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