Quantitative Literacy 1 – Textbook

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This textbook covers basic and intermediate concepts of number sense and quantitative analysis, abstract quantitative concepts as they relate to real-world problems and everyday life and basic number sense, algebraic concepts, geometry and visual modeling, and probability.

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Quantitative Analysis 1

This textbook covers basic and intermediate concepts of number sense and quantitative analysis, abstract quantitative concepts as they relate to real-world problems and everyday life and basic number sense, algebraic concepts, geometry and visual modeling, and probability.

This text contains 10 modules, each with multiple lessons that support varied approaches to help a student learn and engage with the topic, including readings, video, and a knowledge-check quiz.

Course Outcomes

This course focuses on the following learning outcomes. By the end of the course you will be able to:

  • Perform basic mental calculations including estimation, multiplication, division, adding, subtracting, rounding, and factors.
  • Analyze, calculate, and convert basic fraction equations including proper, mixed, improper, equivalent, common and uncommon denominators.
  • Identify, analyze and evaluate problems with decimals, ratios and proportions, and rational proportions.
  • Analyze and evaluate algebraic equations, including basic equations and inequalities.
  • Analyze and evaluate functions, systems of equations, exponential and logarithmic graphics.
  • Identify and analyze elements of a coordinate plane as it relates to linear equations and functions.
  • Analyze and evaluate basic geometric shapes and equations.
  • Analyze data, identify the correct graphic representation, and evaluate graphs to solve problems.
  • Analyze data and calculate descriptive statistics.
  • Analyze and evaluate data to determine basic statistics such as measures of spread, normal distribution, z-scores, confidence intervals, correlation and regression.
  • Analyze and calculate basic probability such as permutations, combinations, events, and simple probability.
  • Analyze and calculate probability such as two events, AND probability, OR probability, and conditional probability.

Technology Requirements

This course is delivered fully online and you will be required to have access to a computer, laptop, or web-capable mobile device – along with consistent access to the internet – to access course material and complete assignments.

Review the information below to ensure your system meets the minimum requirements necessary to complete a course for credit.  

PC Requirements

Hardware

  • Intel Core 2 Duo (or AMD 64×2 Dual-Core) processor
  • 1 GB RAM
  • 80 GB hard drive
  • 1024×768 resolution monitor
  • Soundcard with microphone and speakers
  • Built-in or external webcam
  • Broadband internet connection with speeds of  at least 2 Mbps download and 2 Mbps upload. Hot spots are not recommended. Test internet speed at: http://www.speedtest.net
  • Browser with pop-up blocker disabled

Software

  • Windows 7 or above

Macintosh Requirements

Hardware

  • Intel Core 2 Duo (or AMD 64×2 Dual-Core) processor
  • 1 GB RAM
  • 80 GB hard drive
  • 1024×768 resolution monitor
  • Soundcard with microphone and speakers
  • Built-in or external webcam
  • Broadband internet connection with speeds of  at least 2 Mbps download and 2 Mbps upload. Hot spots are not recommended. Test internet speed at: http://www.speedtest.net
  • Browser with pop-up blocker disabled

Software

  • Mac OS 10.6 “Snow Leopard” or above

Tablet or Smartphone

NOTICE:  Though you can view and interact with all of the available course content on a tablet or smartphone, you MUST USE A DESKTOP OR LAPTOP computer to complete the proctored midterm and final examinations.

Hardware

  • 2 GHz process or faster
  • 1 GB RAM or greater
  • 80 GB hard drive
  • Microphone and speakers
  • Wireless internet connection

Course Outline

 

Module 1 – Number Sense: Part 1

Intro to Number Sense

  • Doubling and Halving
  • Decomposition
  • Extending decomposition
  • Combing our three strategies to multiply
  • Applications for mental math

Estimation

  • Why estimate?
  • Intro to Estimation
  • Place Value
  • How to Round
  • Rounding: Addition
  • Rounding: Accuracy
  • Rounding: When to Use Underestimation and Overestimation
  • Integers: Adding
  • Integers: Subtraction

GCF and LCM

  • Multiples
  • Factors
  • Divisibility Rules
  • Finding GCF and LCM: List Method
  • Finding GCF and LCM: Cake Method

Fractions: Part 1

  • Understanding the meaning of fractions
  • Modeling proper fractions
  • Modeling mixed numbers
  • Modeling improper fractions
  • Modeling equivalent fractions
  • Modeling equivalent fractions
  • Converting from improper fractions to mixed numbers
  • Converting from mixed numbers to improper fractions
  • Comparing the size of fractions

Fractions: Part 2

  • Simplify fractions using GCF
  • Modeling multiplying fractions
  • Multiplying fractions with simplification
  • Dividing proper and improper fractions
  • Add or subtract fractions with common denominators
  • Equivalent fractions using LCD
  • Changing fractions
  • Common pitfalls

Applications: Visually Modeling Fractions

  • Modeling proper fractions, improper fractions, and mixed numbers
  • Modeling adding fractions with like denominators
  • Modeling adding fractions with unlike denominators
  • Modeling multiplying fractions
  • Modeling dividing fractions.

Module 2 – Number Sense: Part 2

Decimals

  • Naming Decimals
  • Convert Decimals to Fractions or Mixed Numbers
  • Ordering Decimals on a Number Line
  • Rounding Decimals
  • Adding or Subtracting Decimals
  • Multiplying Decimals
  • Dividing Decimals

Ratios and Proportions

  • Ratio as a Fraction
  • Rates as a Fraction
  • Finding Unit Rates
  • Finding Unit Price
  • Comparing Unit Prices

Rational Numbers

  • Defining Percents
  • Convert percent to a fraction
  • Convert a percent to a decimal
  • Convert a decimal to a percent
  • Convert fraction to a percent

Percent Applications

  • Solve sales tax applications
  • Solve discount applications
  • Solve simple interest applications

Application: Mental Percents

  • Calculating 100%
  • Calculating 50%
  • Calculating 25%
  • Calculating 200%
  • Calculating 10% and 1%
  • Calculating multiples of 10%
  • Calculating 5%
  • Calculating 15% tip
  • Estimating Direct Percents

Module 3 – Algebra: Part 1

Algebraic Expressions

  • Translating between common verbal expressions and algebraic expressions
  • Combining like terms
  • Distributive property

Solving Equations

  • Verifying a Solution
  • Modeling Addition and Subtraction Properties of Equality
  • Solving Equations: Adding and Subtracting
  • Modeling Multiplication and Division Properties of Equality
  • Solving Equations: Multiplication and Division
  • Solving Equations: Simplification
  • Solving Equations: Combining Properties
  • Solving Equations: Variables on Both Sides

Solving Inequalities

  • Defining Solutions of and Graphing Inequalities
  • Solve Inequalities: Add and Subtract
  • Solve Inequalities: Multiplication and Division
  • Solve Inequalities: Simplification
  • Translate to Inequalities

Coordinate Plane

  • Plot and Identify Points on a Graph
  • Making a Table of Solutions
  • Graphing Lines: Plotting Points
  • Graphing Lines: Intercepts
  • Graphing Lines: Vertical and Horizontal
  • Graphing Lines: Picking the Best Method

Slope and Lines

  • Finding Slope Using a Graph
  • A Different Point of View
  • Slope of Vertical and Horizontal Lines
  • Slope Formula (Two Points)
  • Graph Line with Point and Slope
  • Slope-Intercept Form
  • Graph Using Slope-Intercept Form

Application: Word Problems

  • Approach Word problems with a Positive Attitude
  • A Problem Solving Strategy
  • Applying the Strategy part 1
  • Applying the Strategy part 2
  • Number Word Problems
  • Using Relationships to Simplify Number Problems
  • Number Word Problems in a Real Life Context

Module 4 – Algebra: Part 2

Relations and Functions

  • Domain and Range of Relation
  • Relations and Functions
  • Value of a Function
  • Vertical Line Test
  • Graphing familiar functions
  • Graphing unfamiliar functions

Systems of Equations: Graphs and Substitution

  • A Solution to a System of Equations
  • Graphs of System of Equations
  • Solve a System of Equations by Substitution
  • More Substitution Practice
  • Extra Substitution Practice

Systems of Equations: Elimination and General Strategy

  • Solve a System of Equations by Elimination
  • Using Elimination to solve
  • Infinite or No Solutions
  • Applications of System of Equations
  • Choose the Most Convenient Method

Exponential and Logarithmic Graphs

  • Defining and Comparing Exponential Functions
  • Graphs of Exponential Functions
  • Defining Logarithms
  • Graphing Logarithmic Functions
  • Defining e
  • Natural Exponential and Logarithmic Functions

Application: Interest, Growth, and Decay

  • Interest Formulas
  • Growth and Decay Formula
  • Properties of Logarithms
  • Solve Exponential Equations Using Logarithms
  • Solving Interest Equations
  • Solving Growth and Decay Equations

Module 5 – Geometry

Measurement and Conversions

  • U.S. Unit Conversions
  • Multiple U.S. Unit Conversions
  • Metric Unit Conversions
  • Using Decimals in Metric Conversions
  • Convert Between US and Metric
  • Linear, square, and Cubic Measure

Angles, Triangles, and Pythagorean Theorem

  • Definition of Angles
  • Supplementary and Complementary Angles
  • Sum of Angles in a Triangle
  • Right Triangles
  • Defining perfect squares and square roots
  • Approximating Square Roots
  • Pythagorean Theorem

2-D Shapes

  • Defining perimeter and area
  • How to apply properties of a rectangle to find perimeter and area
  • How to apply properties of a triangle to find perimeter and area
  • How to apply properties of isosceles and equilateral to find perimeter and area
  • How to apply properties of circle to find circumference and area

3-D Shapes

  • Volume and Surface Area of Rectangular Solids
  • Volume and Surface Area of a Cube
  • Volume and Surface Area of Spheres
  • Volume and Surface Area of Cylinders
  • Volume of Cones

Area of Uncommon Figures

  • Defining Net
  • Surface area of triangular prism
  • Surface area of triangular pyramid
  • Surface area of square pyramid
  • Area of Trapezoid
  • Area of Irregular Figures

Application: Scale and Maps

  • Number Scale
  • Bar Scale
  • Estimating on a School Map
  • Issues when Resizing Maps

Module 6 – Visual Modeling

Bar Graphs

  • Label appropriate axis and scale to create bar graph
  • Solve problems by interpreting change between bars

Line Graphs and Scatterplots

  • Label appropriate axis and scales to create a line graph or scatter plot
  • Analyze and interpret changes over time with a line graph
  • Interpret the correlation between two variables with a scatter plot

Pie Graph

  • Label appropriate proportions and percentages to create a pie graph
  • Interpret proportional data with a pie graph
  • Compare pie graphs to solve problems

Frequency Tables and Histograms

  • Label appropriate axes, scales, and intervals
  • Frequency table
  • Two-way table
  • Dot plot
  • Histogram

Comparing Visual Models

  • Determine appropriateness of a table or graph used to represent a set of data (e.g. line graphs vs. bar graphs)
  • Compare alternative displays of the same data set for similarities or differences

Application: Misleading Tables, Graphs, and Charts

  • Identify common ways data can be misrepresented visually (e.g. inappropriate scale, improper labels, incomplete data, disproportionate bars)
  • Identify ways misleading statistics can lead to biased conclusions

Module 7 – Data Analysis: Part 1

What is Statistics?

  • Summarize, Represent, and Analyze Data
  • Two types of Statistics
  • Population and Sample
  • Analyzing Studies

Data and Samples

  • Types of Data
  • Discrete or Continuous Quantitative Data
  • Visual Ways to Represent Data
  • Simple Random Samples
  • Stratified Sampling
  • Cluster Sampling

Experimental Design

  • Parts of an Experiment
  • Lurking Variables
  • Ways to Control Bias
  • The Effects of an Unethical Experiment
  • Protection from Unethical Experiments
  • Ethical Questions

Organizing Data with Frequency Tables

  • Levels of measurement
  • Frequency tables
  • Relative frequency
  • Cumulative relative frequency

Five Number Summary and Percentiles

  • Quartiles and Median
  • IQR and Outliers
  • Percentiles
  • Box Plots

Measures of Center and Shape

  • Mean
  • Median
  • Mode
  • Skew distribution
  • Symmetrical distribution

Module 8 – Data Analysis: Part 2

Measures of Spread

  • Standard deviation
  • Calculating standard deviation
  • Interpreting standard deviation
  • Variability and bias

Normal Distribution and Z-scores

  • Normal Distributions
  • Standard Normal Distribution
  • Calculating and comparing Z-scores
  • Empirical rule

Linear Equations and Predictions

  • Independent and dependent variables
  • Slope and Y-Intercept
  • Making predictions

Scatter Plots and Lines of Best Fit

  • Scatter plots
  • Direction and strength
  • Line of best fit
  • Residuals and SSE
  • Interpreting slope
  • Correlation coefficient
  • Coefficient of determination

Module 9 – Probability By Counting

Simple Probability

  • Define probability
  • Calculate probability of a simple event happening (or not happening) and interpret its level of certainty
  • Evaluate the effectiveness of subjective probability (such as the gambler’s fallacy)

Independent and Dependent Events

  • Define the rules of probability
  • Determine if an event is independent or dependent
  • Calculate and interpret the probability of independent (with replacement) and dependent (without replacement) events

Factorials

  • Calculate the factorials
  • Simplify rational factorials

Permutations

  • Identify when it is appropriate to use permutations to count events
  • Apply the formula to calculate permutations

Combinations

  • Identify when it is appropriate to use combinations to count events
  • Apply the formula to calculate combinations

Application: Understanding Everyday Probability

  • Interpret probability used in weather prediction
  • Interpret probability used in medical research
  • Interpret probability used in politics
  • Interpret probability used in sports
  • Interpret probability used in gaming

Module 10 – Probability By Calculation

Modeling Two Events

  • Create a sample space to model and count compound events
  • Create a tree diagram to model and count compound events
  • Create an area model to model and count compound events
  • Create a Venn diagram to model and count compound events

Calculating “AND” Probability

  • Apply visual representations to calculate the probability of AND events
  • Apply the multiplication rule to calculate the probability of AND events

Calculating “OR” Probability

  • Apply the addition rule to calculate the probability of mutually exclusive events
  • Apply the general addition rule to calculate the probability of non-mutually exclusive events

Conditional Probability

  • Interpret a two way frequency table to calculate and interpret conditional probability
  • Interpret a tree diagram to calculate conditional probability
  • Apply the general multiplication rule to calculate conditional probability

Application: Simulating Experimental Probability

  • Describe possible outcomes and link them to a list of randomly generated values
  • Analyze simulated outcomes
  • Compare experimental probability to theoretical probability

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