ModelCourses/DevelopmentalMath

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Mary Shepherd, Kerry Odjakian, Spyros ..

Contents

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.

Course Objectives

Problem Sets

Use of Problem Sets

Download the 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
  • 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

Chapter 8: Radical Expressions and Equations

  • Set 8.1 Radical-Expressions-Functions
    Students will be able to:
  1. Find square roots
  2. Identify the radicand and index of a radical expression
  3. Evaluate expressions involving square roots
  4. Simplify radical expressions
  5. Evaluate expressions involving nth root expressions
  6. Determine the domain of radical expressions
  • Set 8.2 Rational-Numbers-as-Exponents
    Students will be able to:
  1. Rewrite rational exponents using radical notation
  2. Rewrite radical exponents using rational notation
  3. Rewrite expressions using positive rational exponents
  4. Use laws of exponents to simplify
  5. Simplify radical expressions using rational exponents
  • Set 8.3 Multiplying-Radical-Expressions
    Students will be able to:
  1. Multiply radical expressions
  2. Simplify radical expressions by factoring
  3. Multiply and simplify radical expressions
  • Set 8.4 Dividing-Radical-Expressions
    Students will be able to:
  1. Divide and simplify radical expressions
  2. Rationalize denominators
  3. Rationalize numerators
  • Set 8.5 Expressions-with-Several-Radical-Terms
    Students will be able to:
  1. Add or subtract radical expressions
  2. Find product of two or more radical terms
  3. Rationalize denominators with two terms that contain radicals
  4. Rationalize numerators with two terms that contain radicals
  5. Multiply or divide radical expressions with different indices
  6. Evaluate expressions/functions at values containing radical expressions
  • Set 8.6 Solving-Radical-Equations
    Students will be able to:
  1. Solve radical equations using the principle of powers
  2. Solve radical equations with two radical terms
  3. Find the value of x when given a function of x containing radicals
  • Set 8.7 Distance-Midpoint-Formulas-Applications
    Students will be able to:
  1. Solve word problems involving radicals
  2. Use the Pythagorean Theorem
  3. Find missing lengths of special triangles
  4. Use distance formula
  5. Use midpoint formula


Chapter 9: Quadratic Equations

  • Set 9.1 Introduction-to-Functions
    Students will be able to:
  1. Determine whether a correspondence is a function
  2. Evaluate functions
  3. Find function values, domain and range from a graph
  4. Identify functions from a graph
  5. Solve word problems involving function language
  • Set 9.2 Domain-and-Range
    Students will be able to:
  1. Find domain and range of a function
  2. Find domain and range of a function from a graph
  3. Find the domain of a function
  4. Find the domain of functions in applied problems
  5. Find function values of a piecewise defined function
  • Set 9.3 Graphs-of-Functions
    Students will be able to:
  1. Graph linear functions
  2. Solve word problems by determining and using a linear function model
  3. Classify a function and find its domain
  4. Graph a function and find its domain and range
  • Set 9.4 Complex-Numbers
    Students will be able to:
  1. Rewrite expressions in terms of i
  2. Add or subtract complex numbers
  3. Multiply complex numbers
  4. Divide complex numbers using conjugates
  5. Simplify powers of i
  • Set 9.5 Quadratic-Equations
    Students will be able to:
  1. Solve quadratic equations using the principle of square roots
  2. Complete the square
  3. Solve quadratic equations by completing the square
  4. Find x-intercepts of graphs of quadratic functions
  5. Solve word problems involving quadratic equations
  • Set 9.6 The-Quadratic-Formula
    Students will be able to:
  1. Solve equations using the quadratic formula
  • Set 9.7 Quadratic-Functions-and-Graphs
    Students will be able to:
  1. Graph quadratic functions
  2. Find vertex of quadratic functions
  3. Find axis of symmetry of quadratic functions
  4. Find minimum or maximum values of quadratic functions
  • Set 9.8 More-Graphing-Quadratic-Functions
    Students will be able to:
  1. Complete the square to write a function as f(x)=a(x-h)^2+k
  2. Find vertex, axis of symmetry, min/max of a quadratic function and graph
  3. Find x- and y-intercepts

Chapter 10: Data Representation

  • Set 10.1 Data
    Students will be able to:
  1. Identify variables
  2. Identify the who, what and population
  3. Identify cases, variables and units
  • Set 10.2 Displaying and Describing Categorical Data
    Students will be able to:
  1. Create and analyze relative frequency distributions
  2. Determine if a display of data is appropriate
  3. Examine a contingency table
  4. Find conditional and marginal distributions
  • Set 10.3 Displaying and summarizing Quantitative Data
    Students will be able to:
  1. Describe features of a distribution (center, shape, spread)
  2. Find measures of center and spread
  3. Analyze and compare measures of center and spread
  4. Create a display of data and describe the distribution and unusual features
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