Quantitative Reasoning
Instructor Table of Contents
Before the Semester Begins: Suggestions for Prep & Syllabus
Student Course
Pack Pages
Overview
Practice
Assignment
Lesson Title and Description
Instructor
Notes Pages
Preview
Assignment
Lesson
Table of Contents
p. xv
-
-
p. xxxi
-
-
p. 1
-
p. 1
p. 9
-
p. 5
p. 19
1.C
p. 7
p. 27
1.D
p. 11
p. 35
2.A
p. 13
p. 43
-
p. 15
p. 51
-
p. 17
Complex Numerical Summaries; Graphical Displays
1.A
-
Data for Life
Collect data that will be referred to throughout the
semester; supplemental spreadsheet provided
Our Learning Community
1.B
-
1.C
1.C
1.D
-
2.A
2.A
Student success focus
Establish a sense of shared responsibility; provide key
information about course content and policies
Instant Runoff
Voting schemes
Borda Count
Voting schemes
Graphical Displays
Analysis and communication; dotplots, histograms,
boxplots; mean; median
Forming Effective Study Groups
2.B
2.B
2.C
-
Student success focus
Taking responsibility for own learning and supporting
learning of others; setting norms
Mini-Project: Graphical Displays
Write formal, contextual analysis on compared data;
research-related data; sample rubric provided
The Charles A. Dana Center at
The University of Texas at Austin
Instructor Table of Contents – page vii
Practice
Assignment
Student Course
Pack Pages
3.A
p. 19
p. 67
3.B
p. 21
p. 73
3.C
p. 23
p. 83
4.A
p. 27
p. 91
4.B
p. 31
p. 101
5.A
p. 35
p. 109
5.B
p. 37
p. 117
5.C
p. 39
p. 125
5.D
p. 131
6.A
Preview
Assignment
p. 57
Lesson
Lesson Title and Description
Instructor
Notes Pages
Quantitative Reasoning
Instructor Table of Contents
3.A
3.A
Who Is in the Population?
3.B
3.B
How Much Water Do I Drink?
3.C
3.C
How Much Water Does Our Class Drink?
(Optional)
Populations; sampling
Analyzing class data; Central Limit Theorem
Sample standard deviation
4.A
4.A
4.B
4.B
5.A
5.A
5.B
5.B
5.C
5.C
5.D
5.D
6.A
6.A
Theoretical probability of two or more independent
events
Calculating Risk
Conditional probability of two or more dependent
events
Cost of Living Comparisons
Conversion to create equivalent units; supplemental
spreadsheet
Index Numbers
Using indices such as Consumer Price Index;
supplemental spreadsheet
Polls, Polls, Polls!
Weighted averages
Average Income
Weighted averages and expected value; supplemental
spreadsheet
How Can We Smooth the Data? (Optional)
Simple and weighted moving averages; supplemental
spreadsheet
Mini-Project: Income Disparities (Optional)
6.B
7.A
What Are the Risks?
Written analysis of graphical display of weighted
moving average
7.A
U.S. Budget Priorities
Part-part vs. part-whole ratios
The Charles A. Dana Center at
The University of Texas at Austin
Instructor Table of Contents – page viii
p. 139
p. 149
p. 43
p. 45
p. 47
7.A
p. 49
Practice
Assignment
Student Course
Pack Pages
7.B
p. 53
p. 167
7.C
p. 175
7.D
p. 59
p. 183
7.E
p. 61
p. 193
7.F
p. 65
p. 203
8.A
p. 67
p. 215
8.B
p. 71
p. 223
8.C
p. 73
p. 235
8.D
p. 77
Preview
Assignment
p. 157
Lesson
Lesson Title and Description
Instructor
Notes Pages
Quantitative Reasoning
Instructor Table of Contents
7.B
7.B
Understanding U.S. Budget Priorities
7.C
7.C
Changes to U.S. Budget Priorities
7.D
7.D
Percent of Total U.S. Budget
Decimals, percentages, and part-whole ratios
Absolute and relative change
Dotplots used to introduce symmetry and skewness
p. 57
What’s My Credit Score?
7.E
7.E
7.F
7.F
Application of ratios; Practice assignment can be miniproject. Collect data for Lesson 8, Part D; schedule
lab for 8.D and 10.A.
U.S. Incarceration Rates
Applications of ratios; comparison
Mathematical Modeling
8.A
8.A
More Water, Please!
8.B
8.B
What’s My Car Worth?
8.C
8.C
How Money Makes Money
8.D
8.D
8.E
8.E
Introduction to mathematical modeling
Distinguishing proportionality and linearity
Non-linear models
Have My Choices Affected My Learning?
Regression using student data. Computer lab day, if
possible.
Mini-Project: Progressive and Flat Income
Tax Systems (Optional)
p. 245
p. 81
p. 259
p. 87
Informal piecewise linear function
8.F
8.F
Mini-Project: Estimating the Number of
People in a Crowd (Optional)
Using proportionality to estimate
9.A
9.A
Depreciation
Modeling, interpolation, and extrapolation
The Charles A. Dana Center at
The University of Texas at Austin
Instructor Table of Contents – page ix
p. 271
9.A
p. 91
Practice
Assignment
Student Course
Pack Pages
9.B
p. 97
p. 293
9.C
p. 101
p. 305
9.D
p. 107
p. 315
10.A
p. 111
Preview
Assignment
p. 283
Lesson
Lesson Title and Description
Instructor
Notes Pages
Quantitative Reasoning
Instructor Table of Contents
9.B
9.B
Appreciating Depreciation
9.C
9.C
How Much Should I Be Paid?
9.D
9.D
Why Are You Wearing the Same Old Socks?
10.A
10.A
10.B
10.B
Linear interpolation via similar triangles
Correlation
Correlation vs. causation; strength
Fibonacci’s Rabbits
Exponential growth; limitations. Computer lab day, if
possible.
Is It Getting Crowded?
Exponential growth; limitations
p. 323
p. 113
You may wish to consider various configurations with the upcoming modeling lessons.
For example, you may wish to consider having different groups complete and present
the various logistic lessons or having some groups do logistic models while other groups
do the periodic models. You may also choose to omit either logistic or periodic models.
11.A
11.A
Oh, Deer! (Optional)
11.B
11.B
Population Growth (Optional)
11.C
11.C
11.D
11.D
Hares and Lynxes (Optional)
11.E
11.E
Reindeer and Lichens (Optional)
12.A
12.A
How Long Is the Longest Day? (Optional)
12.B
12.B
What’s My Sine? (Optional)
Logistic models
Time series model of logistic growth
Can You Hear Me Now? (Optional)
Logistic models. Spreadsheet demonstration or
computer lab day, if possible.
Predator-prey
Effects of parameter choices on model predictions
Cyclical data
Periodic functions
The Charles A. Dana Center at
The University of Texas at Austin
Instructor Table of Contents – page x
The Charles A. Dana Center at
p. 331
11.A
p. 115
p. 341
11.B
p. 119
p. 351
11.C
p. 121
p. 359
11.D
p. 125
p. 369
11.E
p. 129
p. 377
12.A
p. 131
p. 389
12.B
p. 135
12.C
SIR Disease (Optional)
Effect of parameters on a model (epidemics)
SIR (Continued) (Optional)
12.D
Create a time-series model using a spreadsheet;
Practice assignment could be a mini-project.
Student Course
Pack Pages
12.C
Practice
Assignment
Preview
Assignment
Lesson Title and Description
Instructor
Notes Pages
Lesson
Quantitative Reasoning
Instructor Table of Contents
p. 397
12.C
p. 139
p. 407
p. 143
Statistical Studies
Mind the Gap in Income Inequality
13.A
13.A
13.B
13.B
13.C
13.C
A Lesson Worth Weighting For
13.D
13.D
Weight . . . There’s More!
14.A
14.A
Blood Pressure and Bias
14.B
14.B
Taking Aim at Bias
14.C
14.C
Conclusions in Observational Studies
15.A
15.A
The Video Game Diet
15.B
15.B
All Things in Moderation
15.C
15.C
The Power of the Pill
15.D
15.D
Designing an Experiment
Introductory vocabulary for statistical studies
When in Rome . . .
Observational and experimental studies and their
conclusions
Sampling processes
Evaluate and design sampling processes
Sampling and non-sampling error
Types of bias
Minimizing bias; appropriate conclusions
Designing experimental studies; cause and effect
Confounding variables
Blinding; placebo effect; placebos
Double blinding; blocking
The Charles A. Dana Center at
The University of Texas at Austin
Instructor Table of Contents – page xi
p. 415
13.A
p. 145
p. 427
13.B
p. 149
p. 437
13.C
p. 151
p. 451
13.D
p. 155
p. 463
14.A
p. 159
p. 471
14.B
p. 163
p. 479
14.C
p. 167
p. 489
15.A
p. 169
p. 497
15.B
p. 171
p. 507
15.C
p. 175
p. 515
15.D
p. 179
Quantitative Reasoning
Instructor Table of Contents
15.E
15.E
In Conclusion
Culminating lesson on conclusions from statistical
studies
p. 527
15.E
p. 183
Complex Quantitative Information and Graphical Displays
You may wish to consider various configurations with the upcoming lessons on
analyzing and writing about graphical displays. For example, you may wish to consider
having different groups complete Lesson 16, Parts B, D, E, and F, and present to the
class.
16.A
16.A
Education Pays
16.B
16.B
Looking for Links
16.C
16.C
It’s About Time!
16.D
16.D
Connecting the Dots
16.E
16.E
Big Data (GIS)
16.F
16.F
Big Brother – They’re Watching
17.A
17.A
17.B
17.B
The Write Approach to Data
17.C
17.C
Numbers Never Lie
17.D
17.D
Can You Feel the Heat?
Analyzing stacked column graphs
Analyzing comparative stacked columns graphs
Building stacked columns graphs from class data
Analyzing motion bubble charts
Analysis problems associated with large, volatile data
Conclusions from heat maps
Decisions, Decisions
Decision making based on multiple pieces of
quantitative information
16.A
16.B
16.C
16.D
16.E
16.F
17.A
Improving written analyses of graphical displays
Misleading and erroneous graphical displays
Using data to understand complex issues
17.C
17.D
Mini-Project: Tornado Climatology
18.A
Choosing appropriate ways to represent data
18.B
18.B
What’s Your Top Ten?
18.C
18.C
What a Wonderful World
Various ways to present mathematical models
Using multiple representations to choose a model
The Charles A. Dana Center at
The University of Texas at Austin
Instructor Table of Contents – page xii
18.B
18.C
Quantitative Reasoning
Instructor Table of Contents
18.D
18.D
Mathematical Models
Limitations of models
18.D
More from Probability and Statistics
19.A
19.A
How Does Amazon Know What You Want?
19.B
19.B
Applications of Probability
19.C
19.C
Heads I Win, Tails You Lose
19.D
19.D
A Little Math is a Dangerous Thing
20.A
20.A
Six Sigma (Optional)
20.B
20.B
20.C
20.C
More Normal
20.D
20.D
Technology and the Normal Curve
(Optional)
21.A
21.A
Poincare’s Bread
21.B
21.B
Loads of Loaves
21.C
21.C
Expressing Confidence
21.D
21.D
Adjusting Confidences
21.E
21.E
Paths to Victory
Probability and the area under a curve
Probability and histograms
Random variables
Probability distribution functions
Using statistics for quality control
That’s Normal
How changes in mean or standard deviation affect
the normal curve
The Empirical Rule
Using technology to find probabilities of events that
are normally distributed
Using a sample mean to estimate a population mean
Applying the Central Limit Theorem
Introduction to confidence intervals
Margin of error
Poll results and levels of confidence
The Charles A. Dana Center at
The University of Texas at Austin
Instructor Table of Contents – page xiii
19.A
19.B
19.C
19.D
20.A
20.B
20.C
20.D
21.A
21.B
21.C
21.D
21.E
Quantitative Reasoning
Instructor Table of Contents
The Charles A. Dana Center at
The University of Texas at Austin
Instructor Table of Contents – page xiv