessment-Operations with complex numbers (Ed Connect)

Primary Assessment- Test on Complex numbers unit

December

Graphing Quadratic Functions Continued

Solving Quadratic Functions Algebraically

20 Days

MA.ALG2.1.7

Graphing Quadratic Functions

Factoring quadratic functions

Graphic Organizer with Practice Graphing Quadratic Functions-Graph a parabola given the function in standard form.

Quiz Graphing Quadratic Functions

Guided Practice Factoring-Guided practice reviewing methods of factoring quadratics

Secondary Assessment-Graphing quadratic functions in standard form

January

Solve quadratic equations using the quadratic formula

Solve quadratic equations by taking the square root

Solve quadratics by completing the square

Graphic Organizer Quadratic Formula-Identify the discriminant and utilize the quadratic formula to solve.  Practice problems solving

Graphic Organizer Square root Method-Solve the quadratic equation by taking the square root. Individual practice problems in notes

Graphic Organizer Complete the Square-Solve the quadratic equation by completing the square.  Individual Practice problems

Quiz solving Quadratics Algebraically

Chapter Review Quadratics

Test Quadratic Equations

Secondary Assessment Solving quadratic equations-Solve the quadratic equations using various algebraic methods

Santa’s Special Delivery-Activity using quadratics and Santa delivering gifts (Secondary)

Primary Assessment-Chapter 5 Test on Quadratic equations

February

Graph quadratic in vertex form and graph circles

Solving Linear and non-Linear systems

15 days

25 Days

MA.ALG2.1.7

MA.ALG2.2.6

MA.ALG2.3.7

MA.ALG2.2.4

MA.ALG2.2.6

Graphing a quadratic in Vertex form

Graphing Circles from standard form

Use the distance formula and completing the square to create the standard form of a circle

Review graphing lines, absolute values, and inequalities

Graphic Organizer Vertex Form-Identify the vertex and locate points  from vertex form

-Practice Graphing in Vertex Form

Graphic Organizer graphing circles Part 1- Use the standard form of a circle to identify the center and the radius

-Practice Graphing Circles

Graphic Organizer graphing circles Part 2- Students will use the distance formula and completing the square to graph circles

-Set up in standard form and graph

Graphing Quadratics and Circles Quiz

Guided Practice-Graphing linear equations

Guided Practice-Graphing Absolute value equations

Guided Practice-Graphing linear inequalities

Performance Assessment-Students will use quadratics to compare 3 different Iphone plans

Secondary Assessment-Graphing quadratics and circles in standard form

Primary Assessment vertex form and circles-Students will graph quadratics in Vertex form and circles in standard form.

March

Graphing Systems of equations

Solving systems of equations algebraically

Solving Systems of Inequalities

Solving systems with 3 variables and 3 equations

Graphic Organizer Graphing systems-Solve a linear system by graphing and locating a point of intersection.

-Practice Graphing systems of linear equations

  Graphic Organizer Elimination-Use the Elimination method to solve the system of equations.

-Practice solving systems using elimination method

Graphic Organizer Substitution-Use the substitution method to solve the system of equations

-Practice solving systems using substitution

Quiz solving systems graphing and algebraically

Graphic Organizer Systems of Inequalities-Graphing systems of inequalities and identifying the solution set

-Practice graphing systems of inequalities

Graphic Organizer Systems with 3 variables-Using substitution and Elimination to solve systems with 3 variables.

-Guided Practice solving systems with 3 variables

Test Systems of Equations

Secondary Assessment Systems-Solve the systems of equations by graphing and algebraically

Secondary Assessment-Solving systems using different methods and comparing solutions. (Small Group)

Primary Assessment Systems of Equations-Solving linear and non-linear systems of equations with various methods

April

Arithmetic and Geometric Sequences and Series

20 days

MA.ALG.2.3.2

Arithmetic Sequences

Geometric Sequences

Arithmetic Series

Geometric Series

Graphic Organizer Arithmetic Sequences-Explore arithmetic patterns and use the explicit formula to find missing terms

-Guided practice using the explicit formula

Graphic Organizer Geometric Sequences-Explore Geometric patterns and find the missing terms

-Guided Practice Exploring geometric sequqences

Quiz Arithmetic and Geometric Sequences

Graphic Organizer Arithmetic Series-Use summation notation to find the sum of an arithmetic series

-Guided Practice Arithmetic Series

Graphic Organizer Geometric Series-Use Sums Formulas to find the sum of finite and infinite geometric series

-Guided Practice Geometric Series

Quiz Arithmetic and Geometric Series

Test Sequences and Series

Performance Assessment-Explore fractals web quest, Create a pattern using iterations

Secondary Assessment Sequences-Find the missing terms and explicit formulas for the patterns

Secondary Assessment Series-Find the sum of finite and infinite series

Primary Assessment Sequences and Series-Use the explicit and sums formulas to find missing terms and sums of all sequences and series

Performance Assessment Patterns-Create fractals and patterns by exploring series and iterations

May

Polynomials

20 days

MA.ALG2.1

Polynomial Functions

Adding and subtracting polynomials

Multiplying polynomials

Long Division of Polynomials

Graphic Organizer Polynomials Intro-Identify polynomials and understand writing in descending order

-Practice identifying polynomials and writing in standard form

Graphic Organizer Adding and Subtracting Polynomials-Perform basic polynomial operations with understanding of like terms

-Practice combining like terms

Graphic Organizer Multiplying Polynomials-Multiply larger polynomials and combine like terms

-Practice multiplying polynomials

Quiz operations with polynomials

Graphic Organizer Long Division of Polynomials-Use long division of polynomials to identify factors

-Guided practice long division

Secondary Assessment operations with polynomials-Perform operations with polynomials to write in simplest terms

Secondary Assessment Dividing Polynomials-Use synthetic and long division to factor polynomials

June

End of Year Benchmark

5 days

Synthetic Division of Polynomials

Prepare for End of Year Benchmark

Graphic Organizer Synthetic Division of Polynomials-Use synthetic division of polynomials to identify factors

-Practice synthetic division

Quiz polynomial division

Guided and Individual Practice-Practice with sequences and series and all polynomial operations

EOY Benchmark Test

Primary Assessment Polynomials-Perform basic operations with polynomials and use division to identify factors of polynomials

End of year Benchmark-Sequences and series and Polynomials Assessment

 GATEWAY GROUP CURRICULUM UNIT PLAN

Content Area: Algebra II

Unit Title: Polynomials

Timeframe:  6 weeks/MP I

Lesson Components

UNIT SUMMARY

In this unit,

Students will be able to…  

  1. Use Properties of operations to add, subtract, and multiply complex numbers.
  2. Solve quadratic equations with real coefficients that have complex solutions.                                           
  3. Show that the fundamental Theorem of Algebra is true for quadratic polynomials.
  4. Restructure by performing arithmetic operations on polynomial/rational expressions.  
  5. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
  6. Use an appropriate factoring technique to factor expressions completely.
  7. Explain the relationship between zeros and factors of polynomials and use zeros to construct a rough graph of the function defined by the polynomial.  

LEARNING TARGETS

ESSENTIAL QUESTIONS

ENDURING UNDERSTANDINGS

What is the Fundamental Theorem of Algebra?  

How are basic elements labeled and used to solve problems?

How do we find the sum of a finite geometric series?  

How do we factor?

How do we apply those formulas?

Use properties of operations for complex numbers.

Restructure polynomials/rational expressions.  

Derive Formulas

Explain relationships of polynomials

21st Century Themes

Global Awareness:  Understanding how rational functions are communicated in other cultures.

Financial, Economic, Business, and Entrepreneurial Literacy: Examining how Geometric series are used in the workplace to make businesses more profitable.

21st Century Skills

Creativity and Innovation: Working in collaborative teams to express original methods for solving real-world problems.

Critical Thinking and Problem Solving:  Learning the components of logical arguments and applying this skill to geometric problems.

Communication and Collaboration:  Using cooperative teams to develop notes and problem solving strategies.

Information Literacy: Maintaining complete and accurate notes of terms and formulas in Algebra.

Media Literacy:  Using conditional statements to examine the veracity of advertisements.

ICT Literacy-Information, Communications and Technology: Accessing necessary information to solve problems using Chrome Books and Smart Phones and demonstrating that information on presentation technology.

Life and Career Skills: Completing self-evaluations throughout the year to gage individual progress.

EVIDENCE OF LEARNING

 Assessment

Students will:

  • Use Properties of operations to add, subtract, and multiply complex numbers.
  • Solve quadratic equations with real coefficients that have complex solutions.                                           
  • Show that the fundamental Theorem of Algebra is true for quadratic polynomials.
  • Restructure by performing arithmetic operations on polynomial/rational expressions.  
  • Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
  • Use an appropriate factoring technique to factor expressions completely.
  • Explain the relationship between zeros and factors of polynomials and use zeros to construct a rough graph of the function defined by the polynomial.  

Integration of Technology:

  • Use of SmartNotebook
  • Use of Mobile Labs
  • Use of Internet
  • Use of SmartBoard/Projector
  • Use of Chromebooks/Smart Phones

Materials/Equipment:

Lined paper

Pencils

Screens/LCD Projector

Transparencies/markers

Colored pencils

Markers

Access to mobile labs/computer lab

Smartboard,

Handouts, texts, articles

Goals/Objectives

Students will:

CPI#

Learning Activities/Instructional Strategies

(Interdisciplinary Connections; Technology;

Integration of 21st Century Skills)

 Assessment Tasks

(More on the summative side)

  1. Use the structure of an expression to identify ways to rewrite it.

A.SSE.2

Notes

Cooperative Teams

Homework

Class Discussion

Smart Board Demonstrations

Assessments

Traditional Assessment

  • Derive the formula for the sum of a finite geometric series

Alternative Assessment

  • Using the Chromebooks students will represent complex numbers.  
  1. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.

A.SSE.4

Notes

Cooperative Teams

Homework

Class Discussion

Smart Board Demonstrations

Assessments

Traditional Assessment

  • Derive the formula for the sum of a finite geometric series Alternative Assessment
  • Students will uses formulas to calculate interest and formulas
  1. Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).

A.APR.2

  1. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

A.APR.3

  • Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior

Differentiation/Adaptations/Modifications:

  •  Study Guides
  •  Individual instruction
  • Use of review guides

Resources Provided

  •  Co-teaching environment
  • Workbooks and reference textbooks


CPI#

Cumulative Progress Indicator (CPI)

A.REI.4b

Solve quadratic equations in one variable.

 b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic

      formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives

      complex solutions and write them as a ± bi for real numbers a and b.

A.SSE.2

Use the structure of an expression to identify ways to rewrite it.

  • For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).

F.IF.7c

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

          c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior


 GATEWAY GROUP CURRICULUM UNIT PLAN

Content Area: Algebra II

Unit Title: Expressions and Equations

Timeframe:  6 weeks/MP I

Lesson Components

UNIT SUMMARY

In this unit,

Students will be able to…  

Extend the properties of exponents to rational exponents.

Understand solving equations as a process of reasoning and explain the reasoning.

Write expressions in equivalent forms to solve problems.

Interpret functions that arise in applications in terms of the content.

 

LEARNING TARGETS

ESSENTIAL QUESTIONS

ENDURING UNDERSTANDINGS

What are the properties of exponents?

How can you solve equations?

How do interpret functions?  

Identify the properties of exponents

Solve equations.

Interpret functions.

21st Century Themes

Global Awareness:  Understanding how Exponents are communicated in other cultures.

Financial, Economic, Business, and Entrepreneurial Literacy: Examining how functions are used in the workplace to make businesses more profitable.

21st Century Skills

Creativity and Innovation: Working in collaborative teams to express original methods for solving real-world problems.

Critical Thinking and Problem Solving:  Learning the components of logical arguments and applying this skill to functions.

Communication and Collaboration:  Using cooperative teams to develop notes and problem solving strategies.

Information Literacy: Maintaining complete and accurate notes of terms and formulas in Algebra II.

Media Literacy:  Using graphs to examine the veracity of advertisements.

ICT Literacy-Information, Communications and Technology: Accessing necessary information to solve problems using Chrome Books and Smart Phones and demonstrating that information on presentation technology.

Life and Career Skills: Completing self-evaluations throughout the year to gage individual progress.

EVIDENCE OF LEARNING

 Assessment

  • Extend the properties of exponents to rational exponents.
  • Understand solving equations as a process of reasoning and explain the reasoning.
  • Write expressions in equivalent forms to solve problems.
  • Interpret functions that arise in applications in terms of the content.

.

Integration of Technology:

  • Use of SmartNotebook
  • Use of Mobile Labs
  • Use of Internet
  • Use of SmartBoard/Projector
  • Use of Chromebooks/Smart Phones

Materials/Equipment:

Screens/LCD Projector

Transparencies/markers

Chromebooks

Smartboard,

Handouts, texts, articles


Goals/Objectives

Students will:

CPI#

Learning Activities/Instructional Strategies

(Interdisciplinary Connections; Technology;

Integration of 21st Century Skills)

 Assessment Tasks

(More on the summative side)

  1. Use properties of integer exponents to explain and convert between expressions involving radicals and rational exponents, using correct notation.

N.RN.1

For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.

Traditional Assessment

  • Convert between expressions involving radicals and rational exponents 

Alternative Assessment

  1. Apply the properties of integers
  1. Solve simple rational and radical equations in one variable and use them to solve problems.

A.REI.1

Justify each step in the process and the solution and in the case of rational and radical equations show how extraneous solutions may arise.  

Traditional Assessment

Simple Rational and Radical Equations

Alternative Assessment

Apply the properties of rational and radical.  

  1. Choose and produce equivalent expressions for exponential functions using the properties of exponents.

Produce equivalent expressions for exponential functions using the properties of exponents.

Produce equivalent expressions for exponential functions using the properties of exponents.

  1. Interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. 

Using Desmos, create graphs and tables to give a visual example of behaviors.  

Differentiation/Adaptations/Modifications:

  1. Study Guides
  2. Individual instruction
  3. Use of review guides  


CPI#

Cumulative Progress Indicator (CPI)

A.REI.2

Expressions and Equations

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to

those values, allowing for a notation for radicals in terms of rational exponents.  For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.

ASSE.3

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

F.IF.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.


 GATEWAY GROUP CURRICULUM UNIT PLAN

Content Area: Algebra II

Unit Title: Expressions and Equations (2)

Timeframe:  3 weeks/MP 2

Lesson Components

UNIT SUMMARY

In this unit,

Students will be able to

Find approximate solutions for the intersections of functions.

Write arithmetic and geometric sequences both recursively and with an explicit formula.

Graph exponential, logarithmic and trigonometric functions.  

LEARNING TARGETS

ESSENTIAL QUESTIONS

ENDURING UNDERSTANDINGS

What do exponential, logarithmic and trigonometric graphs look like?

How can find the intersections of functions?  

What are arithmetic and geometric sequences?    

Show the difference between graphs.

Approximate Intersections

  Find arithmetic and geometric sequences.  

21st Century Themes

Global Awareness:  Understanding how sequences are communicated in other cultures.

Financial, Economic, Business, and Entrepreneurial Literacy: Examining how logarithmic graphs are used in the workplace to make businesses more profitable.

21st Century Skills

Creativity and Innovation: Working in collaborative teams to express original methods for solving real-world problems.

Critical Thinking and Problem Solving:  Learning the components of logical arguments and applying this skill to algebra problems.

Communication and Collaboration:  Using cooperative teams to develop notes and problem solving strategies.

Information Literacy: Maintaining complete and accurate notes of terms and formulas in Algebra.

Media Literacy:  Using graphs to examine the veracity of advertisements.

ICT Literacy-Information, Communications and Technology: Accessing necessary information to solve problems using Chrome Books and Smart Phones and demonstrating that information on presentation technology.

Life and Career Skills: Completing self-evaluations throughout the year to gage individual progress.

EVIDENCE OF LEARNING

 Assessment

  • Find approximate solutions for the intersections of functions.
  • Write arithmetic and geometric sequences both recursively and with an explicit formula.
  • Graph exponential, logarithmic and trigonometric functions.  

Integration of Technology:

  • Use of SmartNotebook
  • Use of Mobile Labs
  • Use of Internet
  • Use of SmartBoard/Projector
  • Use of Chromebooks/Smart Phones

Materials/Equipment:

Lined paper

Pencils

Screens/LCD Projector

Transparencies/markers

Colored pencils

Markers

Access to mobile labs/computer lab

Smartboard,

Handouts, texts, articles

Goals/Objectives

Students will:

CPI#

Learning Activities/Instructional Strategies

(Interdisciplinary Connections; Technology;

Integration of 21st Century Skills)

 Assessment Tasks

(More on the summative side)

Find approximate solutions for the intersections of functions

A.REI.11

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x) involving linear, polynomial, rational, absolute value, logarithmic and exponential functions.

Traditional Assessment

  • Explain why the x-coordinates of the points where the graphs of the equations

Alternative Assessment

  • Desmos Graphing Project

Write arithmetic and geometric sequences both recursively and with an explicit formula.  

4.2.12A

Use them to model situations, and translate between the two forms.  

Traditional Assessment

  • Write arithmetic and geometric sequences

Alternative Assessment

  • Model situations.  

Graph exponential, logarithmic and trigonometric functions.  

F.IF.4

Graph exponential, logarithmic and trigonometric functions expressed symbolically or verbally and show key features of the graph (including intercepts, intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity) by hand in simple cases and using technology for more complicated cases

Traditional Assessment

  • Graphing

Alternative Assessment

  • Desmos Graphing Project

Differentiation/Adaptations/Modifications:

Study Guides

Individual instruction

Use of review guides  

  • Resources Provided
  • Co-teaching environment
  • Workbooks and reference textbooks

CPI#

Cumulative Progress Indicator (CPI)

A.REI.11

Expressions and Equations

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

F.IF.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.  Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity

F.BF.2

Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

 GATEWAY GROUP CURRICULUM UNIT PLAN

Content Area: Geometry

Unit Title: Functions/Inferences & Conclusions

Timeframe:  4 weeks/MP 2

Lesson Components

UNIT SUMMARY

In this unit,

Students will be able to…  

  1. Estimate, calculate and interpret the average rate of change of a function presented symbolically, in a table, or graphically over a specified interval.
  2. Construct a function that combines standard function types using arithmetic operations to model a relationship between two quantities.
  3. Identify different methods and purposes for conducting sample surveys, experiments, and observational studies and explain how randomization relates to each.
  4. Use data from a randomized experiment to compare two treatments and use simulations to decide if differences between parameters are significant; evaluate reports based on data.

LEARNING TARGETS

ESSENTIAL QUESTIONS

ENDURING UNDERSTANDINGS

What is rate of change?

How do you construct a function?

What is the data?  

Identify and apply rate of change

Determine when you construct a function.  

Use data to create reports.

21st Century Themes

Global Awareness:  Understanding how data is communicated in other cultures.

Financial, Economic, Business, and Entrepreneurial Literacy: Examining how data is used in the workplace to make businesses more profitable.

21st Century Skills

Creativity and Innovation: Working in collaborative teams to express original methods for solving real-world problems.

Critical Thinking and Problem Solving:  Learning the components of logical arguments and applying this skill to apple data roblems.

Communication and Collaboration:  Using cooperative teams to develop notes and problem solving strategies.

Information Literacy: Maintaining complete and accurate notes of terms and formulas in Algebra.

Media Literacy:  Using conditional statements to examine the veracity of advertisements.

ICT Literacy-Information, Communications and Technology: Accessing necessary information to solve problems using Chrome Books and Smart Phones and demonstrating that information on presentation technology.

Life and Career Skills: Completing self-evaluations throughout the year to gage individual progress.

EVIDENCE OF LEARNING

 Assessment

Students will be able to…  

  • Estimate, calculate and interpret the average rate of change of a function presented symbolically, in a table, or graphically over a specified interval.
  • Construct a function that combines standard function types using arithmetic operations to model a relationship between two quantities.
  • Identify different methods and purposes for conducting sample surveys, experiments, and observational studies and explain how randomization relates to each.
  • Use data from a randomized experiment to compare two treatments and use simulations to decide if differences between parameters are significant; evaluate reports based on data.

Integration of Technology:

  • Use of SmartNotebook
  • Use of Mobile Labs
  • Use of Internet
  • Use of SmartBoard/Projector
  • Use of Chromebooks/Smart Phones

Materials/Equipment:

Lined paper

Pencils

Screens/LCD Projector

Transparencies/markers

Colored pencils

Markers

Access to mobile labs/computer lab

Smartboard,

Handouts, texts, articles


Goals/Objectives

Students will:

CPI#

Learning Activities/Instructional Strategies

(Interdisciplinary Connections; Technology;

Integration of 21st Century Skills)

 Assessment Tasks

(More on the summative side)

Calculate and interpret the average rate of change of a function.  

4.2.12A

Present symbolically or as a table over a specified interval.  

Estimate the rate of change from a graph 

Write a function that describes a relationship between two quantities.  

Combine standard function types using arithmetic operations.  

Build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model

Use data from a randomized experiment to compare two treatments

Compare two treatments

Use simulations to decide if differences between parameters are significant

Differentiation/Adaptations/Modifications:

  1. Study Guides
  2.  Individual instruction
  3. Use of review guides  

Resources Provided

  • Co-teaching environment
  • Workbooks and reference textbooks

CPI#

Cumulative Progress Indicator (CPI)

F.IF.6

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.  

F.8F.1

Write a function that describes a relationship between two quantities

S.IC.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each