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

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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Quantitative Analysis 1 – Certificate Course

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