Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Curriculum and Instruction – Mathematics Quarter 2 Finite Math 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 standardsaligned 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 • 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. Coherence Rigor 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. 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. 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. 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. Shelby County Schools 2016/2017 Revised 8/31/16 1 of 11 Curriculum and Instruction – Mathematics Quarter 2 8. Look for and express regularity in repeated reasoning 7. Look for and make use of structure 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quatitatively Mathematical Practices(MP) 6. Attend to precision 3. Construct viable arguments and crituqe the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically Finite Math 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: The TN Mathematics Standards The Tennessee Mathematics Standards: Teachers can access the Tennessee State standards, which are featured https://www.tn.gov/education/article/mathematics-standards throughout this curriculum map and represent college and career ready learning at reach respective grade level. Standards for Mathematical Practice Mathematical Practice Standards Teachers can access the Mathematical Practice Standards, which are https://drive.google.com/file/d/0B926oAMrdzI4RUpMd1pGdEJTYkE/view featured throughout this curriculum map. This link contains more a more detailed explanation of each practice along with implications for instructions. Shelby County Schools 2016/2017 Revised 8/31/16 2 of 11 Curriculum and Instruction – Mathematics Quarter 2 Finite Math 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—highquality teaching and learning to grade-level specific standards, including purposeful support of literacy and language learning across the content areas. Additional Instructional Support 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. Shelby County Schools 2016/2017 Revised 8/31/16 3 of 11 Curriculum and Instruction – Mathematics Quarter 2 Finite Math How to Use the Mathematics Curriculum Maps Overview An 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 Standards The 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. Content Teachers 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 District and web-based resources have been provided in the Instructional Resources column. Throughout the map you will find instructional/performance tasks, iReady 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. Shelby County Schools 2016/2017 Revised 8/31/16 4 of 11 Curriculum and Instruction – Mathematics Quarter 2 Finite Math Topics Addressed in Quarter Random Variables, Averages, and Statistics Logic for Finite Math Systems of Linear Equations Overview In quarter two students begin to bridge the study of probability and the application of probability theory to the field of statistics. Students solve problems and use the concepts of random variable, mean, and standard deviation. The normal random variable and the binomial random variable is also studied. Student study a few concepts involving logic including truth tables, statements and deduction. Students conclude the quarter by reviewing systems of linear equations and applying these concepts to analyze and solve real-world problems involving linear systems. Fluency The high school standards do not set explicit expectations for fluency, but fluency is important in high school mathematics. Fluency in algebra can help students get past the need to manage computational and algebraic manipulation details so that they can observe structure and patterns in problems. Such fluency can also allow for smooth progress toward readiness for further study/careers in science, technology, engineering, and mathematics (STEM) fields. These fluencies are highlighted to stress the need to provide sufficient supports and opportunities for practice to help students gain fluency. Fluency is not meant to come at the expense of conceptual understanding. Rather, it should be an outcome resulting from a progression of learning and thoughtful practice. It is important to provide the conceptual building blocks that develop understanding along with skill toward developing fluency. The fluency recommendations for Algebra I listed below should be incorporated throughout your instruction over the course of the school year. A/G A-APR.A.1 A-SSE.A.1b Solving characteristic problems involving the analytic geometry of lines Fluency in adding, subtracting, and multiplying polynomials 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/ Shelby County Schools 2016/2017 Revised 8/31/16 5 of 11 Curriculum and Instruction – Mathematics Quarter 2 TN STATE STANDARDS Conceptual Category: Data Analysis, Statistics, and Probability Domain: Organize and Interpret data D-ID.1 Organize data for problem solving. D-ID.2 Use a variety of counting methods to organize information, determine probabilities, and solve problems. Finite Math CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Chapter 4 Random Variables, Averages, and Statistics (Allow approximately 3 weeks for instruction, review, and assessment) Enduring Understanding(s): Tennessee Finite Math Textbook 4.1 Random Variables and Probability Density Interpretation of data is dependent Functions upon the graphical displays and numerical summaries. The question to be answered Additional Resources determines the data to be collected and Khan Academy Video – Probability Density how best to collect it. Functions The normal distribution is a Khan Academy Video – Random Variables fundamental component of statistical inference. FiniteHelp Practice Problems Density curves are used to mimic FiniteHelp Notation Guide probability. Finite Help The normal distribution is used to Finite Math Student Resources model the spread of data. Probability models are useful tools for making decisions and predictions. Probability is the basis of statistical inference. The notion and behavior of a random variable is foundational to understanding probability distributions. Probability models are useful tools for making decisions and predictions. Essential Question(s): Important Terms & Concepts (Chapter 4) Approximation method, binomial random variable, density function, expected value, expected value of a binomial random variable, mean, normal approximation to a binomial random variable, normal random variable, random variable, standard deviation, standard normal curve, standard normal random variable, variance, variance of a binomial random variable Writing in Math Explain the difference between positively skewed, negatively skewed, and normally distributed sets of data and describe an example of each. Find a real-world data set that appears to represent a normal distribution and one that does not. Describe the characteristics of each distribution. Create a visual representation of each set of data. What is a density function? Glencoe Reading & Writing in the Mathematics Classroom How do density functions relate to probability? Graphic Organizers (9-12) How are measures of central tendency relevant to density functions? Graphic Organizers (dgelman) How can density functions be used to express relative standing? Literacy Skills and Strategies for Content Area Teachers Shelby County Schools 2016/2017 Revised 8/31/16 6 of 11 Curriculum and Instruction – Mathematics Quarter 2 TN STATE STANDARDS Finite Math CONTENT What is a normal distribution? How does one assess normality? INSTRUCTIONAL SUPPORT & RESOURCES What does a normal distribution imply about the spread of data? Objectives: Students will: Conceptual Category: Data Analysis, Statistics, and Probability Domain: Organize and Interpret data D-ID.6 Calculate expected value, e.g., to determine the fair price of an investment. Conceptual Category: Data Analysis, Statistics, and Probability Domain: Organize and Interpret data D-ID.4 Calculate and interpret statistical problem using measures of central tendency and graphs. D-ID.6 Calculate expected value, e.g., to determine the fair price of an investment. Construct a probability distribution for random variables. Objectives: Students will: Determine the expected value of a random variable. Determine the standard deviation of a random variable. Use the expected value to determine the average payoff or loss in a game of chance. Objectives: Students will: Determine the probabilities for a normally distributed variable using a z-score. Determine the binominal probabilities for a normally distributed variable. Tennessee Finite Math Textbook 4.2 Expected Values and Standard Deviations of Random Variables Additional Resources Finite Math Student Resources FiniteHelp Practice Problems TI Activity: It’s To Be Expected Tennessee Finite Math Textbook 4.3 Normal Random Variables and the Normal Approximation to the Binomial Additional Resources Wolfram: Normal Approximation to a Binomial Random Variable Shelby County Schools 2016/2017 Revised 8/31/16 7 of 11 Curriculum and Instruction – Mathematics Quarter 2 Finite Math TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Chapter 11 Logic for Finite Math (Allow approximately 3 weeks for instruction, review, and assessment) Conceptual Category: Geometry and Measurement Domain: Investigate logic G-L.1 Define the order of operations for the logical operators. G-L.2 Define conjunction, disjunction, negation, conditional, and biconditional. Essential Question(s): Can you describe the method used in mathematics to assign a truth value to a compound statement? What is the importance of the concepts implication and proof? Tennessee Finite Math Textbook 11.1 Statements, Connectives, and Negation Additional Resources Wolfram: Logic Objectives: Students will: Define the order of operations for the logical operators. Define conjunction, disjunction, negation, conditional, and biconditional. Important Terms & Concepts (Chapter 11) Biconditional, Conditional, Conjunction, Counterexample, Deduction, Disjunction, Equivalence, Implication, Logical connective “and”, Logical connective “not”, Logical connective ”or”, Negative, Truth table, Valid argument Writing in Math Glencoe Reading & Writing in the Mathematics Classroom Graphic Organizers (9-12) Graphic Organizers (dgelman) Literacy Skills and Strategies for Content Area Teachers Conceptual Category: Geometry and Measurement Domain: Investigate logic G-L.4 Construct and use a truth table to draw conclusions about a statement. G-L.7 Analyze arguments with quantifiers through the use of Venn diagrams. Objectives: Students will: Conceptual Category: Geometry and Measurement Objectives: Students will: Construct and use a truth table to draw conclusions about a statement. Analyze arguments with quantifiers through the use of Venn diagrams Tennessee Finite Math Textbook 11.2 Truth Tables Additional Resources Truth Tables Video Tennessee Finite Math Textbook 11.3 Equivalence, Implication, and Deduction Writing in Math Explain the difference between inductive and deductive reasoning and give an example of Shelby County Schools 2016/2017 Revised 8/31/16 8 of 11 Curriculum and Instruction – Mathematics Quarter 2 TN STATE STANDARDS Domain: Investigate logic G-L.2 Construct and use a truth table to draw conclusions about a statement. G-L.3 Solve a variety of logic puzzles. G-L.5 Apply the laws of logic to judge the validity of arguments. G-L.6 Give counterexamples to disprove statements. Finite Math CONTENT Construct and use a truth table to draw conclusions about a statement. Solve a variety of logic puzzles and apply the laws of logic to judge the validity of arguments. Give counterexamples to disprove statements. INSTRUCTIONAL SUPPORT & RESOURCES Additional Resources Logic Puzzles each. Logic is used in electrical engineering in designing circuits. Find another example of the use of logic in the real world and write a brief report about your findings. Chapter 5 Systems of Linear Equations (Allow approximately 3 weeks for instruction, review, and assessment) HSF.IF.C.7.A Graph linear functions. HSF.LE.A.1.B Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. HSF.LE.A.2 Construct linear functions given a graph, a description of a relationship, or two inputoutput pairs (include reading these from a table). Enduring Understanding(s): A mathematical model consists of both symbolic notations and relations among symbols. Many situations in which mathematical concepts and methods are applied in real world situations involve quantities related to each other through one or more equations. Essential Question(s): How can you model a simulation to represent a real life situation? Objectives: Students will learn: Create and graph linear functions in realworld problems. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. Tennessee Finite Math Textbook 5.1 Review of Equations and Graphs of Lines Additional Resources FiniteHelp Video- 5.1 Finite Math Student Resources Important Terms & Concepts (Chapter 5) Algorithm for solving a system of linear equations, augmented matrix, coefficient matrix, consistent system, coordinates in the plane and in the three-dimensional space, Echelon method, equation of a plane, function, function notation, Gaussian elimination, Gauss-Jordan elimination, general equation of a line, inconsistent system, intercept, line, linear extrapolation, linear interpolation, linear model, reduced row-echelon form, reduction method, row-echelon form, slope, slopeintercept equation of a line, solution of a system of equations, Theorem on the solution of a system of linear equations Writing in Math Explain how the rate of change and slope are related and how to find the slope of a line. Shelby County Schools 2016/2017 Revised 8/31/16 9 of 11 Curriculum and Instruction – Mathematics Quarter 2 TN STATE STANDARDS HAS.REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Conceptual Category: Algebra Domain: Linear systems, matrices, and their applications A-LM.5 Identify and write the general solution to a system of linear equations; in the case of an infinite solution set, select various particular solutions given specific properties. Conceptual Category: Algebra Domain: Linear systems, matrices, and their applications 2. A-LM.5 Identify and write the general solution to a system of linear equations; in the case of an infinite solution set, select various particular solutions given specific properties. Finite Math CONTENT Objectives: Students will: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. INSTRUCTIONAL SUPPORT & RESOURCES Tennessee Finite Math Textbook 5.2 Formulation and Solution of Systems of Linear Equations in Two Variables Additional Resources FiniteHelp Video- 5.2 Writing in Math Explain why you would solve an equation like r = ax + b by solving the system of equations y = r and y = ax + b. Tennessee Finite Math Textbook 5.3 Formulation and Solution of Systems of Linear Equations in Three or More Variables Additional Resources FiniteHelp Video- 5.3 Writing in Math Describe the advantages and disadvantages of using an augmented matrix to solve a system of equations. Identify and write the general solution to a system of linear equations; in the case of an infinite solution set, select various particular solutions given specific properties. Objectives: Students will: Identify and write the general solution to a system of linear equations; in the case of an infinite solution set, select various particular solutions given specific properties. Finite Math Student Resources Shelby County Schools 2016/2017 Revised 8/31/16 10 of 11 Curriculum and Instruction – Mathematics Quarter 2 Finite Math RESOURCE TOOLBOX Textbook Resources Tennessee Finite Math by Dan Maki and Maynard Thompson Published by McGraw Hill 2011 CCSS/PARCC Common Core Standards - Mathematics Common Core Standards - Mathematics Appendix A The Mathematics Common Core Toolbox State Academic Standards (Finite Math) TN Department of Education Math Standards Edutoolbox (formerly TNCore) Videos Khan Academy Illuminations (NCTM) Discovery Education The Futures Channel The Teaching Channel Teachertube.com FiniteHelp Lecture Videos Calculator Texas Instruments Education TI-Nspired http://www.atomiclearning.com/ti_84 TICommonCore.com http://www.casioeducation.com/educators Interactive Manipulatives Rossmanchance.com Additional Sites NCTM Math Illuminations Core Math Tools Math is Fun Wolfram Math World Nrich STatistics Education Web Online Algebra and Trigonometry Tutorial Literacy Glencoe Reading & Writing in the Mathematics Classroom ACT Finite Help Graphic Organizers (9-12) Graphic Organizers (dgelman) Literacy Skills and Strategies for Content Area Teachers TN ACT Information & Resources ACT College & Career Readiness Mathematics Standards Tasks/Lessons UT Dana Center Mars Tasks Inside Math Tasks Math Vision Project Tasks Better Lesson Edutoolbox (formerly TNCore) Shelby County Schools 2016/2017 Revised 8/31/16 11 of 11