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Algebra I Honors

Course Number 1200320

Lake County Schools Curriculum Map

2011-2012 Algebra I Honors Lake County Schools

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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


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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 Pacing o Objective o Essential questions, content and understanding, benchmarks, and assessment o Appendix/ resources


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Next Generation Sunshine State Standards (NGSSS)

Math Benchmark Coding Scheme

MA. 5. A. 1. 1

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

The following benchmarks should be integrated throughout the year as a means to provide more depth of understanding of this math content. 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 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). Italicized topics will not be covered in this level course.


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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

The following benchmarks are new to this math course description. These benchmarks should be integrated throughout the year. LA.910.1.6.1 The student will use new vocabulary that is introduced and taught directly. LA.910.1.6.2 The student will listen to, read, and discuss familiar and conceptually challenging text. LA.910.1.6.5 The student will relate new vocabulary to familiar words. LA.910.3.1.3 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.


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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


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Algebra I Honors 4 X 4 Schedule Pacing Guide

First Quarter I. Equation Solving in One Variable: (2.5 weeks)

A. Variable terms located on both sides of the equal sign

B. Literal equations for a specified variable

C. Incorporate the properties of numbers to justify solutions

D. Solve real-world problems E. Solve algebraic proportions F. Solve real-world applications

II. Solve Inequalities in One Variable: (1.5 weeks)

A. Solve and graph one variable inequalities with justification of steps

B. Solve and graph compound inequalities with justification of steps

C. Solve sentences involving absolute value with one variable

D. Solve real-world problems using inequalities

E. Perform set operations such as union and intersection

Bolded content is required in Algebra I Honors.

Second Quarter III. Functions, Linear Equations, and Inequalities: (2.5 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 two-

variables.

IV. Systems of Equations and Inequalities: (1.5 weeks)

A. Solve systems of equations and inequalities using graphs

B. Solve systems of equations using algebraic methods: Substitution and Elimination

C. Solve real-world problems involving systems

Third Quarter 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: (1 week)

A. Simplify radical expressions B. Perform operations with radical

expressions VII. Study and Application of Quadratic Functions: (1 week)

A. Solve quadratic equations using the quadratic formula

B. Identify characteristics of parabolas

C. Graph quadratic equations D. Solve real-world problems

involving quadratics V. Study of Polynomials Expressions Part B: (1.5 week) D. Factor polynomial expressions E. Solve quadratic equations by factoring F. Simplify algebraic rational

expressions

Fourth Quarter Review and Algebra I EOC (0.5 week) VIII. Study of Basic Rational Expressions: (3.5 weeks)

A. Perform the operations on rational expressions

B. Simplify complex fractions C. Solve rational equations



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Algebra I Honors Traditional Schedule Pacing Guide

First Quarter

2 days Algebra LBA Baseline 2 days 8th Grade LBA Baseline I. Equation Solving in One Variable: (4 weeks)

A. Variable terms located on both sides of the equal sign

B. Literal equations for a specified variable

C. Incorporate the properties of numbers to justify solutions

D. Solve real-world problems E. Solve algebraic proportions F. Solve real-world applications

II. Solve Inequalities in One Variable: (3 weeks)

A. Solve and graph one variable inequalities with justification of steps

B. Solve and graph compound inequalities with justification of steps

C. Solve sentences involving absolute value with one variable

D. Solve real-world problems using inequalities

E. Perform set operations such as union and intersection


Second Quarter

III. Functions, Linear Equations, and Inequalities: (5 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

two-variables. 2 days Algebra I LBA Midyear 2 days 8th Grade LBA Midyear IV. Systems of Equations and Inequalities: (2 weeks)

A. Solve systems of equations and inequalities using graphs

B. Solve systems of equations using algebraic methods: Substitution and Elimination

C. Solve real-world problems involving systems.

Third Quarter

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 of Quadratic Functions: (3 weeks)

A. Solve quadratic equations using the quadratic formula

B. Identify characteristics of parabolas

C. Graph quadratic equations D. Solve real-world problems

involving quadratics.

Fourth Quarter

FCAT – (1 week) V. Study of Polynomials Expressions Part B Continued: (2 weeks)

D. Factor polynomial expressions

E. Solve quadratic equations by factoring

F. Simplify algebraic rational expressions

Review and Algebra I EOC 1 week VIII. Study of Basic Rational Expressions: (4 weeks)

A. Perform the operations on rational expressions

B. Simplify complex fractions C. Solve rational equations



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Algebra I Honors 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 real-world?

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


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How is a proportion used to show the relationship between two quantities in the real-world?

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


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Algebra I Honors Unit II: Solve Inequalities in One Variable Time: 3 weeks [Traditional Schedule]

1.5 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) Solving sentences that include absolute value 5) 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 differences between solving equations and solving inequalities? How do the characteristics of inequalities permit us to compare different quantities in the real-world?

A. Solve an inequality in one variable using 1. The skills of equation solving 2. Graphing the solution on a number line

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 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.



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as the intersection of two sets is a subset of the union of the two sets

C. Solve and graph compound inequalities involving

1. Conjunctions [intersection/and] 2. Disjunctions [union/or]

D. Solve mathematical sentences involving absolute value symbols 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.3.6 Solve and graph the solutions of absolute value equations and inequalities with one variable MA.912.A.3.5 Symbolically represent and solve multi-step and real-world applications that involve linear equations and inequalities.


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Algebra I Unit III: Functions, Linear Equations and InequalitiesTime: 5 weeks [Traditional Schedule] 2.5 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? What are the different ways we can display the equation of a

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

D. Graph a linear equation given: 1. A table of values

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 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

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. Formal:


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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?

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.

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

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


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Algebra I Honors

Unit IV: Systems of Equations and Inequalities Time: 2 weeks [Traditional Schedule] 1.5 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.



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Algebra I Honors

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 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


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property related to factoring? How does simplifying numerical fractions compare to simplifying algebraic fractions?

b. FOIL multiplication c. Product of sum and difference of two

terms d. Perfect squares

4. Division of a polynomial by a. A monomial

Part B 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

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

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.


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Algebra I Honors

Unit VI: Study and Application of Irrational Numbers Time: 2 weeks [Traditional] 1 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.


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Algebra I Honors

Unit VII: Study and Application of Quadratic Functions Time: 3 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 real-world problems MA.912.A.7.10 Use graphing technology to find approximate solutions of quadratic equations.



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Algebra I Honors

Unit VIII: Study of Basic Rational Expressions Time: 4 weeks [Traditional Schedule] 3.5 weeks [4 X 4 Schedule]

Objective: The student will demonstrate their knowledge of algebraic rational numbers by 1) Simplifying the rational expression to lowest terms 2) Finding the sum, difference, product and quotient 3) Simplifying mixed expression and complex rational numbers 4) Solving equations with rational expressions

Vocabulary: complex fraction, constant of variation, inverse variation, rational expression, rational equations, rational function Essential Questions Essential Content and Understandings Essential Skills & Benchmarks Assessment Will knowledge of operations with arithmetic fractions help with solving algebraic fractions?

B. 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

C. Simplify mixed and complex fractions D. Solve rational equations with real-world applications

MA.912.A.5.2 Add, subtract, multiply, and divide rational expressions. MA.912.A.5.3 Simplify complex fractions MA.912.A.5.5 Solve rational equations MA.912.A.5.7 Solve real-world problems involving rational equations (mixture, distance, work, interest, and ratio).

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.


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Algebra I Honors Curriculum Map Appendix for Middle/High Schools

Scope and Sequence Correlated to Textbook

State Approved Course Description Algebra 1 End-of-Course Appendix B


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Algebra I Honors Scope and Sequence Correlated to Holt McDougal Larson Florida Algebra I and NGSSS

Work Word Problems in Every Section

Unit Topic Chapter-Section, Resources NGSSS FIRST QUARTER I. Solve Equations in One Variable – (4 weeks – Traditional)

(2.5 weeks – 4 x 4)

A. Solve equations with variable terms on both sides 3-4 MA.912.A.3.1

B. Solve literal equations for a given variable 3-8 MA.912.A.3.3

C. Incorporate properties to justify solutions Apply throughout unit MA.912.A.3.2

D. Solve real-world problems using equations Apply throughout unit MA.912.A.10.1

E. Solve algebraic proportions 3-5 MA.912.A.5.4 3-6

F. Solve real-world applications 3-7

II. Solve Inequalities in One Variable –(3 weeks – Traditional) (1.5 weeks – 4 x 4)

A. Solve inequalities in one variable 6-1 MA.912.A.3.4 6-2 6-3

B. Perform set operations such as union, intersection, 3-5 MA.912.D.7.1 Venn Diagrams Clouds MA.912.D.7.2

Unions and intersections


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Algebra I Honors Scope and Sequence

Correlated to Holt McDougal Larson Florida Algebra I and NGSSS

Work Word Problems in Every Section Welcome to Venn World

The Eggman: http://themathlab.com/geometry/section2/vennworld.htm

C. Solve compound inequalities 6-4 MA.912.A.3.4

D. Solve sentences involving absolute value 6-5 MA.912.A.3.6

E. Solve real-world problems involving inequalities Apply throughout unit MA.912.A.3.5 SECOND QUARTER III. Functions, Linear Equations, and Inequalities – (5 weeks – Traditional)

(2.5 weeks – 4 x 4)

A. Distinguish between relations and functions 1-6 MA.912.A.2.3

B. Determine the domain and range of relations 1-7 MA.912.A.2.4

C. Determine the slope and intercepts of a linear function 4-2 MA.912.A.3.9 4-3 MA.912.G.1.4 4-4

D. Graph linear functions using various techniques 4-3 MA.912.A.3.7 4-5 MA.912.A.3.8 4-7 MA.912.A.3.9

MA.912.A.3.10

E. Write the equation of a line in various forms 5-1 MA.912.A.3.7 5-2 MA.912.A 3.9


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5-3 MA.912.A.3.10 5-4 MA.912.G.1.4 5-5

F. Apply linear function methods to statistical data 4-6 MA.912.A.3.11 5-6 MA.912.A.2.13 5-7

PROMiSE Algebra Module 4, First Part MA.912.A.3.5, MA.912.A.3.11

G. Graph linear inequalities in two-variables 6-7 MA.912.A.3.5 MA.912.A.3.12 IV. Systems of equations and inequalities – (2 weeks – Traditional)

(1.5 weeks – 4 x 4)

A. Solve systems of equations/inequalities using graphs 7-1 MA.912.A.3.13 7-6 MA.912.A.3.14 MA.912.A.3.15

B. Solve systems of equation using algebraic methods 7-2 MA.912.A.3.14 7-3 MA.912.A.3.15 7-4 7-5

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,

MA.912.A.3.15


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Work Word Problems in Every Section THIRD QUARTER V. Study of Polynomial Expressions (Part A – 3 weeks – Traditional)

(Part A – 1 week – 4 x 4)

A. Apply the laws of integral exponents to monomials 8-1 MA.912.A.4.1 8-2 8-3 8-4

B. Define and classify polynomials 9-1

C. Perform operations on polynomials 9-1 MA.912.A.4.2

9-2 9-3 9-4

VI. Study and Application of Irrational Numbers (2 weeks – Traditional) (1 week – 4 x 4) A. Simplify radical expressions 11-2 MA.912.A.6.1 B. Perform operations on radical expressions 11-3 MA.912.A.6.2

11-4 11-5


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VII. Study and Application of Quadratic Functions – (3 weeks – Traditional) (1 week – 4 x 4)

A. Solve quadratic equations using the quadratic formula 10-6 MA.912.A.7.1 10-7 MA.912.A.7.10

B. Identify the characteristics of parabolas 10-1 MA.912.A.7.1

C. Graph quadratic functions 10-2 MA.912.A.7.1

10-3

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 – 2 weeks – Traditional – Fourth Quarter Starts Here) (Part B – 1.5 weeks – 4 x 4)

D. Factor polynomial expressions 9-5 MA.912.A.4.3

9-6

E. Solve quadratic equations by factoring 10-5 MA.912.A.1.8 MA.912.A.7.2

F. Simplify algebraic rational expressions 12-4 MA.912.A.5.1


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FOURTH QUARTER starts here for 4 x 4 Review for state Algebra I EOC – (1 week – Traditional) (0.5 week – 4 x 4 )

VI. Study of Basic Rational Expressions – (4 weeks – Traditional)

(3.5 weeks – 4 x 4)

A. Perform the operations on rational expressions 12-5 MA.912.A.5.2 12-6

B. Simplify complex fractions 12-5 MA.912.A.5.3

C. Solve rational equations 12-7 MA.912.A.5.5

D. Solve real-world problems with rational equations 12-7 MA.912.A.5.7


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State Approved Course Description

Course Code 1200320 Course Category 6-12 Subject Area Mathematics Course Type Core Course Title Algebra 1 Honors Course Level 3 Course Length Full Year Credit Description 1

Abbreviated Title Algebra 1 Honors

RELATED BENCHMARKS (46) : Scheme Descriptor LA.910.1.6.1 The student will use new vocabulary that is introduced and taught directly; LA.910.1.6.2 The student will listen to, read, and discuss familiar and conceptually challenging text; LA.910.1.6.5 The student will relate new vocabulary to familiar words;

LA.910.3.1.3 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.

MA.912.A.1.8 Use the zero product property of real numbers in a variety of contexts to identify solutions to equations.

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.

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 Solve linear equations in one variable that include simplifying algebraic expressions.


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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. 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. MA.912.A.3.6 Solve and graph the solutions of absolute value equations and inequalities with one variable. 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 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 given 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.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. MA.912.A.4.1 Simplify monomials and monomial expressions using the laws of integral exponents.


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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. MA.912.A.5.1 Simplify algebraic ratios. MA.912.A.5.2 Add, subtract, multiply, and divide rational expressions. MA.912.A.5.3 Simplify complex fractions. MA.912.A.5.4 Solve algebraic proportions. MA.912.A.5.5 Solve rational equations. MA.912.A.5.7 Solve real-world problems involving rational equations (mixture, distance, work, interest, and ratio). 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.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.7.6 Identify the axis of symmetry, vertex, domain, range and intercept(s) for a given parabola. 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.

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.


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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).

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. MA.912.G.1.4 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.


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B–1 | DRAFT Algebra 1 EOC Test Item Specifications © 2010 Florida Department of Education

Algebra 1 EOC Appendix B

MATHEMATICS CONTENT ASSESSED ON THE ALGEBRA 1 EOC ASSESSMENT AND ITEM TYPES BY BENCHMARK

Algebra 1 End-of-Course Assessment

Body of Knowledge Algebra

Standard 1 Real and Complex Number SystemExpand and deepen understanding of real and complex numbers by comparing expressions and performing arithmeticcomputations, especially those involving square roots and exponents. Use the properties of real numbers to simplifyalgebraic expressions and equations, and convert between different measurement units using dimensional analysis.

MA.912.A.1.8Use the zero productproperty of real numbers ina variety of contexts toidentify solutions toequations.

Assessed withMA.912.A.7.2.

Standard 2 Relations and FunctionsDraw 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.2.3 Describe the concept of afunction, use functionnotation, determine whethera given relation is afunction, and link equationsto functions.

Also assessesMA.912.A.2.13.

MC, FR

MA.912.A.2.4Determine the domain andrange of a relation.


MC, FR

MA.912.A.2.13Solve real-world problemsinvolving relations andfunctions.

Assessed withMA.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, thebenchmarks from lower grades will not be assessed in isolation. MC = Multiple Choice FR = Fill-in Response


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Standard 3 Linear Equations and Inequalities

Solve linear equations and inequalities.MA.912.A.3.1Solve linear equations inone variable that includesimplifying algebraicexpressions.


MC, FR

MA.912.A.3.2Identify and apply thedistributive, associative, andcommutative properties ofreal numbers and theproperties of equality.


MA.912.A.3.3Solve literal equations for aspecified variable.

MC

MA.912.A.3.4Solve and graph simple andcompound inequalities inone variable and be able tojustify each step in asolution.

MC

MA.912.A.3.5Symbolically represent andsolve multi-step and realworld applications thatinvolve linear equations andinequalities.

MC, FR

MA.912.A.3.7Rewrite equations of a lineinto slope-intercept formand standard form.


MA.912.A.3.8Graph a line given any ofthe following information: atable of values, the x- andy-intercepts, two points, theslope and a point, theequation of the line inslope-intercept form,standard form, or point-slope form.


MC

MA.912.A.3.9Determine the slope, x-intercept, and y-interceptof a line given its graph, itsequation, or two points onthe line.


MC, FR

MA.912.A.3.10Write an equation of a linegiven any of the followinginformation: two points onthe line, its slope and onepoint on the line, or itsgraph. Also, find anequation of a new lineparallel to a given line, orperpendicular to a givenline, through a given pointon the new line.

Also assessesMA.912.A.3.7,

MA.912.A.3.12, andMA.912.G.1.4.

MC, FR

MA.912.A.3.11Write an equation of a linethat models a data set anduse the equation or thegraph to make predictions.Describe the slope of theline in terms of the data,recognizing that the slope isthe rate of change.


MC, FR



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Standard 3 Linear Equations and InequalitiesSolve linear equations and inequalities.

MA.912.A.3.12Graph a linear equation orinequality in two variableswith and without graphingtechnology. Write anequation or inequalityrepresented by a givengraph.

Assessed withMA.912.A.3.8,MA.912.A.3.9,

MA.912.A.3.10, andMA.912.A.3.11.

MA.912.A.3.13Use a graph to approximatethe solution of a system oflinear equations orinequalities in two variableswith and withouttechnology.


MA.912.A.3.14Solve systems of linearequations and inequalitiesin two and three variablesusing graphical,substitution, andelimination methods.

Also assessesMA.912.A.3.1.13 and

MA.912.A.3.15.

MC, FR

MA.912.A.3.15Solve real-world problemsinvolving systems of linearequations and inequalitiesin two and three variables.


Standard 4 PolynomialsPerform 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.

MA.912.A.4.1 Simplify monomials andmonomial expressionsusing the laws of integralexponents.

MC, FR

MA.912.A.4.2Add, subtract, and multiplypolynomials.

MC, FR

MA.912.A.4.3Factor polynomialexpressions.


MC

MA.912.A.4.4Divide polynomials bymonomials and polynomialswith various techniques,including synthetic division.

MC



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MATHEMATICS CONTENT ASSESSED ON THE FCAT ALGEBRA 1 EOC ASSESSMENT AND ITEM TYPES BY BENCHMARK



Standard 5 Rational Expressions and EquationsSimplify rational expressions and solve rational equations using what has been learned about factoring polynomials.

MA.912.A.5.1Simplify algebraic ratios.


MA.912.A.5.4Solve algebraic proportions.

MC, FR

Standard 6 Radical Expressions and EquationsSimplify and perform operations on radical expressions and equations. Rationalize square root expressions andunderstand 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 Simplify radicalexpressions.

Assessed with A.912.A.6.2. Also assesses MA.912.A.6.1

MA.912.A.6.2Add, subtract, multiply, anddivide radical expressions(square roots and higher).

MC



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MATHEMATICS CONTENT ASSESSED ON THE FCAT ALGEBRA 1 EOC ASSESSMENT AND ITEM TYPES BY BENCHMARK



Standard 7 Quadratic EquationsDraw graphs of quadratic functions. Solve quadratic equations and solve these equations by factoring, completing thesquare and by using the quadratic formula. Use graphing calculators to find approximate solutions of quadraticequations.

MA.912.A.7.1 Graph quadratic equationswith and without graphingtechnology.


MC

MA.912.A.7.2Solve quadratic equationsover the real numbers byfactoring, and by using thequadratic formula.

Also assessesMA.912.A.1.8 and

MA.912.A.7.8.

MC, FR

MA.912.A.7.8 Use quadratic equations tosolve real-world problems.

Assessed withMA.912.A.7.1 and

MA.912.A.7.2.

MA.912.A.7.10Use graphing technology tofind approximate solutionsof quadratic equations.

Not assessed.

Standard 10 Mathematical Reasoning and Problem SolvingIn a general sense, all of mathematics is problem-solving. In all of mathematics, use problem-solving skills, choosehow to approach a problem, explain the reasoning, and check the results.

MA.912.A.10.1 Use a variety of problem-solving strategies, such asdrawing a diagram, makinga chart, guessing and checking, solving a simpler problem, writing an equation,working backwards, andcreating a table.

Assessed throughout.

MA.912.A.10.2 Decide whether a solutionis reasonable in the contextof the original situation.

Assessed throughout.

MA.912.A.10.3Decide whether a givenstatement is always,sometimes, or never true(statements involving linearor quadratic expressions,equations, or inequalitiesrational or radicalexpressions or logarithmicor exponential functions).

Not assessed.



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Body of Knowledge Discrete Mathematics

Standard 7 Set TheoryOperate with sets, and use set theory to solve problems.

MA.912.D.7.1Perform set operations suchas union and intersection,complement, and crossproduct.

MC, FR

MA.912.D.7.2 Use Venn diagrams toexplore relationships andpatterns, and to makearguments aboutrelationships between sets.

MC, FR

Algebra 1 End of Course Assessment

Body of Knowledge Geometry

Standard 1 Points, Lines, Angles, and PlanesUnderstand geometric concepts, applications, and their representations with coordinate systems. Find lengths andmidpoints of line segments, slopes, parallel and perpendicular lines, and equations of lines. Using a compass andstraightedge, patty paper, a drawing program or other techniques, construct lines and angles, explaining and justifyingthe processes used.

MA.912.G.1.4Use coordinate geometry tofind slopes, parallel lines,perpendicular lines, andequations of lines.




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