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Curriculum and Instruction – Office of Mathematics

Quarter 2 Algebra I

Introduction

In 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable goals for school and student performance. The District is committed to these goals, as further described in our strategic plan, Destination2025. By 2025,

80% of our students will graduate from high school college or career ready 90% of students will graduate on time 100% of our students who graduate college or career ready will enroll in a post-secondary opportunity

In order to achieve these ambitious goals, we must collectively work to provide our students with high quality, College and Career Ready standards-aligned instruction. The Tennessee State Standards provide a common set of expectations for what students will know and be able to do at the end of a grade. College and Career Ready Standards are rooted in the knowledge and skills students need to succeed in post-secondary study or careers. The TN State Standards represent three fundamental shifts in mathematics instruction: focus, coherence and rigor.

Focus Coherence Rigor

Thinking across grades:• The Standards are designed around coherent

progressions from grade to grade. Learning is carefully connected across grades so that students can build new understanding onto foundations built in previous years. Each standard is not a new event, but an extension of previous learning.

Linking to major topics:• Instead of allowing additional or supporting

topics to detract from course, these concepts serve the course focus. For example, instead of data displays as an end in themselves, they are an opportunity to do grade-level word problems.

Conceptual understanding:• The Standards call for conceptual understanding

of key concepts, such as place value and ratios. Students must be able to access concepts from a number of perspectives so that they are able to see math as more than a set of mnemonics or discrete procedures.

Procedural skill and fluency:• The Standards call for speed and accuracy in

calculation. While the high school standards for math do not list high school fluencies, there are suggested fluency standards for algebra 1, geometry and algebra 2.

Application:• The Standards call for students to use math

flexibly for applications in problem-solving contexts. In content areas outside of math, particularly science, students are given the opportunity to use math to make meaning of and access content.

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Standards for Mathematical Practice describe varieties of expertise, habits of minds and productive dispositions that mathematics educators at all levels should seek to develop in their students. These practices rest on important National Council of Teachers of Mathematics (NCTM) “processes and proficiencies” with longstanding

importance in mathematics education. Throughout the year, students should continue to develop proficiency with the eight Standards for Mathematical Practice.

This curriculum map is designed to help teachers make effective decisions about what mathematical content to teach so that, ultimately our students, can reach Destination 2025. To reach our collective student achievement goals, we know that teachers must change their practice so that it is in alignment with the three mathematics instructional shifts.

Throughout this curriculum map, you will see resources as well as links to tasks that will support you in ensuring that students are able to reach the demands of the standards in your classroom. In addition to the resources embedded in the map, there are some high-leverage resources around the content standards and mathematical practice standards that teachers should consistently access:

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Mathematical Practices(MP)

1. Make sense of problems and persevere in solving them

2. Reason abstractly and quatitatively

3. Construct viable arguments and

crituqe the reasoning of

others

4. Model with mathematics

5. Use appropriate tools strategically

6. Attend to precision

7. Look for and make use of

structure

8. Look for and express regularity

in repeated reasoning

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Quarter 2 Algebra I

The TN Mathematics StandardsThe Tennessee Mathematics Standards:https://www.tn.gov/education/article/mathematics-standards

Teachers can access the Tennessee State standards, which are featured throughout this curriculum map and represent college and career ready learning at reach respective grade level.

Standards for Mathematical PracticeMathematical Practice Standardshttps://drive.google.com/file/d/0B926oAMrdzI4RUpMd1pGdEJTYkE/view

Teachers can access the Mathematical Practice Standards, which are featured throughout this curriculum map. This link contains more a more detailed explanation of each practice along with implications for instructions.

Purpose of the Mathematics Curriculum Maps

This curriculum framework or map is meant to help teachers and their support providers (e.g., coaches, leaders) on their path to effective, college and career ready (CCR) aligned instruction and our pursuit of Destination 2025. It is a resource for organizing instruction around the TN State Standards, which define what to teach and what students need to learn at each grade level. The framework is designed to reinforce the grade/course-specific standards and content—the major work of the grade (scope)—and provides a suggested sequencing and pacing and time frames, aligned resources—including sample questions, tasks and other planning tools. Our hope is that by curating and organizing a variety of standards-aligned resources, teachers will be able to spend less time wondering what to teach and searching for quality materials (though they may both select from and/or supplement those included here) and have more time to plan, teach, assess, and reflect with colleagues to continuously improve practice and best meet the needs of their students.

The map is meant to support effective planning and instruction to rigorous standards; it is not meant to replace teacher planning or prescribe pacing or instructional practice. In fact, our goal is not to merely “cover the curriculum,” but rather to “uncover” it by developing students’ deep understanding of the content and mastery of the standards. Teachers who are knowledgeable about and intentionally align the learning target (standards and objectives), topic, task, and needs (and assessment) of the learners are best-positioned to make decisions about how to support student learning toward such mastery. Teachers are therefore expected--with the support of their colleagues, coaches, leaders, and other support providers--to exercise their professional judgement aligned to our shared vision of effective instruction, the Teacher Effectiveness Measure (TEM) and related best practices. However, while the framework allows for flexibility and encourages each teacher/teacher team to make it their own, our expectations for student learning are non-negotiable. We must ensure all of our children have access to rigor—high-quality teaching and learning to grade-level specific standards, including purposeful support of literacy and language learning across the content areas.

Additional Instructional SupportShelby County Schools adopted our current math textbooks for grades 9-12 in 2010-2011. The textbook adoption process at that time followed the requirements set forth by the Tennessee Department of Education and took into consideration all texts approved by the TDOE as appropriate. We now have new standards;

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Quarter 2 Algebra I

therefore, the textbook(s) have been vetted using the Instructional Materials Evaluation Tool (IMET). This tool was developed in partnership with Achieve, the Council of Chief State Officers (CCSSO) and the Council of Great City Schools. The review revealed some gaps in the content, scope, sequencing, and rigor (including the balance of conceptual knowledge development and application of these concepts), of our current materials. The additional materials purposefully address the identified gaps in alignment to meet the expectations of the CCR standards and related instructional shifts while still incorporating the current materials to which schools have access. Materials selected for inclusion in the Curriculum Maps, both those from the textbooks and external/supplemental resources (e.g., EngageNY), have been evaluated by district staff to ensure that they meet the IMET criteria.

Topics Addressed in Quarter Functions & Their Graphs Systems of Equations & Inequalities

Overview Continuing with functions in quarter 2, students graph, represent, model, compare and contrast linear, quadratic, and exponential functions. Students continue building their understanding of functions beyond linear functions by investigating tables, graphs, and equations that build on previous understandings of numbers and expressions. They make connections between different representations of the same function. They learn to build functions in a modeling context, and solve problems related to the resulting functions. Note that the focus is on linear, simple exponential, and quadratic equations. Students consider quadratic functions, comparing the key characteristics of quadratic functions to those of linear and exponential functions. They select from among these functions to model phenomena. Students learn to anticipate the graph of a quadratic function by interpreting various forms of quadratic expressions. In particular, they identify the real solutions of a quadratic equation as the zeros of a related quadratic function. Students expand their experience with functions to include more specialized functions—absolute value, step, and those that are piecewise-defined. Finally in this quarter, students will build on the concepts and skills previously acquired to prove and solve systems of linear equations and inequalities exactly and approximately (graphically and algebraically) in multiple contexts. In grade 8 students saw and solved systems for the first time and will compare the given equations or functions in the system. Students will also model real-world problems using equations or functions in the system.

Content Standard Type of Rigor Foundational Standards Sample Assessment Items**F-IF.B.6 Conceptual Understanding & Application 8.F.A.1,2,3; 8.F.B.4,5 Edutoolbox: Bottle RocketF-IF.C.7 Conceptual Understanding & Application 8.F.A.1,2,3; 8.F.B.4,5 Edutoolbox- Buddy Bags

F-BF. A.1, 3 Conceptual Understanding & Application 8.F.A.1,2,3; 8.F.B.4,5 Edutoolbox: Amusement ParkF-BF.B.3 , 4 Conceptual Understanding & Application 8.F.A.1,2,3; 8.F.B.4,5 Illustrative Math: Medieval Archer

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Quarter 2 Algebra I

F-LE.A.2 Conceptual Understanding & Application 8.F.A.1,2,3; 8.F.B.4,5 Illustrative Math: Allergy MedicineA-CED.A.2,3 Procedural Skills & Fluency , Conceptual

Understanding & Application8.EE.C.7 a, b; 8.EE.C.8 a, b, c Inside Mathematics: Number Towers

A-REI.D.11,12 Conceptual Understanding & Application 8.EE.C.8 a, b, c Math Shell: Representing Inequalities Graphically

** TN Tasks are available at http://www.edutoolbox.org/ and can be accessed by Tennessee educators with a login and password.

Fluency The high school standards do not set explicit expectations for fluency, but fluency is important in high school mathematics. Fluency in algebra can help students get past the need to manage computational and algebraic manipulation details so that they can observe structure and patterns in problems. Such fluency can also allow for smooth progress toward readiness for further study/careers in science, technology, engineering, and mathematics (STEM) fields. These fluencies are highlighted to stress the need to provide sufficient supports and opportunities for practice to help students gain fluency. Fluency is not meant to come at the expense of conceptual understanding. Rather, it should be an outcome resulting from a progression of learning and thoughtful practice. It is important to provide the conceptual building blocks that develop understanding along with skill toward developing fluency.

The fluency recommendations for Algebra I listed below should be incorporated throughout your instruction over the course of the school year.

A/G A-APR.A.1 A-SSE.A.1b

Solving characteristic problems involving the analytic geometry of linesFluency in adding, subtracting, and multiplying polynomialsFluency in transforming expressions and seeing parts of an expression as a single object

References:

https://www.engageny.org/ http://www.corestandards.org/

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Quarter 2 Algebra I

http://www.nctm.org/ http://achievethecore.org/

TN STATE STANDARDS CONTENT RESOURCES & TASKS CONNECTIONS

Functions & Their Graphs(Allow approximately 4.5 weeks for instruction, review, and assessment)

Domain: Interpreting FunctionsCluster: Interpret functions that arise in applications in terms of the context F-IF.B.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.

Domain: Linear, Quadratic, and Exponential Models ★Cluster: Construct and compare linear, quadratic, and exponential models and solve problems F-LE.A.1 Distinguish between situations

that can be modeled with linear functions and with exponential functions.b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

Enduring Understanding(s)Calculate, compare and interpret the rate of change from linear and exponential functions in multiple contexts.

Essential Question(s)How can a function's rate of change define its characteristics and the type of real-world phenomena it can model?

Objective(s):F-IF.B.6

i. Students will recognize slope as an average rate of change.

ii. Students will calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval.

iii. Students will estimate the rate of change from a linear or exponential graph.

F-LE.A.1i. Students will recognize that linear

functions grow by equal differences over equal intervals.

Prior to Planning Review the Following:CCSS Flip Book with Examples and Explanations of each Standard (F-IF.B.6 & F-LE.A.1)

To address the objectives within these standards, teach the following lessons.

Prerequisite Skills and Knowledge: Pearson Lesson 5-1 or Glencoe 3-3 (F-IF.B.6-i)• Introduction to Distinguishing Linear

and Exponential from Tables (F-LE.A.1-i & ii)

• Average Rate of Change (Obj. F-IF.B.6 ii. & iii.)

• Recognizing Average Rate of Change (Obj. F-IF.B.6-iii, F-LE.A.1)

• U.S. Census Task and Dwindling Concentrations Task (F-LE.A.1-iii)

Supplemental Task(s)SCS Math Task- High School Gym SCS Math Task- Parachuting Down

VocabularyRate of change, slope

Writing in MathWhat characteristics of a graph represent the rate of change? Explain.

How does finding a line’s slope by counting units of vertical and horizontal change on a graph compare with finding it using the slope formula?PH Algebra I Book Page 297 #39Use KNWS, SQRQCQ, or UPS√ StrategyLiteracy Strategies in Math (p. 22 ) UPS

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TN STATE STANDARDS CONTENT RESOURCES & TASKS CONNECTIONS

ii. Students will recognize and prove that exponential functions grow by exponential functions grow by equal factors over equal intervals.

iii. Students will distinguish and prove between situations that can be modeled with linear and exponential functions to solve mathematical and real world problems.

Additional Lesson(s):Better Lesson: How Will Your Salary Grow? Learn Zillion: Finding Average Rates of Change Using Data in Tables Videos for Prerequisite Support:• Finding slope using rise/run Video • Finding the rate of change using a table

Video• Finding the rate of change using a graph

Video• Finding slope using coordinates Video • Finding the slope of horizontal or vertical

lines Video

Domain: Interpreting FunctionsCluster: Interpret functions that arise in applications in terms of the context. F-IF.B.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.

Enduring Understanding(s)You can utilize essential information to interpret functions when used in applications.

Essential Question(s)What essential information is indicated when recognizing key features and graphing linear and exponential functions?

Objective(s):F.IF.B.4

i. Students will recognize and interpret the key features in tables and graphs of a linear and exponential functions: intercepts; intervals where the function is increasing, decreasing, positive, or negative, and end behavior.

ii. Students will interpret key features of

Prior to Planning Review the Following:CCSS Flip Book with Examples and Explanations of each Standard (F-IF.B.4, A-CED.A.2, F-IF.C.7, F-BF.B.3, F-LE.A.3, F-LE.5)

To address the objectives within these standards, teach the following lessons:

• Prerequisite Knowledge for Interpreting Functions (FOCUS ON REAL WORLD APPLICATIONS) (A.CED.A.2)

o Pearson 5-3 Slope Intercept Formo Pearson 5-4 Point-Slope Formo Pearson 5-5 Standard Formo Glencoe 4-1 Graphing Equations in Slope-

Intercept Form

VocabularyParent function, linear parent function, linear equation, y-intercept, slope-intercept form, x-intercept, standard form of a linear equation.Point-slope form, Absolute value function, translation, step function, piecewise function

Writing in Math

Create a story that would generate a linear function and describe the meaning of key features of the graph as they relate to the story.

Linear equations are useful in predicting future events. Describe some factors in real-world situations that might affect the reliability of the

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TN STATE STANDARDS CONTENT RESOURCES & TASKS CONNECTIONS

Domain: Creating EquationsCluster Create equations that describe numbers or relationships. A-CED.A.2 Create equations in two or

more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Domain: Interpreting FunctionsCluster: Interpret functions that arise in applications in terms of the context. F-IF.C.7 Graph functions expressed

symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★a. Graph linear and quadratic functions and show intercepts, maxima, and minima.b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

graphs and tables of functions in the terms of the contextual quantities each function represents.

iii. Students will sketch graphs showing the key features of a function, modeling a relationship between two quantities, given a verbal description of the relationship.

A-CED.A.2i. Students will create equations in two

or more variables to represent relationships between quantities in a real world context.

ii. Students will graph one ore more created equations in various forms on coordinate axes with appropriate labels and scales.

iii. Students will justify which quantities in a mathematical problem or real-world situation are dependent and independent of one another and which operations represent those relationships.

F.IF.C.7ai. Students will graph linear functions by

hand in simple cases or using technology for more complicated cases and show/label intercepts of the graph.

ii. Students will determine the differences between simple and complicated linear, exponential and quadratic functions and know when the use of technology is appropriate.

F-IF.C.7b• Students will graph square root, cube root,

o Glencoe 4-2 Writing Equations in Slope Intercept Form

o Glencoe 4-3 Writing Equations in Point Slope Form

• TN Task - Buddy Bags (A-CED.A.2, F- IF.B.4)

• Identifying and Interpreting Key Features of Exponential and Linear Functions (F-IF.B.4-i & ii, F-LE.A.3)

• Engage NY Lesson 3: Graphs of Exponential Functions (F-IF.B.4

• Engage NY Lesson 1: Graphs of Piecewise Linear Functions (F-IF.C.7b)

• Pearson Lesson 5-8 or Glencoe 4-7 (F-BF.B.3/F-LE.5)

• Engage NY: Four Interesting Transformations of Functions - Vertical Translation ( F-BF.B.3/F-LE.5)

• Engage NY: Four Interesting Transformations of Functions - Horizontal Translation ( F-BF.B.3/F-LE.5)

• Engage NY: Four Interesting Transformation of Functions - Horizontal Scaling ( F-BF.B.3/F-LE.5)

Additional ResourcesAlgebra II 2-4: Concept Byte PiecewiseFunctionsGlencoe

graph in making predictions.

Describe two methods you can use to write an equation of a line given its graph.

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TN STATE STANDARDS CONTENT RESOURCES & TASKS CONNECTIONS

Domain: Linear, Quadratic, and Exponential ModelsCluster: Interpret expressions for functions in terms of the situation they model. F-LE.A.3 Observe using graphs and

tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratic, or (more generally) as a polynomial function.

Domain: Building FunctionsCluster: Build new functions from existing functions. F-BF.B.3 Identify the effect on the graph

of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.F.LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

and piecewise-defined functions, including step functions and absolute value functions by hand in simple cases or using technology for more complicated cases and show/label key features of the graph.

F-LE.A.3i. Students will fluently compute growth

rates for linear, exponential, and quadratic functions.

ii. Students will compare tables and graphs of exponential and other polynomial functions to observe that a quantity, increasing exponentially, exceeds all others to solve mathematical and real-world problems.

F-BF.B.3/F-LE.5i. Students will describe the differences

and similarities between a parent function and the transformed function.

ii. Students will find the value of k, given the graphs of a parent function, f(x) and the transformed f(x)+k, k f(x), f(kx), or f(x+k) and the representation of k.

iii. Students will interpret parameters of a linear and exponential function.

4-7 Graphing Technology Lab – Piecewise-Linear Functions

• Better Lesson: Sketch Graphs • Better Lesson: Building Quadratic

Functions f(x), kf(x) and f(kx)

Videos for Prerequisite Support• Graphing a linear equation using slope-

intercept form Video• Writing an equation given the slope/y-

intercept Video• Writing an equation from a graph Video • Analyzing Linear Graphs Video • Graphing linear equations using point-

slope form Video• Writing an equation in point-slope form

using a point and the slope Video• Writing an equation in point-slope form

from a graph Video• Writing a linear equation using a table

Video

Supplemental Task(s)SCS Math Task -Real World Linear Equations Stations TN Task - What’s The Point (A-CED.A.2, A- REI.D.10) SCS Math Task- Point-Slope Form Practice Engage NY: Federal Income Tax

What is the difference between a horizontal translation and a vertical translation?

How are the graphs y = │ x │ – 4 andy = │ x – 4 │ the same? How are they different?

PH Algebra I Book Page 317 #28Use KNWS, SQRQCQ, or UPS√ StrategyLiteracy Strategies in Math (p. 22 ) UPS√

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TN STATE STANDARDS CONTENT RESOURCES & TASKS CONNECTIONS

Domain: Building FunctionsCluster: Build a function that models a relationship between two quantities.

F-BF.A.1 Write a function that describes a relationship between two quantities. ★

a. Determine an explicit expression, a recursive process, or steps for calculation from a context.

Domain: Linear, Quadratic, and Exponential Models ★Cluster: Construct and compare linear, quadratic, and exponential models and solve problems

F-LE .A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs

Enduring Understanding(s)From context, either write an explicit expression, define recursive process or describe the calculations needed to model between two quantities.

Essential Question(s)How can arithmetic and geometric sequences can be used to model real-world situations?Objective(s):

F-BF.A.1• Students will write a function that describes

a relationship between two quantities explicit expression, a recursive process or steps for calculation from a context.

F-LE.A.2i. Students will recognize that arithmetic

sequences can be expressed as linear functions and geometric sequences as exponential functions.

ii. Students will construct linear functions including arithmetic sequences and geometric sequences given a graph, description of a relationship, or two input-output pairs (include reading these from a table).

iii. Students will determine when given a graph, a description of a relationship, or two input-output pairs represents a

Prior to Planning Review the Following:CCSS Flip Book with Examples and Explanations of each Standard (F-BF.A.1 & F-LE.A.2)

Engage NY Topic Overview

To address the objectives within these standards, teach the following lessons:

• Engage NY: Integer Sequences (F-BF.A.1)• Engage NY: Recursive Formulas for

Sequence (F-BF.A.1)• Engage NY: Arithmetic and Geometric

Sequences (F-LE.A.2 i & ii)• Engage NY: Why Do Banks Pay You to

Provide Their Services? (F-LE.A.2-iii)• Engage NY: The Power of Exponential

Growth (F-LE.A.2-iii)• Engage NY: Exponential Growth – U.S.

Population and World Population (F-LE.A.2 i & ii)

• Engage NY: Exponential Decay (F-LE.A.2 i & ii)

Additional Resource(s):• Learnzillion: Create a recursive formula (F-

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(include reading these from a table). linear or exponential function in order to solve problems.

LE.A.2 ii)• Learnzillion: Compare explicit expressions

and recursive processes (F-BF.A.1)

Systems of Equations & Inequalities/Graphing(Allow approximately 4.5 weeks for instruction, review, and assessment)

Domain: Reasoning with Equations and InequalitiesCluster: Solve equations and inequalities in one variable. A-REI.C.6 Solve systems of linear

equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Domain: Reasoning with Equations and InequalitiesCluster: Represent and solve equations and inequalities graphically. A-REI.D.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); 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.

Enduring Understanding(s)Systems of linear equations can be used to model problems and can be solved in multiple ways.

Essential Question(s)How is graphing used to solve a system of equations?

Objective(s):• Students will write and use a system of

equations and/or inequalities to solve real world problems.

• Students will justify the method used to solve systems of linear equations exactly and approximately focusing on pairs of linear equations in two variables.

• Students will approximate/find the solution(s) of the functions graphically.

Pearson6-1 Solving Systems by GraphingGlencoe6-1 Graphing Systems of Equations

Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Task(s):Illustrative Math: Quinoa Pasta 2Illustrative Math: Quinoa Pasta 3

Additional Lesson(s):Use the following Engageny Lessons to introduce the concepts/build conceptual understanding. If used, these lessons should be used before the lessons from the textbooks.Engage ny Algebra I Module 1, Topic C • Lesson 20 • Lesson 21 • Lesson 22 • Lesson 23

VocabularySystems of linear equations, solution of a system of linear equations, consistent, independent, dependent, inconsistent

Writing in MathPH Algebra I Book Page 364 #31Use KNWS, SQRQCQ, or UPS√ StrategyLiteracy Strategies in Math (p. 22 ) UPS√

Suppose you graph a system of linear equations. If a point is on only one of the lines, is it a solution to the system? Explain.

Can a system of linear equations have exactly two solutions? Explain.

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• Lesson 24

Additional Resource(s)CCSS Flip Book with Examples of each StandardSolving systems of Linear Equations by Graphing • Solving and interpreting a system of linear

equations by graphing Video• Interpreting solutions of systems of linear

equations Video• Analyzing special types of linear systems

Video

Domain: Reasoning with Equations and InequalitiesCluster: Solve equations and inequalities in one variable. A-REI .C.5 Prove that, given a system of

two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

Enduring Understanding(s)Systems of linear equations can be used to model problems and can be solved in multiple ways.

Essential Question(s)How is substitution used to solve a system of equations?

Objective(s):• Students will write and use a system of

equations and/or inequalities to solve real world problems.

• Students will justify the method used to solve systems of linear equations exactly and approximately focusing on pairs of linear equations in two variables.

Pearson6-2 Solving Systems Using Substitution Glencoe6-2 Substitution

Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Task(s)SCS Math Task - DVD Rentals Task

Additional Lesson(s)LearnZillion: Solving a system of equations by substitution

Additional Resource(s):

VocabularySubstitution method

Writing in MathUse a two-column algebraic proof to provide justifications and explanations when solving each equation and inequality.

When is the substitution method a better method than graphing for solving a system of linear equations?

PH Algebra I Book Page 372 #37Use KNWS, SQRQCQ, or UPS√ StrategyLiteracy Strategies in Math (p. 22 ) UPS√

How can you tell when a system of linear equations has no solutions using a graph? How can you tell when a system of linear

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CCSS Flip Book with Examples of each StandardSolving linear systems using substitution Video

equations has no solution using substitution?

Domain: Reasoning with Equations and InequalitiesCluster: Solve equations and inequalities in one variable A-REI .C.5 Prove that, given a system of

two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

Enduring Understanding(s)Systems of linear equations can be used to model problems and can be solved in multiple ways.Essential Question(s)How is substitution used to solve a system of equations?

Objective(s):• Students will write and use a system

of equations and/or inequalities to solve real world problems.

• Students will justify the method used to solve systems of linear equations exactly and approximately focusing on pairs of linear equations in two variables.

Pearson6-3 Solving Systems Using Elimination

Glencoe6-3 Elimination Using Addition and Subtraction

Additional Lesson(s):LearnZillion: Solve a system of equations by elimination

Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Task(s):SCS Math Task - Solving Systems Variety Task

Additional Resource(s):• Solving linear systems using elimination,

adding Video• Solving linear systems using elimination,

multiplying first Video

VocabularyElimination method

Writing in MathExplain how you would solve a system of equations using elimination.

PH Algebra I Book Page 378 #27Use KNWS, SQRQCQ, or UPS√ Strategy

What do the substitution method and the elimination method have in common? Explain.

Give an example of a system that you would prefer to solve using one method instead of the other. Justify your choice.

Domain: Creating EquationsCluster: Create equations that describe numbers or relationships A-CED.A.3 Represent constraints by

Enduring Understanding(s)Systems of linear equations can be used to model, analyze, and solve real and show the

Pearson6-4 Applications of Linear SystemsGlencoe

Writing in MathPH Algebra I Book Page 387 #18Use KNWS, SQRQCQ, or UPS√ Strategy

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equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

key features situations.

Essential Question(s)How do you determine the best method for solving a system of linear equations?

Objective(s):• Students will create and interpret

equations to model real-world situations.

• Students will represent constraints when solving problems with equations.

6-5 Applying Systems of Linear Equations

Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Task(s):SCS Math Task - Technology The Impossible Task (Teacher Notes) SCS Math Task - Technology The Impossible Task (Students) Performance Assessment – Systems of Equations in Grocery Shopping

Additional Lesson(s):Systems of Equations Lessons

Additional Resource(s):Writing and solving linear systems VideoFinding a break even point Video

Literacy Strategies in Math (p. 22 ) UPS√

Explain how to describe which variable to eliminate when using multiplication.

Domain: Reasoning with Equations and InequalitiesCluster: Represent and solve equations and inequalities graphically. A-REI.D.12 Graph the solutions to a linear inequality in two variables as a half plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-

Enduring Understanding(s)Understand general linear equations and their graphs and extend this to work with absolute value equations, linear inequalities, and systems of linear equations.Essential Question(s)How are inequalities useful in the real world?

Objective(s):

Pearson6-5 Linear Inequalities

Glencoe5-6 Graphing Inequalities in Two Variables

Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

VocabularyLinear inequality, solution of an inequalityWriting in MathUse a graphic organizer to organize the key concepts.Graphic Organizers (9-12)How is a linear inequality in two variables like a linear equation in two variables?How are they different?

PH Algebra I Book Page 394 #35

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planes. • Students will create inequalities in one variable and use them to solve and model real-world problems.

• Students will compare and contrast problems that can be solved by different types of inequalities.

• Students will identify characteristics of a linear inequality and system of linear inequalities, such as: boundary line (where appropriate), shading, and determining appropriate test points to perform tests to find a solution set.

Task(s):TN Task Arc – Algebra I – Equations & Inequalities (Tasks 4-8)

Additional Lesson(s):Engage NY: Solution Sets to Inequalities with Two Variables Recognize and Identify SolutionEngage NY: Solution Sets to Simultaneous Equations - Algebraically or GraphicallyAdditional Resource(s): SCS Math Task - Graph Linear Inequalities Modeling real world situations using linear inequalities Video

Use KNWS, SQRQCQ, or UPS√ StrategyLiteracy Strategies in Math (p. 22 ) UPS√

Domain: Reasoning with Equations and InequalitiesCluster: Represent and solve equations and inequalities graphically. A-REI.D.12 Graph the solutions to a linear inequality in two variables as a half plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Enduring Understanding(s): Understand the structure of algebraic

expressions and polynomials.

Essential Question(s): What are the "pieces" of an algebraic

expression? What do they represent in the context of

the real-world situation?

What do the parts of an expression tell us in a real-world context?

Objective(s): Students will solve a system of linear

inequalities by graphing. Students will model real-world situations

using systems of linear inequalities.

Pearson6-6 Systems of Linear InequalitiesGlencoe6-8 Systems of InequalitiesChoose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Task(s):SCS Math Task - System Word Problem SCS Math Task - Systems of Inequalities Assessment Task: Fishing Adventures

Additional Lesson(s):Engage NY: Applications of Systems of Equations and Inequalities

VocabularySystem of linear inequalities, solution of a system of linear inequalities

Writing in MathHow can you determine whether an ordered pair is a solution of a system of linear inequalities?

How is finding the solution to a system of inequalities different from finding the solution of a system of equations? How is it the same? Explain.

PH Algebra I Book Page 400 #28Use KNWS, SQRQCQ, or UPS√ Strategy

Literacy Strategies in Math (p. 22 ) UPS√

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Additional Resource(s):• Graphing systems of linear inequalities

Video• Writing a system of linear inequalities

Video• Using a system of linear inequalities Video

RESOURCE TOOLBOX

Textbook ResourcesPearsonwww.phschool.com/mathhttp://www.pearsonsuccessnet.comhttp://www.poweralgebra.comGlencoeConnectED Site - Textbook and Resources

StandardsCCSShttp://tncore.org/http://www.ccsstoolbox.org/http://parcconline.org/Common Core Flip BookAchieveTN Algebra I StandardsTN Department of Education Math Standards

VideosKhan AcademyTeacher TubeMath TVThe Futures ChannelThe Teaching Channel Illuminations (NCTM)Discovery Education Get The Math

Calculatorhttp://education.ti.com/educationportal/activityexchange/activityhttp://www.atomiclearning.com/ti_84TICommonCore.comhttp://www.casioeducation.com/educators

Interactive Manipulativeshttp://www.shodor.org/interactivate/activities/http://www.regentsprep.org/Regents/math/ALGEBRA/AV1/indexAV1.htm

Additional SitesState ACT Resourceshttp://www.kutasoftware.com/free.htmlIlluminations Resources for Teaching Mathhttp://www.stemresources.com/http://www.ilovemath.org/index.php?option=com_docmanhttp://www.mathbits.com/http://www.ixl.com/math/algebra-1http://teachers.henrico.k12.va.us/math/hcpsalgebra1/module1-1.html

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TeacherPayTeachers

LiteracyLiteracy Skills and Strategies for Content Area Teachers(Math, p. 22)Formative Assessment Using the UPS StrategyGlencoe Reading & Writing in the Mathematics ClassroomGraphic Organizers (9-12)

TasksMathematics Assessment Project (MARS Tasks)Dan Meyer's Three-Act Math TasksIllustrative Math TasksUT Dana CenterInside Math TasksLearnZillionSCS Math Tasks (Algebra I)

NWEA MAP Resources:https://teach.mapnwea.org/assist/help_map/ApplicationHelp.htm#UsingTestResults/MAPReportsFinder.htm - Sign in and Click the Learning Continuum Tab – this resources will help as you plan for intervention, and differentiating small group instruction on the skill you are currently teaching. (Four Ways to Impact Teaching with the Learning Continuum)https://support.nwea.org/khanrit - These Khan Academy lessons are aligned to RIT scores.

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