Mathematics Curriculum Guide Precalculus Page 1 of 12


 Dorcas Hood
 4 years ago
 Views:
Transcription
1 Mathematics Curriculum Guide Precalculus Page 1 of 12
2 Paramount Unified School District High School Math Curriculum Guides In , PUSD will continue to implement the Standards by providing rigorous math instruction that promotes inquiry based learning, rich math discussions, problem solving and critical thinking. What s Continuing? The Scope and Sequence document sequences instruction for the year for each grade level. Content is organized into instructional units. For each unit of instruction, the scope and sequence cites the standards addressed and the suggested timeframe. What s New? The order of some course units may be different from last year. Adjustments have been made as well so most course content is addressed before SBAC testing. Curriculum Guides The Unit Overview is the big picture of what students will learn throughout the unit. Standards are unpacked to determine specific learning outcomes. Students demonstrate their learning of the standards through Knowledge, Skills and Understandings. Knowledge refers to factual knowledge students must acquire to show mastery, Skills are proficiencies students should demonstrate independently to meet the standard and Understandings are big ideas students come to understand by learning the content. In the Instructional Sequence, the corresponding learning outcomes for each lesson are cited (Knowledge, Skills and Understandings). Focus questions are included to guide instruction while specific textbook lessons and instructional resources are cited to address specific learning targets (e.g., LearnZillion, Smarter Balanced). Units will be posted on the District website as they are completed. Because the Standards require students to demonstrate mastery differently than they did in the past, it is critical for teachers to spend time examining the unit overview to better understand the expectations of the standards and the student learning outcomes. Skills cited in the overview have been revised to align more closely to the standards and to the Smarter Balanced Achievement Level Descriptors. Revisions may be made to the instructional sequence to reflect teacher feedback. Inquiry questions have been included in the units to assist teachers in developing inquiry based lessons that promote problem solving, questioning and rich mathematical discussions. Examples of SBAC type questions are cited in the pacing. Page 2 of 12
3 Instruction Assessments What s Continuing? Unit assessments will continue to reflect a variety of question types including (Part 1) selected response questions, (Part 2) short constructed response and extended constructed response items. Part 2 of the assessments will require students to show their work and explain their thinking. By providing opportunities to demonstrate mathematical reasoning, students apply higherlevel thinking such as analysis, synthesis and evaluation. Unit assessments will be administered at the end of each unit and assessment dates will vary by course and with careful thought to the end of the semester. To review sample items of the Smarter Balanced Assessment which will be implemented in , go to and performance tasks/. For the first three weeks of school, all 9 12 students will receive instruction in an Introduction to a Classroom. The concepts and skills included in this Introduction are to be incorporated into and taught within the context of the Unit 1 content that is taught during this time. The purpose of this unit is to: introduce students to the routines and procedures of the mathematics classroom introduce the skills necessary for building a classroom community review Standards for Mathematical Practice review the proper use of Thinking Maps as tools for discussion and constructing arguments set individual and classroom goals that align to course expectations and SMPs All math classrooms should incorporate these daily practices: thought provoking questioning techniques that develop the habits of mind of the Standards for Mathematical Practice Talk Moves to facilitate discussion and math discourse opportunities to work independently and collaboratively to problem solve inquiry lessons that provide opportunities to explore and investigate concepts opportunities to explain thinking and justify reasoning both orally and in writing What s New? This year, targeted courses will pilot online unit assessments in math to prepare students for Smarter Balanced testing. Inquiry based instruction should be evident in all math classrooms. In an inquiry based math classroom, students persevere to problem solve and think critically as they uncover new concepts. Teachers support this productive struggle by asking guided questions that are planned in advance and scaffolded. This approach is different from a direct instruction where teachers specifically tell students the steps to follow to solve a problem. An inquiry lesson planning template was piloted last year with lead teachers. This year it will be shared with all schools during professional development. In order to support instruction through inquiry, the expectations for posting a daily objective have changed. With inquiry based instruction, students should not be told what they are going to learn as this takes away the opportunity to learn through discovery. Instead, teachers will post a daily Focus Question from the instructional sequence in the curriculum guide. This question guides student thinking as they explore skills and concepts and discover new learning. Teachers can also post Essential Questions from the unit overview to revisit throughout the unit. Page 3 of 12
4 Paramount Unified School District Educational Services Introduction to the Classroom Grades 9 12 Transfer Goals 1) Interpret and persevere in solving complex math problems using strategic thinking and expressing answers with a degree of precision appropriate for the problem context. 2) Express appropriate math reasoning by constructing viable arguments, critiquing the reasoning of others, attending to precision when making mathematical statements, and using tools to support reasoning. 3) Apply mathematical knowledge to analyze and model math relationships in the context of a situation in order to make decisions, draw conclusions, and solve problems. Unit Focus The purpose of this unit is to: introduce students to the routines and procedures of the classroom introduce the skills necessary for building a classroom community (e.g., participate in whole group, small group, and partner conversations using Talk Moves; respond to questions and prompts through academic discussions and writing) review all Standards for Mathematical Practice (especially SMPs #1 3) review the proper use of Thinking Maps as tools for discussion and constructing arguments set individual and classroom goals that align to grade level expectations and SMPs Understandings Students will understand that Mathematical learning is supported with structured routines and procedures Participating in academic conversations requires purposeful listening, speaking and writing in math which leads to greater understanding and shared reasoning Mathematicians don t give up and try different strategies to solve problems (SMP #1) Mathematicians can show their reasoning using both numbers and words (SMP #2) Mathematicians construct arguments and critique the reasoning of others (SMP #3) Thinking Maps are a useful tool for organizing thinking Setting goals is important to monitor both individual and class progress Knowledge Students will know Agreed upon classroom rules and procedures All 8 Talk Moves Linguistic patterns used for partaking in academic discussions The Standards for Mathematical Practices (SMPs) Thinking Maps Individual and classroom goals Essential Questions Students will consider. By following classroom rules and procedures, how does this support my learning? How can I effectively communicate my ideas orally and in writing to construct a viable argument about what I am learning and thinking? What strategies can I use to persevere in problem solving? How can I respectfully critique the reasoning of others? How can Thinking Maps be used during math to help me organize and explain my thinking? By setting goals, how will this help me to progress in meeting my grade level expectations and develop the habits of mind of a mathematician? Skills Students will be skilled at and able to Follow classroom rules and procedures Participate in academic conversations using Talk Moves, appropriate body language and a variety of active participation strategies Respond to questions and prompts orally and in writing using academic language Use a variety of strategies to persevere in solving problems (e.g., numbers, words) Construct viable arguments and critique the reasoning of others Use Thinking Maps to represent mathematical thinking Set individual and classroom goals Suggested Timeframe: Within first 3 weeks Instructional Activities Collaboratively establish classroom rules and procedures (behavior, retrieve materials, independent work, group work) Review each Talk Move individually model first, check for understanding and use in context to promote shared reasoning Establish appropriate behaviors for listening and speaking (e.g., eye contact, lean in, strong voice, speak clearly, linguistic patterns, etc.) Review expectations for working collaboratively (everyone contributes, listen to each other, add on to classmates thinking, disagree with and critique others respectfully) Establish individual and classroom goals for the year, quarter, etc. that align to grade level expectations and the SMPs Use Thinking Maps for the activities cited above (e.g., Circle Map to identify practices for each of the SMPs, Multi flow Map to show the effects of effective collaboration, etc.) Resources Talk Moves posters SMP posters Problem solving response frames Thinking Maps posters Goal setting documents Page 4 of 12
5 Paramount Unified School District Educational Services Topic 1: Functions and Graphs Mathematics Topic 1 Overview Course: Precalculus Transfer Goals 1) Interpret and persevere in solving complex math problems using strategic thinking and expressing answers with a degree of precision appropriate for the problem context. 2) Express appropriate math reasoning by constructing viable arguments, critiquing the reasoning of others, attending to precision when making mathematical statements, and using tools to support reasoning. 3) Apply mathematical knowledge to analyze and model math relationships in the context of a situation in order to make decisions, draw conclusions, and solve problems. Understandings Standard s ALGEB RA A CED 1 A CED 2 A REI 10, 11 F IF 1 F IF 2 F IF 4 F IF 5 F IF 6 F IF 7, F IF 8 F IF 9 F BF 1 F BF 3 F BF 4 A SSE 3 Quantities N Q 1 Students will understand that Functions are use usually given in terms of equations involving x and y. (F IF 1) Functions are used to determine the function s domain and its range. (F IF 1, 3) Ordered pair describes the order of the coordinate and makes a difference in a point s location. (A REI 10) A parent function is the simplest form of a set of functions that forma a family. Each function in the family is a transformation of the parent function. (F IF 7) A function involving more than one transformation can be graphed in the following order: horizontal shifting, stretching or shrinking, reflecting and vertical shifting. (F BF 3) Transformations help to understand the relationship between graphs that have similarities but are not the same. (F BF 3) Functions and graphs form the basis for understanding mathematics and applications. (A CED 1, 2) The ratio of the vertical change to the horizontal change is constant. That constant ratio describes the slope of the line. (F IF 6) Linear functions can be graphed using the slope and the y intercept. Linear equations in standard form can be graphed using the x and y intercepts. (A REI 10) Operations of functions are performed same as for real numbers. One difference is that the domain of each function must be considered. (F BF 1) Numerical, algebraic, and graphical models provide different methods to visualize, analyze, and understand data. (A CED 1, 2) Knowledge Students will know Vocabulary: Zeros, intercepts, domain, range, function, interval notation, vertical line test, increasing, decreasing, minimum, maximum, regression, vertical and horizontal shift and stretch, reflection, composition, inverse functions, horizontal line test, one to one function, verbal models Properties of the twelve basic functions. The graph of f has x intercepts at the real zeros, intervals of increasing, decreasing, and relative maximum and minimum. A function involving more than one transformation can be graphed in the following order: horizontal shifting, stretching or shrinking, reflecting and vertical shifting. Transformations help to understand the relationship between graphs that have similarities but are not the same. If a function does not model a verbal condition, its domain is the largest set of real numbers for which the value of f(x) is a real number, excluding real numbers that cause division by zero and real numbers that result in an event root of a negative numbers. Most functions can be created by combining or modifying other functions. Essential Questions Students will keep considering Suggested Timeframe: 4 weeks, 20 days Assessment Dates: Sept , 2015 How do represent functions graphically and interpret information given by the graphs? How are domains affected when functions are combined arithmetically or composed? How can inverse functions be determined, verified, and graphed? How can verbal models are used to obtain functions from verbal descriptions? Skills Students will be skilled at and able to do the following Investigate end behavior. Identify different forms of linear equations. Know the different forms of a linear function. Graph linear equations from a given form. Identify graphs of the twelve basic functions. Analyze functions both algebraically and graphically for various properties including domain, range, continuity, intervals of increasing and decreasing, local extrema, symmetry, and end behavior. Identify algebraically and graphically representations of translations, reflections, stretches, and shrinks of functions. Perform transformations of graph, which include vertical and horizontal shifts, reflections, vertical stretching and shrinking, and horizontal stretching and shrinking. Perform operations that apply to all types of functions and build new functions from existing functions. Consider the domain of functions as the largest set of real numbers, excluding real numbers that cause division by zero and real numbers that result in an event root of a negative numbers. Find the inverse functions by restricting the domain using algebraic method, using tables, and using graphs. Verify inverse functions by composing the functions in both orders. Identify appropriate basic functions with which to model real world problems and be able to produce specific functions to model data, formulas, graphs, and verbal descriptions. Page 5 of 12
6 Paramount Unified School District Educational Services Topic 1: Functions and Graphs Essential Questions: How do represent functions graphically and interpret information given by the graphs? How are domains affected when functions are combined arithmetically or composed? How can inverse functions be determined, verified, and graphed? How can verbal models are used to obtain functions from verbal descriptions? Lesson/ Time Activity 3 days Review concepts of Algebra (Sections P.1,P.5, P.9) Focus Questions for Lessons Focus Question How do you recognize subsets of the real numbers and identify their properties to simplify algebraic expressions? Is a rule that can help to determine the factors of an expression? Standards: A CED 1, 2, F IF 1, 2, 4, 5, 6, 7, 8, 9, A REI 11, F BF 1, 3, 4, N Q 1 Suggested Timeframe: 4 weeks, 20 days Start Date: August 19, 2015 Assessment Dates: September 15 16, 2015 Understandings Knowledge Skills Resources The set of real numbers contains rational and irrational numbers Absolute value expresses distance Mathematical modeling is the process of finding an equation to describe realworld phenomena Rules of factorization Domain of an inequality Vocabulary: absolute value, mathematical modeling, setbuilder notation, intersection of sets, union of sets, rea; numbers, factoring, domain, inequalities, interval notation. Simplify algebraic expressions Identify intersection and union of sets Use the properties of real numbers Factoring expressions Solving linear, compound and absolute value inequalities Use interval notation to determine the domain of an inequality Mathematics Topic 1 Pacing Course: Precalculus P.1: # , P.5: # , P.9: # days Lesson 1.4: Linear Functions and Slope A REI 10 Lesson 1.5: More on Slope F IF 6, 7, 8, 9 Focus Question. How do you write and graph linear equations? Explain how to derive the slopeintercept form of line s equation, y = mx +b from the point intercept form, y y 1 = m(x x 1 ) The ratio of the vertical change to the horizontal change is constant. That constant ratio describes the slope of the line. Linear functions can be graphed using the slope and the y intercept. Linear equations in standard form can be graphed using the x and y intercepts. Vocabulary: slope, scatter plot, intercept form, point slope form, horizontal and vertical lines, parallel and perpendicular lines, rate of change. Parallel lines have the same slope. Perpendicular lines slopes are opposite reciprocals. Identify different forms of linear equations. Know the different forms of a linear function. Graph linear equations from a given form. 1.4: #87 99, : #27 38, : #25 34, 87 88, 118, : #5 12, day Topic 1 Opening Activity Introduction to the Performance Task (see attached) Practices Instruction in the Standards for Mathematical Practices Use of Talk Moves Note taking Use of Manipulatives Use of Technology Use of Real world Scenarios Project based Learning Thinking Maps Page 6 of 12
7 Time Lesson/ Activity Focus Questions for Lessons Understandings Knowledge Skills Additional Resources 1 day Lesson 1.1: Graphs and graphing utilities F IF 1 Focus Question. How do you graph functions and interpret information given by the graphs? Are single numbers the only way to represent intercepts? Can ordered pairs also be used? Functions are use usually given in terms of equations involving x and y Functions are used to determine the function s domain, range and intercepts. Ordered pair describes the order of the coordinates and makes a difference in a point s location. Vocabulary: x and y axis, quadrants, ordered pair, x and y intercept, origin, equation in two variables. Ordered pairs satisfy solutions of equations. Plot points and graph equations in the rectangular system. Use a graph to determine intercepts. Interpret information given by graphs. Use a graphing Utility 1.1: #55 65, 67 74, : # days Lessons 1.2: Basics of Functions and Their Graphs F IF 5, 7, 9 Lesson 1.3: More on Functions and Their Graphs Focus Question How do you graph relations and identify their properties? Pg. 185 Chose from A relation is identified as a function if it passes the vertical line test and its domain values appear only once. Dots, open dots, or arrows on the left and right sides of a graph give information about a function. The x coordinate and not the y coordinate describe the interval where the functions increase, decrease, or are constant. Vocabulary: domain, range, function, vertical line test, intercepts, intervals notation, open interval, interval of increasing, decreasing, or constant, symmetry, local maximum and minimum. F(x) notation describes the value of the function at x. Identify the graphs of twelve basic functions. Obtain information about a function from its graph and visualize that lines will or will not extend on both sides of the line depending on a dot, open dot or arrow. Analyze functions both algebraically and graphically for various properties including domain and range, intervals of increasing and decreasing, local and absolute extrema, symmetry, asymptotes and end behavior. 1.2: #99 116, : #79 82, , : #1 10, : #33 36, 37 42, Practices Instruction in the Standards for Mathematical Practices Use of Talk Moves Note taking Use of Manipulatives Use of Technology Use of Real world Scenarios Project based Learning Thinking Maps Page 7 of 12
8 Time Lesson/ Activity Focus Questions for Lessons Understandings Knowledge Skills Additional Resources 2 days Lesson 1.6: Transformation s of functions 2 days F IF 7 F BF 3 Lesson 1.7: Combinations of functions: Composite Functions F BF 1 Focus Question How transformations could help you to understand the relationship between graphs that have similarities but are not the same? Pg. 229 # 128 Focus Question How are domains affected when functions are combined arithmetically or composed? Describe the values of x that must be excluded from the domain of (f g)(x) A parent function is the simplest form of a set of functions that forma a family. Each function in the family is a transformation of the parent function. A function involving more than one transformation can be graphed in the following order: horizontal shifting, stretching or shrinking, reflecting and vertical shifting. Transformations help to understand the relationship between graphs that have similarities but are not the same. Operations of functions are performed same are for real numbers. One difference is that the domain of each functions must be considered If a function does not model a verbal condition, its domain is the largest set of real numbers for which the value of f(x) is a real number, excluding real numbers that cause division by zero and real numbers that result in an event root of a negative numbers. Vocabulary: common functions, vertical and horizontal shift, reflections, vertical and horizontal stretching and shrinking, Graphing procedures Transformation of a familiar graph makes graphing easier. Vocabulary: inequality symbols and related operations, solid and dashed lines, region of solutions The composition of two functions involves replacing the variable of one function with the expression equal to the other function. Identify algebraically and graphically representations of translations, reflections, stretches, and shrinks of functions. Perform transformations of graph, which include vertical and horizontal shifts, reflections, vertical stretching and shrinking, and horizontal stretching and shrinking. Perform operations that apply to all types of functions and build new functions from existing functions. Consider the domain of functions as the largest set of real numbers, excluding real numbers that cause division by zero and real numbers that result in an event root of a negative numbers. 1.6: # , : #17 24, 53 66, : #97 107, : p #a d, p #8 12, 25 26, 51 66, day Lesson 1.8: Inverse Functions F BF 4 Focus Question How can a function s inverse be determined, verify, and graphed? Pg. 256 # 89, 90 The inverse of a may be or not be a function. The range of the relation is the domain of the inverse and domain of the relation is the range of the inverse. If f and f 1 are functions and if either maps a to b, then the other maps b to a. Vocabulary: inverse relation, inverse function, one to one function, horizontal line test, The inverse of a function will only be a function if the function is a one toone. Find the inverse functions by restricting the domain using algebraic method, using tables, and using graphs. Verify inverse functions by composing the functions in both orders. 1.8: #65 75, : #1 10, 11 28, Instruction in the Standards for Mathematical Practices Use of Talk Moves Note taking Practices Use of Manipulatives Use of Technology Use of Real world Scenarios Project based Learning Thinking Maps Page 8 of 12
9 Time Lesson/ Activity Focus Questions for Lessons Understandings Knowledge Skills Additional Resources 1 day Lesson 1.10: Modeling with Functions A CED 1,2 Focus Question How can you construct functions from verbal descriptions and from formulas? Pg. 281 # 68 Data can be modeled from real world situations with equations, formulas, or graphs. These tools can be used to draw conclusions about the situations. Real world situations can be analyzed and solved by functions.. Vocabulary: verbal models When developing functions that model situations, it is helpful to draw a diagram Identify appropriate basic functions with which to model real world problems and be able to produce specific functions to model data, formulas, graphs, and verbal descriptions. This whole lesson has cc problems. 1.10: #21 22, days 1 day Review & Assess Chapter 1 Concepts & Skills Use Textbook Resources and/or Teacher Created Items for Assessment Topic 1 Performance Task Have students work collaboratively to reflect on the Performance Task 2 days Unit 1 Assessment (Created and provided by PUSD) Instruction in the Standards for Mathematical Practices Use of Talk Moves Note taking Practices Use of Manipulatives Use of Technology Use of Real world Scenarios Project based Learning Thinking Maps Page 9 of 12
10 Topic 1 Performance Task Page 1 Precalculus Name: Date: Per: Page 10 of 12
11 Topic 1 Performance Task Page 2 Page 11 of 12
12 Page 12 of 12
CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREERREADY FOUNDATIONS IN ALGEBRA
We Can Early Learning Curriculum PreK Grades 8 12 INSIDE ALGEBRA, GRADES 8 12 CORRELATED TO THE SOUTH CAROLINA COLLEGE AND CAREERREADY FOUNDATIONS IN ALGEBRA April 2016 www.voyagersopris.com Mathematical
More informationAlgebra II Unit Number 4
Title Polynomial Functions, Expressions, and Equations Big Ideas/Enduring Understandings Applying the processes of solving equations and simplifying expressions to problems with variables of varying degrees.
More informationHow To Understand And Solve Algebraic Equations
College Algebra Course Text Barnett, Raymond A., Michael R. Ziegler, and Karl E. Byleen. College Algebra, 8th edition, McGrawHill, 2008, ISBN: 9780072867381 Course Description This course provides
More informationhttp://www.aleks.com Access Code: RVAE4EGKVN Financial Aid Code: 6A9DBDEE3B74F5157304
MATH 1340.04 College Algebra Location: MAGC 2.202 Meeting day(s): TR 7:45a 9:00a, Instructor Information Name: Virgil Pierce Email: piercevu@utpa.edu Phone: 665.3535 Teaching Assistant Name: Indalecio
More informationFlorida Math for College Readiness
Core Florida Math for College Readiness Florida Math for College Readiness provides a fourthyear math curriculum focused on developing the mastery of skills identified as critical to postsecondary readiness
More informationSouth Carolina College and CareerReady (SCCCR) Algebra 1
South Carolina College and CareerReady (SCCCR) Algebra 1 South Carolina College and CareerReady Mathematical Process Standards The South Carolina College and CareerReady (SCCCR) Mathematical Process
More informationEQUATIONS and INEQUALITIES
EQUATIONS and INEQUALITIES Linear Equations and Slope 1. Slope a. Calculate the slope of a line given two points b. Calculate the slope of a line parallel to a given line. c. Calculate the slope of a line
More informationPrentice Hall Connected Mathematics 2, 7th Grade Units 2009
Prentice Hall Connected Mathematics 2, 7th Grade Units 2009 Grade 7 C O R R E L A T E D T O from March 2009 Grade 7 Problem Solving Build new mathematical knowledge through problem solving. Solve problems
More informationAdministrative  Master Syllabus COVER SHEET
Administrative  Master Syllabus COVER SHEET Purpose: It is the intention of this to provide a general description of the course, outline the required elements of the course and to lay the foundation for
More informationAlgebra I Credit Recovery
Algebra I Credit Recovery COURSE DESCRIPTION: The purpose of this course is to allow the student to gain mastery in working with and evaluating mathematical expressions, equations, graphs, and other topics,
More informationPolynomial Operations and Factoring
Algebra 1, Quarter 4, Unit 4.1 Polynomial Operations and Factoring Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned Identify terms, coefficients, and degree of polynomials.
More informationLAKE ELSINORE UNIFIED SCHOOL DISTRICT
LAKE ELSINORE UNIFIED SCHOOL DISTRICT Title: PLATO Algebra 1Semester 2 Grade Level: 1012 Department: Mathematics Credit: 5 Prerequisite: Letter grade of F and/or N/C in Algebra 1, Semester 2 Course Description:
More informationAlgebra 1 Course Information
Course Information Course Description: Students will study patterns, relations, and functions, and focus on the use of mathematical models to understand and analyze quantitative relationships. Through
More informationMATH 095, College Prep Mathematics: Unit Coverage Prealgebra topics (arithmetic skills) offered through BSE (Basic Skills Education)
MATH 095, College Prep Mathematics: Unit Coverage Prealgebra topics (arithmetic skills) offered through BSE (Basic Skills Education) Accurately add, subtract, multiply, and divide whole numbers, integers,
More informationMathematics Georgia Performance Standards
Mathematics Georgia Performance Standards K12 Mathematics Introduction The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by
More informationSouth Carolina College and CareerReady (SCCCR) PreCalculus
South Carolina College and CareerReady (SCCCR) PreCalculus Key Concepts Arithmetic with Polynomials and Rational Expressions PC.AAPR.2 PC.AAPR.3 PC.AAPR.4 PC.AAPR.5 PC.AAPR.6 PC.AAPR.7 Standards Know
More informationCRLS Mathematics Department Algebra I Curriculum Map/Pacing Guide
Curriculum Map/Pacing Guide page 1 of 14 Quarter I start (CP & HN) 170 96 Unit 1: Number Sense and Operations 24 11 Totals Always Include 2 blocks for Review & Test Operating with Real Numbers: How are
More informationHigher Education Math Placement
Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication
More informationAlgebra 2 YearataGlance Leander ISD 200708. 1st Six Weeks 2nd Six Weeks 3rd Six Weeks 4th Six Weeks 5th Six Weeks 6th Six Weeks
Algebra 2 YearataGlance Leander ISD 200708 1st Six Weeks 2nd Six Weeks 3rd Six Weeks 4th Six Weeks 5th Six Weeks 6th Six Weeks Essential Unit of Study 6 weeks 3 weeks 3 weeks 6 weeks 3 weeks 3 weeks
More informationPreCalculus Semester 1 Course Syllabus
PreCalculus Semester 1 Course Syllabus The Plano ISD eschool Mission is to create a borderless classroom based on a positive studentteacher relationship that fosters independent, innovative critical
More informationNEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS
NEW YORK STATE TEACHER CERTIFICATION EXAMINATIONS TEST DESIGN AND FRAMEWORK September 2014 Authorized for Distribution by the New York State Education Department This test design and framework document
More informationVocabulary Words and Definitions for Algebra
Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms
More informationCourse Outlines. 1. Name of the Course: Algebra I (Standard, College Prep, Honors) Course Description: ALGEBRA I STANDARD (1 Credit)
Course Outlines 1. Name of the Course: Algebra I (Standard, College Prep, Honors) Course Description: ALGEBRA I STANDARD (1 Credit) This course will cover Algebra I concepts such as algebra as a language,
More informationGRADE 8 MATH: TALK AND TEXT PLANS
GRADE 8 MATH: TALK AND TEXT PLANS UNIT OVERVIEW This packet contains a curriculumembedded Common Core standards aligned task and instructional supports. The task is embedded in a three week unit on systems
More informationRUTHERFORD HIGH SCHOOL Rutherford, New Jersey COURSE OUTLINE STATISTICS AND PROBABILITY
RUTHERFORD HIGH SCHOOL Rutherford, New Jersey COURSE OUTLINE STATISTICS AND PROBABILITY I. INTRODUCTION According to the Common Core Standards (2010), Decisions or predictions are often based on data numbers
More informationThe program also provides supplemental modules on topics in geometry and probability and statistics.
Algebra 1 Course Overview Students develop algebraic fluency by learning the skills needed to solve equations and perform important manipulations with numbers, variables, equations, and inequalities. Students
More informationPerformance Level Descriptors Grade 6 Mathematics
Performance Level Descriptors Grade 6 Mathematics Multiplying and Dividing with Fractions 6.NS.12 Grade 6 Math : SubClaim A The student solves problems involving the Major Content for grade/course with
More informationAlgebra I Vocabulary Cards
Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Absolute Value Order of Operations Expression
More informationPrerequisite: MATH 0302, or meet TSI standard for MATH 0305; or equivalent.
18966.201610 COLLIN COLLEGE COURSE SYLLABUS Course Number: MATH 0305.XS1 Course Title: Beginning Algebra Course Description: With an emphasis on developing critical thinking skills, a study of algebraic
More informationSuccessful completion of Math 7 or Algebra Readiness along with teacher recommendation.
MODESTO CITY SCHOOLS COURSE OUTLINE COURSE TITLE:... Basic Algebra COURSE NUMBER:... RECOMMENDED GRADE LEVEL:... 811 ABILITY LEVEL:... Basic DURATION:... 1 year CREDIT:... 5.0 per semester MEETS GRADUATION
More informationMTH124: Honors Algebra I
MTH124: Honors Algebra I This course prepares students for more advanced courses while they develop algebraic fluency, learn the skills needed to solve equations, and perform manipulations with numbers,
More informationNorth Carolina Math 2
Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4.
More informationInteger Operations. Overview. Grade 7 Mathematics, Quarter 1, Unit 1.1. Number of Instructional Days: 15 (1 day = 45 minutes) Essential Questions
Grade 7 Mathematics, Quarter 1, Unit 1.1 Integer Operations Overview Number of Instructional Days: 15 (1 day = 45 minutes) Content to Be Learned Describe situations in which opposites combine to make zero.
More informationTennessee Department of Education. Task: Sally s Car Loan
Tennessee Department of Education Task: Sally s Car Loan Sally bought a new car. Her total cost including all fees and taxes was $15,. She made a down payment of $43. She financed the remaining amount
More informationClovis Community College Core Competencies Assessment 2014 2015 Area II: Mathematics Algebra
Core Assessment 2014 2015 Area II: Mathematics Algebra Class: Math 110 College Algebra Faculty: Erin Akhtar (Learning Outcomes Being Measured) 1. Students will construct and analyze graphs and/or data
More informationGeorgia Department of Education Kathy Cox, State Superintendent of Schools 7/19/2005 All Rights Reserved 1
Accelerated Mathematics 3 This is a course in precalculus and statistics, designed to prepare students to take AB or BC Advanced Placement Calculus. It includes rational, circular trigonometric, and inverse
More informationALGEBRA I (Created 2014) Amherst County Public Schools
ALGEBRA I (Created 2014) Amherst County Public Schools The 2009 Mathematics Standards of Learning Curriculum Framework is a companion document to the 2009 Mathematics Standards of Learning and amplifies
More informationHIBBING COMMUNITY COLLEGE COURSE OUTLINE
HIBBING COMMUNITY COLLEGE COURSE OUTLINE COURSE NUMBER & TITLE:  Beginning Algebra CREDITS: 4 (Lec 4 / Lab 0) PREREQUISITES: MATH 0920: Fundamental Mathematics with a grade of C or better, Placement Exam,
More informationWhat are the place values to the left of the decimal point and their associated powers of ten?
The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything
More informationMATH 60 NOTEBOOK CERTIFICATIONS
MATH 60 NOTEBOOK CERTIFICATIONS Chapter #1: Integers and Real Numbers 1.1a 1.1b 1.2 1.3 1.4 1.8 Chapter #2: Algebraic Expressions, Linear Equations, and Applications 2.1a 2.1b 2.1c 2.2 2.3a 2.3b 2.4 2.5
More informationCreating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities
Algebra 1, Quarter 2, Unit 2.1 Creating, Solving, and Graphing Systems of Linear Equations and Linear Inequalities Overview Number of instructional days: 15 (1 day = 45 60 minutes) Content to be learned
More informationGlencoe. correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 33, 58 84, 87 16, 49
Glencoe correlated to SOUTH CAROLINA MATH CURRICULUM STANDARDS GRADE 6 STANDARDS 68 Number and Operations (NO) Standard I. Understand numbers, ways of representing numbers, relationships among numbers,
More informationAcademic Standards for Mathematics
Academic Standards for Grades Pre K High School Pennsylvania Department of Education INTRODUCTION The Pennsylvania Core Standards in in grades PreK 5 lay a solid foundation in whole numbers, addition,
More informationThe PointSlope Form
7. The PointSlope Form 7. OBJECTIVES 1. Given a point and a slope, find the graph of a line. Given a point and the slope, find the equation of a line. Given two points, find the equation of a line y Slope
More informationCurrent Standard: Mathematical Concepts and Applications Shape, Space, and Measurement Primary
Shape, Space, and Measurement Primary A student shall apply concepts of shape, space, and measurement to solve problems involving two and threedimensional shapes by demonstrating an understanding of:
More informationFor example, estimate the population of the United States as 3 times 10⁸ and the
CCSS: Mathematics The Number System CCSS: Grade 8 8.NS.A. Know that there are numbers that are not rational, and approximate them by rational numbers. 8.NS.A.1. Understand informally that every number
More informationFunctional Math II. Information CourseTitle. Types of Instruction
Functional Math II Course Outcome Summary Riverdale School District Information CourseTitle Functional Math II Credits 0 Contact Hours 135 Instructional Area Middle School Instructional Level 8th Grade
More informationHigh School Functions Interpreting Functions Understand the concept of a function and use function notation.
Performance Assessment Task Printing Tickets Grade 9 The task challenges a student to demonstrate understanding of the concepts representing and analyzing mathematical situations and structures using algebra.
More informationGeorgia Standards of Excellence 20152016 Mathematics
Georgia Standards of Excellence 20152016 Mathematics Standards GSE Coordinate Algebra K12 Mathematics Introduction Georgia Mathematics focuses on actively engaging the student in the development of mathematical
More informationThis unit will lay the groundwork for later units where the students will extend this knowledge to quadratic and exponential functions.
Algebra I Overview View unit yearlong overview here Many of the concepts presented in Algebra I are progressions of concepts that were introduced in grades 6 through 8. The content presented in this course
More informationIndiana Academic Standards Mathematics: Algebra I
Indiana Academic Standards Mathematics: Algebra I 1 I. Introduction The college and career ready Indiana Academic Standards for Mathematics: Algebra I are the result of a process designed to identify,
More informationMATH. ALGEBRA I HONORS 9 th Grade 12003200 ALGEBRA I HONORS
* Students who scored a Level 3 or above on the Florida Assessment Test Math Florida Standards (FSAMAFS) are strongly encouraged to make Advanced Placement and/or dual enrollment courses their first choices
More informationIndiana State Core Curriculum Standards updated 2009 Algebra I
Indiana State Core Curriculum Standards updated 2009 Algebra I Strand Description Boardworks High School Algebra presentations Operations With Real Numbers Linear Equations and A1.1 Students simplify and
More informationPearson Algebra 1 Common Core 2015
A Correlation of Pearson Algebra 1 Common Core 2015 To the Common Core State Standards for Mathematics Traditional Pathways, Algebra 1 High School Copyright 2015 Pearson Education, Inc. or its affiliate(s).
More informationF.IF.7e Analyze functions using different representations. Graph exponential and logarithmic functions, showing intercept and end behavior.
Grade Level/Course: Algebra and PreCalculus Lesson/Unit Plan Name: Introduction to Logarithms: A Function Approach Rationale/Lesson Abstract: This lesson is designed to introduce logarithms to students
More informationGrade 6 Mathematics Performance Level Descriptors
Limited Grade 6 Mathematics Performance Level Descriptors A student performing at the Limited Level demonstrates a minimal command of Ohio s Learning Standards for Grade 6 Mathematics. A student at this
More informationFactoring Quadratic Trinomials
Factoring Quadratic Trinomials Student Probe Factor x x 3 10. Answer: x 5 x Lesson Description This lesson uses the area model of multiplication to factor quadratic trinomials. Part 1 of the lesson consists
More informationCOLLEGE ALGEBRA LEARNING COMMUNITY
COLLEGE ALGEBRA LEARNING COMMUNITY Tulsa Community College, West Campus Presenter Lori Mayberry, B.S., M.S. Associate Professor of Mathematics and Physics lmayberr@tulsacc.edu NACEP National Conference
More informationCommon Core Unit Summary Grades 6 to 8
Common Core Unit Summary Grades 6 to 8 Grade 8: Unit 1: Congruence and Similarity 8G18G5 rotations reflections and translations,( RRT=congruence) understand congruence of 2 d figures after RRT Dilations
More informationMathematics. Accelerated GSE Analytic Geometry B/Advanced Algebra Unit 7: Rational and Radical Relationships
Georgia Standards of Excellence Frameworks Mathematics Accelerated GSE Analytic Geometry B/Advanced Algebra Unit 7: Rational and Radical Relationships These materials are for nonprofit educational purposes
More informationBookTOC.txt. 1. Functions, Graphs, and Models. Algebra Toolbox. Sets. The Real Numbers. Inequalities and Intervals on the Real Number Line
College Algebra in Context with Applications for the Managerial, Life, and Social Sciences, 3rd Edition Ronald J. Harshbarger, University of South Carolina  Beaufort Lisa S. Yocco, Georgia Southern University
More informationDRAFT. Algebra 1 EOC Item Specifications
DRAFT Algebra 1 EOC Item Specifications The draft Florida Standards Assessment (FSA) Test Item Specifications (Specifications) are based upon the Florida Standards and the Florida Course Descriptions as
More informationEstimated Pre Calculus Pacing Timeline
Estimated Pre Calculus Pacing Timeline 20102011 School Year The timeframes listed on this calendar are estimates based on a fiftyminute class period. You may need to adjust some of them from time to
More informationAlgebra 1. Curriculum Map
Algebra 1 Curriculum Map Table of Contents Unit 1: Expressions and Unit 2: Linear Unit 3: Representing Linear Unit 4: Linear Inequalities Unit 5: Systems of Linear Unit 6: Polynomials Unit 7: Factoring
More informationAnswer Key for California State Standards: Algebra I
Algebra I: Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences.
More informationChapter 111. Texas Essential Knowledge and Skills for Mathematics. Subchapter B. Middle School
Middle School 111.B. Chapter 111. Texas Essential Knowledge and Skills for Mathematics Subchapter B. Middle School Statutory Authority: The provisions of this Subchapter B issued under the Texas Education
More informationPrentice Hall Mathematics, Algebra 1 2009
Prentice Hall Mathematics, Algebra 1 2009 Grades 912 C O R R E L A T E D T O Grades 912 Prentice Hall Mathematics, Algebra 1 Program Organization Prentice Hall Mathematics supports student comprehension
More informationAlgebra 1 Course Title
Algebra 1 Course Title Course wide 1. What patterns and methods are being used? Course wide 1. Students will be adept at solving and graphing linear and quadratic equations 2. Students will be adept
More informationTo represent mathematical relationships using graphs. 41 Activity: Relating Quantities See Department Chair for File 1 day A.REI.10, F.IF.
CCSS for Mathematical Practice: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model
More informationMath at a Glance for April
Audience: School Leaders, Regional Teams Math at a Glance for April The Math at a Glance tool has been developed to support school leaders and region teams as they look for evidence of alignment to Common
More informationKEANSBURG SCHOOL DISTRICT KEANSBURG HIGH SCHOOL Mathematics Department. HSPA 10 Curriculum. September 2007
KEANSBURG HIGH SCHOOL Mathematics Department HSPA 10 Curriculum September 2007 Written by: Karen Egan Mathematics Supervisor: Ann Gagliardi 7 days Sample and Display Data (Chapter 1 pp. 447) Surveys and
More informationAnchorage School District/Alaska Sr. High Math Performance Standards Algebra
Anchorage School District/Alaska Sr. High Math Performance Standards Algebra Algebra 1 2008 STANDARDS PERFORMANCE STANDARDS A1:1 Number Sense.1 Classify numbers as Real, Irrational, Rational, Integer,
More informationLinear Equations. Find the domain and the range of the following set. {(4,5), (7,8), (1,3), (3,3), (2,3)}
Linear Equations Domain and Range Domain refers to the set of possible values of the xcomponent of a point in the form (x,y). Range refers to the set of possible values of the ycomponent of a point in
More informationCORE Assessment Module Module Overview
CORE Assessment Module Module Overview Content Area Mathematics Title Speedy Texting Grade Level Grade 7 Problem Type Performance Task Learning Goal Students will solve reallife and mathematical problems
More informationMathematics Online Instructional Materials Correlation to the 2009 Algebra I Standards of Learning and Curriculum Framework
Provider York County School Division Course Syllabus URL http://yorkcountyschools.org/virtuallearning/coursecatalog.aspx Course Title Algebra I AB Last Updated 2010  A.1 The student will represent verbal
More informationUnit 1 Equations, Inequalities, Functions
Unit 1 Equations, Inequalities, Functions Algebra 2, Pages 1100 Overview: This unit models realworld situations by using one and twovariable linear equations. This unit will further expand upon pervious
More informationGrade 6 Mathematics Assessment. Eligible Texas Essential Knowledge and Skills
Grade 6 Mathematics Assessment Eligible Texas Essential Knowledge and Skills STAAR Grade 6 Mathematics Assessment Mathematical Process Standards These student expectations will not be listed under a separate
More informationMeasurement with Ratios
Grade 6 Mathematics, Quarter 2, Unit 2.1 Measurement with Ratios Overview Number of instructional days: 15 (1 day = 45 minutes) Content to be learned Use ratio reasoning to solve realworld and mathematical
More informationPrentice Hall. California Edition of Algebra 1  Classics Edition (Smith/Charles) 2008. Grade 8
Prentice Hall Grade 8 California Edition of Algebra 1  Classics Edition (Smith/Charles) 2008 C O R R E L A T E D T O California s Map for a Basic Grade Level Program Grade 8 PROGRAM DESCRIPTION Prentice
More informationStandards for Mathematical Practice: Commentary and Elaborations for 6 8
Standards for Mathematical Practice: Commentary and Elaborations for 6 8 c Illustrative Mathematics 6 May 2014 Suggested citation: Illustrative Mathematics. (2014, May 6). Standards for Mathematical Practice:
More informationProblem of the Month Through the Grapevine
The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards: Make sense of problems
More informationDELAWARE MATHEMATICS CONTENT STANDARDS GRADES 910. PAGE(S) WHERE TAUGHT (If submission is not a book, cite appropriate location(s))
Prentice Hall University of Chicago School Mathematics Project: Advanced Algebra 2002 Delaware Mathematics Content Standards (Grades 910) STANDARD #1 Students will develop their ability to SOLVE PROBLEMS
More informationAlgebra I. In this technological age, mathematics is more important than ever. When students
In this technological age, mathematics is more important than ever. When students leave school, they are more and more likely to use mathematics in their work and everyday lives operating computer equipment,
More informationWelcome to Math 7 Accelerated Courses (Preparation for Algebra in 8 th grade)
Welcome to Math 7 Accelerated Courses (Preparation for Algebra in 8 th grade) Teacher: School Phone: Email: Kim Schnakenberg 402443 3101 kschnakenberg@esu2.org Course Descriptions: Both Concept and Application
More informationWentzville School District Algebra 1: Unit 8 Stage 1 Desired Results
Wentzville School District Algebra 1: Unit 8 Stage 1 Desired Results Unit Title: Quadratic Expressions & Equations Course: Algebra I Unit 8  Quadratic Expressions & Equations Brief Summary of Unit: At
More informationMath 1280/1300, PreCalculus
Math 1280/1300, PreCalculus Instructor: Office: Office Hours: Phone: Email: MyMathLab Course Code: Text and Materials: ISBN: 1269594060 Author: Blitzer Title: Precalculus, Books a la Carte Edition Package
More informationUnit 3  Lesson 3. MM3A2  Logarithmic Functions and Inverses of exponential functions
Math Instructional Framework Time Frame Unit Name Learning Task/Topics/ Themes Standards and Elements Lesson Essential Questions Activator Unit 3  Lesson 3 MM3A2  Logarithmic Functions and Inverses of
More informationPrentice Hall Mathematics: Algebra 2 2007 Correlated to: Utah Core Curriculum for Math, Intermediate Algebra (Secondary)
Core Standards of the Course Standard 1 Students will acquire number sense and perform operations with real and complex numbers. Objective 1.1 Compute fluently and make reasonable estimates. 1. Simplify
More informationMAT 113701 College Algebra
MAT 113701 College Algebra Instructor: Dr. Kamal Hennayake Email: kamalhennayake@skipjack.chesapeake.edu I check my email regularly. You may use the above email or Course Email. If you have a question
More informationCHICAGO PUBLIC SCHOOLS (ILLINOIS) MATH & SCIENCE INITIATIVE COURSE FRAMEWORK FOR ALGEBRA Course Framework: Algebra
Chicago Public Schools (Illinois) Math & Science Initiative Course Framework for Algebra Course Framework: Algebra Central Concepts and Habits of Mind The following concepts represent the big ideas or
More informationPRECALCULUS GRADE 12
PRECALCULUS GRADE 12 [C] Communication Trigonometry General Outcome: Develop trigonometric reasoning. A1. Demonstrate an understanding of angles in standard position, expressed in degrees and radians.
More informationMarch 2013 Mathcrnatics MATH 92 College Algebra Kerin Keys. Dcnnis. David Yec' Lscture: 5 we ekly (87.5 total)
City College of San Irrancisco Course Outline of Itecord I. GENERAI DESCRIPI'ION A. Approval Date B. Departrnent C. Course Number D. Course Title E. Course Outline Preparer(s) March 2013 Mathcrnatics
More informationIndiana Academic Standards Mathematics: Algebra II
Indiana Academic Standards Mathematics: Algebra II 1 I. Introduction The college and career ready Indiana Academic Standards for Mathematics: Algebra II are the result of a process designed to identify,
More informationSlopeIntercept Equation. Example
1.4 Equations of Lines and Modeling Find the slope and the y intercept of a line given the equation y = mx + b, or f(x) = mx + b. Graph a linear equation using the slope and the yintercept. Determine
More informationIV. ALGEBRAIC CONCEPTS
IV. ALGEBRAIC CONCEPTS Algebra is the language of mathematics. Much of the observable world can be characterized as having patterned regularity where a change in one quantity results in changes in other
More informationPreAlgebra 2008. Academic Content Standards Grade Eight Ohio. Number, Number Sense and Operations Standard. Number and Number Systems
Academic Content Standards Grade Eight Ohio PreAlgebra 2008 STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express large numbers and small
More informationHow To Factor Quadratic Trinomials
Factoring Quadratic Trinomials Student Probe Factor Answer: Lesson Description This lesson uses the area model of multiplication to factor quadratic trinomials Part 1 of the lesson consists of circle puzzles
More informationMcDougal Littell California:
McDougal Littell California: PreAlgebra Algebra 1 correlated to the California Math Content s Grades 7 8 McDougal Littell California PreAlgebra Components: Pupil Edition (PE), Teacher s Edition (TE),
More informationAlgebra 1 2008. Academic Content Standards Grade Eight and Grade Nine Ohio. Grade Eight. Number, Number Sense and Operations Standard
Academic Content Standards Grade Eight and Grade Nine Ohio Algebra 1 2008 Grade Eight STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express
More informationINDIANA ACADEMIC STANDARDS. Mathematics: Grade 6 Draft for release: May 1, 2014
INDIANA ACADEMIC STANDARDS Mathematics: Grade 6 Draft for release: May 1, 2014 I. Introduction The Indiana Academic Standards for Mathematics are the result of a process designed to identify, evaluate,
More information