Statistics, 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 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 numbers (including grouping symbols). 
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 Compound Inequalities

1. Find the union of two sets. 
2. Find the intersection of two sets. 
3. Graph compound inequalities on a number line.
4. Solve compound inequalities and write the solution sets in set-builder and interval notation.

 

2.5 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 and Scientific Notation

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 with integer exponents

       6. Simplify exponential expressions using 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. 

 

Module 5:  Absolute Value Equations and Inequalities

5.1 Absolute Value Equations

1. Solve absolute value equations.
   
   

5.2 Absolute Value Inequalities

1. Solve absolute value inequalities.
2. Identify absolute value inequalities that are contradictions or identities.

 

Module 6: Introduction to Statistics

6.1 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. 
   
   

6.2 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. 

 

6.3 Linear Regression

1. Graph the best-fit line for a set of data. 
2. Use the equation of a best-fit line to predict values of x. 

Module 7:  Introduction to Probability

7.1 Counting Techniques 

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

7.2 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. 

 

7.3 Permutations and Combinations 

1. Calculate permutations. 
2. Calculate combinations. 
3. Solve applications involving permutations and combinations. 

7.4 Odds

1. Calculate odds in favor of and against an event. 
2. Use odds to determine if a game is fair.