Curriculum and Instruction – Mathematics

Quarter 1 Finite Math

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

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

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

Focus Coherence Rigor

• 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 concepts of each subject 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.

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 onto foundations built in previous years. Each standard is not a new event, but an extension of previous learning.

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

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

Conceptual understanding:• The TN Standards call for conceptual

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

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

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

Application:• The Standards call for students to use math

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

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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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Mathematical Practices(MP)

1. Make sense of problems and persevere in solving them

2. Reason abstractly and quatitatively

3. Construct viable arguments and

crituqe the reasoning of

others

4. Model with mathematics

5. Use appropriate tools strategically

6. Attend to precision

7. Look for and make use of

structure

8. Look for and express regularity

in repeated reasoning

Curriculum and Instruction – Mathematics

Quarter 1 Finite Math

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

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

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

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

Purpose of the Mathematics Curriculum Maps

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

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

Additional Instructional Support

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Shelby County Schools adopted our current math textbooks for grades 6-8 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.

Topics Addressed in Quarter Sets, Partitions, and Tree Diagrams Probabilities, Counting, and Equally Likely Outcomes Probability

Overview During this quarter students develop a common notation and terminology for sets and set notation which will be useful in understanding probability. Sets, ways of combining sets, set operations and a technique of representing sets with diagrams is developed. Students are introduced to a special type of set needed for the work on probability, and three methods of counting the elements in particular kinds of sets are developed: partitions, tree diagrams, and the multiplication principle. Concepts from set theory are used to develop probability and the counting principles/tools to compute probabilities in special situations. Finally in this quarter students will see how the properties of probabilities which hold in general settings are related to those which hold when outcomes are equally likely. Also, students will study experiments and the concept of tree diagrams to represent certain types of experiments as a way of representing experiments and as an aid to solving problems.

Fluency

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

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

A/G A-APR.A.1

Solving characteristic problems involving the analytic geometry of linesFluency in adding, subtracting, and multiplying polynomials

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A-SSE.A.1b Fluency in transforming expressions and seeing parts of an expression as a single object

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

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESChapter 1 Sets, Partitions, and Tree Diagrams

(Allow approximately 2 weeks for instruction, review, and assessment)Conceptual Category: Geometry and MeasurementDomain: Set TheoryG-ST1. Define sets, subsets, proper subsets, and

empty sets with correct notation.G-ST3. Perform set operations such as union,

intersection, complement, and set difference.

Enduring Understanding(s): Mathematical models can be used to

interpret and predict the behavior of real world phenomena.

Recognizing the predictable patterns in mathematics allows the creation of functional relationships.

Varieties of mathematical tools are used to analyze and solve problems and explore concepts.

Clear and precise notation and mathematical vocabulary enables effective communication and comprehension.

Using prior knowledge of mathematical ideas can help discover more efficient problem solving strategies.

Essential Question(s): How do I use the language of math (i.e.

symbols, words) to make sense of/solve a problem?

How does the math I am learning in the classroom relate to the real-world?

How do I effectively communicate about

Tennessee Finite Math Textbook1.1 Review of Sets and Set Operations

Additional ResourcesFiniteHelp Video - 1.1FiniteHelp Chapter 1 Notation GuideFinite HelpFinite Math Student Resources

Important Terms & Concepts (Chapter 1)Cartesian product, complement, de Morgan’s law, disjoint sets, element, empty(null) set, experiment, intersection, Multiplication Principle, number of elements in a set, pairwise disjoint, partition, partition principle, sample space, set, set equality, subset, tree diagram, union, universal set, Venn DiagramWriting in MathGlencoe Reading & Writing in the Mathematics Classroom

Graphic Organizers (9-12)

Graphic Organizers (dgelman)

Literacy Skills and Strategies for Content Area Teachers

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

math with others in verbal form? In written form?

How do I explain my thinking to others, in written form? In verbal form?

How do I effectively represent quantities and relationships through mathematical notation?

Objectives:Students will: Develop a common notation and

terminology for sets and set operations. Discuss the meaning of a universal set.

Conceptual Category: Geometry and MeasurementDomain: Set TheoryG-ST2. Analyze and compare sets, including

using Venn Diagrams.

Objectives:Students will: Represent sets and relations

between sets using diagrams or pictures.

Tennessee Finite Math Textbook1.2 Venn Diagrams and PartitionsAdditional ResourcesFiniteHelp Video- 1.2Finite Math Student Resources

TaskQ1_finiteresource_GreatExpectinProb

Conceptual Category: Geometry and MeasurementDomain: Set TheoryG-ST3. Perform set operations such as union,

intersection, complement, and set difference.

Conceptual Category: Data Analysis. Statistics, and ProbabilityDomain: Organize and Interpret data

Objectives:Students will: Determine the number of subsets of a set. Perform operations with sets.

Tennessee Finite Math Textbook1.3 Sizes of SetsAdditional ResourcesFiniteHelp Video- 1.3

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

D-ID3. Analyze survey data using Venn

Diagrams

Conceptual Category: Geometry and MeasurementDomain: Set TheoryG-ST4. Operate with sets and use set theory to

solve problems.

Objectives:Students will: Use three methods to represent sets.

Tennessee Finite Math Textbook1.4 Sets of Outcomes and TreesAdditional ResourcesFiniteHelp Video- 1.4

Chapter 2 Probabilities, Counting, and Equally Likely Outcomes(Allow approximately 3 weeks for instruction, review, and assessment)

Conceptual Category: Data Analysis, Statistics, and ProbabilityDomain: Organize and interpret dataD-ID2. Use a variety of counting methods to

organize information, determine probabilities, and solve problems.

Enduring Understanding(s): How to distinguish between types of

probability How to find the probability of two events

occurring in sequence How to find the probability that at least

one of two events will occur How to count the number of ways an

event can occur How to represent and interpret binomial

probability distributionsEssential Question(s): How can one differentiate between the

three types of probability? What is conditional probability? How can one determine if two events will

occur in sequence? How can one determine if two events are

mutually exclusive?Objectives:

Tennessee Finite Math Textbook2.1 Probabilities, Events, and Equally Likely OutcomesAdditional ResourcesFiniteHelp Video- 2.1Finite HelpFinite Math Student Resources

Important Terms & Concepts (Chapter 2)Assignment of probabilities, binomial coefficients, combination principle, deductive method of assigning probabilities, dependent events, equally likely outcomes, equiprobable measures, event, experiment, mutually exclusive events, performance, permutation, permutation principle, probability of an event, probability of E, probability measure, Relative frequency method of assigning probabilities, simple event, weight

Writing in MathGlencoe Reading & Writing in the Mathematics Classroom

Graphic Organizers (9-12)

Graphic Organizers (dgelman)

Literacy Skills and Strategies for Content Area Shelby County Schools 2016/2017

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

Students will: Use the Fundamental Counting Principle

to determine the number of possible outcomes in a given situation.

Use the possible outcomes to determine the probability of an event/experiment.

Teachers

Conceptual Category: Data Analysis, Statistics, and ProbabilityDomain: Develop concepts in probabilityD-CP2. Evaluate expressions indicating

permutations or combinations.D-CP3. Define the relationship between

permutations and the multiplication principle.

Objectives:Students will: Use the permutations formula to find the

number of ways a group of objects can be arranged in order.

Tennessee Finite Math Textbook2.2 Counting Arrangements: Permutations

Additional ResourcesFiniteHelp Video- 2.2Finite Math Student Resources

Conceptual Category: Data Analysis, Statistics, and ProbabilityDomain: Develop concepts in probabilityD-CP2. Evaluate expressions indicating

permutations or combinations.

Objectives:Students will: Use the combinations formula to find

the number of ways to choose several objects from a group without regard to order.

Tennessee Finite Math Textbook2.3 Counting Partitions: Combinations

Additional ResourcesFiniteHelp Video- 2.3

Conceptual Category: Data Analysis, Statistics, and ProbabilityDomain: Develop concepts in probabilityD-CP1. Differentiate between permutations and

combinations.4. Use permutations and combinations to

compute probabilities of compound

Objectives:Students will: Distinguish between using permutations and

combinations to solve problems. Use counting principles (permutations,

combinations, and fundamental counting principle) to find probabilities.

Tennessee Finite Math Textbook2.4 Computing Probabilities by Using Equally Likely Outcomes

Additional ResourcesFiniteHelp Video- 2.4

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

events and solve problems. Task(s)Q1_finiteactivity_PermComb (or see TI Activity: Permutations & Combinations)

Chapter 3 Probability(Allow approximately 4 weeks for instruction, review, and assessment)

Conceptual Category : Data Analysis, Statistics, and ProbabilityDomain: Organize and interpret data D-ID2. Use a variety of counting methods to

organize information, determine probabilities, and solve problems.

3. Analyze survey data using Venn Diagrams

Enduring Understanding(s):Probability is a tool for measuring long-term behavior.Essential Question(s):• What is probability theory?• How can probability be simulated?• What is a probability distribution?

• How does one determine probability for a given event?

Objectives:Students will learn: Axioms for a Probability Measure Properties for a Probability Measure

Tennessee Finite Math Textbook3.1 Probability Measures: Axioms and PropertiesAdditional ResourcesFiniteHelp Video- 3.1Finite Math Student Resources

Important Terms & Concepts (Chapter 3)Axioms of a probability measure, Bayes probabilities, Bayes’ Theorem, Bernoulli process, Bernoulli trial, conditional probability, equiprobable measure, independence, probability measure, properties of a probability measure, probabilities on trees, stochastic processWriting in MathGlencoe Reading & Writing in the Mathematics Classroom

Graphic Organizers (9-12)

Graphic Organizers (dgelman)

Literacy Skills and Strategies for Content Area Teachers

Conceptual Category: Data Analysis, Statistics, and ProbabilityDomain: Develop concepts in probabilityD-CP5. Understand and apply the relationship

between conditional probabilities and the probabilities of individual events.

Conceptual Category: Data Analysis,

Objectives:Students will: Distinguish between independent and

dependent events. Compute conditional probabilities.

Tennessee Finite Math Textbook3.2 Conditional Probability and IndependenceAdditional ResourcesFiniteHelp Video- 3.2

Task(s)Q1_finitetask_Independence

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESStatistics, and ProbabilityDomain: Organize and interpret dataD-ID2. Use a variety of counting methods to

organize information, determine probabilities, and solve problems.

D-ID3. Analyze survey data using Venn

diagrams

(or see TI Activity: Statistics: Independence is the Word)

Conceptual Category: Data Analysis, Statistics, and ProbabilityDomain: Develop concepts in probabilityD-CP5. Understand and apply the relationship

between conditional probabilities and the probabilities of individual events.

Conceptual Category : Data Analysis, Statistics, and ProbabilityDomain : Organize and interpret data D-ID2. Use a variety of counting methods to

organize information, determine probabilities, and solve problems.

Objectives:Students will: Use pictures, diagrams, and trees to find

conditional probabilities.

Tennessee Finite Math Textbook3.3 Stochastic Process and TreesAdditional ResourcesFiniteHelp Video- 3.3

Finite Math Student Resources

Conceptual Category: Data Analysis, Statistics, and ProbabilityDomain: Develop concepts in probabilityD-CP6. Calculate conditional probabilities using

Bayes’ Theorem.

Conceptual Category : Data Analysis, Statistics, and ProbabilityDomain : Organize and interpret data

Objectives:Students will: Find the probability of an event using Bayes’

Theorem.

Tennessee Finite Math Textbook3.4 Bayes Probabilities

Additional ResourcesFiniteHelp Video- 3.4

Task(s)Q1_finitetask_BayesTheorem

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

D-ID2. Use a variety of counting methods to

organize information, determine probabilities, and solve problems.

Conceptual Category: Data Analysis, Statistics, and ProbabilityDomain: Develop concepts in probabilityD-CP5. Understand and apply the relationship

between conditional probabilities and the probabilities of individual events.

Conceptual Category: Data Analysis, Statistics, and ProbabilityDomain: Organize and interpret data D-ID 2. Use a variety of counting methods to

organize information, determine probabilities, and solve problems.

Objectives:Students will: Determine if an event is a Bernoulli trial. Compute the probability of an event that is a

Bernoulli trial.

Tennessee Finite Math Textbook3.5 Bernoulli Trials

Additional ResourcesFiniteHelp Video- 3.4

Finite Math Student Resources

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RESOURCE TOOLBOXTextbook ResourcesTennessee Finite Math by Dan Maki and Maynard Thompson Published by McGraw Hill 2011

Finite Help

CCSS/PARCCCommon Core Standards - MathematicsCommon Core Standards - Mathematics Appendix AThe Mathematics Common Core ToolboxState Academic Standards (Finite Math)TN Department of Education Math StandardsEdutoolbox (formerly TNCore)

VideosKhan AcademyIlluminations (NCTM)Discovery Education The Futures ChannelThe Teaching Channel

Teachertube.com FiniteHelp Lecture Videos

CalculatorTexas Instruments EducationTI-Nspiredhttp://www.atomiclearning.com/ti_84TICommonCore.comhttp://www.casioeducation.com/educators

Interactive ManipulativesRossmanchance.com

Additional SitesNCTM Math IlluminationsCore Math ToolsMath is FunWolfram Math WorldNrichST atistics E ducation W eb

LiteracyGlencoe Reading & Writing in the Mathematics Classroom

Graphic Organizers (9-12)

Graphic Organizers (dgelman)

Literacy Skills and Strategies for Content Area Teachers

ACTTN ACT Information & ResourcesACT College & Career Readiness Mathematics Standards