mth420 – college algebrasharepoint.pthsd.k12.nj.us/ci/approved curriculum/mth420 college... ·...

MTH420 College Algebra 1

Parsippany-Troy Hills School District

MTH420 – College Algebra A Course Outline for Mathematics

Approved by the Board of Education October 22, 2015

Developed: October 2015 Revised: Approved:


Table of Contents STATEMENT OF PURPOSE……………………………………………………………………………………………………………………………………………………………………………………………3 THE LIVING CURRICULUM ................................................................................................................................................................................................... 4

AFFIRMATIVE ACTION ......................................................................................................................................................................................................... 4

GENERAL GOALS ................................................................................................................................................................................................................. 5

METHODS ............................................................................................................................................................................................................................ 5

EVALUATION / ASSESSMENT .............................................................................................................................................................................................. 6

GRADING PROCEDURES ...................................................................................................................................................................................................... 7

COURSE PROFICIENCIES ...................................................................................................................................................................................................... 8

I. COMPARING, ORDERING, ROUNDTAG WHOLE NUMBERS AND DECIMALS .................................................................................................... 10

II. FRACTIONS AND MIXED NUMBERS .................................................................................................................................................................. 11

III. DECIMALS ......................................................................................................................................................................................................... 13

IV. INTRODUCTION TO ALGEBRA AND THE REAL NUMBER SYSTEM..................................................................................................................... 14

V. RATIO, PROPORTION AND PERCENT ................................................................................................................................................................ 15

VI. LINEAR EQUATIONS AND INEQUALITIES .......................................................................................................................................................... 16

VII. INTRODUCTION TO GRAPHIING ....................................................................................................................................................................... 17

VIII. SYSTEMS OF LINEAR EQUATIONS ..................................................................................................................................................................... 19

IX. POLYNOMIALS .................................................................................................................................................................................................. 21

X. FACTORING POLYNOMIALS .............................................................................................................................................................................. 23

XI. RATIONAL EXPRESSIONS AND FUNCTIONS ...................................................................................................................................................... 25

XII. ROOTS AND RADICALS ...................................................................................................................................................................................... 26

BIBLIOGRAPHY .................................................................................................................................................................................................................. 27

APPENDIX A SAMPLE AUTHENTIC ASSESSMENT ............................................................................................................................................ 28

APPENDIX B SELF ASSESSMENT ...................................................................................................................................................................... 30

MTH420 College Algebra

APPENDIX C NEW JERSEY STUDENT LEARNING STANDARDS ......................................................................................................................... 33

APPENDIX D CURRICULUM MODIFICATIONS AND ADAPTATIONS .................................................................... Error! Bookmark not defined.

STATEMENT OF PURPOSE

Separately we assess students to gauge progress and inform instruction. Benchmark assessments for students in grades 9 through 12 are administered in the form of a midterm and final exam for full year courses. *Special Note: Only final exams are administered at the end of quarter courses and semester courses.


THE LIVING CURRICULUM

Curriculum guides are designed to be working documents. Teachers are encouraged to make notes in the margins. Written comments can serve as the basis for future revisions. In addition, the teachers and administrators are invited to discuss elements of the guides as implemented in the classroom and to work collaboratively to develop recommendations for curriculum reforms as needed.

AFFIRMATIVE ACTION

During the development of this course of study, particular attention was paid to material, which might discriminate on the basis of sex, race, religion, national origin, or creed. Every effort has been made to uphold both the letter and spirit of affirmative action mandates as applied to the content, the texts and the instruction inherent in this course.

MODIFICATIONS AND ADAPTATIONS For guidelines on how to modify and adapt curricula to best meet the needs of all students, instructional staff should refer to the Curriculum Modifications and Adaptations included as an Appendix in this curriculum. Instructional staff of students with Individualized Education Plans (IEPs) must adhere to the recommended modifications outlined in each individual plan.


GENERAL GOALS

This course offers students the opportunity to prepare for success in their college experience by addressing the skills needed for successful completion of college entrance exams. Students will integrate topics of arithmetic and introductory Algebra, including whose numbers, fractions, decimals, percents, linear equations and inequalities in one variable, operations of polynomials, factoring integer exponents, and graphing. Student will integrate topics of systems of equations, polynomials, factoring, rational expressions, radicals and solving quadratic equations.

METHODS

This course has been designed as an integration elementary mathematics and algebraic symbols and the corresponding graphing interpretation and extrapolation. A variety of assessments strategies including open-ended questions, multiple choice, and short constructed responses in combinations with traditional methods will provide a complete picture of student’s performance and progress. Pearson’s My Foundation Lab will be utilized daily by students to explore and assess their progress.


EVALUATION / ASSESSMENT

“Assessment must be more than testing; it must be continuous, dynamic and often informal process,” according to NCTM Curriculum and Evaluation Standards for School Mathematics. With this in mind, the assessment tools for the College Algebra course should be completed on the My Foundations Lab and include, but not be limited to:

- open-ended questions - problem-solving experiences using real-life data - labs - individual/partner/group - projects - individual/partner/group - concepts and application of technology - partner quizzes/tests - notebook quizzes - unit tests/quizzes - student self-assessment

Utilizing a variety of assessment techniques enables the teacher and the student to understand more fully the mathematical strengths and weaknesses of the student and the program.


GRADING PROCEDURES

Marking Period Grades: Long- and Short-Term Assessments 90% Publisher-prepared tests, quizzes and/or worksheets Teacher-prepared tests, quizzes and/or worksheets Authentic Assessments Technology Applications Projects Reports Labs Daily Assessments 10% Homework Do Now / Exit Questions Class Participation Journal Writing Notebook - checks and open notebook assessments Explorations High School

Final Grade – Full Year Course

Full Year Course • Each marking period shall count as 20%

of the final grade (80% total).

The midterm assessment will count as 10% of the final grade, and the final assessment will count as 10% of the final grade.


PARSIPPANY-TROY HILLS TOWNSHIP SCHOOLS COURSE PROFICIENCIES

Course: MTH420 Title: COLLEGE ALGEBRA

In accordance with district policy as mandated by the New Jersey Administrative Code and the New Jersey Student Learning Standards, the following are proficiencies required for the successful completion of the above named course. The student will:

1. compare, order, round whole numbers and decimals. 2. add, subtract, multiply, divide whole numbers. 3. find powers and roots of whole numbers. 4. use the order of operations. 5. find factors and least common multiples of whole numbers. 6. add and subtract fractions with like and unlike denominators. 7. multiply and divide fractions. 8. find equivalent fractions including writing a fraction in lowest terms. 9. work with mixed numbers and improper fractions. 10. order fractions. 11. add, subtract, multiply, and divide decimals. 12. convert from fraction to decimal form and vice versa. 13. work with integers, opposites, and absolute value. 14. add, subtract, multiply, & divide integers. 15. simplify algebraic expressions. 16. do calculations with real numbers. 17. use ratios, rates, proportions. 18. convert from percent to fractions to decimals and vice versa. 19. complete calculations with percents. 20. solve word problems with percents. 21. calculate simple interest. 22. solve linear equations in one variable.


Course Proficiencies (continued)

23. apply linear equations. 24. rewrite formulas. 25. solve linear inequalities. 26. finding slope & intercepts of linear functions. 27. graph linear equations. 28. write equations of lines. 29. find parallel and perpendicular lines. 30. graph linear inequalities. 31. solve linear systems. 32. classify polynomials. 33. add and subtract polynomials. 34. Using the product rule and the power rules for exponents. 35. multiply polynomials, including special products. 36. apply the properties of exponents. 37. divide a polynomial by a monomial. 38. factor out the greatest common factor. 39. factor trinomials in the form x^2+bx+c. 40. factor trinomials in the form ax^2+bx+c. 41. factor difference of two squares and perfect square trinomials. 42. multiply and divide rational expressions. 43. add and subtract rational expressions. 44. simplify complex fractions. 45. solve rational equations. 46. solve systems of linear equations graphically and algebraically. 47. solve systems of linear inequalities (optional). 48. factor polynomials that are not quadratic. 49. evaluate and simplify radicals (square roots only). 50. perform operations on radicals (square roots only). 51. solve radical equations (square roots only).

solve quadratic equations by factoring and the quadratic formula.


I. COMPARING, ORDERING, ROUNDTAG WHOLE NUMBERS AND DECIMALS Essential Question(s): a) How can you describe the value of a digit through the hundred thousands?

b) How can you round numbers? c) How can you compare and order numbers? d) What strategies can you use to find factors and multiples?

Enduring Understanding(s): a) Generalize place value understanding for multi-digit whole numbers.

b) Use place value understanding and properties of operations to perform multi-digit arithmetic.

COMPARING, ORDERING, ROUNDTAG WHOLE NUMBERS AND DECIMALS

PROFICIENCY / OBJECTIVE Standards SUGGESTED ACTIVITY EVALUATION/ ASSESSMENT

TEACHER NOTES

The student will be able to: Students will:

1. use and compare whole numbers. (1, 2, 3, 4, 5)

8.1.12.A.3 6.EE.2.C

• perform operations with whole numbers, including order of operations.

8.1.12.A.3 3.NBT.A.1

• estimate to different place values. Round 45,327 to the nearest thousands and tenths

8.1.12.A.3 8.EE.A.1 8.EE.A.2

• estimate exponents and square roots.

8.1.12.A.3 4.OA.B.4

• find factors and multiples of whole numbers.

Find the factors and multiples of 32.


II. FRACTIONS AND MIXED NUMBERS Essential Question(s): a) How can you rewrite a pair of fractions so that they have a common denominator?

b) How can you use a common denominator to add and subtract fractions with unlike denominators? c) How can you make reasonable estimates of fraction sums and differences? d) How can you represent division? e) How can you find a fractional part of a group? f) How does the size of the product compare to the size of one factor when multiplying fractions? g) How do you multiply mixed numbers? h) How do you divide a whole number by a fraction and divide a fraction by a whole number?

Enduring Understanding(s): a) Use equivalent fractions as a strategy to add and subtract fractions. b) Apply and extend previous understandings of multiplication and division to multiply and divide

fractions. c) Add and subtract mixed numbers. d) Convert improper fractions to mixed numbers.

FRACTIONS AND MIXED NUMBERS

PROFICIENCY/OBJECTIVE Standards SUGGESTED ACTIVITY EVALUATION/ ASSESSMENT

TEACHER NOTES


2. use fractions and mixed numbers. (6, 7, 8, 9, 10)

8.1.12.A.3 5.NF.A.1

• add and subtract fractions with like and unlike denominators.

Solve:

8.1.12.A.3 5.NF.B.4 5.NF.B.7

• multiply and divide fractions.


FRACTIONS AND MIXED NUMBERS


TEACHER NOTES

The student will be able to: Students will: 2. (continued) 8.1.12.A.3

4.NF.A.1 • find equivalent fractions including

writing a fraction in lowest terms. Write in lowest term: Simplify:

3256

Find two additional equivalent fractions

8.1.12.A.3 5.NF.A.1

• perform operations with mixed numbers and improper fractions.

8.1.12.A.3 4.NF.A.2

• order fractions. List the following fractions in order from least to greatest:

23

43

34

12

32

13


III. DECIMALS Essential Question(s): a) How can you describe the relationship between two place value positions?

b) How can you read, write and represent numbers? c) How can you use place value to compare and order decimals? d) How can you use place value to round decimals to a given place? e) How can you use concrete models to add, subtract, multiply and divide decimals to hundredths?

Enduring Understanding(s): a) Understand the place value system. b) Perform operations with multi-digit whole numbers and with decimals to hundredths.

DECIMALS


TEACHER NOTES


3. add, subtract, multiply and divide decimals. (11)

8.1.12.A.3 5.NBT.B.7

• perform operations with decimals, include order of operations.

4. reading and writing decimals and place values. (1)

8.1.12.A.3 5.NBT.A.3.A 5.NBT.A.4

• review place values and how to read and speak decimals.

Write 47,238 in words Round 47,238 to the tenths and hundredths

8.1.12.A.3 5.NBT.A.3.b

• place decimals on a number line. List the following numbers in order from least to greatest:

5.12 5.01 0.5 5.2 0.05 5.21 0.052


IV. INTRODUCTION TO ALGEBRA AND THE REAL NUMBER SYSTEM

Essential Question(s): a) What techniques can be used to solve equations in one variable? b) How can we translate verbal models into algebraic models to represent and solve real-life situations? c) How can you check the reasonableness of your solution? d) What techniques can be used to simplify numerical and exponential expressions?

Enduring Understanding(s): a) Rules of arithmetic and algebra can be used together with the concept of equivalence to transform equations so solutions can be found to solve problems.

b) Algebraic Concepts and processes can be utilized to concisely express real-life situations and expand the ability to solve problems.

c) The relationships among numbers, operations, and their properties promote computational fluency.

INTRODUCTION TO ALGEBRA AND THE REAL NUMBER SYSTEM


TEACHER NOTES


5. work with the real number system. (1, 13, 14, 15, 16)

8.1.12.A.3 6.NS.C.6 6.NJ.C.7.C

• work with integers, opposites, and absolute value.

8.1.12.A.3 7.NS.A.1 7.NS.A.2

• add, subtract, multiply and divide integers.

8.1.12.A.3 6.EE.A.3

• simplify algebraic expressions.

8.1.12.A.3 • perform calculations with real numbers.


V. RATIO, PROPORTION AND PERCENT Essential Question(s):

a) How can we make numbers more manageable? b) How do we use rates and ratios to describe changes in our daily life? c) How can ratios and proportional relationships be used to determine unknown quantities? d) How can you use a graph to show the relationship between two quantities?

Enduring Understanding(s): a) Any number, measure, or numerical expression can be represented in a number of ways that will have the same value.

b) Representations of constant rates of change can be used to model real world conditions. c) Proportional reasoning can be used to model and understand relationships which exist throughout

numerous aspects of real life. d) Ratios and proportional relationships are used to express how quantities change in relation to each

other. e) A graph can be used to show a proportional relationship (direct variation).

RATIO, PROPORTION AND PERCENT


TEACHER NOTES


6. work with ration, rate and proportions. (17, 18, 19, 20)

8.1.12.A.3 6.RP.3.A

• use ratio, rate and proportions. Solve:

8.1.12.A.3 6.RP.A.3.C

• convert percent to fractions/decimals and vice versa.

Convert 3.125 to a fraction. Convert 7 2/3 to a decimal rounded to the nearest tenths.

8.1.12.A.3 6.RP.A.3.C 7.RP.A.3

• solve word problems with percents. Find the % of discount when the original price of a TV is $1,500 and the sale price is $975.

8.1.12.A.3 7.RP.A.3

• calculate simple interest. Determine the interest earned when you invest $1,000 for 1 year on an account paying 3 ½% interest annually.


VI. LINEAR EQUATIONS AND INEQUALITIES Essential Question(s): a) What techniques are used for solving linear equations systematically?

b) What real-life situations can be solved by writing and graphing linear equations? c) How can patterns, relations, and functions be used as tools to best describe and help explain real-life

situations? d) How can we translate verbal models into algebraic models to represent and solve real-life situations? e) How can change be best represented mathematically? f) How can we use an inequality to describe a real life statement? g) How can we use addition or subtraction to solve an inequality? h) How can we solve a multistep inequality? i) How can we use inequalities to describe intervals on the real number line?

Enduring Understanding(s): a) Functional relationships can be expressed in real contexts, graphs, algebraic equations, tables, and words; each representation of a given function is simply a different way of expressing the same idea.

b) The value of a particular representation depends on its purpose. c) Proportionality involves a relationship in which the ratio of two quantities remains constant as the

corresponding values of the quantities change d) Inequalities can be used to model and solve real world situations. e) Inverse operations can be used to solve inequalities. f) There are a variety of techniques used to solve and graph absolute value equations.

LINEAR EQUATIONS AND INEQUALITIES


TEACHER NOTES


7. solve linear equations and linear inequalities. (22, 23, 24, 26, 27, 28, 29, 30, 31)

8.1.12.A.3 A.REI.B.3 7.EE.B.4

• solve linear equations in one variable with applications.

Solve:

8.1.12.A.3 A.REO.B.3

• rewrite formulas. Solve for “w”


VII. INTRODUCTION TO GRAPHIING Essential Question(s): a) How can technology be used to investigate properties of linear functions and their graphs?

b) How can technology be used to investigate properties of linear functions and their graphs? c) What techniques can be used to graph linear equations? d) How can we determine whether an equation or a graph is a function?

Enduring Understanding(s): a) Graphs and equations are alternative (and often equivalent) ways for depicting and analyzing patterns of change.

b) The value of a particular representation depends on its purpose. c) A variety of families of functions can be used to model and solve real world situations.

INTRODUCTION TO GRAPHING


TEACHER NOTES


7. (continued) 8.1.12.A.3 8.F.A.3 8.EE.B.5

• find the slope and intercepts of a line.

Identify the slope given a graph of Y=2x-8.

Induce tables of values, slope intercept form and point slope form

8.1.12.A.3 8.1.12.A.1 A.REID.10 F.F.C.7.A.

• graph a linear equation. Graph using a table or the slope and y-intercept form:

5 1y x= +

8.1.12.A.3 8.1.12.A.1 A.REID.12

• graph a linear inequality. Graph: 3 74

y x≤ −


INTRODUCTION TO GRAPHING


TEACHER NOTES


7. (continued) 8.12.A.3 G.GPE.B.5

• determine if lines are parallel, perpendicular or neither.

Determine if: 3 4 9x y+ =

and 3 74

y x= +

Represent parallel lines.


VIII. SYSTEMS OF LINEAR EQUATIONS Essential Question(s): a) What techniques can be used to solve and graph a system of linear equations or inequalities in one or

two variables? b) How can we model and solve real-life situations using a system of linear equations or inequalities? c) How can functional relationships be used to express real contexts, graphs, algebraic equations, tables

and words? d) How is each representation of a function a different way of expressing the same idea? • How are

functions and their graphs related? e) How can systems of equations be used to solve real-life situations?

Enduring Understanding(s): a) Systems of linear equations or inequalities can be used to model and solve real world situations. b) Systems of equations and inequalities can be solved with a variety of different methods. c) The solutions to a system of linear inequalities can be represented by an intersection of two half

planes.

SYSTEMS OF LINEAR EQUATIONS


TEACHER NOTES


8. solve systems of two linear equations.

8.1.12.A.3 A.REI.C.6 A.REI.D.11

• solve systems graphically. Solve: 2 10x y+ =

3 9x y− + =

8.1.12.A.3 A.REI.C.5 A.REI.C.6

• solve systems algebraically by substitution and elimination.

Solve: 2 3 7x y+ =

9x y− + = 4 3 6x y+ =

2 6 6x y− − =


SYSTEMS OF LINEAR EQUATIONS


TEACHER NOTES

The student will be able to: Students will: 8. (continued) 8.1.12.A.3

F.BF.A.1 • applications of linear systems. A test has twenty questions worth

100 pts. The test consists of true/false questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?


IX. POLYNOMIALS Essential Question(s): a) What techniques can be used to simply expressions with exponents?

b) How can we use mathematical language to describe non-linear change? c) How can we model situations using exponents? d) How can we use mathematical language to describe exponential change? e) How can we use exponential models for real life situations? f) How can we use algebraic representation to analyze patterns? g) Why are number and algebraic patterns important as rules? h) How can we add, subtract, and multiply polynomials? i) What techniques can be used to factor polynomials and solve polynomial equations?

Enduring Understanding(s): a) Mathematical models can be used to describe physical relationships; these relationships may be linear, quadratic, or exponential.

b) Real world situations, involving exponential relationships, can be solved using multiple representations.

POLYNOMIALS


TEACHER NOTES


9. work with polynomials and exponent properties. (32, 33, 37)

8.1.12.A.3 8.EE.A.1

• use the exponent properties (product rule, power rule, negative exponents, quotient rule).

Simplify:

3 2 55 (3 )a x a

8.1.12.A.3 A.SSE.A.1.A

• classify polynomials. Identify the leading coefficient, degree and type:

8.1.12.A.3 A.APR.A.1

• add, subtract and multiply polynomials.

Include special products


POLYNOMIALS


TEACHER NOTES

The student will be able to: Students will: 9. (continued)

8.1.12.A.3 • divide a polynomial by a monomial. Simplify:


X. FACTORING POLYNOMIALS Essential Question(s): a) How do you translate real-world problems into mathematics?

b) How do you translate mathematical solutions into real-world meaning? c) What methods can be used to find solutions to quadratic functions? How can these solutions be

interpreted? d) What techniques can we use to solve quadratic equations or inequalities? e) How can we model and solve real-life situations using quadratic equations? f) How can we use mathematical language to describe non-linear change? g) How do we model situations using quadratics?

Enduring Understanding(s): a) Graphs and equations are alternative ways for depicting and analyzing patterns of non-linear change. b) Mathematical models can be used to describe physical relationships; these relationships are often non-

linear. c) The characteristics of quadratic functions and their representations are useful in solving real-world

problems.

FACTORING POLYNOMIALS


TEACHER NOTES


10. factor polynomials. (38, 39, 40, 41)

8.1.12.A.3 8.1.12.C.1 A.REEI.B.4.B A.APR.B.3

• factor polynomials by greatest common factor, grouping, difference of two squares and perfect square trinomials.

Factor:

Include: x^2+bx+c ax^2+bx+c Be sure to also include polynomials that are not quadratics like ax^4+bx^2+c

11. solve quadratic equations. 8.1.12.A.3 8.1.12.C.1 A.REI.B.4.B

• solve quadratic equations by factoring and by the quadratic formula.

Solve:

2 5 24 0x x+ − =


FACTORING POLYNOMIALS


TEACHER NOTES


12. apply quadratics to real-life problem.

8.1.12.A.3 8.1.12.C.1 F.LE.A.1

• use quadratic equations to answer questions about applications.

You are a member of a theater production crew. You use manila rope and wire rope to support lighting, scaffolding, and other equipment. The weight W (in pounds) that can be safely supported by a rope with diameter d (in inches) is given below for both types of rope. Manila rope: 21480W d≤ Wire Rope: 28000W d≤ Graph the inequalities in separate coordinate planes for

10 1 .2

d≤ ≤

Based on your graphs, can 1000 pounds of theater equipment be

supported by a 12

inch manila

rope? by a 12

wire rope?


XI. RATIONAL EXPRESSIONS AND FUNCTIONS Essential Question(s): a) How can you add, subtract and multiply rational expressions?

b) What are the methods that can be used to simplify complex fractions? Enduring Understanding(s): a) Describe a function that is represented by more than one linear/non-linear equations.

b) Describe the methods used in solving rational equations.

RATIONAL EXPRESSIONS AND FUNCTIONS

CONTENT OUTLINE Standards SUGGESTED ACTIVITY EVALUATION/ ASSESSMENT

TEACHER NOTES


13. simplify rational expressions. (42, 43, 44, 45)

8.1.12.C.1 8.1.A.3 A.APR.D.7

• simplify, add, subtract and multiply and divide rational expressions.

Simplify:

8.1.12.C.1 8.1.A.3 A.APR.D.7

• simplify complex fractions. Simplify:

A,REI.A.2 • solve rational equations. Solve:

A variety of problems should be used, include proportions & using the LCD to “clear” the fractions. Problems should also result in a quadratics that are factorable & those requiring the quadratic formula.


XII. ROOTS AND RADICALS Essential Question(s): a) How do properties of radicals facilitate computation?

b) How can you check the reasonableness for your solution? c) How could writing an expression or equation to model a problem or real life situation facilitate solving it?

Enduring Understanding(s): a) Mathematical models can be used to describe physical relationships; these relationships may be radical. b) Real world situations, involving radical relationships, can be solved using multiple representations.

ROOTS AND RADICALS

CONTENT OUTLINE Standards SUGGESTED ACTIVITY EVALUATION/ ASSESSMENT

TEACHER NOTES


14. work with square roots. (49, 50, 51)

8.1.12.C.1 8.1.A.3 8.EE.A.2

• find square roots of perfect squares without a calculator and use a calculator to verify an estimate of the square root of a number that is not a perfect square.

• approximate irrational roots.

Simplify:

Students should be able to estimate square roots & place them on a number line

8.1.12.C.1 8.1.A.3

• simplify, multiply, and divide square roots and rationalize denominators.

Simplify:

12 18•

8.1.12.C.1 8.1.A.3

• add and subtract square roots. Simplify:

15. solve square root equations. (51, 52)

8.1.12.C.1 8.1.A.3 A.REI.A.2

• solve square root equations algebraically.

Solve:


BIBLIOGRAPHY TEXTBOOKS Larson, Ron, Boswell, Laurie Big Ideas Math Algebra 2. Erie, Pa. Big Ideas Learning, LLC, 2015 SUPPLEMENTAL TEXTBOOK MATERIALS Lial, Margaret L., Hornsby, John, McGinnis, Terry Beginning Algebra; Pearson 2014 My Foundations Lab; Pearson WEBSITES www.domath.org www.enc.org www.forum.swarthmore.edu www.illuminations.nctm.org www.mathforum.com www.mathgoodies.com www.nctm.org www.state.nj.us/education/

http://www.domath.org/

http://www.enc.org/

http://www.forum.swarthmore.edu/

http://www.illuminations.nctm.org/

http://www.mathforum.com/

http://www.mathgoodies.com/

http://www.nctm.org/

http://www.state.nj.us/education/


APPENDIX A SAMPLE AUTHENTIC ASSESSMENT


TASK 1: You want to talk your parents into buying you a car. They tell you that in addition to your college fund they have been saving so you could have at least $2,000 each year for books and the various miscellaneous items you will need to purchase when you go to college. You find a car for $12,500, and tell your parents that the money you will receive from selling this car when you go to college, in two years, will be enough for books and the miscellaneous expenses. Prove to your parents that even though the car will depreciate 12.5% per year, there will be enough money remaining for you after it is sold. TASK 2: You want to have a vegetable garden that is safe from the deer and rabbits! You have 24 meters of fencing to use to enclose a rectangular garden. What should the dimensions of your garden be if you want to maximize the area in which to plant your veggies? Please provide all diagrams, considered, and the final one with reasons for your selection.


APPENDIX B SELF ASSESSMENT


SELF-ASSESSMENT SHEET FOR STUDENT WORK FOLDER

Name ______________________________ Course______________________________

Date Assessment Concepts I understand and can explain to someone else

Concepts I need to further develop


Name ______________________________ Course______________________________

Date Assessment Concepts I understand and can explain to someone else

Concepts I need to further develop


APPENDIX C NEW JERSEY STUDENT LEARNING STANDARDS

MTH420 College Algebra Page

NEW JERSEY STUDENT LEARNING STANDARDS

4 - Mathematics 8 - Technology 9 - 21st Century Life and Careers

http://www.state.nj.us/education/cccs/2016/math/

http://www.state.nj.us/education/aps/cccs/tech/

http://www.state.nj.us/education/aps/cccs/career/


APPENDIX D CURRICULUM MODIFICATIONS & ADAPTATIONS

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