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Mathematics Department Math for College Readiness Curriculum Map Volusia County Schools 1200700/IND Revised June 8, 2012

Volusia County Mathematics Curriculum Map

Math for College Readiness

Course Number 1200700/IND

KEY TERMINOLOGY OF THE CURRICULUM MAP

Unit/Organizing Principle: the overarching organizational structure used to group content and concepts within the curriculum map Pacing: the recommended time period within the year for instruction related to the essential questions to occur Essential Questions: the overarching question(s) that will serve to guide instruction and push students to higher levels of thinking; essential questions should guide students to the heart of the content Measurement Topics: a list of the major underlying concepts covered in the development of the essential questions Learning Targets/Skills: the content knowledge, processes and enabling skills that will ensure successful mastery of the essential questions Benchmarks: the Next Generation Sunshine State Standards Academic Language: the content vocabulary and other key terms and phrases with which students should be familiar and that support mastery of the learning targets, skills and essential questions Activities and Resources: a listing of available, high quality and appropriate materials, strategies, lessons, textbooks, videos and other media sources that are aligned with the learning targets, skills and essential questions; developed to save teachers time when planning for instruction Assessment: a list of required formative assessments as well as suggested assessments that are available to use as formative or summative assessments

UNIT/ORGANIZING PRINCIPLE: The Rational Number System PACING: 1

st 9 weeks

3 days

ESSENTIAL QUESTIONS: How do you apply properties and order of operations to algebraically add, subtract, multiply and divide rational numbers?

MEASUREMENT

TOPICS LEARNING TARGETS/SKILLS BENCHMARKS ACADEMIC LANGUAGE

Evaluating rational expressions

Add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

MACC.7.NS.1.1 Rational Numbers Quotient Product Reciprocal LCM Ratio

Multiply and divide rational numbers MACC.7.NS.1.2

Solve real-world and mathematical problems involving the four operations with rational numbers

MACC.7.NS.1.3

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision. Look for and make use of structure.

Look for and express regularity in repeated reasoning.

MACC.K12.MP.1 MACC.K12.MP.2 MACC.K12.MP.3 MACC.K12.MP.4 MACC.K12.MP.5 MACC.K12.MP.6 MACC.K12.MP.7 MACC.K12.MP.8

Activities and Resources Assessment

Suggested Resources

Holt McDougal (Algebra 1)

1.1 Evaluating Expressions

1.2 Apply Order of Operation(only rational numbers)

1.3 Write Expressions

2.1 Use Integers and rational numbers

2.2 Add real numbers

2.3 Subtract real numbers

2.4 Multiply real numbers

2.5 Divide real numbers

Pearson (Algebra 1)

1.2 Order of operation (only rational numbers)

1.3 Real numbers and the number line (only rational numbers)

1.4 Properties of real numbers (only rational numbers)

1.5 Add and subtract real numbers (only rational numbers)

1.6 Multiply and Divide real numbers (only rational numbers)

Safari Montage

Math’scool Lesson 1

Internet Resources

www.pearsonsuccessnet.com reteaching worksheets and power points http://my.hrw.com

Power points and worksheets

http://people.ucsc.edu/~miglior/chapter%20pdf/Ch01_SE.pdf

Review of basic algebraic concepts

http://www.pearsonsuccessnet.com/

http://my.hrw.com/


UNIT/ORGANIZING PRINCIPLE: Solve Real-Life and Mathematical Problems Using Numerical and

Algebraic Expressions and Equations

PACING: 1st 9 weeks

9 days

ESSENTIAL QUESTIONS: How can you use algebraic expressions, equations and inequalities to solve real-life problems

MEASUREMENT


Applying algebraic equations/ inequalities

Translate verbal phrases into algebraic expressions and vice versa

MACC.7.EE.2.4b

Expression Equation Inequalities Linear Equations Inverse Operations Set Builder Notation Interval Notation Null Set Universal Set

Solve linear equations and inequalities MACC.912.A-REI.2.3

Graph the solution set for the inequalities MACC.7.EE.2.4b

Understand the graph of an equation or inequalities in two variables is the set of all its solutions plotted in the coordinate plane

MACC.912.A-REI.4.10










Suggested Resources


1.1 Evaluate expressions

1.2 Order of operations

1.3 Write expressions

1.4 Write equations and inequalities

1.5 Use a problem solving plan

2.5 Distributive properties

3.1 Solve one step equations

3.2 Solve two step equations

3.3 Solve multi step equations

3.4 Solve equations with variables on both sides

3.5 Write ratios and proportions

3.6 Solve percent problems

3.7 Rewrite equations and formulas

All of Chapter 6 Solving and Graphing Linear inequalities

Pearson (Algebra 1)

1.1 Variable and expressions

1.2 Order of operations and expression

1.7 Distributive property

1.8 Intro to Equations

1.9 Patterns, Equations and Graphs

2.1 Solve one step equations

2.2 Solve two step equations

2.3 Solve multi step equations

2.4 Modeling equations with variables on both sides

2.6 Ratios, rates and conversions

2.7 Solve proportions

2.8 Proportions and similar figures

2.9 Percents

2.10Change expressed as percent

All of Chapter 3 Solving Inequalities




Review of basic algebraic concepts


http://my.hrw.com/


UNIT/ORGANIZING PRINCIPLE: Use Functions to Model Relationships Between Quantities PACING: 1

st 9 weeks

10 days

ESSENTIAL QUESTIONS: Can a student recognize and represent linear functions in table graph and equation forms

MEASUREMENT


Relations & Functions

Use the functions to translate model relationships between quantities

MACC.8.F.2.4 Direct Variation Domain Function Indirect Variation Range Relation Vertical Line Test Function Notation Slope Rate of Change Intercept

Build a function that models a relationship between two quantities

MACC.912.F-BF.1.1

Understand the concept of a Function and use of function notation

MACC.912.F-IF.1.1

Interpret linear functions that arise in applications in terms of context

MACC.912.F-IF.2.4

Understand the connections between proportional relationships, lines, and linear equations

MACC.8.EE.2.5

Interpret linear models

Interpret the slope (rate of change) and intercept (constant tem) of a linear model in the context

MACC.912.S-ID.3

MACC.912.S-ID.3.7










Suggested Resources


1.6 Represent Functions and rules and tables

1.7 Represent functions as graphs

4.4 Find slope and rate of change

All of Chapter 4 Graphing linear equations and functions Pearson (Algebra 1)

All of Chapter 4 An Introductions to functions

5.1 Rate of change and slope

5.2 Direct variation

Daytona State College (Intermediate Algebra MAT1033)

Chapter 3

Safari Montage

Algebra’scool Lesson 9

Internet Resources www.pearsonsuccessnet.com reteaching worksheets and power points http://my.hrw.com



Introduction to Functions & Relations


Logarithmic & Exponential Functions


http://my.hrw.com/



UNIT/ORGANIZING PRINCIPLE: Reasoning and Creating Equations and Inequalities PACING: 1

st 9 weeks

20 days

ESSENTIAL QUESTIONS: How can you use linear equations and inequalities , their graphs, and relationship tables to model real world

situations?

MEASUREMENT


Applying linear equations/ inequalities

Explain each step in solving equations and inequalities and construct a viable argument to justify a solution method

MACC.912.A-REI.1.1 Literal Equations Standard form Slope-intercept form Point-slope form x-intercept y-intercept constant variable slope rate of change

Create linear equations and inequalities in one variable and use them to solve problems.

MACC.912.A-CED.1.1

Solve literal equations

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales

MACC.912.A-CED.1.4

MACC.912.A-CED.1.2










Suggested Resources


5.1 Write linear equations in slope intercept form

5.2 Use linear equations in slope intercept fprm

5.3 Write linear equations in point slope form

5.4 write linear equations in standard form

5.5write equations of parallel and perpendicular lines

All of Chapter 6 Solving and Graphing Linear inequalities Pearson (Algebra 1)

All of Chapter 3 Solving inequalities

5.3 Slope intercept form

5.4 Point slope form

5.5 Standard form

5.6 Parallel and perpendicular lines

2.5 literal equations and formulas


Chapter 1

Safari Montage




http://people.ucsc.edu/~miglior/chapter%20pdf/Ch02_SE.pdf Linear Equations in Two Variables


http://my.hrw.com/


UNIT/ORGANIZING PRINCIPLE: Solving Systems of Equations PACING: 2

nd 9 weeks

15 days

ESSENTIAL QUESTIONS: How do you solve systems of equations by graphing, substitution, elimination?

MEASUREMENT


Solve linear systems

Solve systems of equations using substitution and elimination MACC.912.A-REI.3.5

Systems of linear equations Solutions of systems of equations Elimination Substitution Dependent Indepentent Consistent Inconsistent

Solve systems of equations by graphing exactly and approximately

MACC.912.A-REI.3.6

Explain why the x-coordinate points where the graphs of the equations intersect are the solutions of the equations; find the solutions approximately (include linear, polynomials, rational, absolute value, exponential, and logarithmic functions.

MACC.912.A-REI.4.11

Prove slope criteria for parallel and perpendicular lines and use them to solve geometric problems

MACC.912.G-GPE.2.5









Suggested Resources


All of chapter 7 Systems of equations and inequalities Pearson (Algebra 1)

All of chapter 6 Systems of equations and inequalities


Chapter 2

Safari Montage





Solving Systems of Linear Equations


http://my.hrw.com/


UNIT/ORGANIZING PRINCIPLE: Expressions and Equations PACING: 2

nd 9 weeks

2 days

ESSENTIAL QUESTIONS: How do you manipulate radicals and integer exponents?

MEASUREMENT


Simplifying monomial exponents

Know and apply the properties of integer exponents to generate equivalent numerical expressions.

MACC.8.EE.1.1

Power Base Exponent Radical Radicand Scientific notation

Perform operations with number expressed in scientific notation. MACC.8.EE.1.4










Suggested Resources


All of Chapter 8 Exponents and exponential functions Pearson (Algebra 1)

All of Chapter 7 Exponents

Safari Montage

Math’scool Lesson 5.6 Exponents and Powers

Algebra’scool Lesson 11.1 Applying Rules of Exponents

Algebra’scool Lesson 1.4 Simplifying expressions with exponents and roots

Math’scool Lesson 5.7 Scientific Notation www.pearsonsuccessnet.com reteaching worksheets and power points http://my.hrw.com



http://my.hrw.com/

UNIT/ORGANIZING PRINCIPLE: The irrational numbers and the real number system PACING: 2

nd & 3

rd 9 weeks

30 days

ESSENTIAL QUESTIONS: How do you use properties or rational and irrational numbers to solve rational and radical equations

MEASUREMENT


Radical & Rational

Expressions Identifying and approximating irrational numbers MACC.8.NS.1.1 Rational Expression Equivalent rational expressions Complex Fraction Radical Expression Domain of a rational & radical expression Range of a rational & radical expression Index Radicand Square root Cubed Root Conjugate pair Rationalize (the denominator) Extraneous solutions Asymptote

Extend the properties of exponents to rational exponents MACC.912.N-RN.1.1

Use properties of rational and irrational numbers MACC.912.N-RN.2.3

Simplifying and rationalizing radical expressions MACC.912.A-APR.4.7

Solve simple rational and radical equations in one variable, and give examples showing extraneous solutions may arise

MACC.912.A-REI.2.3

Create simple rational equations in two variables and use them to solve problems.

MACC.912.A-CED.1.1

Represent constraints by equations and inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context

MACC.912.A-CED.1.3










Suggested Resources


2.7 Finding square roots and compare real numbers

11.1 Graphing square root functions

11.2 Simplify radical expressions

11.3 Solve radical equations

All of Chapter 12 Pearson (Algebra 1)

Chapter 1 Foundations for algebra (irrational numbers)

Chapter 10 Radical Expressions


Chapter 5

Chapter 6

Chapter 7 Section 7.1

Safari Montage

Algebra’scool Lesson 15: Rational Expressions

Algebra’scool Lesson 17: Radical Expressions www.pearsonsuccessnet.com reteaching worksheets and power points http://my.hrw.com

Power points and worksheets http://people.ucsc.edu/~miglior/chapter%20pdf/Ch06_SE.pdf Rational Expressions & Rational Equations http://people.ucsc.edu/~miglior/chapter%20pdf/Ch07_SE.pdf Radicals & Complex Numbers


http://my.hrw.com/



UNIT/ORGANIZING PRINCIPLE: Polynomials PACING: 3

rd 9 weeks

15 days

ESSENTIAL QUESTIONS: How do you identify, interpret and simplify polynomial expressions?

MEASUREMENT


Operations with

polynomials

Interpret parts of a polynomial expressions MACC.912.A-SSE-1.1 Monomial Binomial Trinomial Polynomial Coefficient Degree of a monomial Degree of a polynomial Constant Linear Quadratic Cubic Quartic Leading Term Synthetic Division Distance formula Midpoint Pythagorean Theorem

Perform arithmetic operations on polynomials MACC.912.A-APR.1.1

Simplify and divide polynomials MACC.912.A-APR.4.6

Use polynomial identities to solve problems MACC.912.A-APR.3.4

Find the point on a directed line segment between two given points that partitions the segment given the ratio

MACC.912.G-GPE.2.6

Use coordinates to compute perimeters of polygons and areas of a triangles and rectangles, e.g., using the distance formula.

MACC.912.G-GPE.2.7










Suggested Resources


9.1 Add and subtract polynomials

9.2 Multiply Polynomials

9.3 Find Special products and polynomials

11.4 Apply the Pythagorean Theorem and Its converse

11.5 Apply the distance and midpoint formulas Pearson (Algebra 1)

8.1 adding and subtracting polynomials

8.2 multiplying and factoring

8.3 Multiplying binomials

8.4 Multiplying special cases


4.1 Division of Polynomials

4.2 Greatest common factor and factoring by grouping


Power points and worksheets http://people.ucsc.edu/~miglior/chapter%20pdf/Ch05_SE.pdf Introduction to Polynomials


http://my.hrw.com/


UNIT/ORGANIZING PRINCIPLE: Factoring and solving polynomial equations PACING: 3

rd 9 weeks

20 days

ESSENTIAL QUESTIONS: How do you solve a polynomial equation?

MEASUREMENT


Solving quadratic

equations Use GCF to factor polynomials MACC.912.A-SSE.2.3 Factor Factor by grouping Factor completely GCF Difference of Squares Difference of cubes Perfect Square Trinomial Sum of cubes Zeros (of a function) Zero product rule Roots

Identify zeros of polynomials when suitable factorization are available, and use the zeros to construct a rough graph of the function define by the polynomial

MACC.912.A-APR.2.3

Factor quadratic expressions to reveal the zeros of the function it defines

MACC.912.A-SSE.2.3a

Solve quadratic equations of the type ax 2 + bx + c and x 2

+ bx + c in one variable MACC.912.A-REI.2.4

Factoring special cases MACC.912.A-SSE.1.2

Completing the squares MACC.912.A-REI.2.4a

Factor using various methods (completing squares, factoring,etc) MACC.912.A-REI.2.4b










Suggested Resources


9.4 Solve polynomial equations in factored form

9.5 Factor xˆ2+bx+c

9.6 Factor ax^2+bx+c

9.7 Factor special products

9.8 Factor polynomials completely

10.4 Use square roots to solve quadratic equations

10.5 Solve quadratic equations by completing the square

10.6 Solve quadratic equations by the quadratic formulas

10.7 Interpret the discriminate Pearson (Algebra 1)

8.5 Factoring x^2+bx+c

8.6 Factoring ax^2+bx+c

8.7 Factoring special cases

8.8 Factoring by grouping


4.3 Factoring Trinomials

4.4 Factoring binomials

4.5 Additional Factoring Strategies

4.6 Solving equations using the zero product rule

7.2 Square Root Property & completing the square

7.3 Quadratic Formula

Safari Montage

Algebra’scool Lesson 11: Polynomials

Algebra’scool Lesson 12: Factoring Polynomials




http://my.hrw.com/

UNIT/ORGANIZING PRINCIPLE: Graphing quadratic functions PACING: 4

th 9 weeks

10 days

ESSENTIAL QUESTIONS: How do you use the various techniques to graph a quadratic function?

MEASUREMENT


Graphing quadratics Identify key features of a quadratic function by hand

and using technology MACC.912.F-IF.3.7

Parabola Vertex Axis of symmetry Extreme value (of a quadratic function) Maxima Minima Intercepts Completing the square Quadratic Formula Discriminant Real root Imaginary root Standard Form Vertex Form Parent function End behavior Periodicity

Graph quadratic functions and show intercepts, maxima and minima

MACC.912.F-IF.3.7a

Write a function define by an expression in different but equivalent forms to reveal and explain different properties of the function

MACC.912.F-IF.3.8

Use factoring and completing squares to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context

MACC.912.F-IF.3.8a

Shifting and stretching functions MACC.912.F-BF.2.3

Interpret functions that arise in applications in terms of context. Interpret key features: intercepts, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity

MACC.912.F-IF.2.4










Suggested Resources


10.1 Graph y=ax^2+c

10.2 Graph y=ax^2+bx+c

10.3Solving quadratic equations by graphing Pearson (Algebra 1)

All of Chapter 9 Quadratic Functions and Equations

Safari Montage

Algebra’scool Lesson 13: Solving quadratic equations

Algebra’scool Lesson 14: Graphing quadratic relations


Power points and worksheets Ck12.org/flexbook


Quadratic Equations & Functions


http://my.hrw.com/


UNIT/ORGANIZING PRINCIPLE: Data Analysis PACING: 4

th 9 weeks

10 days

ESSENTIAL QUESTIONS: How do you use analyze data given in various forms?

MEASUREMENT


Data Analysis Summarize Categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data

MACC.912.S-ID.2.5

Data Data analysis Frequency table Joint frequency Marginal frequency Conditional relative frequency Scatterplot Line of best fit (trend line) Regression Correlation (positive & negative) Direct variation Indirect variation Rate of change Residual Error Independent variable Dependent variable

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related

MACC.912.S-ID.2.6

Fit a function to the data; use functions to data to solve problems in the context of the data.

MACC.912.S-ID.2.6a

Plotting and analyzing residuals MACC.912.S-ID.2.6b

Fit linear function for a scatter plot that suggests a linear association

MACC.912.S-ID.2.6c










Suggested Resources


5.6 Fit a line to data

5.7 Predict with linear models

10.8 Compare linear, exponential, and quadratic models Pearson (Algebra 1)

5.7 Scatter plots and trend lines


Power points and worksheets Safari Montage Algebra’scool Lesson 19 Ck12.org/flexbook

PERT Review/Study Materials: http://www.khanacademy.org/ http://www.fldoe.org/schools/pdf/PERT-StudentStudyGuide.pdf http://www.mdc.edu/testing_information/PERT/ http://www.fscj.edu/mydegree/assessment-certification/cpt/assets/documents/pert-math-study-guide.pdf http://www.seminolestate.edu/academic-success/cptrefresh.htm http://www.colpsc.com/index.php?option=com_weblinks&view=category&id=64&Itemid=33 http://valenciacollege.edu/assessments/cpt/


http://my.hrw.com/

http://www.khanacademy.org/

http://www.fldoe.org/schools/pdf/PERT-StudentStudyGuide.pdf

http://www.mdc.edu/testing_information/PERT/

http://www.fscj.edu/mydegree/assessment-certification/cpt/assets/documents/pert-math-study-guide.pdf

http://www.fscj.edu/mydegree/assessment-certification/cpt/assets/documents/pert-math-study-guide.pdf

http://www.seminolestate.edu/academic-success/cptrefresh.htm

http://www.colpsc.com/index.php?option=com_weblinks&view=category&id=64&Itemid=33

http://www.colpsc.com/index.php?option=com_weblinks&view=category&id=64&Itemid=33

http://valenciacollege.edu/assessments/cpt/

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