Major Content Supporting Content Additional Content Curriculum and Instruction – Mathematics Quarter 1 Algebra II 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 Shelby County Schools 2016/2017 Revised 6/29/16 1 of 35 Focus The TN Standards call for a greater focus in mathematics. Rather than racing to cover topics in a mile-wide, inch- deep curriculum, the Standards require us to significantly narrow and deepen the way time and energy is spent in the math classroom. We focus deeply on the major work of each grade so that students can gain strong foundations: solid conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom. For algebra 2, the major clusters account for 65% of time spent on instruction. Supporting Content - information that supports the understanding and implementation of the major work of the grade. Additional Content - content that does not explicitly connect to the major work of the grade yet it is required for proficiency. Coherence Thinking across grades: The TN Standards are designed around coherent progressions from grade to grade. Learning is carefully connected across grades so that students can build new understanding on to 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 the focus of the grade, these concepts serve the grade level focus. For example, instead of data displays as an end in themselves, they are an opportunity to do grade- level word problems. Rigor Conceptual understanding: The TN Standards call for conceptual understanding of key concepts. 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. Students are given opportunities to practice core functions such as single-digit multiplication so that they have access to more complex concepts and procedures. 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.
Transcript
Major Content Supporting Content Additional Content
Curriculum and Instruction – Mathematics
Quarter 1 Algebra II
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 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 readiness is 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.
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Focus
The TN Standards call for a greater focus in mathematics. Rather than racing to cover topics in a mile-wide, inch-deep curriculum, the Standards require us to significantly narrow and deepen the way time and energy is spent in the math classroom. We focus deeply on the major work of each grade so that students can gain strong foundations: solid conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom. For algebra 2, the major clusters account for 65% of time spent on instruction.Supporting Content - information that supports the understanding and implementation of the major work of the grade.Additional Content - content that does not explicitly connect to the major work of the grade yet it is required for proficiency.
Coherence
Thinking across grades:The TN Standards are designed around coherent progressions from grade to grade. Learning is carefully connected across grades so that students can build new understanding on to 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 the focus of the grade, these concepts serve the grade level focus. For example, instead of data displays as an end in themselves, they are an opportunity to do grade-level word problems.
Rigor
Conceptual understanding: The TN Standards call for conceptual understanding of key concepts. 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. Students are given opportunities to practice core functions such as single-digit multiplication so that they have access to more complex concepts and procedures.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.
Major Content Supporting Content Additional Content
Curriculum and Instruction – Mathematics
Quarter 1 Algebra II
The 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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Quarter 1 Algebra II
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.
Major Content Supporting Content Additional Content
Curriculum and Instruction – Mathematics
Quarter 1 Algebra II
Shelby 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; 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.
How to Use the Mathematics Curriculum Maps
OverviewAn overview is provided for each quarter. The information given is intended to aid teachers, coaches and administrators develop an understanding of the content the students will learn in the quarter, how the content addresses prior knowledge and future learning, and may provide some non-summative assessment items.
Tennessee State StandardsThe TN State Standards are located in the left column. Each content standard is identified as the following: Major Work, Supporting Content or Additional Content.; a key can be found at the bottom of the map. The major work of the grade should comprise 65-85% of your instructional time. Supporting Content are standards that supports student’s learning of the major work. Therefore, you will see supporting and additional standards taught in conjunction with major work. It is the teacher’s responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard.
ContentTeachers are expected to carefully craft weekly and daily learning objectives/ based on their knowledge of TEM Teach 1. In addition, teachers should include related best practices based upon the TN State Standards, related shifts, and knowledge of students from a variety of sources (e.g., student work samples, MAP, etc.). Support for the development of these lesson objectives can be found under the column titled ‘Content’. The enduring understandings will help clarify the “big picture” of the standard. The essential questions break that picture down into smaller questions and the objectives provide specific outcomes for that standard(s). Best practices tell us that clearly communicating and making objectives measureable leads to greater student mastery.
Instructional Support and Resources
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District and web-based resources have been provided in the Instructional Resources column. Throughout the map you will find instructional/performance tasks, i-Ready lessons and additional resources that align with the standards in that module. The additional resources provided are supplementary and should be used as needed for content support and differentiation.
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Topics Addressed in Quarter Expressions, Equations, and Inequalities Various Functions, Equations & Their Graphs Linear Systems Quadratic Functions & Equations
Overview During this quarter students will extend their understanding of functions and the real numbers system, and increase their toolset for modeling in the real world. Students extend their notion of number to include complex numbers and see how the introduction of this set of numbers yields the solutions of quadratic equations. Students deepen their understanding of the concept of function, and apply equation-solving and function concepts to many different types of functions. Students also build upon previous units and prior courses that explored linear equations and expressions, and apply equation-solving and function concepts to many different types of functions. Students continue to interpret graphs and reason about rates of change of functions. Students learned in Grade 8 that the rate of change of a linear function is equal to the slope of its graph. And because the slope of a line is constant, the phrase “rate of change” is clear for linear functions. For nonlinear functions, however, rates of change are not constant, and students therefore discuss and understand average rates of change over an interval.
Students build on their work with linear and quadratic functions in this quarter. Students work closely with the expressions that define the functions and continue to expand and refine their abilities to model situations and to solve equations, including simplifying radical expressions and solving quadratic equations over the set of complex numbers.
Content Standard Type of Rigor Foundational Standards Sample Assessment Items**A-CED.A.1 Procedural Skill, Conceptual
Major Content Supporting Content Additional Content
Curriculum and Instruction – Mathematics
Quarter 1 Algebra II
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 II listed below should be incorporated throughout your instruction over the course of the school year. A APR.D.6‐ Divide polynomials with remainder by inspection in simple cases A SSE.A.2‐ See structure in expressions and use this structure to rewrite expressions F.IF.A.3 Fluency in translating between recursive definitions and closed forms
Major Content Supporting Content Additional Content
Curriculum and Instruction – Mathematics
Quarter 1 Algebra II
TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESDomain: Creating EquationsCluster: Create equations that describe number relationships. A-CED.A.1Create equations and
inequalities in one variable and use them to solve problems. ★
Domain: Reasoning with Equations and InequalitiesCluster: Create equations that describe numbers or a relationship. A-REI.A.1 Explain each step in solving a
simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Enduring Understanding(s):Relationships with numbers can be represented by equations, inequalities, and systems.
Essential Question(s):How can algebra describe the relationship between a set of numbers?
Objective(s):Students will write and solve equations and justify the solution path chosen.
Additional Resource(s)CCSS Flip Book with Examples of each Standard Solving equations with variables on both sides VideoSolving multi-step equations by combining like terms VideoWriting a multi-step equation to solve problems VideoUsing formulas to solve real-world problems VideoTransforming formulas VideoUse the following Engageny Lessons to introduce the concepts/build conceptual understanding. If used, these lessons should be used before the lessons from the textbooks.
Additional Lesson(s):Engage ny Algebra I Module 1, Topic C, Lesson 10, True and False Equations
Engage ny Algebra I Module 1, Topic C, Lesson 12, Solving Equations
Engage ny Algebra I Module 1, Topic C, Lesson 13, Some Potential Dangers When Solving Equations
Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.
Major Content Supporting Content Additional Content
Curriculum and Instruction – Mathematics
Quarter 1 Algebra II
TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES A-CED.A.1Create equations and
inequalities in one variable and use them to solve problems. ★
Domain: Reasoning with Equations and InequalitiesCluster: Create equations that describe numbers or a relationship. A-REI.A.1 Explain each step in solving
a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
problems.
Essential Question(s):How can a problem be solved and why is one method chosen over another?
Objective(s):Students will write, solve and graph inequalities and justify the solution path chosen.
Glencoe1-5 Solving Inequalities
Additional Resource(s):Writing and solving a compound inequality containing “And” VideoWriting and solving a compound inequality containing “Or” VideoSolving and graphing multi-step inequalities VideoInequalities with no solutions or all real numbers as solutions Video
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.
Additional Lesson(s):Engage ny Algebra I Module 1, Topic C, Lesson 11, Solution Sets for Equations and Inequalities
Engage ny Algebra I Module 1, Topic C, Lesson 14, Solving Inequalities
Engage ny Algebra I Module 1, Topic C, Lesson 15, Solution Sets of Two or More Equations (or Inequalities) Joined by “And” or “Or”
Engage ny Algebra I Module 1, Topic C, Lesson 16, Solving and Graphing Inequalities Joined by “And” or “Or”
Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.
Task(s)Ivy Smith Grows Up
Writing in MathWhat is the difference between solutions to a compound inequality joined by and compared to those joined by or?
Have students to write a sentence(s) and create examples about their thinking. Students could also make a Venn diagram to explain their thoughts and examples.
Functions, Equations, and Graphs(Allow approximately 2 weeks for instruction, review, and assessment)
Domain: Interpreting FunctionsCluster: Interpret functions that arise in
Enduring Understanding(s):Functions can be used to model all kinds of
Major Content Supporting Content Additional Content
Curriculum and Instruction – Mathematics
Quarter 1 Algebra II
TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESapplications 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.
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: Conduct 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 (include reading these from a table).
Domain: Linear, Quadratic, and Exponential Models ★Cluster: Interpret expressions for functions in terms of the situation they model.
F-LE.B.5 Interpret the parameters in a linear or exponential function in terms of a context.
real-world problems.
Essential Question(s):What is a relation and when is a relation a function?
Objective(s):Students will identify, interpret, and graph relations and functions.
Glencoe2-1 Relations and Functions
Additional Lesson(s):Domain Representations
Additional Resource(s)CCSS Flip Book with Examples of each StandardIdentifying functions using a mapping diagram VideoIdentifying functions using the vertical line test VideoGraphing relations VideoFinding domain and range of a relation Video
Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.
Major Content Supporting Content Additional Content
Curriculum and Instruction – Mathematics
Quarter 1 Algebra II
TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES
Cluster: 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. ★
change/slope.
Essential Question(s):How can the relationship between quantities best be represented?
Objective(s):Students will graph and write linear equations and calculate and interpret the rate of change of a function.
Glencoe2-3 Rate of Change and Slope
Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.
Additional Lesson(s)Armstrong Numbers National Debt and WarsHow to Weigh an Alligator Weight of Money-linear function Weight of Money Reflect and Apply
Tasks:TN Task, Alg. 1 – Downloads TN Task, Alg. 1-What’s the Point Oil spills on land Medical Testing Television and Test Grades You’re Toast Dude!
intercept, y-intercept, slope-intercept
Writing in MathDescribe the process of finding the rate of change for each of the following:a. a table of values b. a graph c. an equationHave students to write a sentence(s) and create an example about each choice. Students could also tell when each of the options is best utilized in their example.
Graphic OrganizerSlope-intercept Form (dgelman)
Domain: Interpreting Categorical and Quantitative Data
Cluster: Summarize, represent, and interpret data on a single count or measurement. variable S-ID.B.6 Represent data on two
quantitative variables on a scatter plot, and describe how the variables are related.a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Uses given functions or choose a function suggested by the context. Emphasize linear, quadratic, and
Enduring Understanding(s):Many real-world problems involve modeling data with a linear equation. The equation can be used to draw conclusions about the situation.Essential Question(s):How can you model data with a linear function?
Objective(s):• Students will write linear equations that
model real-world data.• Students will make predictions from linear
Pearson 2-5 Using Linear Models Glencoe 2-5 Scatter Plots and Lines of Regression and
Correlation
Additional Resource(s): Writing an equation for a trend line Video Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.
Additional Lesson(s):Guess the Age
VocabularyScatter plot, correlation, line of best fit, correlation coefficient
Writing in MathWhat is the difference between a positive correlation and a negative correlation? Provide real-world quantities that represent each.
Have students to write a sentence(s) and create examples about their thinking. Students could also make a Venn diagram to explain their
Major Content Supporting Content Additional Content
Curriculum and Instruction – Mathematics
Quarter 1 Algebra II
TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES
exponential. models based upon the data. Price of Apples Exploring Linear Data Line of Best Fit
Tasks:Bird Eggs
Having Kittens
thoughts and examples.
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):The absolute value function is a good parent function to use to apply translations, stretches, compressions, and reflections.Essential Question(s):What is an absolute value function?
Objective(s):Students will graph and find solutions of absolute value functions using a variety of strategies.
Pearson 2-7 Absolute Value Functions and Graphs Glencoe 2-7 Parent Functions and Transformations
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.
Additional Lesson(s):Engage ny Algebra I Module 3, Topic C, Lesson 15, Piecewise Functions
Additional Resource(s)CCSS Flip Book with Examples of each Standard
Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.Absolute Value Functions Lesson & resources
VocabularyAbsolute value function, axis of symmetry, vertex
Writing in MathExplain why the reflection of the graph off(x) = x2 in the y-axis is the same as the graph of f(x) = x2. Is this true for all reflections of quadratic equations? If not, describe a case when it is false.
Have students to write a sentence(s) about their thinking and create an example of the false case, and tell why it is false.
Linear Systems(Allow approximately 2 weeks for instruction, review, and assessment)
Domain: Reasoning with Equations and InequalitiesCluster: Solve systems of equations.
Enduring Understanding(s):A system of equations can be solved by finding a set of values that replace the variables in the equations and make each
Pearson 3-1 Solving Systems Using Tables and Graphs
Glencoe
VocabularySystem of equations, linear system, solution of a system
Major Content Supporting Content Additional Content
Curriculum and Instruction – Mathematics
Quarter 1 Algebra II
TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES
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.
true.
Essential Question(s):How does representing functions graphically help you solve systems of equations?
Objective(s):Students will solve a linear system using a graph or a table.
3-1 Solving Systems of Equations by GraphingUse the following Engageny Lessons to introduce the concepts/build conceptual understanding. If used, these lessons should be used before the lessons from the textbooks.
Additional Lesson(s): Engage ny Algebra II Module 1, Topic C, Lesson 31,
Systems of Equations Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.
Additional Resource(s)CCSS Flip Book with Examples of each Standard Solving and interpreting a system of linear
equations by graphing Video Interpreting solutions of systems of linear
equations Video Classifying systems of equations without
graphing Video
Writing in MathExplain how you can determine the consistency and dependence of a system without graphing the system.
Have students to write a sentence(s) and create examples about their thinking. Students could also make a Venn diagram to explain their thoughts and examples.
Domain: Reasoning with Equations and InequalitiesCluster: Solve systems of equations. A-REI.C.5 Prove that, given a system of
two equations in two variables, replacing one equation by the sum of that equation
Enduring Understanding(s):A system of equations can be solved by utilizing various methods including substitution, elimination, and using matrices.
Pearson 3-2 Solving Systems Algebraically 3-2 Solving Systems Algebraically (Part 2)
Major Content Supporting Content Additional Content
Curriculum and Instruction – Mathematics
Quarter 1 Algebra II
TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES
and a multiple of the other produces a system with the same solutions.
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.
Essential Question(s):When can you use substitution to solve a system?When can you use elimination to solve a system of linear equations?Why is it helpful to use matrices to solve systems of linear equations?
Objective(s):Students will solve a linear system using substitution.Students will solve a linear system using elimination.• Students will represent a system of linear
equations with a matrix.• Students will solve a system of linear
equations with matrices.
Glencoe 3-2 Solving Systems of Equations Algebraically
4-6 Augmented MatricesUse the following resources to ensure that the intended outcome and level of rigor of the standards are met.
Tasks:Best Buy Tickets Cash Registers System of Equations and Inequalities Accurately Weighing Pennies
Flying Through the St Louis Gateway Arch Stacking Cups
Additional Resource(s):CCSS Flip Book with Examples of each Standard Solving linear systems using substitution Video Solving linear systems for real-world situations
using substitution Video Solving linear systems using elimination,
adding Video Solving linear systems using elimination,
multiplying first Video Writing the dimensions of a matrix Video Identifying a matrix element Video Using matrices to organize data Video
Writing in MathWhy might you use different methods for solving a system of equations?
Have students to write a sentence(s) and create examples about their thinking. Students could also make a Venn diagram to explain their thoughts and examples.
Graphic OrganizerSystems by Substitution(dgelman)
Quadratic Functions and Equations( Allow approximately 4 weeks for instruction, review, and assessment)
Domain: Interpreting FunctionsCluster: Analyze functions using different representations. F-IF.C.7 Graph functions expressed
Enduring Understanding(s):A parabola is the graph of the quadratic function f(x) = ax2 + bx + cThe vertex form of a quadratic function is
Pearson 4-1 Quadratic Functions and TransformationsGlencoe 5-1 Graphing Quadratic Functions
VocabularyParabola, quadratic function, vertex form, axis of symmetry, vertex of the parabola, minimum value, maximum value
Major Content Supporting Content Additional Content
Curriculum and Instruction – Mathematics
Quarter 1 Algebra II
TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES
symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★
F-IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
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.★
f(x) = a(x – h)2 + k, where a ≠ 0.
Objective(s):• Students will identify, compare, and graph
quadratic functions.• Students will find and explain solutions of
equations using various methods.
Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.
Tasks: TN Task, Alg. 2 –Forms of a Function TN Task, Alg. 1 -Vegetable Garden TN Alg. 1 Task Arc, Task 1 -Log Flume Ride TN Alg. 1 Task Arc, Task 2 -Linear or Quadratic Quadratic Function Dominos Season Pass Throwing a Ball Breaking Distance Building Functions
Additional Resource(s)CCSS Flip Book with Examples of each Standard Graphing Families of Quadratic Functions
(Texas Instruments) Changing Lots Finding the minimum of a parabola Video Using the maximum or minimum of a parabola
Video Using vertex form of a parabola to graph the
parabola Video Using vertex form to write the equation of a
parabola Video Using vertex form of a parabola to solve real
world problems Video
Writing in MathDescribe how you determine whether a function is quadratic and if it has a maximum or minimum value.
Have students to write a sentence(s) and create examples of a graph and an equation about their thinking. Students could also make a Venn diagram to explain their thoughts and examples.
Domain: Seeing Structure in ExpressionsCluster: Interpret the structure of expressions. A-SSE.A.2 Use the structure of an
expression to identify ways to rewrite it.
Enduring Understanding(s): Any quadratic function is a stretch or
compression, reflection, and/or a translation of y = x2.
• The standard form of a quadratic function is f(x) = ax2 + bx + c, where a ≠ 0.
Pearson4-2 Standard Form of a Quadratic FunctionGlencoe5-1 Graphing Quadratic FunctionsUse the following resources to ensure that the intended outcome and level of rigor of the standards are met.
VocabularyStandard form
Writing in MathIs standard form or vertex form the best way to write a quadratic equation?
Major Content Supporting Content Additional Content
Curriculum and Instruction – Mathematics
Quarter 1 Algebra II
TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES
Essential Question(s):Why is the standard form of a quadratic function useful?
Objective(s):Students will identify and graph quadratic functions written in standard form.
Additional Lesson(s): Kangaroo Conundrum/Tower of Hanoi Hanging Chains The Winning Three Pointer The Winning Three Pointer Reflect
and Apply Over Da Watta Math Shadows
Tasks:TN Task, Alg. 1 –Bottle Rocket
TN Task, Alg. 2 – One Rocket Three Equations TN Alg. 1Task Arc, Task 3, Roller Coaster Ride
TN Alg. 1Task Arc, Task 4 , Fireworks at the Park
TN Alg. 1Task Arc, Task 5 -Riding the Ramp TN Alg. 1Task Arc, Task 8 -Skywalking the Grand Canyon
Additional Resource(s) Identifying points on a parabola Video Using a quadratic function to model the height
of an object - Example 1- Video Graphing a quadratic function, y = ax^2 + bx
+ c Video Using a quadratic function to model the
height of an object - Example 2- Video
Have students to write a sentence(s) about their thinking and create examples of the two equations that would prove their answer. Students could also make a Venn diagram to explain the pros and cons of each form that would prove their answer.
Domain: Creating EquationsCluster: Create equations that describe numbers or relationships. A-CED.A.1 Create equations and
inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.★
Essential Question(s):How can you write the equation of a parabola without knowing the vertex?
Objective(s):Students will model data with quadratic functions.
Pearson 4-3 Modeling With Quadratic Functions
Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.
Tasks:TN Alg.2 Task Arc, Task 5 –The Root of the Problem TN Alg. 1 Task Arc, Task 6 -Food to Go
VocabularyStandard form
Writing in MathName two real world situations that need the quadratic function and explain your reasoning.
Major Content Supporting Content Additional Content
Curriculum and Instruction – Mathematics
Quarter 1 Algebra II
TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESTN Alg. 1 Task Arc, Task 5 -Circus Acts Sidewalk Patterns in Prague
Additional Resource(s):CCSS Flip Book with Examples of each
Standard Math Nspired: Modeling with a quadratic
function Ball Bounce (Texas Instruments) Mirror, Mirror Reflect and Apply Fitting a quadratic function to 3 points Video Using quadratic models Video Graphing a quadratic function using a table, y
= ax^2 + c Video
Have students to write a sentence(s) about their thinking and draw a picture of the situations, labelling important features.
Domain: Seeing Structure in ExpressionsCluster: Write expressions in equivalent forms
to solve problems. A-SSE.B.3 Choose and produce an
equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. ★
Enduring Understanding(s):• Expressions can be written in a variety
of ways.• Many quadratic trinomials can be
factored into products of two binomials.Essential Question(s):How is factoring related to the Distributive Property?
Objective(s):• Students will find common and binomial
factors of quadratic expressions and explain their properties.
• Students will factor special quadratic expressions and solve problems using equivalent forms.
Additional Lesson(s): Polynomial puzzler Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.
Tasks:The Protein Bar Toss Task ,p.18Two Squares are Equal
Additional Resource(s): Factoring trinomials of the type x^2 + bx + c
where b is positive Video Factoring trinomials of the type x^2 + bx + c
where b is negative Video
VocabularyFactoring, greatest common factor (GCF) of an expression, perfect square trinomial, difference of two squares
Writing in MathWhy do you need different methods to factor?Have students to write a sentence(s) about their thinking and create examples of problems that would require the different factoring methods Students could also make a Venn diagram to compare and contrast the different features of the expressions.
Major Content Supporting Content Additional Content
Curriculum and Instruction – Mathematics
Quarter 1 Algebra II
TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Factoring trinomials of the type x^2 + bx - c
Video Factoring trinomials of the type ax^2 + bx + c
where c is positive Video Factoring trinomials of the type ax^2 + bx + c
where c is negative Video
Domain: The Complex Number SystemCluster: Use complex numbers in polynomial identities and equations. N-CN.B. 7 Solve quadratic
equations with real coefficients that have complex solutions.
Domain: Arithmetic with Polynomials and Rational ExpressionsCluster: Understand the relationship between zeros and factors of polynomials. A-APR 3 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.
Enduring Understanding(s):Operations and properties of the real number system can be extended to situations involving complex numbers.
Essential Question(s):How can features of polynomial functions such as the equation, solutions, axis of symmetry, vertex, etc. be represented in tables, equations, and in “real world” contexts?
Objective(s):• Students will solve quadratic equations by
factoring, by using a table, and by graphing.• Students will identify the zeros of a
polynomial where appropriate and graph the function defined by the polynomial.
Pearson4-5 Quadratic Equations (Parts 1& 2)Glencoe5-2 Solving Quadratic Equations by GraphingUse the following resources to ensure that the intended outcome and level of rigor of the standards are met.
Tasks:TN Task , Alg. 2 - Boxed In TN Task, Alg. 1 - Cliffhanger TN Task , Alg. 1 - Fencing For Josephine’s garden (linear and quadratic) The Pig Problem
Additional Resource(s): Solving quadratic equations by graphing Video Solving quadratic equations by factoring Video
VocabularyZero of a function, Zero-Product Property
Writing in MathExplain how to solve a quadratic equation by graphing its related quadratic function.
Have students to write a sentence(s) about their thinking and create an example of an equation with its graph that would prove their answer.
Domain: The Real Number SystemCluster: Extend the properties of exponents to rational exponents. N-RN.A.1 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.
N-RN.A.2 Rewrite expressions involving
Enduring Understanding(s):• A single quantity may be represented
by many different expressions.• Corresponding to every power, there is
a root.Essential Question(s):What does it mean to take the nth root of a number?
Pearson6-1 Roots and Radical ExpressionsGlencoe7-4 Nth Roots
Additional Resource(s):CCSS Flip Book with Examples of each
Standard Simplifying radical expressions Video
VocabularyNth root, principal root, radicand, index
Writing in MathExplain when and why absolute value symbols are needed when taking an nth root.
Major Content Supporting Content Additional Content
Curriculum and Instruction – Mathematics
Quarter 1 Algebra II
TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES
radicals and rational exponents using the properties of exponents.
Objective(s):Students will find and explain the roots of an expression.
Simplifying radical expressions with cube roots Video
their thinking and create examples of roots that need absolute value and roots that do not.
Domain: Reasoning with Equations and InequalitiesCluster: Solve systems of equations. A-REI.B.4 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.
Enduring Understanding(s):There are various methods of solving equations and inequalities when solving problems.
Essential Question(s):Why structure expressions in different ways?
Objective(s):• Students will find common and binomial
factors of quadratic expressions.• Students will solve equations, and solve
problems involving functions by completing the square.
Pearson 4-6 Completing the Square (Parts 1 & 2)Glencoe5-5 Completing the Square
Additional Lesson(s):Building Connections
Additional Resource(s): Math Nspired: Completing the Square Math Nspired: Completing the square
algebraically Solving quadratic equations using square roots
Video Solving quadratic equations using completing
the square Video Solving quadratic equations using completing
the square when a does not equal 1 Video Rewriting a function in vertex form by
completing the square Video
VocabularyCompleting the square
Writing in MathExplain what it means to complete the square. Describe each step.Have students to write a sentence(s) about their thinking and create two examples of expressions that could be created by completing the square.
Enduring Understanding(s):There are various methods of solving equations and inequalities when solving problems.
Essential Question(s):Why is the Quadratic Formula important?
Objective(s):• Students will solve quadratic equations
using the Quadratic Formula.
Pearson 4-7 The Quadratic Formula Glencoe 5.6 Quadratic Formula and the Discriminant
Additional Resource(s): Math Nspired: Discriminant testing Solving quadratic equations using the
quadratic formula Video Using the discriminant to find the number of
solutions and solve problems Video
VocabularyQuadratic Formula, discriminant
Writing in MathDescribe four different ways to solvex2 – 2x – 15 = 0. Which method do you prefer and why?
Have students to write a sentence(s) about their thinking and show the solving of the
Major Content Supporting Content Additional Content
Curriculum and Instruction – Mathematics
Quarter 1 Algebra II
TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES
• Students will determine the number of solutions by using the discriminant.
Solving quadratic equations using the quadratic formula, complex solution Video
equation in all four ways.
Domain: The Complex Number System Cluster: Perform arithmetic operations with complex numbers. N-CN.A.1 Know there is a complex
number i such that i2 = –1, and every complex number has the form a + bi with a and b real.
N-CN.A.2 Use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
Enduring Understanding(s):Operations and properties of the real number system can be extended to situations involving complex numbers.
Essential Question(s):What are complex numbers?
Objective(s):• Students will identify, graph, and perform
operations with complex numbers.• Students will determine the number of
solutions by using the discriminant.
Pearson4-8 Complex Numbers (Parts 1 & 2)Glencoe5.4 Complex Numbers and the Complex PlaneUse the following resources to ensure that the intended outcome and level of rigor of the standards are met.
Additional Lesson(s):Classifying Complex Numbers Complex Number Properties
Additional Resource(s): Math Nspired: Complex Numbers Simplifying the square root of negative
numbers Video Simplifying imaginary numbers Video Adding complex numbers Video Multiplying complex numbers Video Finding complex solutions Video
VocabularyImaginary unit, imaginary number, complex number, pure imaginary number, complex number plane, absolute value of a complex number, complex conjugates
Writing in MathExplain how are complex number related to the solutions of quadratic equations?
Have students to write a sentence(s) about their thinking and create one example of an equation that would need to have a complex solution- showing through the quadratic formula or completing the square AND a graph.
Domain: Reasoning with Equations and InequalitiesCluster: Solve systems of equations. A-REI.C.7 Solve a simple system
consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x2
+ y2 = 3.
Enduring Understanding(s):A system of equations and inequalities can be solved by utilizing various methods.
Essential Question(s):What are the various methods that one can use to solve quadratic inequalities?
Objective(s):• Students will investigate and use different
PearsonConcept Byte - Quadratic Inequalities (p.279)Glencoe5.8 Quadratic Inequalities Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.
Major Content Supporting Content Additional Content
Curriculum and Instruction – Mathematics
Quarter 1 Algebra II
TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES
methods to solve quadratic inequalities.
Domain: Expressing Geometric Properties with EquationsCluster: Translate between the geometric description and the equation for a conic section. G-GPE.A.2 Derive the equation of a
parabola given a focus and directrix.
Enduring Understanding(s):Algebra can be used to efficiently and effectively describe and apply geometric properties.
Essential Question(s):How can algebra be useful when expressing geometric properties?
Objective(s):Students will write the equation of a parabola, graph parabolas and translate between the description and the equation.
Pearson10-2 Parabolas
Glencoe10.1 Midpoint and Distance Formulas10.2 Parabolas
Additional Resource(s): Parabola Word Problem Writing the equation of a parabola Video Finding the equation of a parabola Video Graphing the equation of a parabola Video
VocabularyFocus of a parabola, directrix, focal length
Writing in MathWhat is true about the set of points on a parabola, its focus, and its directrix?
What can you determine about the orientation of a parabola by looking at its vertex equation?
Have students to write a sentence(s) about their thinking and create a sketch that would prove their answer.
Major Content Supporting Content Additional Content
Curriculum and Instruction – Mathematics
Quarter 1 Algebra II
Shelby County Schools 2016/2017Revised 6/29/16
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RESOURCE TOOLBOXTextbook Resources
Pearson Tools:www.phschool.com/mathhttp://www.poweralgebra.comhttp://www.pearsonsuccessnet.com( ELL, Enrichment, Re-teaching, Quizzes/Tests, Think About a Plan, Test Prep, Extra Practice, Find the Errors, Activities/Games/Puzzles, Video Tutor, Chapter Project, Performance Task, and Student Companion)Glencoe Tools:Student EditionTeacher EditionProblem SolvingVocabulary Puzzle Maker
Pearson Textbookshttp://interactmath.com/
StandardsCommon Core State Standards InitiativeCommon Core Standards - MathematicsCommon Core Standards - Mathematics Appendix AEdutoolbox (formerly TNCore)The Mathematics Common Core ToolboxTennessee BlueprintsPARCC Blueprints and Test Specifications FAQCCSS ToolboxNYC tasksNew York Education Department TasksPARCC High School Math TasksPARCC Practice TestTICommonCore.comTN Department of Education Math StandardsAlgebra 2 TN State StandardsCCSS Flip Book with Examples of each Standard
VideosBrightstormThe Futures ChannelKhan AcademyMath TVLamar University Tutorial
Literacy:Literacy Skills and Strategies for Content Area Teachers(Math, p. 22)Glencoe Reading & Writing in the Mathematics ClassroomGraphic Organizers (9-12)Graphic Organizers (dgelman)University of Idaho Literacy Strategies
Additional SitesUT Dana CenterMars TasksInside Math TasksMath Vision Project Tasks Better LessonAlgebra II BlueprintDana Center Algebra 2 AssessmentsIllinois State Assessment strategiesSCS Math Tasks (Algebra II)NYC tasksNew York Education Department Tasks
Interactive ManipulativesKuta SoftwareIlluminations (NCTM)Stem ResourcesNational Math ResourcesMARS Course 2NASA Space MathMath Vision ProjectPurple Math
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.
ACTTN ACT Information & ResourcesACT College & Career Readiness Mathematics Standards
