## Quantitative Analysis 1

This course 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 is a self-paced online course. It 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.

To earn a Certificate of Completion for this course, you must compete all of the content in the course lessons, as well as earn a passing grade of at least 80% on each of the 10 module quizzes.

## 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

**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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