ModelCourses/DevelopmentalMath

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Mary Shepherd, Kerry Odjakian, Spyros ..

General Description

These objectives are based on a course redesign developed at Northwest Missouri State University. The book used is Elementary and Intermediate Algebra by Bittinger, Ellenbogen and Johnson. The course is designed in 10 modules with each module broken into several sections. The learning objectives are given for each section. The material in each module was based on the CCSS as given in about 2010-11. Although nearly all objectives are “calculational”, conceptual questions for each objective should be included.

Problem Sets

Description of Problem Sets

Chapter 1: Real Numbers

• Set 1.1 Commutative-Associative-Distributive-Laws
  Students will be able to:

1. Use the commutative laws of addition and multiplication
2. Use the associative laws of addition and multiplication
3. Use the commutative and associative laws together
4. Use the distributive law to multiply
5. Use the distributive law to factor
6. List the terms and factors in simple algebraic expressions
7. Identify and combine like terms

• Set 1.2: Fractions
  Students will be able to:

1. Write the prime factorization of a number
2. Identify a number as prime, composite, or neither
3. Determine the least common multiple (LCM) of a set of integers
4. Simplify fractions
5. Multiply fractions and simplify
6. Divide fractions and simplify
7. Add fractions and simplify
8. Subtract fractions and simplify
9. Add, subtract, multiply and divide, proper, improper and mixed fractions
10. Word problems and coceptual problems

• Set 1.3 Positive-and-Negative-Real-Numbers
  Students will be able to:

1. State which real number corresponds to a situation
2. Estimate the location of rational numbers on a number line
3. Write decimal notation for fractions*
4. Classify real numbers
5. Use inequalities with real numbers*
6. Work with absolute value*

• 1.4 Addition-of-Real-Numbers (whole, decimal and fraction)
  Students will be able to:

1. Add signed numbers on a number line
2. Add signed numbers without a number line*
3. Combine like terms*
4. Solve word problems involving adding of signed numbers
5. Solve word problems involving perimeter*

• Set 1.5 Subtraction-of-Real-Numbers
  Students will be able to:

1. Find additive inverse of a number
2. Translate subtraction problem into words
3. Translate a phrase (with difference or subtract) into symbols and simplify
4. Subtract real numbers
5. Add and subtract series of numbers
6. Identify and combine like terms
7. Solve word problems involving adding and subtraction

• Set 1.6 Multiplication-and-Division-of-Real-Numbers
  Students will be able to:

1. Multiply real numbers
2. Divide real numbers (if possible)
3. Write equivalent forms of signed fractions
4. Perform operations on mixed fractions
5. Find reciprocal/multiplicative inverse of a number
6. Perform mixed operations on signed fractions

• Set 1.7 Exponential-Notation-and-Order-of-Operations
  Students will be able to:

1. Write in exponential notation*
2. Simplify numbers written in exponential notation*
3. Use the order of operations on signed numbers*
4. Evaluate expressions at a specific real number*
5. Simplify expressions by removing parentheses*

• Set 1.8 Applications-with-Percent
  Students will be able to:

1. Convert between decimal and percent notation*
2. Solve simple word problems involving percents*

Chapter 2: Solving and Graphing Linear Equations

• Set 2.1 Introduction-to-Algebra
  Students will be able to:

1. Evaluate algebraic expressions*
2. Translate phrases to algebraic expressions
3. Determine whether the given number is a solution of the given expressions
4. Translate word problems to equations

• Set 2.2 Solving-Linear-Equations
  Students will be able to:

1. Solve equations using the addition principle
2. Solve equations using the multiplication principle
3. Select the correct approach by identifying the operation to perform to an equation to isolate variable in a simple linear equation

• Set 2.3 Using-Addition-Multiplication-Principles-Together (to solve simple linear equations)
  Students will be able to:

1. Solve equations using the multiplication and addition principles
2. Combining like terms to solve equations
3. Clear fractions and decimals in equations

• Set 2.4 Formulas
  Students will be able to:

1. Evaluate formulas
2. Solve formulas for a variable

• Set 2.5 Read-Graphs-Plot-Points-Scaling-Graphs
  Students will be able to:

1. Solve problems with bar, circle and line graphs*
2. Plot ordered pairs*
3. Number (and scale) axes appropriately
4. Identify quadrants

• Set 2.6 Graphing-Linear-Equations
  Students will be able to:

1. Determine whether an ordered pair is a solution to an equation
2. Graph linear equations
3. From a word problem graph a linear equation and solve a problem

• Set 2.7 Graphing-and-Intercepts
  Students will be able to:

1. Find x- and y-intercepts of a graph
2. List coordinates of x- and y-intercepts
3. Graph linear equations using intercepts
4. Graph horizontal and vertical lines
5. Write the equation of a horizontal or vertical line

• Set 2.8 Rates-of-Change
  Students will be able to:

1. Solve word problems about rates
2. Draw graphs showing rates
3. Find rates from graphs

• Set 2.9 Slope
  Students will be able to:

1. Find slope from a graph
2. Use 2 points to find slope
3. Find slopes of vertical and horizontal lines
4. Solve word problems involving slopes and linear graphs

• Set 2.10 Slope-Intercept-Form
  Students will be able to:

1. Use y-intercept and slope to graph a line
2. Find slope and y-intercept from a linear equation
3. Write an equation in slope-intercept form given the slope and y-intercept
4. Write an equation in slope-intercept form from a graph
5. Graph an equation given in slope-intercept form
6. Write the slope-intercept equation given a description of the graph
7. Determine whether a pair of lines are parallel, perpendicular or neither

• Set 2.11 Point-Slope-Form
  Students will be able to:

1. Analyze equations in point-slope form
2. Write equations in point-slope form
3. Write a slope-intercept equation given a point and slope
4. Write equations of parallel lines
5. Graph lines given a point and slope
6. Graph lines given as a point-slope equation
7. Solve word problems involving points and slopes

Chapter 3: Solving and Graphing Linear Inequalities

• Set 3.1 Solving-Inequalities
  Students will be able to:

1. Determine whether a number is a solution of an inequality
2. Graph inequalities on a number line
3. Graph inequalities and write in set builder and interval notation
4. Solve inequalities using addition principle
5. Solve inequalities using multiplication property
6. Solve inequalities using both addition and multiplication property

• Set 3.2 Solving-Applications-with-Inequalities
  Students will be able to:

1. Translate words to linear inequalities
2. Solve linear inequality word problems

• Set 3.3 Inequalities-and-Domain
  Students will be able to:

1. Find domain of a radical expression/function
2. Solve inequalities graphically
3. Solve inequality word problems

• Set 3.4 Intersections-Unions-Compound-Inequalities
  Students will be able to:

1. Find intersection or union of sets
2. Graph and write in interval notation compound inequalities
3. Solve and graph compound inequalities
4. Find domain of a function/expression

• Set 3.5 Absolute-Value-Equations-and-Inequalities
  Students will be able to:

1. Solve equations with absolute value
2. Solve equations with two absolute values
3. Solve inequalities with absolute value

Chapter 4: Polynomials

• Set 4.1 Exponents-and-Properties
  Students will be able to:

1. Multiply powers with like bases
2. Divide powers with like bases
3. Use zero as an exponent
4. Raise a power to a power
5. Raise a product or quotient to a power

• Set 4.2 Negative-Exponents-Scientific-Notation
  Students will be able to:

1. Express using positive exponents
2. Express using negative exponents
3. Simplify expression with negative exponents
4. Convert between scientific and decimal notation
5. Calculate using scientific notation

• Set 4.3 Polynomials
  Students will be able to:

1. Identify terms of a polynomial
2. Determine the coefficients and degree of terms in a polynomial
3. Combine like terms
4. Evaluate polynomials
5. Solve word problems involving polynomials

• Set 4.4 Addition-Subtraction-Polynomials
  Students will be able to:

1. Add polynomials
2. Write equivalent expressions for opposites of polynomials
3. Subtract polynomials
4. Solve word problems involving adding/subtracting polynomials

• Set 4.5 Multiplication-of-Polynomials
  Students will be able to:

1. Multiply monomials
2. Multiply a monomial and a polynomial
3. Multiply two polynomials

• Set 4.6 Special-Products
  Students will be able to:

1. Multiply two binomials
2. Multiply sums and differences of two terms
3. Square binomials
4. Multiply various types of polynomials
5. Find areas of rectangles

• Set 4.7 Polynomials-Several-Variables
  Students will be able to:

1. Evaluate polynomials in several variables
2. Identify coefficients and degrees in polynomials of several variables
3. Combine like terms involving several variables
4. Add and subtract polynomials in several variables
5. Multiply polynomials in several variables
6. Use geometric figures to illustrate products

• Set 4.8 Polynomials
  Students will be able to:

1. Divide monomials
2. Divide polynomials

Chapter 5: Factoring

• Set 5.1 Introduction to Factoring
  Students will be able to:

1. Factor monomials
2. Factor when terms have a common factor
3. Factor by grouping

• Set 5.2 Factoring Trinomials: Lead Coefficient one
  Students will be able to:

1. Factor trinomials with leading coefficient of 1

• Set 5. 3 Factoring Trinomials: Lead Coefficient not one
  Students will be able to:

1. Factor trinomials with leading coefficient not equal 1
2. Factor by grouping
3. Factor completely

• Set 5.4 Factoring-Perfect-Square-Trinomials-Differences-of-Squares
  Students will be able to:

1. Recognize perfect-square trinomials
2. Factor perfect-square trinomials
3. Recognize difference of squares
4. Factor difference of squares
5. Factor completely

• Set 5.5 Factoring-Sums-Differences-of-Cubes
  Students will be able to:

1. Factor the sum of cubes
2. Factor the difference of cubes

• Set 5.6 Factoring-General-Strategy
  Students will be able to:

1. Factor using all factoring tools

• Set 5.7 Solving-Polynomial-Equations-by-Factoring
  Students will be able to:

1. Use the principle of zero products
2. Factor and solve equations using the principle of zero products
3. Use graphs to solve polynomial equations

• Set 5.8 Solving-Applications
  Students will be able to:

1. Solve work problems involving quadratic equations

Chapter 6: Rational Expressions and Equations

• Set 6.1 Rational-Expressions
  Students will be able to:

1. List numbers for which rational expressions are undefined
2. Simplify rational expressions by removing a factor equal to 1
3. Simplify rational expressions with opposite factors

• Set 6.2 Multiplication-Division
  Students will be able to:

1. Multiply rational expressions
2. Multiply rational expressions and simplify if possible
3. Find reciprocals of rational expressions
4. Divide rational expressions and simplify

• Set 6.3 Addition-Subtraction-LCD
  Students will be able to:

1. Add or subtract rational expressions with like denominators
2. Find LCM
3. Find equivalent expressions that have the LCD

• Set 6.4 Addition-Subtraction-Unlike-Denominators
  Students will be able to:

1. Add or subtract rational expressions with different denominators and simplify

• Set 6.5 Complex-Rational-Expressions
  Students will be able to:

1. Simplify complex rational expressions

• Set 6.6 Solving-Rational-Equations
  Students will be able to:

1. Solve rational equations

• Set 6.7 Applications-Rational-Equations-Proportions
  Students will be able to:

1. Solve word problems involving work
2. Solve word problems involving motion
3. Solve word problems involving proportions

Chapter 7: Systems of Equations and Inequalities

• Set 7.1 Systems-Equations-2-Variables
  Students will be able to:

1. Translate problems to systems of linear equations
2. Determine whether an ordered pair is a solution to a given system
3. Solve systems of equations graphically

• Set 7.2 Solving-Substitution-or-Elimination
  Students will be able to:

1. Solve systems of equations using substitution
2. Solve systems of equations using elimination
3. Solve systems of equations using an appropriate method

• Set 7.3 Applications-Systems-Two-Equations
  Students will be able to:

1. Solve word problems using systems of two equations
2. Solve word problems involving mixture
3. Solve word problems involving investments
4. Solve word problems involving geometric figures

• Set 7.4 Business-Economics-Applications
  Students will be able to:

1. Find the total profit function
2. Find the break even point
3. Find the equilibrium point

• Set 7.5 Inequalities-in-Two-Variables
  Students will be able to:

1. Determine whether an ordered pair is a solution of a system of inequalities
2. Graph linear inequalities
3. Graph systems of linear inequalities