## 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

**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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