TCMS
Transition to College Mathematics and Statistics
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TCMS Overview


Transition to College Mathematics and Statistics (TCMS) is a problem-based, technology-rich, fourth-year course developed to serve the large and diverse population of college-bound students whose intended program of study does not require calculus.

The content of the text, as summarized below, has been organized to permit different pathways through the units depending on the background and interests of the class. Possible alternative pathways are provided in the Teacher's Guide.

As indicated in the table of contents, each lesson of a unit is followed by a set of On Your Own tasks designed for student work outside of class.


Each On Your Own section includes a set of distributed review tasks that revisit previously learned mathematics essential for college readiness and to enable students to refine their skills in using that mathematics.

Additionally, the teaching support materials for the end of each lesson include a print and online 10-item College Readiness Assessment (CRA) that mirrors college placement tests common on most campuses today. The online CRA can be taken at any time by students and they are provided with immediate feedback on their strengths and weaknesses that need further attention.

Unit focus and key topics along with sample student and teacher material are available.
Transition to College Mathematics and Statistics
Table of Contents
1
Interpreting Categorical Data
Lesson 1 Comparing the Risk
 
Investigations
  1 Summarizing and Displaying the Risk
  2 Comparing Risk
  3 Design of Experiments
On Your Own
Lesson 2 A Test of Significance
 
Investigations
  1 Homogeneous Groups
  2 The Chi-Square Statistic
  3 Statistical Significance
On Your Own
Lesson 3 The Relationship Between Two Variables
 
Investigations
  1 Diagnostic Testing
  2 Independence
  3 The Chi-Square Test of Independence
On Your Own
Lesson 4 Looking Back
2
Functions Modeling Change
Lesson 1 Function Models Revisited
 
Investigations
  1 Modeling Atmospheric Change
  2 Modeling Change in Business Prospects
  3 Modeling Periodic Change
  4 Function Families
On Your Own
Lesson 2 Customizing Models by Translation and Reflection
 
Investigations
  1 Vertical Translation
  2 Reflection Across the x-Axis
  3 Horizontal Translation
On Your Own
Lesson 3 Customizing Models by Stretching and Compressing
 
Investigations
  1 Vertical Stretching and Compressing
  2 Horizontal Stretching and Compressing
On Your Own
Lesson 4 Looking Back
3
Counting Methods
Lesson 1 Systematic Counting
 
Investigations
  1 Methods of Counting
  2 Principles of Counting
On Your Own
Lesson 2 Order and Repetition
 
Investigations
  1 Permutations and Combinations
  2 Collections, Sequences, This or That
On Your Own
Lesson 3 Counting Throughout Mathematics
 
Investigations
  1 Counting and Probability
  2 Combinations, the Binomial Theorem, and Pascal's Triangle
On Your Own
Lesson 4 Looking Back
4
Mathematics of Financial Decision-Making
Lesson 1 Financial Decision-Making: Saving
 
Investigations
  1 Simple-Interest Investments
  2 Compound-Interest Investments
  3 Investment Strategies and Tools
  4 Compound Interest and the Number e
On Your Own
Lesson 2 Financial Decision-Making: Borrowing
 
Investigations
  1 Credit Card Options
  2 Borrowing and Lending
  3 Purchasing vs. Leasing
On Your Own
Lesson 3 Looking Back
5
Binomial Distributions and Statistical Inference
Lesson 1 Binomial Distributions
 
Investigations
  1 Rules of Probability and Binomial Situations
  2 The Binomial Probability Formula
  3 Statistical Significance
On Your Own
Lesson 2 Sample Surveys
 
Investigations
  1 Trustworthy Surveys
  2 How Surveys Can Go Wrong
On Your Own
Lesson 3 Margin of Error: From Sample to Population
 
Investigations
  1 Variability from Sample to Sample
  2 The Margin of Error
  3 Confidence Intervals
On Your Own
Lesson 4 Looking Back
6
Informatics
Lesson 1 Access: Set Theory, Logic, Searching, and Sorting
 
Investigations
  1 Intersection, Union, and Set Difference
  2 Subsets and Complements
  3 Searching and Sorting
On Your Own
Lesson 2 Security: Cryptography
 
Investigations
  1 Symmetric-Key Cryptography
  2 Modular Arithmetic (video clips of a class session)
  3 Public-Key Cryptography
On Your Own
Lesson 3 Accuracy: Error-Detecting and -Correcting Codes
 
Investigations
  1 ID Numbers and Error-Detecting Codes
  2 Transmit Information Using Error-Correcting Codes
On Your Own
Lesson 4 Efficiency: Data Compression
 
Investigation
  1 Huffman Codes
On Your Own
Lesson 5 Looking Back
7
Spatial Visualization and Representations
Lesson 1 Representing Three-Dimensional Objects
 
Investigations
  1 Using Data to Determine Surfaces
  2 Visualizing and Reasoning with Cross Sections
On Your Own
Lesson 2 A Three-Dimensional Coordinate System
 
Investigations
  1 Relations Among Points in Three-Dimensional Space
  2 The Graph of Ax + By + Cz = D
  3 Systems of Equations
On Your Own
Lesson 3 Linear Programming: A Graphical Approach
 
Investigations
  1 Linear Programming with Two Variables
  2 Linear Programming with Three Variables
  3 Linear Programming with Spreadsheets
On Your Own
Lesson 4 Looking Back
8
Mathematics of Democratic Decision-Making
Lesson 1 Social Choice and Voting
 
Investigations
  1 Ranked-Choice Voting
  2 Fair Is Fair, Isn't It?
  3 Weighted Voting and Voting Power
On Your Own
Lesson 2 Fair Division
 
Investigations
  1 Political Apportionment
  2 Getting Your Fair Share
On Your Own
Lesson 3 Looking Back

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