PREREQUISITE: MAT098 – Prealgebra, equivalent, or placement

COREQUISITE: RDG095 – Reading Foundations, if required by placement

• Online homework platform: MyQuantway ISBN #9781926902623
• Students are required to have access to a computer and internet outside of class. There is a computer lab available to students each Monday through Friday in our Tutoring Center (room 217 of the main building.)
• Access to an electronic spreadsheet (Excel or Google Sheets)
• Three-ring binder
• Scientific calculator (not a cell phone)

OBJECTIVES FOR QUANTWAY SEQUENCE:

Quantitative with Multiple Literacies Goal: Students will develop their quantitative reasoning abilities through learning and practicing other essential literacies and reasoning skills. In particular, students will practice and make explicit connections with the following reasoning skills and literacies:

L.1  Quantitative Literacy: Students will demonstrate the Quantitative Literacy “habit of mind.” In particular, students will:

• L.1.1   Demonstrate an appreciation for QL by reading about and discussing the importance of QL in the world both globally and in their lives.
• L.1.2   Show confidence in quantitative reasoning through perseverance in quantitative thinking and ability to transfer prior knowledge from one context to the next.
• L.1.3   Check the reasonableness of quantities that have been presented to them or numbers that they calculate or estimate.
• L.1.4   Use correct units when using numbers based on the context.

L.2  Critical Reading: Students will be able to read and interpret quantitative information from a variety of real-world sources. Students will be able to recognize and evaluate quantitative assumptions.

L.3  Communication: Students will communicate quantitative results by:

• L.3.1   Writing and orally presenting their work using appropriate language, symbolism, data and graphs.
• L.3.2   Analyzing and using quantitative information to support an argument.

L.4  Information Literacy: Students will be develop critically thinking skills about quantitative information by:

• L.4.1   Evaluating sources of information.
• L.4.2   Locating reliable and appropriate quantitative data.

L.5  Visual/Graphical Literacy: Students will be able to read, interpret, and make decisions based on visual displays of data including line graphs, bar graphs, scatter plots, histograms, and maps with multiple parameters.

L.6  Technology Literacy: Students will be able to use technology appropriately as a tool including:

• L.6.1   Knowing when and how to use calculators appropriately.
• L.6.2   Using computers and the Internet to gather, research and analyze quantitative information.
• L.6.3   Questioning and evaluating the output from a computer application.
• L.6.4   Using spreadsheets to create and/or investigate mathematical models whenever possible.
• L.6.5   Facility with other appropriate technologies, such as: math or statistical applications on smart phones, or java applets.

L.7  Spatial/Geometric Reasoning: Students will be able to apply spatial reasoning to solve geometric problems involving area, perimeter, and volume of basic shapes including using and translating between different units of measurement.

 

Numeracy Skills Goal: Students will develop and apply the concepts of numeracy to investigate and describe quantitative relationships and solve problems in a variety of contexts. Students will be able to:

N.1  Demonstrate operation sense and communicate verbally and symbolically the effects of common operations on numbers.

N.2  Demonstrate an understanding of and competency in using magnitude in the context of place values, fractions, and numbers written in scientific notation.

N.3  Use estimation skills, knowing how and when to estimate results and to what precision, to solve problems, detect errors, and check accuracy.

N.4  Demonstrate measurement sense including units, precision, accuracy and error.

N.5  Be able to use and distinguish between statements involving absolute change and relative change.

N.6  Be able to use and interpret percentages in a variety of contexts including but not limited to: Parts to whole comparisons, decimal representations of percentages, quantifying risks and other probabilities, rates, change, and margins of error.

 

Proportional Reasoning Goal: Students will represent proportional relationships and solve problems that require an understanding of ratios, rates, proportions, and scaling. Students will be able to:

P.1  Recognize proportional relationships from verbal and numeric representations.

P.2  Compare proportional relationships represented in different ways.

P.3  Apply quantitative reasoning strategies to solve real-world problems with proportional relationships based on an understanding that derived quantities can be described with whole numbers, fractions, or decimals, or in a combination of these, and that to fully explain these relationships, units must be used.

 

Algebraic Reasoning Goal: Students will reason using the language and structure of algebra to investigate, represent, and solve problems.

A.1  Understand various uses of variables to represent quantities or attributes.

A.2  Describe the effect that a change in the value of one variable has on the value(s) of other variables in the algebraic relationship.

A.3  Construct and use equations to represent relationships involving one or more unknown or variable quantities to solve problems.

 

Mathematical Modeling Goal: Students will reason using the language and structure of mathematics to investigate, represent, and solve problems. Students will be able to:

M.1  Create models of authentic contextual situations, including:

• M.1.1 Using multiple representations of mathematical models such as tables, graphs, equations, and words.
• M.1.2 Using multiple variables to represent quantities or attributes.
• M.1.3 Describing why these tools are a useful strategy for understanding the world.
• M.1.4 Describing limitations present in these models.

M.2  Demonstrate an extensive understanding of linear models by:

• M.2.1 Creating and using linear models of real world situations.
• M.2.2 Describing the behavior of linear models using words, algebraic symbols, graphs, and tables.
• M.2.3 Identifying when a linear model or trend is reasonable for given data or context.
• M.2.4 Determining a reasonable domain of the model based on the scenario.
• M.2.5 Using appropriate terms and units to describe rate of change. (For example: Describe the rate of change using appropriate units: slope for linear relationships or average rate of change over an interval for nonlinear relationships.)

M.3  Demonstrate an understanding of exponential models by:

• M.3.1 Creating and using exponential models of real world situations including growth and decay models beyond financial concepts.
• M.3.2 Describing the behavior of exponential models using words, algebraic symbols, graphs, and tables.
• M.3.3 Identifying when an exponential model or trend is reasonable for given data or context.
• M.3.4 Determining a reasonable domain of the model based on the scenario.

M.4  Develop mathematical modeling skills in personal finance that move beyond basic exponential models.

M.5  Understand and describe models beyond linear and exponential models. Students will be able to:

• M.5.1 Identify when a linear and/or exponential model is not reasonable.
• M.5.2 Identify important characteristics of models (e.g. increasing/decreasing, cyclic, piecewise, etc.) that represent real world contexts.
• M.5.3 Identify multiple parameters in a scenario.

M.6  Identify important characteristics of models in various representations.

M.7  Understand that abstract mathematical models used to characterize real-world scenarios or physical relationships are not always exact and may be subject to error from many sources, including variability.

Statistical Thinking Goal: Students will reason using the language and structure of statistics to investigate, represent, and solve problems. Students will be able to:

S.1  Critically evaluate statistics being presented in a media report including:

• S.1.1 Identifying the reference value for a reported percentage.
• S.1.2 Evaluating the sampling strategy.
• S.1.3 Determining sources of bias.
• S.1.4 Describing the difference between correlation and causation.
• S.1.5 Identifying confounding variables.

S.2  Use the language of probability to describe and evaluate statements involving risk.

S.3  Calculate and interpret measures of center including mean, median, expected value, and weighted average.

S.4  Use and interpret measures of spread and position including standard deviation, quartiles, percentiles, and range.

 

SUMMARY OF COURSE CONCEPTS AND SKILLS:

Module 1 Concepts and Skills

Working with and Understanding Large Numbers

• Place Value and Naming Large Numbers (1.1)
• Scientific Notation (1.6)
• Calculations with Large Numbers (1.6)
• Relative Magnitude and Comparison of Numbers (1.6)

Estimation and Calculation

• Rounding (1.1)
• Fractions and Decimals (1.3)
• Relationship of Multiplication and Division (1.4)
• Order of Operations (1.4)
• Properties that Allow Flexibility in Calculations: Distributive and Commutative Properties (1.4)

Percentages and Ratios

• Estimations with Fractions and Percent Benchmarks (1.2, 1.3)
• Calculate Percentages (1.3)
• Write and Understand Ratios (1.6)
• Calculate Percentages from a Two-Way Table (1.8)
• Use Percentages as Probabilities and Ratios (1.9)

Module 2 Concepts and Skills

Using Ratios

• Understand the Meaning of Equivalent Ratios in Context (2.1)
• Use Units with Ratios (2.1)
• Calculate a Unit Rate (2.2)
• Use Ratios and Proportionality to Calculate New Values (2.2)
• Interpret and Use Index Numbers to Calculate New Values (2.8, 2.9)

Applications of Percentages

• Calculate and Interpret Absolute Change between Two Quantities (2.3)
• Calculate and Interpret Relative Change between Two Quantities (2.3)
• Calculate and Interpret Absolute Change between Two Percentages (2.3)
• Calculate and Interpret Relative Change between Two Percentages (2.3)
• Make and Interpret Comparisons of Absolute Measurements versus Relative     Measurements (2.4)

Graphical Displays

• Read and Interpret Pie Graphs, Bar Graphs, and Line Graphs (2.4)
• Recognize Distortion of Graphs Due to Different Scales (2.4)
• Calculate Absolute and Relative Change from a Graph (2.4)
• Create Bar Graphs to Represent Absolute and Relative Change (2.5)

Measures of Central Tendency

• Calculate Mean, Median, and Mode of a Data Set (2.6)
• Interpret the Meaning of and Difference Between the Mean, Median, and Mode (2.6, 2.7)

Module 3 Concepts and Skills

Making Conversions

• Understand Use of Units in Making Conversions (3.1, 3.2)
• Use Dimensional Analysis to Make a Conversion Involving Multiple Conversion Factors (3.1, 3.2)

Geometric Reasoning

• Understand Concepts of and Units for Linear Measurement, Area, and Volume (3.3)
• Identify and Use the Appropriate Geometric Formula to Apply in a Given Situation (3.3)

Using Formulas and Algebraic Expressions

• Understand the Use of Variables in Formulas and Algebraic Expressions, Including the Appropriate Way to Define a Variable (3.4)
• Understand the Role of a Constant in a Formula (3.4)
• Use a Formula to Solve for a Value (3.4, 3.6, 3.8)

Use Graphical Displays

• Read and Interpret a Pictograph (3.5)
• Understand the Limitations and Potential for Distortion in Pictographs (3.5)

Creating and Solving Equations

• Solve a Linear Equation in One Variable (3.6, 3.8)
• Interpret the Solution to an Equation (3.6, 3.7, 3.8)
• Solve an Equation or Formula for a Variable (3.8)
• Write and Solve Proportions (3.7)

Module 4 Concepts and Skills

Linear Models

• Create, Interpret, and Use the Four Representations of a Linear Model: Verbal, Table, Graph, and Equation (4.1, 4.2, 4.3, 4.7, 4.8)
• Translate between the Four Representations of a Linear Model (4.1, 4.2, 4.3)
• Identify and Interpret Vertical Intercept, Horizontal Intercept, and Slope from a Graph (4.1, 4.2, 4.3, 4.7, 4.8)
• Identify the Slope and Vertical Intercept from an Equation (4.1, 4.2)
• Understand that a Linear Model is Defined by a Constant Rate of Change (4.1, 4.2, 4.7, 4.8)
• Identify a Model as Linear Based on Any of the Four Representations (4.1, 4.2, 4.7, 4.8)
• Understand the Role of Units in a Linear Equation (4.1)
• Calculate and Interpret Slope (4.2, 4.3)
• Create a Linear Equation to Model Data (4.3)
• Use Equations, Tables, and Graphs to Solve or Estimate Solutions to Problems (4.1, 4.2, 4.3, 4.7, 4.8)
• Write and Use Linear Equations Based Upon a Percentage Increase or Decrease (4.4)

Exponential Models

• Create, Interpret, and Use the Four Representations of an Exponential Model: Verbal, Table, Graph, and Equation (4.5, 4.6, 4.7, 4.9)
• Write and Use an Exponential Model (4.5, 4.6, 4.7, 4.9)
• Understand that an Exponential Model is Defined by a Percentage Change (4.6, 4.7, 4.9)
• Identify and Exponential Model as Growth or Decay (4.6, 4.7, 4.9)

The Math Department at CCC recommends that you review the following prerequisite topics to be successful in MAT100Q:

1) Fractions: Reducing, adding and subtracting, multiplying and dividing.

2) Translating: Sentences into Algebraic Expressions and Equations, then simplifying and solving them.

3) Solving: Equations containing one variable.

Review of these topics will prepare you to be successful in the first four weeks when you are getting situated and accustomed to your new environment.

Feel free to contact a member of the Math Department or the Math Department Chair.