Chapter 1

1.1     Functions     (2-3 days)

This important concept is the foundation for many concepts in the book. It is especially important to emphasize that there are four ways to examine a problem: verbally (a description); symbolically (with numbers and letters); graphically (with a statistical graph, a scatter plot or a line graph); or numerically (with numbers). Other important concepts include scaling the axes and functional notation. The experiment on page 10 will help get the class involved and working in groups. A presentation by the groups could be beneficial.

1.2 & 1.3     Models & Investigating the Models     (5-10 days)

The amount of time spent on this section depends on the level of experience of your students. One way to approach this section is to cover A (Tax Rate Table) and save the others for later. A again emphasizes the different ways of analyzing a problem. The basic skills can also be reviewed when covering A. Additional work for each of these problems is in Section 1.3. You can pick and choose from the other problems. You can assign the problems to groups in the class and have the groups explain the problem and pre-requisite skills to the rest of the class. I think it is important not to "lecture" or "tell" the class about these problems. Most of this material has been seen (or heard) before. By assigning the problems to groups (or to individuals), you put the burden of understanding on the students.

Optional Activity: Calculator

Chapter 2     (2-3 days)

This chapter can be covered in sequence, or covered in bits and pieces as the time presents itself. If covered in sequence, it would probably mean more group work. Or one activity could be covered at a time, like at the beginning or end of each week. The work with proportions is important.

Optional Activity: A Simulation

Chapter 3     (5-7 days)

3.1     Sampling

This is an important section to discuss with the class. The ideas of population, sample, bias, random selection, ... must be clearly understood. Try some different ways to assess the class' understanding of the topics. Have them write about a topic and read selected paragraphs, or do a "plus/delta" analysis that allows the students to tell you what they did or didn't understand.

3.2     Describing Data

Use technology to present this material. Either bring the spreadsheet into the class, have the class in a lab, or use powerpoint to display your results. (prepared slides will also work) The dice problem (1C) is important for later chapters.

3.3 & 3.4     Experiments

These experiments are designed to help students understand variability and error, bias, and samples and populations. The amount of time spent on these can vary.

Optional Activity: Ratio and Proportion

3.5     Line Graphs

The important idea is that line graphs show a trend in the data. Trends are important in many applications. Scatter plots may be used (over line graphs) when there may be several y-values for any x-value. They too show a trend. The ability to find a maximum or minimum from a line graph or a table is important. Also discuss how the rate of change of y with respect to x appears on a graph and in a table. X-bar charts are important and can be introduced here.

3.6     Using Technology

The student should use technology to build these graphics. Students should be familiar with spreadsheets, but may need help with their initial endeavors with graphics. The amount of time spent on this section is dependent upon the background of the student and the computer resources of the college. If you have been using technology in your presentations on histograms, pie charts and line graphs, this section should be a breeze.

Chapter 4     (8-10 days)

4.1     Relations and Functions

Using functional notation helps build the concept of dependence, one variable upon another. Helping the student to understand and use the notation f(x) is crucial. Discuss continuous and discrete functions.

Optional Activity: Numerical Study of Functions

Review

Some students may need to review the basic concepts of signed numbers and rearranging equations before going on.

4.2     Linear Functions-The Slope

The slope is stressed as being a rate of change. The rate that y changes is dependent upon the coefficient of x.

4.3     Linear Functions-Intercepts and Applications

The slope and intercepts are covered here in the context of meaningful applications. The slope is again stressed as a rate of change. Having the student write down the answers to #4 is important. You may even assign the student to write problems like these.

Optional Activity: Kanban I

4.4     Linear Functions-Finding the Equation

This section is crucial. Being able to find the equation of a line given a set of parameters demands that the student possess a good understanding of dependent and independent variable, what a solution is, and what slope means.

4.5     More on Linear Functions-Applications and Models

This is the important conclusion to this work with linear functions-being able to use them to make models for physical situations.

4.6     Other Functions

It is also important for the student to realize that not all phenomenon can be modeled with linear functions. So, this section includes several non-linear functions. Again, use the spreadsheet in class to build tables of values for these functions.

4.7 Spreadsheets

If you have been using spreadsheets in class and the student for homework, this section will be a simple review.

Chapter 5     (5-6 days)

5.1     Measures of Central Tendency

The basic concepts of mean, median and mode are covered in this section.

5.2     Standard Deviation

Students should learn to perform the necessary calculations "by hand" before using technology. They should understand how the standard deviation normalizes data, in that the standard deviation shows the relative position of the data to the mean. Having students do #2 (p 156) together (the day after the homework is assigned) can be beneficial. Use a spreadsheet to investigate the possibilities with a different data set. Sections 1 and 2 can be covered together.

5.3     Box-and-whisker plots

These are useful to make nice pictures of the data but also provide a context for the discussion of quartiles and then z-scores.

5.4     Linear Models of Best Fit

After you complete the chart on page 166, have the students complete the others in groups and share information. Don't tell them the answers to questions 1, 2 and 3 on page 166. That should be a good discussion.

Optional Activity: Kanban II

5.5     Help! Using Spreadsheets for Lines of Best Fit

After performing the calculations necessary to complete the tables, students should have sufficient motivation to learn more about using spreadsheets to do linear regression. Lotus and Quattro have built-in regression analysis while Excel has a Slope Formula, an Intercept Formula, and others related to regression that must be done separately.

Chapter 6     (9-11 days)

6.1     Systems of Linear Equations

This section introduces the topic. It is important that students understand when a solution is approximate or exact and can use graphs and tables to find solutions.

6.2     Solving Systems of Linear Equations-Algebraic Procedures

Students should be able to use either the substitution or elimination procedure to solve a system. It is important that they be able to build models from an applications and solve the resulting system.

6.3     Multiple Approaches to Systems of Linear Equations

The concept behind numerical investigations of systems of equations is very useful. Students should be able to visualize this concept and identify the proximity of solutions. Use a spreadsheet template to present this topic that allows the initial value and increment to be changed easily.

6.4     Matrices - An Introduction

The idea that data is organized into rows and columns in important. Therefore, matrices can be an important tool. Students should be able to perform matrix operations by hand before using technology. Use technology, though, when the necessary calculations become too tedious.

6.5     Matrices and Their Inverse

Using matrices to solve systems should be motivation for the study of the previous sections. In fact, you may want to show that this can be done before discussing 6.4.

6.6     Linear Programming-Inequalities

This section provides the tools that students will need to solve linear programming problems. To be able to graph inequalities, select the correct corner points, and use the correct equations to find the corner points is an involved process for students. Be sure and provide examples where your work is clearly marked and labeled and organized. The latter feature is one that is often lacking in students-and one that we have to help build.

6.7     Linear Programming-Introduction

This section introduces the student to LP problems. Working through a problem with "random" solutions provides time for the student to digest this complicated process. Group work should provide time for them to find additional feasible solutions and consider why one solution yields more profit than another. This is time well spent. Problems 2 and 3 (p 266) have three variables, but can still be used in this section. A similar problem is assigned in the next section, but with only two variables.

6.8 & 6.9     Linear Programming

These sections use many of the skills the students have mastered so far in the course. Many students view these problems as fun and wonder why they have never used math like this before. It is important that students define the variables to the problem initially before building a table or writing constraints.

Chapter 7     (3-5 days)

7.1     Introduction to Probability

The basics of probability. Problem 7 (p 246) should set the stage for the next section.

7.2     Area and Probability-Introducing the Normal Curve

This section establishes the connection between histograms, the area under a curve and probability. Students should perform an exercise like the one on page 251.

7.3     The Normal Curve, An Application of Probability

This section builds on the last section and provides the essentials for work with problems with normal distributions.

Optional Activity: Making the Cuts Count

Chapter 8     (4-7 days)

8.1     The Exponential Function

This section investigates the exponential function graphically and numerically using compound interest as the application. Other models are shown and students will need to be able to evaluate them with certain values.

8.2     The Logarithmic Function

The logarithmic function is presented as a necessary tool to solve exponential functions. This section investigates this function numerically and graphically. The log function is also used to linearize (or re-express) data.

8.3     Applications of the Exponential and Logarithmic Functions

Applications that involve the exponential and logarithmic functions require the student to exercise their skills with these functions.