Quantitative Reasoning or Liberal Arts Math, 1st edition

Module 1:  Number Arithmetic

1.1 Fractions

1. Simplify fractions.  
2. Plot fractions on a number line.
3. Add or subtract like fractions. 
4. Find the least common denominator of a list of fractions.
5. Write equivalent fractions
6. Compare fractions.
7. Add or subtract unlike fractions. 
8. Multiply or divide fractions. 
9. Evaluate exponential expressions with fractional bases.
10. Use the order of operations on fractions. 
11. Solve applications involving fractions. 

 

1.2 Decimals

1. Identify place values of decimals. 
2. Compare decimals.
3. Add or subtract decimals. 
4. Multiply or divide decimals. 
5. Evaluate exponential expressions with decimal bases.
6. Use the order of operations on decimals. 
7. Round decimals. 
8. Solve problems involving estimation with decimals.
9. Convert decimals to fractions.
10. Convert fractions to decimals.
11. Solve applications involving decimals. 

 

1.3 Percents

1. Interpret the meaning of percent.
2. Write fractions as percents. 
3. Write percents as fractions in simplest form. 
4. Write decimals as percents. 
5. Write percents as decimals. 

6.     Convert among fractions, decimals, and percents. 

7.     Perform calculations involving percents. 

8.     Compute percent change.

9.     Solve applications involving percents. 

 

1.4 Ratios and Rates

1. Write ratios in different notations, including fractions. 
2. Simplify ratios.
3. Determine unit rates. 
4. Determine the better buy. 

 

1.5 Proportions 

1. Solve proportions.
2. Solve applications involving proportions. 

 

1.6 Measurement

1. Identify U.S. units of length, weight, and capacity.
2. Perform unit conversions among U.S. units (including mixed units).
3. Identify metric units of length, mass, and capacity.
4. Perform unit conversions among metric units.
5. Convert between U.S. and metric units.
6. Solve applications involving units of measurement.

 

1.7 Real Numbers

1. Classify sets of numbers. 
2. Find square roots.  
3. Approximate square roots. 
4. Use the properties of real numbers. 
5. Use the order of operations with real

  6. Solve applications involving real numbers. 

 

Module 2: Linear Equations and Inequalities; Formulas

2.1 Algebraic Expressions

1. Evaluate algebraic expressions. 
2. Combine like terms.
3. Simplify algebraic expressions.
4. Translate English phrases into algebraic expressions.

 

2.2 Linear Equations in One Variable

1. Distinguish between expressions and equations.
2. Solve linear equations in one variable using the addition property of equality.
3. Solve linear equations in one variable using the multiplication property of equality.
4. Solve linear equations in one variable using both properties of equality. 
5. Translate sentences into equations.
6. Solve applications involving linear equations in one variable.

 

2.3 Linear Inequalities in One Variable

1. Write inequality statements using real numbers and inequality symbols.
2. Graph linear inequalities in one variable on a number line.
3. Write solutions to inequalities in set-builder notation.
4. Write solutions to inequalities in interval notation.
5. Solve linear inequalities in one variable.
6. Translate sentences into linear inequalities in one variable.
7. Solve applications involving linear inequalities in one variable.

 

2.4 Formulas

1. Solve a formula for a specific variable. 
2. Find the perimeter of a figure.
3. Find the circumference of a circle.
4. Find the area of a figure.
5. Find the volume of a figure.
6. Solve applications involving distance, rate, and time.

 

Module 3: Graphing Linear Equations in Two Variables

3.1 The Rectangular Coordinate System

1.     Write ordered pairs.

2.     Plot points in the rectangular coordinate system.

3.     Complete a table of values of ordered pair solutions for a linear equation in two variables.

4.     Graph linear equations in two variables using a table of values.

 

3.2 Intercepts

1. Find the intercepts of a line.
2. Graph a linear equation in two variables given its intercepts.

 

3.3  Slope

1. Find the slope of a line given two points on the line.
2. Find the slope of a line given its graph.
3. Graph a line given its equation in slope-intercept form.
4. Graph a line given one point on the line and the slope.
5. Graph vertical lines.
6. Graph horizontal lines.
7. Use slope with parallel and perpendicular lines.
8. Interpret slope as a rate of change.

 

3.4 Equations of Lines

1. Find the slope of a line given its equation.
2. Write the slope-intercept form of a line. 
3. Write the equation of a line given the slope and a point on the line. 
4. Write the equation of a line through two given points.
   
   

Module 4:  Exponents, Polynomials, and Quadratic Models

4.1 Exponential Expressions and Rules for Exponents

1. Evaluate exponential expressions with positive exponents.
2. Use the product rule for exponents.
3. Use the power rules for exponents.
4. Use the quotient rule for exponents.
5. Evaluate exponential expressions with integer exponents.
6. Simplify exponential expressions using the rules for exponents. 

 

4.2 Scientific Notation

1. Convert between scientific and standard notation.
2. Perform calculations involving scientific notation.
3. Solve applications involving scientific notation. 

 

4.3 Polynomial Expressions

1. Identify parts of a polynomial (coefficient, term, degree, factor, constant).
2. Classify polynomials.
3. Evaluate polynomial expressions. 
4. Add polynomials. 
5. Subtract polynomials.
6. Multiply monomials.
7. Multiply a monomial and a polynomial.
8. Multiply polynomials.
9. Multiply the sum and difference of two terms.
10. Square binomials.

 

4.4 Factoring

1. Factor out the GCF of a polynomial. 
2. Factor trinomials with a leading coefficient of 1. 
3. Factor trinomials with a leading coefficient other than 1. 
4. Factor polynomials by grouping.
5. Factor a difference of squares.
6. Factor the sum or difference of two cubes.
7. Factor polynomials completely.

 

4.5 Quadratic Equations and Models

1. Solve quadratic equations by factoring.
2. Solve quadratic equations by the square root property. 
3. Solve quadratic equations by completing the square. 
4. Solve quadratic equations by using the quadratic formula. 

5.     Distinguish between linear and quadratic models in real world situations.

6.     Solve applications involving quadratic equations and models. 

 

Module 5:  Financial Math

5.1 Percent Applications:  Sales Tax, Commission, Discount

1. Calculate sales tax, total price, and sale price.
2. Calculate commission.
3. Calculate tips.
4. Calculate original price, discount, total cost, tax, and markup.

 

5.2 Simple Interest

1. Compute simple interest.
2. Find principal, interest rate, or time in the simple interest formula.
3. Solve applications involving simple interest.

 

5.3 Compound Interest

1. Compute compound interest.
2. Find principal, interest rate, or time in the compound interest formula.
3. Solve applications involving compound interest.

 

Module 6:  Introduction to Functions

6.1 Relations and Functions

1. Identify relations and functions. 
2. Evaluate functions using function notation. 
3. Find the domain and range of a function.
4. Use the vertical line test to determine if a graph is a function.

 

6.2 Linear Functions

1. Identify linear functions. 
2. Evaluate linear functions. 
3. Interpret the graph of a linear function (domain, range, slope, intercepts).
4. Solve applications that involve linear functions as models.
   
   

Module 7: Introduction to Statistics

7.1 Data Displays 

       1. Interpret and draw line graphs. 

       2. Interpret and draw bar graphs. 

       3. Construct frequency distributions and relative frequency distributions for a data set. 

       4. Interpret and draw histograms. 

       5. Interpret and draw circle graphs.

       6. Interpret and build scatterplots. 

 

7.2 Measures of Center 

1. Find the mean of a data set. 
2. Find the weighted mean. 
3. Find the median of a data set. 
4. Find the mode of a data set. 
5. Find the range and midrange of a data set. 

 

Module 8:  Introduction to Probability

8.1 Counting Techniques 

1. Evaluate factorial expressions. 
2. Use counting techniques. 

8.2 Introduction to Probability 

1. Identify sample spaces, outcomes, and events. 
2. Find the probability of an event.
3. Use tree diagrams to find sample spaces and compute probabilities. 
   
   

Module 9:  Sets and Logic

9.1 Sets

1. Define terminology associated with sets.
2. Describe the members of a set using various notations.
3. Find subsets of a set.
4. Find equivalent sets.
5. Find the union of two sets. 
6. Find the intersection of two sets. 
7. Find the complement of a set. 

 

9.2 Reasoning, Arguments, and Statements

1. Distinguish between inductive and deductive reasoning.
2. Distinguish between valid and invalid arguments.

       3.    Identify types of statements.