Course Number Lake County Schools Curriculum Map

Transcription

1 Algebra I Course Number Curriculum Map Page 1 of 38

2 PREFACE Teams of Lake County teachers created the curriculum maps in order to ensure that all students throughout the district receive a common curriculum. The maps help ensure that all state requirements are taught and that the content is divided into teachable segments with appropriate pacing. The curriculum maps will guide your instruction but provide flexibility based on the individual needs of students. The maps are living documents and feedback is requested of teachers to ensure continuous improvement. All teachers are expected to use the curriculum maps, in conjunction with data, to drive instruction. The maps were designed for the instruction to take place by quarter. There is some flexibility within the quarters for mastery and re-teaching. The expectation is that teachers will finish the content within each quarter in its entirety. The maps have been structured in such a way as to scaffold student learning. Listed below are a few of the new or updated features common to all curriculum maps: Essential Question(s): o Provide application of the skills/concepts o Have more than one right answer which promotes student discourse o Increase the rigor in the classroom, by changing from teacher-centered to student-centered learning o Are referred to at the beginning, middle, and end of the lesson o Require you to make a decision o Promote critical thinking and problem solving o Encourage interdependence o Are open-ended Academic Vocabulary are: o Unfamiliar vocabulary that are essential to understanding new content within explicit instruction o Not necessarily the bold words in the chapter. o Cumulative and continuously used throughout the year. o Integrated into word walls, a research-based strategy that will facilitate vocabulary acquisition. Common Board Configuration Elements (specific layouts may vary by sites, but must include each of these): Purpose: For the student to know what is being taught and what the student will learn o Date o Benchmark o Measurable, student-friendly objective o Essential Question o Bell work o Agenda (Specific daily schedule) o Homework o Exit Strategy/Card Page 2 of 38

3 Lessons that infuse reading, writing, and discussion are imperative components of every subject area. There should be daily: o Teacher to student and student to student discourse utilizing academic vocabulary. o Reading and authentic writing o Writing that includes higher-order thinking o Incorporation of effective reading and writing instructional strategies Maps are organized to include the following: o o o o Pacing Objective Essential questions, content and understanding, benchmarks, and assessment Appendix/ resources Page 3 of 38

4 Algebra I Next Generation Sunshine State Standards (NGSSS) Math Benchmark Coding Scheme MA. 5. A Subject Grade Level Body of Knowledge Big Idea / Supporting Idea Benchmark Body of Knowledge Key A ~ Algebra G ~ Geometry C ~ Calculus P ~ Probability D ~ Discrete Mathematics S ~ Statistics F ~ Financial Literacy T ~ Trigonometry Math Process Benchmarks These math process benchmarks should be incorporated throughout the entire course. MA.912.A.1.8 MA.912.A.10.1 MA.912.A.10.2 MA.912.A.10.3 Use the zero product property of real numbers in a variety of contexts to identify solutions to equations. Use a variety of problem-solving strategies, such as drawing a diagram, making a chart, guess- and-check, solving a simpler problem, writing an equation, working backwards, and create a table. Decide whether a solution is reasonable in the context of the original situation. Decide whether a given statement is always, sometimes, or never true (statements involving linear or quadratic expressions, equations, or inequalities, rational or radical expressions or logarithmic or exponential functions). Topic will not be covered in this level course Page 4 of 38

5 Differentiated Instruction Strategies The following differentiated instruction strategies should be incorporated throughout the entire course: Cooperative Groups Computer Assisted Instruction Tiered Assignments Centers Flexible Grouping Curriculum Compacting/Contracts Learning Stations Scaffolding Hands-on Instruction Leveled Texts/Resources Teacher Led Small Groups Web Quest Language Arts Benchmarks These language arts benchmarks should be incorporated throughout the entire course. LA LA LA LA The student will use new vocabulary that is introduced and taught directly. The student will listen to, read, and discuss familiar and conceptually challenging text. The student will relate new vocabulary to familiar words. The student will pre-write by using organizational strategies and tools (e.g., technology, spreadsheet, outline, chart, table, graph, Venn diagram, web, story map, plot pyramid) to develop a personal organizational style. Page 5 of 38

6 Reading Writing Discussion in the classroom everyday (50% RWD) This means that during each class period the students should be reading, writing, and/or talking about Math for 50% of the time. Many of these overlap incorporating a combination of reading, writing, and discussion. Reading Writing Discussion in the Math Classroom: What do these look like in the Math classroom? What does the READING process look like? Modeling - reading and thinking out loud Students in small groups or pairs Whole group when referring to a specific portion of the text Use of graphic organizers Incorporation of word wall activities/vocabulary strategies Reading word problems and translating to mathematical problem by analyzing key vocabulary words What does the WRITING process look like? Journal writing Literacy logs Student created word problems Written responses to word wall activities Written answer to essential questions Cornell Notes Summarizing hands-on activities Exit cards Writing the steps needed to work a problem Quick writes Three-column vocabulary Graphic Organizers Cartoons Question stems Math poems, jingles, or raps Student created math stories Reports What does the DISCUSSION process look like? Student discourse discussion among and between the students. (Could be in small group, pair share, hands-on activity) Student to teacher discourse - responses to open ended questions, essential questions, higher order thinking prompts, etc. Imbedding vocabulary terms/word wall, academic vocabulary, into the discussion Page 6 of 38

7 Algebra I 4 X 4 Schedule Pacing Guide First Quarter Second Quarter Third Quarter Fourth Quarter I. Equation Solving in One Variable: (2.5 weeks) A. One- and two-step equations B. Variable terms located on both sides of the equal sign C. Parentheses removal using the distributive property D. Literal equations for a specified variable E. Incorporate the properties of numbers to justify solutions F. Solve real-world problems using equations G. Solve algebraic proportions using cross products II. Solve Inequalities in one Variable: (1.5 weeks) A. Solve and graph one variable inequalities with justification of steps B. Perform set operations such as union and intersection C. Use Venn diagrams to explore relationships D. Solve and graph compound inequalities with justification of steps E. Solve real-world problems using inequalities DO NOT TEACH ABSOLUTE VALUE III. Functions, Linear Equations, and Inequalities: (3 weeks) A. Relations and Functions B. Determine domain and range C. Determine slope and intercepts of a linear function D. Graph a linear equation. E. Write an equation of a line in various forms. F. Apply linear functions to statistical data. G. Graph a linear inequality in twovariables. IV. Systems of equations and inequalities: (1 week) A. Solve systems of equations and inequalities using the Graphing method B. Solve systems of equations using algebraic methods: Substitution and Elimination C. Solve real-world problems involving systems V. Study of Polynomial Expressions Part A: (1 week) A. Apply the Laws of Integral Exponents to Monomials B. Define and classify polynomials C. Perform operations on polynomials VI. Study and Application of Irrational Numbers: (.5 week) A. Simplify radical expressions B. Perform operations with radical expressions VII. Study and Application Quadratic Functions : (1 week) A. Solve quadratic equations using the quadratic formula B. Identify characteristics of parabolas C. Graph quadratic functions D. Solve real-world problems involving quadratics V. Study of Polynomials Expressions Part B: (1.5 weeks) A. Factor polynomial expressions B. Solve quadratic equations by factoring C. Simplify algebraic rational expressions Review and Algebra I EOC (1 week) VIII. Work for mastery: (3 weeks) 1) Re-teach concepts not yet mastered. 2) Strengthen students learning for those passing at minimal level. 3) Extend learning for students demonstrating exceptional performance on grade level expectations. 4) Continue to problem solve in all areas. OR VIII. Study of Basic Rational Expressions: (3weeks) A. Perform operations on rational expressions B. Solve rational equations Page 7 of 38

8 Algebra I Traditional Schedule Pacing Guide First Quarter Second Quarter Third Quarter Fourth Quarter 2 days for Algebra I LBA Baseline 2 days for 8 th grade LBA Baseline I. Equation Solving in One Variable: (4 weeks) A. One- and two-step equations B. Variable terms located on both sides of the equal sign C. Parentheses removal using the distributive property D. Literal equations for a specified variable E. Incorporate the properties of numbers to justify solutions F. Solve real-world problems using equations G. Solve algebraic proportions using cross products II. Solve Inequalities in One Variable: (3 weeks) A. Solve and graph one variable inequalities with justification of steps B. Perform set operations such as union and intersection C. Use Venn diagrams to explore relationships D. Solve and graph compound inequalities with justification of steps E. Solve real-world problems using inequalities III. Functions, Linear Equations, and Inequalities: (6 weeks) A. Relations and Functions B. Determine domain and range C. Determine slope and intercepts of a linear function D. Graph a linear equation. E. Write an equation of a line in various forms. F. Apply linear functions to statistical data. G. Graph a linear inequality in twovariables. 2 days for Algebra I LBA Midyear 2 days for 8 th grade LBA Midyear IV. Systems of Equations and Inequalities Part A : (1 week) A. Solve systems of equations and inequalities using the Graphing method B. Solve systems of equations using substitution IV. Systems of Equations and Inequalities Part B : (1.5 weeks) B. Solve systems of equations using elimination method C. Solve real-world problems involving systems V. Study of Polynomial Expressions Part A: (3 weeks) A. Apply the Laws of Integral Exponents to Monomials B. Define and classify polynomials C. Perform operations on polynomials VI. Study and Application of Irrational Numbers: (2 weeks) A. Simplify radical expressions B. Perform operations with radical expressions VII. Study and Application Quadratic Functions : (2 weeks) A. Solve quadratic equations using the quadratic formula B. Identify characteristics of parabolas C. Graph quadratic functions D. Solve real-world problems involving quadratics FCAT 1 week V. Study of Polynomials Expressions Part B: (2.5 weeks) A. Factor polynomial expressions B. Solve quadratic equations by factoring C. Simplify algebraic rational expressions Review and Algebra I EOC (1 week) VIII. Work for mastery: (3 weeks) 1) Re-teach concepts not yet mastered. 2) Strengthen students learning for those passing at minimal level. 3) Extend learning for students demonstrating exceptional performance on grade level expectations. 4) Continue to problem solve in all areas. OR VIII. Study of Basic Rational Expressions: (3weeks) A. Perform operations on rational expressions B. Solve rational equations. DO NOT TEACH ABSOLUTE VALUE Page 8 of 38

9 Algebra I Unit I: Solve Equations in One Variable Time: 4 weeks [Traditional Schedule] 2.5 weeks [4 X 4 Schedule] Objective: The student will demonstrate their ability to solve algebraic equations in one variable 1) With one-, two-, or multi-step equations by using inverse operations 2) When solving for a specified variable 3) When translating a verbal problem into an algebraic equation 4) Investigate their ability to apply proportional solving techniques to a) Cross products b) Real-world problems Vocabulary: algebraic expression, equivalent expression, equivalent equations, isolate, like terms, term Essential Questions Essential Content and Understandings Essential Skills & Benchmarks Assessment What techniques are available to prove that you have solved a linear equation? How do equations help us analyze and solve problems when working in the realworld? A. Solve an equation in one variable using 1. Additive inverse 2. Multiplicative inverse 3. Involving an opposite sign on the variable 4. Using multiple operations B. Solve an equation in one variable with algebraic terms on both sides of the equal sign C. Solve an equation in one variable with parentheses in the equation requiring the use of the distributive property and combining of like terms D. Solving literal equations for a given variable E. Incorporate the properties of numbers to justify solutions F. Solve real-world problems using equations MA.912.A.3.1 Solve linear equations in one variable that include simplifying algebraic expressions MA.912.A.3.2 Identify and apply the distributive, associative, and commutative properties of real numbers and the properties of equality. MA.912.A.3.3 Solve literal equations for a specified variable. Formal: Chapter Test Vocabulary Test Mini-quizzes Informal: Check for understanding with the use of 5-minute checks FCAT Explorer FCAT style bell ringers Word Wall activity: Use writing strategies to display the connection between the various vocabulary terms Page 9 of 38

10 How is a proportion used to show the relationship between two quantities in the realworld? G. Solve proportions using the cross products and the techniques of equation solving H. Real-world applications 1. Similar figures 2. Indirect measurement MA.912.A.5.4 Solve algebraic proportions Page 10 of 38

11 Algebra I Unit II: Solve Inequalities in One Variable Time: 4 weeks [Traditional Schedule] 2 weeks [4 X 4 Schedule] Objective: The student will apply their ability to solve algebraic inequalities in one variable by 1) Using equation solving techniques 2) Graphing sets of real numbers on a number line 3) Solving compound inequalities 4) Applying inequalities to real-world situations Vocabulary: complement of a set, disjoint set, empty set, intersection, union, roster form, set-builder notation, universal set, cross product, subsets, element, compound inequality, conjunctions, disjunctions Essential Questions Essential Content and Understandings Essential Skills & Benchmarks Assessment What are the similarities and A. Solve an inequality in one variable using Formal: differences between solving equations and solving inequalities? The skills of equation solving Graphing the solution on a number line Chapter Test Vocabulary Test Mini-quizzes How do the characteristics of inequalities permit us to compare different quantities in the realworld? B. Operations on sets by finding the 1. union a. role model with groups of students 2. intersection a. role model with groups of students 3. complement a. role model with groups of students 4. cross product a. role model with groups of students 5. subsets a. role model with groups of students C. Venn Diagrams will be employed to 1. Show the Relationships and patterns between two sets a. role model with string circles/hula hoops and groups of students 2. Defend statements regarding sets such MA.912.A.3.4 Solve and graph simple and compound inequalities in one variable and be able to justify each step in a solution MA.912.D.7.1 Perform set operations such as union and intersection, complement, and cross product. MA.912.D.7.2 Use Venn diagrams to explore relationships and patterns, and to make arguments about relationships between sets. Informal: Check for understanding with the use of 5-minute checks FCAT Explorer FCAT style bell ringers Word Wall activity: Use writing strategies to display the connection between the various vocabulary terms Page 11 of 38

12 as the intersection of two sets is a subset of the union of the two sets D. Solve and graph compound inequalities involving 1. Conjunctions [intersection/and] 2. Disjunctions [union/or] Do Not Teach Absolute Value E. Solve real-world applications using inequalities with terms such as 1. Not more than and not less than 2. At least and at most MA.912.A.3.5 Symbolically represent and solve multi-step and real-world applications that involve linear equations and inequalities. Page 12 of 38

13 Algebra I Unit III: Functions, Linear Equations and InequalitiesTime: 6 weeks [Traditional Schedule] 3 weeks [4 X 4 Schedule] Objective: The student will demonstrate their ability to 1) Distinguish between relations and functions 2) Determine domain and range of relations 3) Graph a linear function 4) Find the slope and intercepts of a linear function 5) Find the equation of a line 6) Apply linear functions to statistical measurements 7) Graph inequalities in two variables Vocabulary: function notation, coordinate plane, parallel lines (in term of slopes), perpendicular lines (in terms of slopes), m = slope, b = y-intercept, slope-intercept form for equation of a line, point-slope form for equation of a line, continuous graph, discrete graph, causation, extrapolation, interpolation, trend line, linear inequality, solution of an inequality, standard form of a linear equation Essential Questions Essential Content and Understandings Essential Skills & Benchmarks Assessment When does a relation become a function? How can graphing real world situations help us to determine a range of possible answers? A. Distinguish between relations and functions using 1. Sets of ordered pairs 2. Tables 3. Mappings 4. The definition 5. Vertical line test 6. Employ the use of functional notation B. Determine the domain and range of relations C. Determine the slope and intercepts of a linear function given a(n) 1. Graph 2. Equation 3. Table MA.912.A.2.3 Describe the concept of a function, use function notation, determine whether a give relation is a function, and link equations to functions. MA.912.A.2.4 Determine the domain and range of a relation MA.912.A.2.13 Solve real-world problems involving relations and functions MA.912.A.3.7 Rewrite equations of a line into slopeintercept form and standard form. MA.912.A.3.8 Graph a line given any of the following information: a table of Formal: Chapter Test Vocabulary Test Mini-quizzes Informal: Check for understanding with the use of 5-minute checks FCAT Explorer FCAT style bell ringers Word Wall activity: Use writing strategies to display the connection between Page 13 of 38

14 What are the different ways we can display the equation of a line? When does a specific form of an equation help us to draw its picture and relate the information to real world situations? How does knowing the equation of a line help us to make predictions in the business world? How would recognizing the connection between two sets of numbers help you to make predictions? D. Graph a linear equation given: 1. A table of values 2. x- and y-intercepts 3. Two points 4. A slope and a point 5. Standard equation form 6. Slope-intercept equation form 7. Point-slope equation form E. Write the equation of a line in 1. Slope-intercept form 2. Point-slope form 3. Standard form 4. Parallel to a given line 5. Perpendicular to a given line through a specific point on the given line F. Apply linear function methods to statistical data 1. Finding the line of best fit 2. Making predictions 3. Recognizing the slope is the rate of change G. Graph a linear inequality in two variables. values, the x- and y-intercepts, two points, the slope and a point, the equation of the line in slope-intercept form, standard form or point-slope form. MA.912.A.3.9 Determine the slope, x-intercept, and y-intercept of a line given its graph, its equation, or two points on the line. MA.912.A.3.10 Write an equation of a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, find an equation of a new line parallel to a given line, or perpendicular to a given line, through a give point on the new line. MA.912.A.3.11 Write an equation of a line that models a data set and use the equation or the graph to make predictions. Describe the slope of the line in terms of the data, recognizing that the slope is the rate of change. MA.912.A.3.12 Graph a linear equation or inequality in two variables with and without graphing technology. Write an equation or inequality represented by a given graph. MA.912.G.1.4 Use coordinate geometry to find slopes, parallel lines, perpendicular lines and equations of lines the various vocabulary terms. Formal: Chapter Test Vocabulary Test Mini-quizzes Informal: Check for understanding with the use of 5-minute checks FCAT Explorer FCAT style bell ringers Word Wall activity: Use writing strategies to display the connection between the various vocabulary terms Page 14 of 38

15 Algebra I Unit IV: Systems of Equations and Inequalities Time: 2.5 weeks [Traditional Schedule] 1 week [4 X 4 Schedule] Objective: The student will demonstrate their knowledge of systems of equations [inequalities] using 1) Graphing method 2) Algebraic methods Vocabulary: elimination method, solution of a system of linear equations, consistent, independent, dependent, {all numbers}, no solution/empty set, inconsistent, substitution method, system of linear equations, systems of linear inequalities Essential Questions Essential Content and Understandings Essential Skills & Benchmarks Assessment What is the best method to use to solve a system of equations? How do you explain how a system of equations will help a businessman determine the break-even point and help to analyze future trends? Can you describe other uses for systems of equations in the real-world? A. Solve systems of equations and inequalities by graphing. 1. Graph systems of equations and classify them as: a. Consistent or inconsistent b. Dependent or independent 2. Graph systems of inequalities B. Solve system of equations with two variables algebraically by using the 1. Substitution method 2. Elimination methods a. Addition and subtraction b. Multiplication C. Applications to real-world situations MA.912.A.3.13 Use a graph to approximate the solution of a system of linear equations or inequalities in two variables with and without technology. MA.912.A.3.14 Solve systems of linear equations and inequalities in two and three variables using graphical, substitution, and elimination methods. MA.912.A.3.15 Solve real-world problems involving systems of linear equations and inequalities in two and three variables. Topic will not covered in this level course. Formal: Chapter Test Vocabulary Test Mini-quizzes Informal: Check for understanding with the use of 5-minute checks FCAT Explorer FCAT style bell ringers Word Wall activity: Use writing strategies to display the connection between the various vocabulary terms Page 15 of 38

16 Algebra I Unit V: Study of Polynomials Part A (A-C) Time: 3 weeks Third Quarter [Traditional} 1 week Third Quarter [4 x 4] Teach Units VI and VII between Part A and B Part B (D-F) Time: 2.5 weeks Fourth Quarter [Traditional] 1.5 weeks Third Quarter [4 x 4] Objective: The student will demonstrate their knowledge of monomials and polynomials by 1) Applying the laws of integral exponents to monomials 2) Describing the characteristics 3) Applying basic arithmetic operations 4) Factor into a product of primes 5) Simplifying the rational expression to lowest terms Vocabulary: binomial, trinomial, polynomial, degree of a monomial and polynomial, FOIL, difference of two squares, perfect square trinomial, factoring by grouping, rational expression Essential Questions Essential Content and Understandings Essential Skills & Benchmarks Assessment How can adding polynomials help you model sales? How is multiplying polynomials related to finding area of a rectangle? How are the prefixes used in English related to the prefixes used in mathematics? How is the distributive Part A A. Apply the laws of integral exponents to monomials when 1. Adding 2. Subtracting 3. Multiplying 4. Dividing B. Define and classify polynomials according to 1. Number of terms 2. Degree 3. Order of the powers of the terms C. Perform operations on polynomials 1. Addition 2. Subtraction 3. Multiplication using a. Distributive property MA.912.A.4.1 Simplify monomials and monomial expressions using the laws of integral exponents. MA.912.A.4.2 Add, subtract, and multiply polynomials. MA.912.A.4.3 Factor polynomial expressions MA.912.A.4.4 Divide polynomials by monomials and polynomials with various techniques, including synthetic division. Topic will not be covered in this level course. Formal: Chapter Test Vocabulary Test Mini-quizzes Informal: Check for understanding with the use of 5-minute checks FCAT Explorer FCAT style bell ringers Word Wall activity: Use writing strategies to display the connection between the various Page 16 of 38

17 property related to factoring? Part B b. FOIL multiplication c. Product of sum and difference of two terms d. Perfect squares 4. Division of a polynomial by a. A monomial D. Factor polynomial expressions 1. Monomials using greatest common factors 2. Polynomials using a. Greatest common factor b. Trinomials with a = 1 and a > 1 c. Difference of two squares d. Perfect squares e. Grouping f. Combinations of the above vocabulary terms Formal: Chapter Test Vocabulary Test Mini-quizzes Informal: Check for understanding with the use of 5-minute checks FCAT Explorer FCAT style bell ringers How does simplifying numerical fractions compare to simplifying algebraic fractions? E. Solve quadratic equations 1. By factoring F. Simplifying algebraic rational expressions and ratios to lowest terms 1. Review rules of factoring 2. Apply the rules to the numerator and denominator 3. Divide out the common factors MA.912.A 5.1 Simplify algebraic ratios Word Wall activity: Use writing strategies to display the connection between the various vocabulary terms Page 17 of 38

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19 Algebra I Unit VI: Study and Application of Irrational Numbers Time: 2 weeks [Traditional].5 weeks [4 x 4] Objective: The student will demonstrate their knowledge of irrational numbers by 1) Simplifying into a product of a rational number and an irrational number 2) Applying basic arithmetic operations to irrational numbers Vocabulary: rationalize the denominator, unlike radicals Essential Questions Essential Content and Understandings Essential Skills & Benchmarks Assessment Why is it necessary to express numbers using different forms? A. Determining when a radical expression is simplified using 1. Product property of square roots 2. Quotient property of square roots 3. Definition of Irrational numbers B. Performing operations with radical expressions: 1. Addition 2. Subtraction 3. Multiplication 4. Division MA.912.A.6.1 Simplify radical expressions MA.912.A.6.2 Add, subtract, multiply and divide radical expressions (square roots and higher). MA.912.A.1.4(Extension from Algebra IA) Topic will not be covered in this level course. Formal: Chapter Test Vocabulary Test Mini-quizzes Informal: Check for understanding with the use of 5-minute checks FCAT Explorer FCAT style bell ringers Word Wall activity: Use writing strategies to display the connection between the various vocabulary terms. Page 19 of 38

20 Algebra IB Unit VII: Study and Application of Quadratic Functions Time: 2 weeks [Traditional] 1 week [4 x 4 ] Objective: The student will demonstrate their knowledge of quadratic functions by 1) Solving and graphing quadratic equations 2) Using them to solve real-world problems Vocabulary: quadratic equation, standard form of a quadratic equation, quadratic formula, axis of symmetry, vertex, domain, range, x-intercepts, discriminant, maximum, minimum, parabola, root of an equation, vertex, zero of a function Essential Questions Essential Content and Understandings Essential Skills & Benchmarks Assessment How do you explain the quadratic function as it relates to: 1. The hang time of a football? 2. The flight of a golf ball? 3. The shape of an arch? 4. The management of water resources? 5. The study of science? A. Solve quadratic equations using 1. The quadratic formula B. Identify the following characteristics of parabola 1. Axis of symmetry 2. Vertex 3. Domain and range 4. x-intercepts (roots of equation) C. Graph quadratic functions 1. Use graphing calculator to approximate solutions 2. Use function tables 3. Use the Equation of the Axis of Symmetry of a parabola and the coordinates of the vertex 4. Select the correct equation given parabolic graphs D. Use quadratics to solve real-world problems MA.912.A.7.1 Graph quadratic equations with and without graphing technology. MA.912.A.7.2 Solve quadratic equations over the real numbers by factoring, and by using the quadratic formula. MA.912.A.7.8 Use quadratic equations to solve realworld problems MA.912.A.7.10 Use graphing technology to find approximate solutions of quadratic equations. Formal: Chapter Test Vocabulary Test Mini-quizzes Informal: Check for understanding with the use of 5-minute checks FCAT Explorer FCAT style bell ringers Word Wall activity: Use writing strategies to display the connection between the various vocabulary terms Page 20 of 38

21 Algebra I Review Algebra I concepts for final Time: 1 week Unit V: Study of Basic Rational Expressions- Time: 3 weeks [Traditional] OPTIONAL 3 weeks [4 x 4 ] OPTIONAL Objective: The student will demonstrate their knowledge of algebraic concepts. The student will demonstrate their knowledge of algebraic rational numbers by 1) Simplifying the rational expression to lowest terms 2) Solve rational equations Vocabulary: no new vocabulary Essential Questions Essential Content and Understandings Essential Skills & Benchmarks Assessment Will knowledge of operations with arithmetic fractions help with solving algebraic fractions? MA.912.A.5.2 Add, subtract, multiply, and divide rational expressions. A. Find the sum, difference, product and quotient of algebraic fractions by 1. Applying the rules of factoring 2. Perform the indicated operation 3. Applying the rules of simplifying B. Solve rational equations MA.912.A.5.5 Solve rational equations. Formal: Chapter Test Vocabulary Test Mini-quizzes Informal: Check for understanding with the use of 5-minute checks FCAT Explorer FCAT style bell ringers Word Wall activity: Use writing strategies to display the connection between. Page 21 of 38

22 Algebra I Curriculum Map Appendix for Middle/High Schools Scope and Sequence Correlated to Textbook State Approved Course Description Algebra 1 End-of-Course Appendix B Page 22 of 38

23 Algebra 1 Scope and Sequence Correlated to Prentice Hall Algebra I and NGSSS Work Word Problems in Every Section Topic Chapter-Section, Resources NGSSS FIRST QUARTER I. Solve Equations in One Variable- (4 x weeks) (Traditional 4 weeks) A. Solve one- and two-step equations in one variable 2-1 MA.912.A B. Solve equations with variable terms on both sides 2-4 MA.912.A.3.1 C. Solve equations involving simplifying 2-3 MA.912.A.3.1 D. Solve literal equations for a given variable 2-5 MA.912.A.3.3 E. Incorporate properties to justify solutions Apply throughout unit MA.912.A.3.2 F. Solve real-world problems using equations Apply throughout unit MA.912.A.10.1 G. Solve algebraic proportions 2-7 MA.912.A.5.4 II. Solve Inequalities in One Variable- (4 x weeks) (Traditional 3 weeks) A. Solve inequalities in one variable 3-1 MA.912.A Page 23 of 38

24 Algebra 1 Scope and Sequence Correlated to Prentice Hall Algebra I and NGSSS Work Word Problems in Every Section B. Perform set operations such as union and intersection 3-5 MA.912.D.7.1 Clouds Unions and Intersections Lake Algebra I NGSSS Resources C. Use Venn diagrams to explore relationships 3-8 MA.912.D.7.2 Welcome to Venn World The Eggman: D. Solve compound inequalities 3-6 MA.912.A.3.4 E. Solve real-world problems involving inequalities Apply throughout unit MA.912.A.3.5 SECOND QUARTER III. Functions, Linear Equations, and Inequalities- (4 x 4-3 weeks) (Traditional 6 weeks) A. Distinguish between relations and functions 4-6 MA.912.A.2.3 B. Determine the domain and range of relations 4-6 MA.912.A C. Determine the slope and intercepts of a linear function 5-1 MA.912.A.3.9 MA.912.G.1.4 Page 24 of 38

25 Algebra 1 Scope and Sequence Correlated to Prentice Hall Algebra I and NGSSS Work Word Problems in Every Section D. Graph linear functions using various techniques 5-3 MA.912.A MA.912.A MA.912.A.3.9 MA.912.A.3.10 E. Write the equation of a line in various forms 5-3 MA.912.A MA.912.A MA.912.A MA.912.G.1.4 F. Apply linear function methods to statistical data 5-7 MA.912.A.3.11 MA.912.A.2.13 PROMiSE Algebra Module 4,First Part MA.912.A.3.5, MA.912.A.3.11 G. Graph linear inequalities in two-variables 6-5 MA.912.A.3.5 MA.912.A.3.12 IV. Systems of equations and inequalities - (4 x 4 1 week) (Traditional 2.5 weeks Start Third Quarter at section B) A. Solve systems of equations/inequalities using graphs 6-1 MA.912.A MA.912.A.3.14 MA.912.A.3.15 Page 25 of 38

26 Algebra 1 Scope and Sequence Correlated to Prentice Hall Algebra I and NGSSS Work Word Problems in Every Section B. Solve systems of equation using algebraic methods 6-2 MA.912.A MA.912.A.3.15 C. Solve real-world problems involving systems Apply throughout unit MA.912.A.3.15 PROMiSE Algebra Module 4, Second Part MA.912.A.3.13, V. Study of Polynomial Expressions Part A (4 x 4 1 week start Third Quarter) (Traditional 3 weeks) A. Apply the laws of integral exponents to monomials 7-3 MA.912.A B. Define and classify polynomials 8-1 C. Perform operations on polynomials 8-1 MA.912.A Concept Byte p. 538 MA.912.A.4.4 Page 26 of 38

27 Algebra 1 Scope and Sequence Correlated to Prentice Hall Algebra I and NGSSS Work Word Problems in Every Section VI. Study and Application of Irrational Numbers (4 x weeks) (Traditional 2 weeks) A. Simplify radical expressions 10-1 MA.912.A B. Perform operations on radical expressions 10-3 MA.912.A.6.2 VII. Study and Application of Quadratic Functions (4 x 4 1 week) (Traditional 2 weeks) A. Solve quadratic equations using the quadratic formula 9-2 MA.912.A MA.912.A.7.10 B. Identify the characteristics of parabolas 9-1 MA.912.A.7.1 C. Graph quadratic functions 9-1 MA.912.A.7.1 D. Solve real-world problems involving quadratics Apply throughout unit MA.912.A.7.8 PROMiSE Algebra Module 5 MA.912.A.7.8 V. Study of Polynomial Expressions Part B (4 x weeks) (Traditional 2.5 weeks Start Fourth Quarter) D. Factor polynomial expressions 8-2 MA.912.A.4.3 Page 27 of 38

28 Scope and Sequence Correlated to Prentice Hall Algebra I and NGSSS Algebra 1 Work Word Problems in Every Section E. Solve quadratic equations by factoring 9-4 MA.912.A.1.8 MA.912.A.7.2 F. Simplify algebraic rational expressions Supplement 11-3 from Glencoe MA.912.A.5.1 Algebra I textbook (Algebra IA/IB Textbook) Review for state Algebra I EOC (1 week) VIII. Study of Basic Rational Expressions (3 weeks) Optional A. Perform operations on rational expressions MA.912.A.5.2 B. Solve rational equations MA.912.A This curriculum map is designed to cover the core curriculum for your math course. If your students are not successful per the specifications of RtI please use the RtI materials provided with your textbook, for Intensive Math classes, or other additional math resources that are available at your school for RtI interventions. Page 28 of 38

29 State Approved Course Description Course Code Course Category 6-12 Subject Area Mathematics Course Type Core Course Title Algebra 1 Course Level 2 Course Length Full year Credit Description 1 Abbreviated Title Algebra 1 RELATED BENCHMARKS (40) : Scheme Descriptor LA The student will use new vocabulary that is introduced and taught directly; LA LA LA MA.912.A.1.8 MA.912.A.2.3 The student will listen to, read, and discuss familiar and conceptually challenging text; The student will relate new vocabulary to familiar words; The student will pre-write by using organizational strategies and tools (e.g., technology, spreadsheet, outline, chart, table, graph, Venn Diagram, web, story map, plot pyramid) to develop a personal organizational style. Use the zero product property of real numbers in a variety of contexts to identify solutions to equations. Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions. Page 29 of 38

30 MA.912.A.2.4 Determine the domain and range of a relation. MA.912.A.2.13 Solve real-world problems involving relations and functions. MA.912.A.3.1 MA.912.A.3.2 MA.912.A.3.3 MA.912.A.3.4 MA.912.A.3.5 MA.912.A.3.7 MA.912.A.3.8 MA.912.A.3.9 MA.912.A.3.10 MA.912.A.3.11 Solve linear equations in one variable that include simplifying algebraic expressions. Identify and apply the distributive, associative, and commutative properties of real numbers and the properties of equality. Solve literal equations for a specified variable. Solve and graph simple and compound inequalities in one variable and be able to justify each step in a solution. Symbolically represent and solve multi-step and real-world applications that involve linear equations and inequalities. Rewrite equations of a line into slope-intercept form and standard form. Graph a line given any of the following information: a table of values, the x- and y-intercepts, two points, the slope and a point, the equation of the line in slope-intercept form, standard form, or point-slope form. Determine the slope, x-intercept, and y-intercept of a line given its graph, its equation, or two points on the line. Write an equation of a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, find an equation of a new line parallel to a given line, or perpendicular to a given line, through a given point on the new line. Write an equation of a line that models a data set and use the equation or the graph to make predictions. Describe the slope of the line in terms of the data, recognizing that the slope is the rate of change. Page 30 of 38

31 MA.912.A.3.12 MA.912.A.3.13 MA.912.A.3.14 Graph a linear equation or inequality in two variables with and without graphing technology. Write an equation or inequality represented by a given graph. Use a graph to approximate the solution of a system of linear equations or inequalities in two variables with and without technology. Solve systems of linear equations and inequalities in two and three variables using graphical, substitution, and elimination methods. MA.912.A.3.15 Solve real-world problems involving systems of linear equations and inequalities in two and three variables. MA.912.A.4.1 MA.912.A.4.2 MA.912.A.4.3 MA.912.A.4.4 MA.912.A.5.1 MA.912.A.5.4 MA.912.A.6.1 MA.912.A.6.2 MA.912.A.7.1 Simplify monomials and monomial expressions using the laws of integral exponents. Add, subtract, and multiply polynomials. Factor polynomial expressions. Divide polynomials by monomials and polynomials with various techniques, including synthetic division. Simplify algebraic ratios. Solve algebraic proportions. Simplify radical expressions Add, subtract, multiply and divide radical expressions (square roots and higher). Graph quadratic equations with and without graphing technology. Page 31 of 38

32 MA.912.A.7.2 MA.912.A.7.8 Solve quadratic equations over the real numbers by factoring, and by using the quadratic formula. Use quadratic equations to solve real-world problems. MA.912.A.7.10 Use graphing technology to find approximate solutions of quadratic equations. MA.912.A.10.1 Use a variety of problem-solving strategies, such as drawing a diagram, making a chart, guess- and-check, solving a simpler problem, writing an equation, working backwards, and create a table. MA.912.A.10.2 Decide whether a solution is reasonable in the context of the original situation. MA.912.A.10.3 MA.912.D.7.1 MA.912.D.7.2 MA.912.G.1.4 Decide whether a given statement is always, sometimes, or never true (statements involving linear or quadratic expressions, equations, or inequalities rational or radical expressions or logarithmic or exponential functions). Perform set operations such as union and intersection, complement, and cross product. Use Venn diagrams to explore relationships and patterns, and to make arguments about relationships between sets. Use coordinate geometry to find slopes, parallel lines, perpendicular lines, and equations of lines. Italicized words indicate topics that will not be covered in this level course. The Page 32 of 38

33 Algebra 1 EOC Algebra 1 End-of-Course Assessment Body of Knowledge Algebra Appendix B MATHEMATICS CONTENT ASSESSED ON THE ALGEBRA 1 EOC ASSESSMENT AND ITEM TYPES BY BENCHMARK Standard 1 Real and Complex Number System Expand and deepen understanding of real and complex numbers by comparing expressions and performing arithmetic computations, especially those involving square roots and exponents. Use the properties of real numbers to simplify algebraic expressions and equations, and convert between different measurement units using dimensional analysis. MA.912.A.1.8 Use the zero product property of real numbers in a variety of contexts to identify solutions to equations. Standard 2 Assessed with MA.912.A.7.2. MA.912.A.2.3 Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions. Relations and Functions Draw and interpret graphs of relations. Understand the notation and concept of a function, find domains and ranges, and link equations to functions. MA.912.A.2.4 Determine the domain and range of a relation. MA.912.A.2.13 Solve real-world problems involving relations and functions. Also assesses MA.912.A MC, FR Also assesses MA.912.A MC, FR Assessed with MA.912.A.2.3 and MA.912.A.2.4. Prior Knowledge: Items may require the student to apply mathematical knowledge described in NGSSS benchmarks from lower grades; however, the benchmarks from lower grades will not be assessed in isolation. MC = Multiple Choice FR = Fill-in Response B 1 DRAFT Algebra 1 EOC Test Item Specifications 2010 Florida Department of Education Algebra I Page 33 of 38

34 Algebra 1 EOC Appendix B Algebra 1 End-of-Course Assessment Body of Knowledge Standard 3 MA.912.A.3.1 Solve linear equations in one variable that include simplifying algebraic expressions. Algebra Linear Equations and Inequalities MATHEMATICS CONTENT ASSESSED ON THE ALGEBRA 1 EOC ASSESSMENT Solve linear equations and inequalities. MA.912.A.3.2 Identify and apply the distributive, associative, and commutative properties of real numbers and the properties of equality. AND ITEM TYPES BY BENCHMARK MA.912.A.3.3 Solve literal equations for a specified variable. MA.912.A.3.4 Solve and graph simple and compound inequalities in one variable and be able to justify each step in a solution. MA.912.A.3.5 Symbolically represent and solve multi-step and real world applications that involve linear equations and inequalities. Also assesses MA.912.A.3.2. Assessed with MA.912.A.3.1. MC, FR MA.912.A.3.7 Rewrite equations of a line into slope-intercept form and standard form. MA.912.A.3.8 Graph a line given any of the following information: a table of values, the x- and y-intercepts, two points, the slope and a point, the equation of the line in slope-intercept form, standard form, or pointslope form. MC MA.912.A.3.9 Determine the slope, x-intercept, and y-intercept of a line given its graph, its equation, or two points on the line. MC MA.912.A.3.10 Write an equation of a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, find an equation of a new line parallel to a given line, or perpendicular to a given line, through a given point on the new line. MC, FR MA.912.A.3.11 Write an equation of a line that models a data set and use the equation or the graph to make predictions. Describe the slope of the line in terms of the data, recognizing that the slope is the rate of change. Assessed with MA.912.A Also assesses MA.912.A Also assesses MA.912.A Also assesses MA.912.A.3.7, MA.912.A.3.12, and MA.912.G.1.4. Also assesses MA.912.A MC MC, FR MC, FR MC, FR Prior Knowledge: Items may require the student to apply mathematical knowledge described in NGSSS benchmarks from lower grades; however, the benchmarks from lower grades will not be assessed in isolation. MC = Multiple Choice FR = Fill-in Response B 2 DRAFT Algebra 1 EOC Test Item Specifications 2010 Florida Department of Education Algebra I Page 34 of 38

35 Algebra 1 EOC Algebra 1 End-of-Course Assessment Body of Knowledge Standard 3 MA.912.A.3.12 Graph a linear equation or inequality in two variables with and without graphing technology. Write an equation or inequality represented by a given graph. Algebra Appendix B MATHEMATICS CONTENT ASSESSED ON THE ALGEBRA 1 EOC ASSESSMENT Linear Equations and Inequalities Solve linear equations and inequalities. MA.912.A.3.13 Use a graph to approximate the solution of a system of linear equations or inequalities in two variables with and without technology. AND ITEM TYPES BY BENCHMARK MA.912.A.3.14 Solve systems of linear equations and inequalities in two and three variables using graphical, substitution, and elimination methods. MA.912.A.3.15 Solve real-world problems involving systems of linear equations and inequalities in two and three variables. Assessed with MA.912.A.3.8, MA.912.A.3.9, MA.912.A.3.10, and MA.912.A Assessed with MA.912.A Also assesses MA.912.A and MA.912.A Assessed with MA.912.A Standard 4 MA.912.A.4.1 Simplify monomials and monomial expressions using the laws of integral exponents. MC, FR Polynomials Perform operations on polynomials. Find factors of polynomials, learning special techniques for factoring quadratics. Understand the relationships among the solutions of polynomial equations, the zeros of a polynomial function, the x-intercepts of a graph, and the factors of a polynomial. MC, FR MA.912.A.4.2 Add, subtract, and multiply polynomials. MC, FR MA.912.A.4.3 Factor polynomial expressions. Also assesses MA.912.A.5.1. MC MA.912.A.4.4 Divide polynomials by monomials and polynomials with various techniques, including synthetic division. Prior Knowledge: Items may require the student to apply mathematical knowledge described in NGSSS benchmarks from lower grades; however, the benchmarks from lower grades will not be assessed in isolation. MC = Multiple Choice FR = Fill-in Response MC B 3 DRAFT Algebra 1 EOC Test Item Specifications 2010 Florida Department of Education Algebra I Page 35 of 38

36 Algebra 1 EOC Appendix B Algebra 1 End-of-Course Assessment Body of Knowledge Standard 5 MA.912.A.5.1 Simplify algebraic ratios. Algebra MATHEMATICS CONTENT ASSESSED ON THE FCAT ALGEBRA 1 EOC ASSESSMENT AND ITEM TYPES BY BENCHMARK Rational Expressions and Equations Simplify rational expressions and solve rational equations using what has been learned about factoring polynomials. Assessed with MA.912.A.4.3. MA.912.A.5.4 Solve algebraic proportions. MC, FR Standard 6 Radical Expressions and Equations Simplify and perform operations on radical expressions and equations. Rationalize square root expressions and understand and use the concepts of negative and rational exponents. Add, subtract, multiply, divide, and simplify radical expressions and expressions with rational exponents. Solve radical equations and equations with terms that have rational exponents. MA.912.A.6.1 MA.912.A.6.2 Simplify radical Add, subtract, multiply, and expressions. divide radical expressions (square roots and higher). Assessed with A.912.A.6.2. Also assesses MA.912.A.6.1 MC Prior Knowledge: Items may require the student to apply mathematical knowledge described in NGSSS benchmarks from lower grades; however, the benchmarks from lower grades will not be assessed in isolation. MC = Multiple Choice FR = Fill-in Response B 4 DRAFT Algebra 1 EOC Test Item Specifications 2010 Florida Department of Education Algebra I Page 36 of 38

37 Algebra 1 EOC Algebra 1 End-of-Course Assessment Body of Knowledge Standard 7 MA.912.A.7.1 Graph quadratic equations with and without graphing technology. Algebra Appendix B MATHEMATICS CONTENT ASSESSED ON THE FCAT ALGEBRA 1 EOC ASSESSMENT AND ITEM TYPES BY BENCHMARK Quadratic Equations Draw graphs of quadratic functions. Solve quadratic equations and solve these equations by factoring, completing the square and by using the quadratic formula. Use graphing calculators to find approximate solutions of quadratic equations. MA.912.A.7.2 Solve quadratic equations over the real numbers by factoring, and by using the quadratic formula. MA.912.A.7.8 Use quadratic equations to solve real-world problems. MA.912.A.7.10 Use graphing technology to find approximate solutions of quadratic equations. Also assesses MA.912.A.7.8. Also assesses MA.912.A.1.8 and MA.912.A.7.8. Assessed with MA.912.A.7.1 and MA.912.A.7.2. Not assessed. Standard 10 MA.912.A.10.1 Use a variety of problemsolving strategies, such as drawing a diagram, making a chart, guessing and checking, solving a simpler problem, writing an equation, working backwards, and creating a table. MC MC, FR Mathematical Reasoning and Problem Solving In a general sense, all of mathematics is problem-solving. In all of mathematics, use problem-solving skills, choose how to approach a problem, explain the reasoning, and check the results. MA.912.A.10.2 Decide whether a solution is reasonable in the context of the original situation. MA.912.A.10.3 Decide whether a given statement is always, sometimes, or never true (statements involving linear or quadratic expressions, equations, or inequalities rational or radical expressions or logarithmic or exponential functions). Assessed throughout. Assessed throughout. Not assessed. Prior Knowledge: Items may require the student to apply mathematical knowledge described in NGSSS benchmarks from lower grades; however, the benchmarks from lower grades will not be assessed in isolation. MC = Multiple Choice FR = Fill-in Response B 5 DRAFT Algebra 1 EOC Test Item Specifications 2010 Florida Department of Education Algebra I Page 37 of 38