Mohawk Valley Community College s17

MOHAWK VALLEY COMMUNITY COLLEGE UTICA and ROME, NEW YORK

COURSE OUTLINE

INTRODUCTORY ALGEBRA

Prepared by Emily Hantsch, December 2013 Reviewed and Revised by Emily Hantsch, May 2014 Reviewed by Emily Hantsch, May 2016 COURSE OUTLINE

Title: Introductory Algebra

Catalog Number: MA091

Contact Hours: 3

Practicum Hours: 0

Credit Hours: 0

Prerequisite: An appropriate placement test score or MA089 Arithmetic.

Catalog Description: This course is for students enrolled in STEM programs or for students who need to take either MA115 or MA171 who, according to placement test results, need preparation for subsequent mathematics courses. It develops basic skills and the understanding of elementary algebra. Topics include arithmetic computations, measurement and geometry, percentages, ratio and proportion, linear equations, polynomials, and an introduction to graphing lines. Prerequisite: An appropriate placement test score or MA089 Arithmetic.

Major Topics:

For each of the following topics the student will:

Topic 1. Whole Numbers 1.1 Perform basic operations with whole numbers and identify their properties. 1.2 Approximate quantities using estimation. 1.3 Simplify and/or evaluate arithmetic and variable expressions, including exponential form, involving whole numbers using order of operations. 1.4Translate a given verbal expression to symbolic form.

Topic 2. Integers 2.1 Locate integer values on a real number line and use order relations to compare given integers. 2.2 Add, subtract, multiply and divide integers. 2.3 Simplify and/or evaluate variable expressions involving verbal and/or symbolic expressions for the operations on integers. 2.4 Simplify and/or evaluate expressions, including exponential form, additive inverse and absolute value involving integers using order of operations. Topic 3. Rational Numbers 3.1 Simplify fractions. 3.2 Use order relations to compare given fractions. 3.3 Determine the prime factorization of given composite numbers. 3.4 Determine a common denominator for given fractions. 3.5 Add, subtract, multiply and divide given fractions. 3.6 Evaluate variable expressions involving verbal and/or symbolic expressions for the operations on fractions. 3.7 Simplify and/or evaluate expressions involving fractions using the order of operation agreements.

Topic 4. Decimals: 4.1 Perform basic operations on decimals. 4.2 Convert given fractional expressions to decimals including fractions that are equal to repeating decimals, and convert given decimals to fractional expressions. 4.3 Use order relations to compare given decimals. 4.4 Approximate the (principal) square root of a given number with the aid of a calculator. 4.5 Evaluate variable expressions involving verbal and/or symbolic expressions for the operations on decimals. 4.6 Convert numbers between standard notation and scientific notation.

Topic 5. Measurements 5.1 Convert, using conversion factors (rates), measurements of length and time in the U.S. System. 5.2 Convert, using conversion factors (rates), measurements of length, capacity and mass in the Metric System of measurement. 5.3 Convert between U.S. Units and metric units of length using provided conversion factors.

Topic 6. Geometry 6.1 Calculate the perimeter of plane geometric figures. 6.2 Know and use the formulas to calculate the area and circumference of a circle. 6.3 Calculate the area of triangles, rectangles, and squares. 6.4 Recognize the symbol  and use its approximation (from the  key on a scientific calculator or by using 3.14) to evaluate formulas.

Topic 7. Ratio, Proportion, and Percents 7.1 Write ratios as fractions and simplify. 7.2 Write rates as fractions and find unit rates. 7.3 Write and solve proportions. 7.4 Solve application problems which use proportions. 7.5 Perform conversions between percents and fractions and between decimals and percents. 7.6 Use either the basic percent equation (percent X base = amount) or the percent proportion to solve application problems including percent increase and decrease.

Topic 8. Algebraic Expressions and Linear Equations 8.1 Simplify algebraic expressions using the operations of addition and subtraction and distribution of a constant over an expression. 8.2 Evaluate algebraic expressions. 8.3 Evaluate formulas, including when the desired variable is not isolated. 8.4 Determine solutions to first degree equations by applying the addition and multiplication properties of equations. 8.5 Translate given verbal sentences into equations and solve the resulting equations.

Topic 9. Lines 9.1 Graph ordered pairs on a rectangular coordinate system. 9.2 Determine solutions of given linear equations in two variables. 9.3 Graph solutions of given linear equations in two variables on a rectangular coordinate system. 9.4 Recognize and graph horizontal and vertical lines from given equations. 9.5 Determine the x and y-intercepts of given linear equations in two variables. 9.6 Determine and interpret the slopes of lines given two points on the line and/or given the equation of the line. 9.7 Determine an equation of a line given a point and the slope and/or given the graph of a linear equation.

Topic 10. Polynomials 10.1 Use the Rules of Exponents to simplify an expression. 10.2 Add and subtract polynomials 10.3 Multiply a monomial by a polynomial, a binomial by a binomial, and divide a polynomial by a monomial. 10.4 Factor the Greatest Common Factor from a polynomial. Teaching Guide

Title: Introductory Algebra

Catalog Number: MA091

Contact Hours: 3

Practicum Hours: 0

Credit Hours: 0

Prerequisite: An appropriate placement test score or MA089 Arithmetic.

Catalog Description: This course is for students enrolled in STEM programs or for students who need to take either MA115 or MA171 who, according to placement test results, need preparation for subsequent mathematics courses. It develops basic skills and the understanding of elementary algebra. Topics include arithmetic computations, measurement and geometry, percentages, ratio and proportion, linear equations, polynomials, and an introduction to graphing lines. Prerequisite: An appropriate placement test score or MA089 Arithmetic.

Text: Prealgebra and Introductory Algebra, (Custom), Wright: Hawkes Learning Systems/Quant Systems Inc. 2012 MVCC Supplement written by Anna Radlowski and bundled with the text book.

NOTE: Chapter 1, 2, and 3 has mainly review material. Chapter 1 6 Hours 1.1 Introduction to Whole Numbers – Review 1.2 Addition and Subtraction with Whole Numbers – Review 1.3 Multiplication and Division with Whole Numbers – Review. Long Division is supplemented by Topic 1 of the supplement. 1.4 Problem Solving with Whole Numbers – New Material 1.5 Solving Equations with Whole Numbers – New Material 1.6 Exponents and Order of Operations – Review 1.7 Introduction to Polynomials – New 1.8 Introduction to Integers – Review 1.9 Addition with Integers – Review 1.10 Subtraction with Integers – Review 1.11 Multiplication, Division, and Order of Operations with Integers – Review 1.12 Applications: Change in Value and Mean -- OMIT 1.13 Introduction to Like Terms and Polynomials – New Material 1.14 Solving Equations with Integers – New Material

Chapter 2 5 Hours 2.1 Tests for Divisibility – OMIT 2.2 Prime Numbers – Review Material 2.3 Prime Factorization – Review Material 2.4 Least Common Multiple – OMIT 2.5 Introduction to Fractions – Review 2.6 Division with Fractions – Review 2.7 Addition and Subtraction with Fractions – Review 2.8 Introduction to Mixed Numbers 2.9 Multiplication and Division with Mixed Numbers – OMIT 2.10 Addition and Subtraction with Mixed Numbers – OMIT 2.11 Complex Fractions and Order of Operations – Complex fractions are new, Order of Operations is review. 2.12 Solving Equations with Fractions – New 2.13 Ratios and Proportions – New. This section is supplemented by Topic 5 in the supplement.

Chapter 3 5 Hours 3.1 Reading, Writing, and Rounding Decimal Numbers – Review 3.2 Addition and Subtraction with Decimal Numbers – Review 3.3 Multiplication and Division with Decimal Numbers – Review 3.4 Measures of Center – OMIT 3.5 Decimal Numbers, Fractions, and Scientific Notation – Converting between decimals and fractions is review but scientific notation is new material. Scientific Notation is supplemented by Topic 4 in the supplement, converting fractions to decimals is found in Topic 2 of the supplement. 3.6 Basics of Percent – Review 3.7 Applications of Percent – New Material 3.8 Simple and Compound Interest – OMIT 3.9 Square Roots -- Review

Chapters 4-7 contain only new material. Chapter 4 6 Hours 4.1 The Metric System - OMIT Objectives D, F, OMIT all questions from Objective E dealing with equivalent measures of volume. This section is supplemented by Topic 7. 4.2 U.S. Customary and Metric Equivalents – OMIT Objective A and exercises 17- 30. This topic is supplemented by Topic 6. 4.3 Introduction to Geometry – OMIT 4.4 Perimeter. Supplement Topic 8 4.5 Area – Supplement Topic 8. 4.6 Volume – OMIT 4.7 Similarity – OMIT 4.8 The Pythagorean Theorem – OMIT 4.9 Reading Graphs – OMIT

Chapter 5 6 Hours 5.1 Simplifying and Evaluating Algebraic Expressions 5.2 Translating English Phrases and Algebraic Expressions 5.3 Solving Linear Equations: x+b=c and ax=c 5.4 Solving Linear Equations: ax+b=c 5.5 Solving Linear Equations: ax+b=cx+d 5.6 Applications: Number Problems and Consecutive Integers 5.7 Applications: Percent Problems 5.8 Working with Formulas 5.9 Applications: Distance – Rate – Time, Interest, Mean, Cost – OMIT

Chapter 6 6 Hours 6.1 The Cartesian Coordinate System 6.2 Graphing Linear Equations in Two Variables 6.3 The Slope – Intercept Form 6.4 The Point – Slope Form 6.5 Linear Inequalities in One or Two Variables – OMIT 6.6 Introduction to Functions and Function Notation - OMIT

Chapter 7: Exponents, Polynomials, and Factoring Techniques 6 Hours 7.1 Exponents 7.2 Introduction to Polynomials 7.3 Addition and Subtraction with Polynomials 7.4 Multiplication with Polynomials 7.5 Special Products of Polynomials – OMIT 7.6 Greatest Common Factor (GCF) and Factoring by Grouping 7.7 Factoring Trinomials: x2+bx+c – OMIT 7.8 Factoring Trinomials: ax2+bx+c – OMIT 7.9 Special Factoring Techniques – OMIT 7.10 Solving Quadratic Equations by Factoring – OMIT 7.11 Applications of Quadratic Equations – OMIT

The teaching guide leaves 3 hours for in class assessment. There will be a two hour proctored comprehensive final examination. Study guides are prohibited on the final exam according to math department policy.

Grading Structure – Instructors must explicitly state their grading policy on their syllabus. 3 hour in class tests, together 50-60% Final exam 30% Attendance 0-5% Other (homework, groupwork, quizzes, etc.) 5–25%