Major Content Supporting Content Additional Content

Curriculum and Instruction –Mathematics

Quarter 3 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 3 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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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

The Shelby County Schools curriculum maps are intended to guide planning, pacing, and sequencing, reinforcing the major work of the grade/subject. Curriculum maps are NOT meant to replace teacher preparation or judgment; however, it does serve as a resource for good first teaching and making instructional decisions based on best practices, and student learning needs and progress. Teachers should consistently use student data differentiate and scaffold instruction to meet the needs of students. The curriculum maps should be referenced each week as you plan your daily lessons, as well as daily when instructional support and resources are needed to adjust instruction based on the needs of your students.

How to Use the Mathematics Curriculum Maps

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 the 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 teachers' responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard.

ContentWeekly and daily objectives/learning targets should be included in your plan. These 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 learning targets/objectives provide specific outcomes for that standard(s). Best practices tell us that making objectives measureable increases student mastery.

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Instructional Support and ResourcesDistrict and web-based resources have been provided in the Instructional Support and Resources column. The additional resources provided are supplementary and should be used as needed for content support and differentiation.

Topics Addressed in Quarter Rational Expressions and Functions Sequences and Series Probability and Statistics

Overview During this quarter students will extend their understanding of functions and the real numbers and increase their toolset for modeling in the real world. Students extend their notion of number to include rational exponents. Students deepen their understanding of the concept of function, and apply equation-solving and function concepts to rational functions. They will explore rational functions through graphing, solving, and learning their properties. The field of rational functions is analogous to the rational numbers and the graphs of these functions are explored. Building on their work with linear, quadratic, exponential, and radical functions, in Algebra II students extend their repertoire of functions to include rational functions. Students work closely with the expressions that define the functions and continue to expand and hone their abilities to model and analyze situations that involve polynomial, radical, exponential, and logarithmic equations over the set of real and complex numbers.

Content Standard Type of Rigor Foundational Standards Sample Assessment Items**A-APR Procedural Skill, Conceptual Understanding &

ApplicationA-APR.C.6 Chemistry Example: Alcohol Solution

A-CED Procedural Skill, Conceptual Understanding & Application

A-CED-A.1 Direct variation (oil spills on land)

A-REI Conceptual Understanding & Application A-REI.1,2, 11 Painting a room-pg. 11.10

A-SSE Procedural Skill, Conceptual Understanding & A-SSE.B.4 Applications of Adding and Subtracting

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Application Rational ExpressionsF-IF Conceptual Understanding & Application F-IF.3,4,7 Summer Intern

F-BF Conceptual Understanding & Application F-BF.1,2 Math Nspired: Airport Impact Study S-IC Procedural Skill, Conceptual Understanding &

ApplicationS-IC. 3,4,5,6,7 Math Nspired: Birthday Problem

S-ID Procedural Skill, Conceptual Understanding & Application

S-ID.4 Is This Your Normal?

S-CP Procedural Skill, Conceptual Understanding & Application

S-CP. 1,2,3,4,5,6,7 Rolling twice

** 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 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

References:

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

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TN STATE STANDARDS CONTENT RESOURCES & TASKS CONNECTIONSRational Functions

(Allow approximately 3 weeks for instruction, review, and assessment)Domain: Creating Equations

Cluster: Create equations that describe numbers or relationships.

A-CED.A.1 Creating Equations★Create equations that describe numbers or relationships.

Enduring Understanding(s):If a product is constant, a decrease in the value of one factor must accompany an increase in the value of the other factor.

Essential Question(s):How is and inverse variation different than a direct variation?

Objective(s):• Students will recognize and use inverse

variation.• Students will use joint and other variations.

Use the textbook resources to address procedural skill and fluency.

Pearson 8.1 Inverse Variation

Glencoe9.5 Variation Functions

Lesson VideosUsing inverse variationsUsing joint and other variations

Use the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.CSS Flip Book with Examples of each Standard

Task(s):Direct variation (oil spills on land)

VocabularyInverse variation, combined variation, joint variation

Writing in MathHow do you recognize an inverse variation given data?

A-CED.A.1

Domain: Interpreting FunctionsCluster: Interpret functions that arise in

Enduring Understanding(s):• Transformations of the parent reciprocal

functions include stretches, compressions, reflections, and horizontal and vertical

Use the textbook resources to address procedural skill and fluency.Pearson

VocabularyReciprocal function, branch

Writing in Math

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TN STATE STANDARDS CONTENT RESOURCES & TASKS CONNECTIONSapplications 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: Interpreting FunctionCluster: Analyze functions.

F-IF.C.7 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.

translations.• A rational function may have zero or one

horizontal or oblique asymptote and zero or more vertical asymptotes.

Essential Question(s):How do the a, h, and k values effect the graph of the reciprocal function?

Objective(s):• Students will graph reciprocal functions.• Students will graph translations of

reciprocal functions.

8.2 Reciprocal Function FamilyGlencoe9.3 Graphing the Reciprocal FamilyLesson VideosGraphing reciprocal functionUse the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.CSS Flip Book with Examples of each Standard

Tasks:Math Vision Project: Module 1-Functions and Their Inverses (five tasks)Summer Intern

What are the key components of the graph of a reciprocal function? Write a few sentences and create and graph an example about your thinking.

F-IF.B.4

F-IF.C.7

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.

Enduring Understanding(s):• A rational function is a ratio of

polynomial functions.

• If a function has a polynomial in its denominator, its graph has a gap at each zero of the polynomial. The gap could be a one-point hole in the graph, or it could be the location of a vertical asymptote for the graph.

• A rational function may have no asymptotes, one horizontal or oblique asymptote, and any number of vertical asymptotes.

Essential Question(s):By looking at an equation, how do you recognize points of discontinuity?

Use the textbook resources to address procedural skill and fluency.Pearson

8.3 Rational Functions and Their Graphs Glencoe 9.4 Graphing Rational Functions

Lesson VideosGraphing rational functions

Use the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.CSS Flip Book with Examples of each Standard

Task(s):

VocabularyRational function, continuous graph, discontinuous graph, point of discontinuity, removable discontinuity, non-removable discontinuity

Writing in MathHow do you know there is a vertical asymptote in a rational function and how do you find it?

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Objective(s):• Students will identify properties of rational

functions.• Students will recognize and graph rational

functions.

Math Nspired: Airport Impact Study Math Vision Project: Module 4- Rational Functions (seven tasks)

Domain: Arithmetic with Polynomials and Rational Expressions

Cluster: Understand the relationship between zeros and factors of Polynomials

A-APR.C.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

Enduring Understanding(s):A rational expression is in its simplest form when its numerator and denominator are polynomials that have no common divisors.

Essential Question(s):What are the rules for multiplying and dividing fractions? Multiplying and dividing polynomials?

Objective(s):• Students will simplify rational expressions.• Students will multiply and divide rational

expressions.

Use the following Lesson(s) to introduce concepts/build conceptual understanding.Engageny Algebra II Module 1, Topic C, Lesson 22,Rational Expressions

Engageny Algebra II Module 1, Topic C, Lesson 23,Equivalent Rational Expressions

Engageny Algebra II Module 1, Topic C, Lesson 24,Multiply and Divide Rational Expressions

Use the textbook resources to address procedural skill and fluency.Pearson8.4 Rational ExpressionsGlencoe9.1 Multiplying and Dividing Rational ExpressionsLesson VideosSimplifying a rational expressionMultiplying rational expressionsDividing rational expressionsUse the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.CSS Flip Book with Examples of each

VocabularyRational expression, simplest form, restrictions

Writing in MathHow do you find the restrictions when multiplying and dividing polynomial expressions?

Graphic OrganizerGraphic Organizer division(dgelman)

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TN STATE STANDARDS CONTENT RESOURCES & TASKS CONNECTIONSStandard

Task(s):Chemistry Example: Alcohol Solution

A-APR.A.2

A-APR.C.6 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):• Rational expressions can be added or

subtracted by first finding the least common denominator (LCM).

• The LCM of denominators is the product of their prime factors, each raised to the greatest power that occurs ion any of the expressions.

Essential Question(s):How do you find the LCM of expressions?

Objective(s):• Students will add and subtract rational

expressions..

Use the following Lesson(s) to introduce concepts/build conceptual understanding.Engageny Algebra II Module 1, Topic C, Lesson 22,Rational Expressions Engageny Algebra II Module 1, Topic C, Lesson 23,Equivalent Rational Expressions

Engageny Algebra II Module 1, Topic C, Lesson 25, Add and Subtract Rational Expressions

Use the textbook resources to address procedural skill and fluency.Pearson8.5 Adding and Subtracting Rational Expressions Glencoe9.2 Adding and Subtracting Rational Functions

Lesson VideosAdding rational expressionsSubtracting rational expressionsUse the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.CSS Flip Book with Examples of each Standard

VocabularyComplex fraction

Writing in MathHow do you find the restrictions when adding and subtracting polynomial expressions?

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Task(s):Applications of Adding and Subtracting Rational Expressions

Domain: Reasoning with Equations and InequalitiesCluster: Understand solving equations as a process of reasoning and explain the reasoning.

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.

A-REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise

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):• Solving an equation containing rational

expressions begins by multiplying each side by the LCM of the rational expressions. This can cause extraneous solutions.

Essential Question(s):When do you have extraneous solutions?

Objective(s): Students will solve rational

equations. Students will use rational

equations to solve problems.

Use the following Lesson(s) to introduce concepts/build conceptual understanding.Engageny Algebra II Module 1, Topic C, Lesson 26,Solve Rational Expressions

Engageny Algebra II Module 1, Topic C, Lesson 27,Solve Word Problems with Rational Expressions

Use the textbook resources to address procedural skill and fluency.Pearson8.6 Solve Rational EquationsGlencoe9.6 Solving Rational Equations and InequalitiesLesson Video:Using rational equations

Use the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.CSS Flip Book with Examples of each Standard

Task(s):Painting a room-pg. 11.10

Vocabulary Rational equation

Writing in MathExplain why a rational equation could have extraneous solutions.

Have students to write a sentence(s) and create two different examples about their thinking- one equation that has an extraneous solution and one that does not.

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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.

Sequences and Series(Allow approximately 3 weeks for instruction, review, and assessment)

Domain: Interpreting FunctionsCluster: Understand the concept of a function and use function notation.

F-IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.

Domain: Building FunctionsCluster: Build a function that models a relationship between two quantities F-BF.A.1a 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.

F-BF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Enduring Understanding(s): In an arithmetic sequence, the

difference between any two consecutive terms is always the same number. An arithmetic sequence can be built by adding the same number to each term.

A sequence can be defined explicitly by describing its nth term with a formula using n or recursively by stating its first term and a formula for its nth term using the (n-1) term.

Essential Question(s):When is the best to use an explicit formula?

Objective(s):Students will define, identify, and apply arithmetic sequences.

Use the textbook resources to address procedural skill and fluency.Pearson9.2 Arithmetic SequencesGlencoe

11.1 Sequences as Functions11.2 Arithmetic Sequences11.5 Recursion and Iteration

Lesson VideosFinding the value of the nth term of an arithmetic sequenceUsing the arithmetic mean

Use the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.CSS Flip Book with Examples of each Standard

Task(s):

VocabularySequence, term of a sequence, explicit formula,

recursive formula, arithmetic sequence, common difference, arithmetic mean

Writing in MathWhen is it easier to use a recursive formula?

Have students to write a sentence(s) and create two different examples -one explicit and one recursive- about their thinking.

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TN Task Arc –Interior Angle Sum The Devil and Daniel Webster Trout PondGenerating Polynomials from PatternsArithmetic Sequence Word Problems Illustrative: Susita's Account

F-IF.A.3

F-BF.A.1aF-BF.A.2

Enduring Understanding(s):In a geometric sequence, the ratio of any term, after the first, to its preceding term is a constant value, no matter what two terms are compared. A geometric sequence can be built by multiplying each term by that constant.

Essential Question(s):How do you find the next term in a geometric sequence?

Objective(s):Students will define, identify, and apply geometric sequences.

Use the textbook resources to address procedural skill and fluency.Pearson9.3 Geometric SequencesGlencoe

11.1 Sequences as Functions 11.3 Geometric Sequences

11.5 Recursion and Iteration Lesson VideosFinding the value of the nth term of a geometric sequenceUsing the geometric meanUse the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.CSS Flip Book with Examples of each Standard Task(s):TN Task Arc –Honeybees Common Differences

VocabularyGeometric sequence, geometric mean, common ratio

Writing in MathExplain the difference between an arithmetic and geometric sequence.

Have students to write a sentence(s) and create examples of the arithmetic and geometric sequences, showing their differences.

Domain: Seeing Structure in ExpressionsCluster: Interpret the structure of expressions.

A-SSE.B.4 . Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example,

Enduring Understanding(s):The sum of a finite geometric series can be found using a formula. It is necessary to know the first term, number of terms, and common ratio.

Use the following Lesson(s) to introduce concepts/build conceptual understanding.

Engageny Algebra II Module 3, Topic E, Lesson 29,Finite Geometric Series

VocabularySeries, Geometric series, converge, diverge, finite series, infinite series, limits

Writing in Math

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calculate mortgage payments. The sum of an infinite geometric series is the number that the sequence of partial sums approaches.

Essential Question(s):What are the differences between a finite and infinite geometric series?

Objective(s):Students will define geometric series and find their sums.

Engageny Algebra II Module 3, Topic E, Lesson 30,Using Finite Geometric Series for a Car Loan

Engageny Algebra II Module 3, Topic E, Lesson 31,Using Finite Geometric Series for a Credit Card Balance

Engageny Algebra II Module 3, Topic E, Lesson 32,Using Finite Geometric Series for a Buying a House

Engageny Algebra II Module 3, Topic E, Lesson 33,Using Finite Geometric Series for saving a million dollars Use the textbook resources to address procedural skill and fluency.Pearson9.5 (Finite)Geometric SeriesGlencoe11.3 Geometric SeriesLesson VideosEvaluating a finite geometric seriesUsing the geometric series formula to solve problemsEvaluating an infinite geometric seriesUse the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.CSS Flip Book with Examples of each Standard Task(s):

How do you decide if an infinite geometric series converges or diverges?

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TN Task Arc-Patterns in PatternsProbability and Statistics

( Allow approximately 3 weeks for instruction, review, and assessment)Domain: Interpreting Categorical and Interpretive DataCluster: Summarize, represent, and interpret data on a single count or measurement variable

S-IC.A.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?

Enduring Understanding(s):The probability, p, of an event is a number between 0 and 1 inclusive. The probability of an impossible event is 0. The probability of a certain event is 1.

Essential Question(s):What is the difference between theoretical and experimental probability?

Objective(s):Students will find the probability of an event using theoretical, experimental, and simulation methods.

Use the textbook resources to address procedural skill and fluency.Pearson

11.2 Probability – SimulationGlencoe

12.4 Probability and Probability DistributionsLesson VideosFinding experimental probabilityFinding theoretical and geometric probabilityUse the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

CSS Flip Book with Examples of each Standard

Task(s):Mathshell: A Fair Game Illuminations: Stick or SwitchMathshell: Charity FairMath Nspired: Birthday Problem

VocabularyExperimental probability, simulation, sample space, equally likely outcomes, theoretical probability

Writing in MathWhy is a simulation better the more times you perform it?

Domain: Conditional Probability and the Rules of ProbabilityCluster: Understand independence and conditional probability and use them to interpret data

S-CP.A.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics(or categories) of the

Enduring Understanding(s):To find the probability of two events occurring together, it is necessary to determine whether the occurrence of one event affects the probability that the other event will occur.

Essential Question(s):What is the difference independent and

Use the textbook resources to address procedural skill and fluency.Pearson11.3 Probability of Multiple EventsGlencoe12.4 Probability and Probability Distributions

Lesson VideosFinding the Probability of Independent Events

VocabularyDependent events, independent events, mutually exclusive events

Writing in MathMake up a sample problem that would show mutually exclusive events.

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outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).

S-CP.A.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

dependent events?Objective(s):

Students will find the probability of the events A and B.

Students will find the probability of event A or B.

Finding the Probability of Mutually Exclusive EventsUse the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.CSS Flip Book with Examples of each Standard

Task(s):Rolling twice

Have students to write a sentence(s) about their thinking and make up the example.

Domain: Conditional Probability and the Rules of ProbabilityCluster: Use the rules of probability to compute probabilities of compound events in a uniform probability model

S-CP.B.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.

S-CP.B.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.

Domain: Conditional Probability and the Rules of ProbabilityCluster: Understand independence and conditional probability and use them to interpret data

S-CP.A.3 . Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as

Enduring Understanding(s):• A conditional probability is the probability

that one event occurs, given that another event has occurred.

Essential Question(s):What makes a probability conditional?

Objective(s): Students will find conditional

probabilities Students will use tables and tree

diagrams to determine conditional probabilities.

Use the textbook resources to address procedural skill and fluency.

Pearson11-4 Conditional Probability Glencoe12.3 Conditional ProbabilityLesson VideosFinding Conditional Probabilities Using a FormulaFinding Conditional Probability using a Tree diagram

Use the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.CSS Flip Book with Examples of each Standard

Task(s):Gamers

VocabularyConditional probability

Writing in MathWrite about a conditional situation in your everyday life.

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Quarter 3 Algebra II

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saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

S-CP.A.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.

S-CP.A.5 . Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.

Enduring Understanding(s):Data sets can be described using various statistical measures, depending on what characteristics are being studied.

Essential Question(s): What situations are the mean, median, and mode the most useful measures of central tendency?

Use the following Lesson(s) to introduce concepts/build conceptual understanding.Engageny Algebra I Module 2, Topic A, Lesson 1,Using a Box Plot to show Variablility with Data

Engageny Algebra I Module 2, Topic A, Lesson 2,Finding Mean and Median

VocabularyMeasure of central tendency, mean, median, mode, bimodal, outlier, range of a set of data, quartile, interquartile range, box and whisker plot, percentile

Writing in MathHow does an outlier effect the various measures of central tendency?

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Quarter 3 Algebra II

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Objective(s):• Students will calculate measures of central

tendency.• Students will draw and interpret box and

whisker plots.

Engageny Algebra I Module 2, Topic A, Lesson 3,Choosing the Best Measure of Central Tendency for Data

Engageny Algebra I Module 2, Topic B, Lesson 7,Interquartile Range

Engageny Algebra I Module 2, Topic B, Lesson 8, Variablity of Interquartile Range Use the textbook resources to address procedural skill and fluency.

Pearson11.5 Analyzing DataLesson VideosMaking a box-and-whisker plotUse the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.CSS Flip Book with Examples of each Standard

Task(s):Illuminations: NBA statistics

Mathshell: Suzi's Company

Domain: Interpreting Categorical and Interpretive DataCluster: Summarize, represent, and interpret

data on a single count or measurement variable

S-IC.A.2

Enduring Understanding(s):Collecting data enables analysis.

Essential Question(s):How many samples should be collected to have valid data?

Use the following Lesson(s) to introduce concepts/build conceptual understanding.

Engageny Algebra II Module 4, Topic D, Lesson 23, Randomness of Experiments

Engageny Algebra II Module 4, Topic D, Lesson 24, Differences due to Randomness

Writing in MathWas there any bias in your data collection? Why/Why not?

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Quarter 3 Algebra II

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Objective(s):• Students will collect a random sample of

data and analyze it..

Alone

Engageny Algebra II Module 4, Topic D, Lesson 25, Randomized Distribution

Engageny Algebra II Module 4, Topic D, Lesson 26, Randomized Distribution of Experiments

Engageny Algebra II Module 4, Topic D, Lesson 27, Randomized Distribution of Experiments continued

Engageny Algebra II Module 4, Topic D, Lesson 28, Randomized Distribution of Experiments continued

Engageny Algebra II Module 4, Topic D, Lesson 29, Comparison of Treatments

Engageny Algebra II Module 4, Topic D, Lesson 30, Comparison of Treatments continued

Use the textbook resources to address procedural skill and fluency.Pearsonp.724 Describing DataUse the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.CSS Flip Book with Examples of each Standard

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Quarter 3 Algebra II

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Task(s):Increase Minimum Wage task

Domain: Making Inferences and Justifying ConclusionsCluster: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

S-IC.A.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

Domain: Making Inferences and Justifying ConclusionsCluster: Make inferences and justify conclusions from a sample

S-IC.B.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.Domain: Making Inferences and Justifying ConclusionsCluster: Make inferences and justify conclusions from a sample

S-IC.B.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

S-IC.B.5 Use data from a randomized

Enduring Understanding(s):You can get good statistical information about a population by studying a sample of that population.

Essential Question(s):What are the different ways that you can collect data?

Objective(s):• Students will identify sampling methods.• Students will recognize bias in samples and

surveys.

Use the textbook resources to address procedural skill and fluency.

Pearson11.7 Samples and Surveys

Glencoe12.1 Experiments, Surveys, and Observational StudiesLesson Videos

Using margin of error

Task(s):Chocolicious

VocabularyPopulation, sample, convenience sample, self-selected sample, systematic sample, random sample, bias, observational study, controlled experiment, survey

Writing in MathWhat are the key features to an observational study?

Have students to write a sentence(s) and create one example about their thinking.

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experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

Domain: Interpreting Categorical and Interpretive DataCluster: Summarize, represent, and interpret

data on a single count or measurement variable

S-ID.A.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

Domain: Making Inferences and Justifying ConclusionsCluster: Make inferences and justify conclusions from a sample

S-IC.B.6 Evaluate reports based on data.

Enduring Understanding(s):Normal distributions model many common natural phenomena. A normal distribution has a symmetric bell curve shape centered on the mean of the data.

Essential Question(s):What percent of data falls within three standard deviations?

Objective(s):Students will use a normal distribution and make inferences/draw conclusions from the data.

Use the following Lesson(s) to introduce concepts/build conceptual understanding.Engageny Algebra I Module 2, Topic B, Lesson 4, Interpret Deviations

Engageny Algebra I Module 2, Topic B, Lesson 5, Calculate Standard Deviation

Engageny Algebra I Module 2, Topic B, Lesson 6, Standard Deviation Using the Calculator

Use the textbook resources to address procedural skill and fluency.Pearson11.9 Normal DistributionGlencoe12.5 Normal Distribution

Lesson VideosUsing a normal distributionUsing the standard normal curveUse the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.Tasks:Math Vision Project 2014- Module 8- Statistics (eight tasks) Is This Your Normal?

VocabularyDiscrete probability distribution, continuous probability distribution, normal distribution

Writing in MathHow do outliers fit in with the normal curve?

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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

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 TasksTICommonCore.comTN Department of Education Math StandardsAlgebra 2 TN State StandardsPARCC Practice TestCCSS Flip Book with Examples of each Standard

VideosBrightstormTeacher TubeThe 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)

CalculatorMath NspiredTexas Instrument ActivitiesCasio Activities

Others:UT Dana CenterMars Tasks (Mathshell) Inside Math TasksMath Vision Project Tasks Better LessonLearnZillionSCS Math TasksGSE - Adv. Algebra/Algebra II Tasks; Units 1 – 7

Interactive ManipulativesKuta SoftwareIlluminations (NCTM)Stem ResourcesNational Math ResourcesMARS Course 2NASA Space MathMath Vision ProjectPurple MathACTTN ACT Information & ResourcesACT College & Career Readiness Mathematics Standards

Additional SitesDana Center Algebra 2 AssessmentsIllinois State Assessment strategiesUniversity of Idaho Literacy StrategiesNWEA 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.