Weekly Course Announcements

Welcome to MATH 2133: Understanding Elemntary Math II

Great Students,

Greetings to everyone.
Welcome to our class. It is great to have you on board.

I am Samuel Chukwuemeka, your instructor for the class. Please do not bite your tongue trying to pronounce my last name 😊
You can call me Mr. Samuel or Mr. C.
Chukwuemeka is a name of Ibo tribe in Nigeria.
Chukwu means GOD; emeka means has done a lot.
So, Chukwuemeka means GOD has done a lot for me.
I have a Bachelor of Engineering degree in Civil Engineering, an Associate in Applied Technology degree in Computer Information Systems, a Master of Education degree in Mathematics Education, and a Master of Science degree in Computer Science. I have taught several mathematics courses at several secondary schools, colleges, and universities for 15 years.
My personal quote is: The Joy of a Teacher is the Success of his Students.
Yes, I mean it. I want you to succeed in your academic profession and I want to be part of that success.

We shall cover these topics: Problem Solving; Numbers and Numeration Systems; Number Theory; Integers; Rational Numbers and Proportional Reasoning; Rational Numbers as Decimals, and Percent among others.
We shall apply the knowledge of the topics to real-world problems.
Procrastination is inimical to time. It is important to complete each assessment by the due date. I would plan my time accordingly.

May you please do the following tasks?
Review the course syllabus and all the information in the course.
Weekly Office Hours/Live Sessions will be held on Fridays from 10:30 am – 11:30 am MDT.
Click the invite link (https://wnmu.zoom.us/j/89080119210)  and join each week.
There will be a recording of the sessions, so we ask that you do not say or type any information that is insensitive to someone else.
The sessions are optional, however, please make plans to attend.
If the day and time do not suit your schedule, no worries. You can always send an email to me, and we shall communicate accordingly.
Ensure you review all the information for each page and each module. Complete every assessment as applicable. Do not skip.
Feel free to ask questions. I am here to help.
Thank you.



Mathematically Yours,
Samuel Chukwuemeka
Working together for success

Welcome to Week 1: Basic Geometry: Points, Lines, Planes, and Angles

Great Students,

Greetings to everyone.
Welcome to Module 1.

In this module, we shall begin our study of Introductory Geometry.
Specifically, we shall define and explain several terms in Geometry.
Then, we shall solve some problems involving these terms.
Let us briefly look at a real-world example.

(Taken from: LibreTexts K12 Education: Coordinate Locations on a Map
4.1.4: Coordinate Locations on a Map. (2020, July 21). K12 LibreTexts. https://k12.libretexts.org/Bookshelves/Mathematics/Algebra/04%3A_Graphs_and_Functions/01%3A_Graphing_in_the_Coordinate_Plane/1.04%3A_Coordinate_Locations_on_a_Map)



Ian finds an old map when he's going through his grandfather's attic.
It seems to be a pirate map of the Spanish Main.
On the back of it, he sees scrawled a hasty X and the numbers: 26.5 and 81.
He suspects that this map leads to treasure. But where is it?

A coordinate grid is a grid in which points are graphed.
It usually has two or more intersecting lines which divide a plane into quadrants, and in which ordered pairs, or coordinates, are defined.
Maps also use coordinates. Around the edges of maps are numbers and sometimes letters.
These define the location of cities, states, and other physical entities and landmarks. Most maps use degrees.
These define the latitude and longitude.
Longitude is the measure, in degrees, (angle measure) of lines vertically on a map. Depending on how the map is made, these lines are sometimes curved.
Latitude is the measure, in degrees, (angle measure) of lines horizontally on a map.

Notice those vocabulary terms in bold.
If Ian does not know these terms, do you think he will locate the treasure?

Welcome to Basic Geometry: Points, Lines, Planes, and Angles

May you please:
(1.) Review the Overview and Objectives.
(2.) Review the Readings/Assessments.
(3.) Complete the assessments initially due this week.
(4.) Participate in the Week 1 Discussion.
(5.) Attend the Live Sessions/Office Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 2: Polygons and Curves

Great Students,

Greetings to everyone.
Welcome to Module 2.
In the previous module (Module 1), we started our introduction to geometry by discussing Points, Lines, Planes, and Angles.
In this module, we shall extend our study to objects that have lines, angles, and surfaces...known as Geometric Figures.
These geometric figures may be closed plane shapes with straight sides known as Polygons.
They may also be open or closed shapes with non-straight sides known as Curves.
We shall analyze the properties of these polygons including Triangles, Quadrilaterals, and other Polygons.
We shall also continue our study on Angles.

Where are you right now?
Hmmmm...Mr. C, are you trying to monitor me? 😊
No, I'm not monitoring you. I just want to make a connection to what we are about to discuss this week.
If you are in the classroom, library, church, or your room, there is a high probability that you will see at least one geometric shape.
What do you see?
Do you see any geometric figure/shape?
Is it closed or open?
Is it a polygon or a curve?
Is it a plane shape (two-dimensional shape) or a solid shape (three-dimensional shape)?
Is it regular or irregular?
Can you list and analyze the properties of the figure?

Welcome to Polygons and Curves.

May you please:
(1.) Review the Overview and Objectives.
(2.) Review the Readings/Assessments.
(3.) Complete the assessments initially due this week.
(4.) Participate in the Week 2 Discussion.
(5.) Attend the Live Sessions/Office Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 3: Measurements and Units: Linear Measures

Great Students,

Greetings to everyone.
Welcome to Module 3.

In the previous module (Module 2), we discussed Geometric Figures.
In this module, we shall discuss the measurements of some of the properties of geometric figures and the measurements of other physical quantities.
This is an introduction to Mensuration: the branch of mathematics that deals with the measurements of geometric figures and their parameters.
In addition, we shall discuss the units of the measurements.
Further, we shall discuss the two basic systems of measurements and units.
So we have two terms: the measurement and the unit of the measurement.
Specifically, we shall focus on Linear Measures.
Let us begin with an overview.

Look around you.
Do you find any containers/geometric figures such as containers of food, drinks, soap, paint, lotion?
Look at the entire container.
Do you see any measurements? any units?
How many measurements (values) do you see?
How many units do you see?
Most likely, you will see at least two different measurements and two different units.

Questions for Thought
(1.) Which unit is the United States/Customary unit?
(2.) Which unit is the International/Metric unit?
(3.) Why are there at least two different measurements and two different units?
(Hint: If an American company that produces food in containers wants to market it to Mexico, is it not appropriate for the company to use the unit that Mexico uses for the measurement of food?
Similarly, If an Mexican company that produces food in containers wants to market it to America, is it not appropriate for the company to use the unit that America uses for the measurement of food?)
(4.) Is it possible to have errors in measurements?
What are the errors in measurements?
If two or more people measure the length of a desk, would they obtain the same measurement to the: nearest integer, tenth, hundredth, ..., unit?
...and so on and so forth.

Specifically to understand Linear Measures:
(1.) Are you familiar with the unit: meter (m)?
(2.) What quantity is measured in meters?
(3.) Are you familiar with the unit: square meter (m²)?
(4.) What quantity is measured in square meters?
(5.) Are you familiar with the unit: cubic meter (m³)?
(6.) What quantity is measured in cubic meters?
(7.) Which of these quantities and units is a linear measure?
(8.) Which of these quantities and units is a quadratic (square) measure?
(9.) Which of these quantities and units is a cubic measure?

Welcome to Measurements and Units: Linear Measures

May you please:
(1.) Review the Overview and Objectives.
(2.) Review the Readings/Assessments.
(3.) Complete the assessments initially due this week.
(4.) Participate in the Week 3 Discussion.
(5.) Attend the Live Sessions/Office Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 4: Mensuration: Polygons and Circles

Great Students,

Greetings to everyone.
Welcome to Module 4.

In the previous module (Module 3), we discussed the mensuration of some of the properties of geometric figures and other physical quantities.
We also discussed the units of the measurements and the two basic systems of measurements.
In this module, we shall extend our knowledge to the measurements of the properties of polygons and circles.
Specifically, we shall discuss the measurements of the areas of: polygons and circles.

Welcome to Mensuration: Polygons and Circles

May you please:
(1.) Review the Overview and Objectives.
(2.) Review the Readings/Assessments.
(3.) Complete the assessments initially due this week.
(4.) Participate in the Week 4 Discussion.
(5.) Attend the Live Sessions/Office Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 5: The Pythagorean Theorem, Distance Formula, and Equation of a Circle

Great Students,

Greetings to everyone.
Welcome to Module 5.

In the previous module (Module 4), we discussed the the measurements of the areas of: polygons and circles.
As we already know:
The measurement of the length, width, height, distance is linear: the highest exponent of the independent variable is 1
The measurement of the area is square or quadratic: the highest exponent of the independent variable is 2
The measurement of the volume is cubic: the highest exponent of the independent variable is 3
In this module, we shall apply the knowledge we acquired last week regarding the areas of polygons and circles.
How do we apply it?

For Polygons, specifically, we shall focus on triangles.
For Triangles, we shall focus on Right Triangles.
For Right Triangles, an application is the Pythagorean Theorem.

$ hypotenuse^2 = leg^2 + leg^2 \\[3ex] $ Notice the square
Please Note: The Pythagorean Theorem is not $c^2 = a^2 + b^2$ unless the variables: $c$, $a$, $b$ are clearly defined as hypotenuse, leg, and leg respectively.
It is much better to avoid those variables because the hypotenuse and the legs can be any variable.
If $a$, $b$, $c$ are defined as hypotenuse, leg, and leg respectively, the Pythagorean Theorem would be: $a^2 = b^2 + c^2$
This can be confusing to someone who is already fixed-minded on $c^2 = a^2 + b^2$
So, unless you define the variables accordingly, it is better to use: $hyp^2 = leg^2 + leg^2$

Further application of the Pythagorean Theorem leads us to the Distance Formula

$ distance^2 = (\Delta x)^2 + (\Delta y)^2 \\[4ex] distance^2 = (x_2 - x_1)^2 + (y_2 - y_1)^2 \\[4ex] Compare\;\;to\;\;the\;\;Pythagorean\;\;Theorem \\[3ex] distance = hypotenuse \\[3ex] \Delta x = leg \\[3ex] \Delta y = leg \\[3ex] $ Notice the square
where:
Point 1 = (x₁, y₁)
Point 2 = (x₂, y₂)
x₁ = x-coordinate of Point 1
y₁ = y-coordinate of Point 2
x₂ = x-coordinate of Point 2
y₂ = y-coordinate of Point 2
Δx = change in the x-coordinate
Δy = change in the y-coordinate

For Circles, further application of the Distance Formula leads us to the Equation of Circle Did you notice the trend: an application of the first leads to the application of the second, which leads to the application of the third?

$ \underline{Standard\;\;Form\;\;of\;\;the\;\;Equation\;\;of\;\;a\;\;Circle} \\[3ex] radius^2 = (x - h)^2 + (y - k)^2 \\[3ex] Compare\;\;to\;\;the\;\;Pythagorean\;\;Theorem \\[3ex] radius = hypotenuse \\[3ex] x - h = leg \\[3ex] y - k = leg \\[3ex] $ Notice the square
where:
(h, k) = coordinate of the circle center
(x, y) = coordinate of the point on the circle circumference

For this announcement, let us focus on the Pythagorean Theorem
Classroom Activity
Teacher: Hosea, please come.
Take that chair and mark as your starting point.
Walk four steps in a horizontal line.
Then, turn around at an angle of 90°
In other words, rotate left 90°
Walk three steps in a vertical line.
Then, turn towards me to face me.
If I asked you to come to me, how many steps would you walk to reach me?
Student: About 5 steps I guess...
Ask your students and note their responses.
Ask them to give reasons for their answers.
Teacher: About...indicates you are not so sure?
Well, it is 5 steps.
That is correct.
But, how did you get 5 steps?
Student: Mr. C, it's just a guess...a correct guess.
I'll just walk towards you 😊
Teacher: Let's find out.
Welcome to the Pythagorean Theorem

Welcome to The Pythagorean Theorem, Distance Formula, and Equation of a Circle

May you please:
(1.) Review the Overview and Objectives.
(2.) Review the Readings/Assessments.
(3.) Complete the assessments initially due this week.
(4.) Participate in the Week 5 Discussion.
(5.) Attend the Live Sessions/Office Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 6: Measurements and Units: Surface Area, Volume, and Mass

Great Students,

Greetings to everyone.
Welcome to Module 6.

In Module 3, we discussed the measurements of units for linear measures.
In this module, we shall discuss the measurements and units for volume and mass measures.

In Module 4, we discussed the measurements and units for area measures.
We also discussed the mensuration of polygons and circles.
In this module, we shall discuss the mensuration of solids.

So, we are still discussing Measurements and Units and Mensuration.
Welcome to Measurements and Units: Surface Area, Volume, and Mass and Mensuration: Solids

May you please:
(1.) Review the Overview and Objectives.
(2.) Review the Readings/Assessments.
(3.) Complete the assessments initially due this week.
(4.) Participate in the Week 6 Discussion.
(5.) Attend the Live Sessions/Office Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 7: Variables, Linear Expressions and Linear Equations

Great Students,

Greetings to everyone.
Welcome to Module 7.

In Modules 1 – 6, we discussed Geometry.
We used Algebra in several calculations we did in Geometry.
Do you realize that the formulas we used consists of variables?
In this module, we shall discuss Algebra.
Specifically, we shall discuss the concept of Variables.
Next, we shall use variables to write Linear Algebraic Expressions.
Setting the expressions to equal some number or variable makes it a Linear Algebraic Equation.

Let us begin with Variables:
Before I immigrated to the United States, I looked like this:


Then, I came here, ate a lot of cheeseburgers, gained a lot of weight, and now look like this:

(Please don't laugh at me) 😊

So we have two variables: weight and the number of cheeseburgers.
Which one depends on the other?
In other words:
(1.) Which of the variables is the dependent variable?
(2.) Which one is the independent variable?
(Hint: Does my weight depend on the number of cheeseburgers I eat, or does the number of cheeseburgers I eat depend on my weight?)

Then move to Linear Algebraic Expressions:
Can we do something fun for Year 2024?...Determining your Age in 2024
(1.) Pick an integer between 0 and 10 (0 and 10 excluded).
(2.) Multiply the integer by two.
(3.) Add five to the product.
(4.) Multiply the sum by fifty.
(5.) If you already had your birthday this year, add the product to one thousand, seven hundred and seventy-four.
If you have not had your birthday this year, add the product to one thousand, seven hundred and seventy-three.
(6.) Subtract your four-digit birth year from the sum.
(7.) What is the difference?
What do you notice: How many digits do you have?
What is the first digit?
What is the second digit?

Can we do another one?: Determining your Date of Birth.
(1.) Pick the integer that is your month of birth.
(2.) Multiply the integer by two hundred.
(3.) Add three hundred and eighty-two to the product.
(4.) Divide the sum by two.
(5.) Add your day of birth to the quotient.
(6.) Multiply the sum by one hundred.
(7.) Add thirteen thousand, eight hundred and forty to the product.
(8.) Add the last two digits of your year of birth to the sum.
(9.) Subtract thirty-two thousand, nine hundred and forty from the sum.
(10.) What is the difference?
What do you notice: How many digits are there?
If you have five digits, may you add make it six digits by including a zero as the first digit?
What do the first two digits represent?
What do the middle two digits represent?
What do the last two digits represent?

Would you not like to know how these expressions were set up so you do more fun activities with your students?
How many variables was used to set it up? What do you think?

Now, onto Linear Algebraic Equations
How young was Mr. C in 2008?
[Question Number (18.) on Applications of Linear Equations]
Three hundred reduced by three times my age is one hundred and ninety two.
What was my age?

Welcome to Variables, Linear Expressions, and Linear Equations

May you please:
(1.) Review the Overview and Objectives.
(2.) Review the Readings/Assessments.
(3.) Complete the assessments initially due this week.
(4.) Participate in the Week 7 Discussion.
(5.) Attend the Live Sessions/Office Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 8: Linear Functions

Great Students,

Greetings to everyone.
Welcome to Module 8.

In the previous module (Module 7), we discussed the topics of: Variables, Linear Expressions, and Linear Equations.
In this module (Module 8), we shall extend our knowledge to the topic of Linear Functions.
But before we discuss linear functions, let us discuss the meaning of functions.
But before we discuss functions, we need to know the meaning of relations.
So, we have it in this order: Relations → Functions → Linear Functions.

Recall the pictures I used in the previous module:
Before I immigrated to the United States, I looked like this:


Then, I came here, ate a lot of cheeseburgers, gained a lot of weight, and now look like this:

(Please don't laugh at me) 😊

Questions for Thought: First Set
(1.) Did you notice any relationship?
What is the relationship?
Any input-output relationship?
Which variable is the input?
Which variable is the output?
Can you express the relationship as a:
(2.) Set of ordered pairs (set of points)
(3.) Function Rule (Equation)?
(4.) Table of Values
(5.) Graph
(6.) Mapping or Correspondence

The example is a two-variable relationship where the:
weight is the dependent variable and the
number of cheeseburgers is the independent variable.
In the example, we say that the weight, w is a function of the number of cheeseburgers, c
We can write it as:
w = f(c)

Let us make some interdisciplinary connections:
Bring it to Algebra and Calculus
y is the dependent variable
x is the independent variable

Bring it to Statistics
y is the response variable
x is the predictor or explanatory variable

Bring it to Philosophy (Cause-Effect Relationship)
y is the effect
x is the cause

Bring it to Economics/Business (Input-Output Relationship)
y is the output
x is the input

Bring it to Psychology/Human Behavior/Sociology
y is the consequence
x is the action

So, for any input, there is at least an output. This is defined as a Relation.
Welcome to Relations.

Notice the word, at least in the definition of a Relation.
At least one output means one or more output.
But, is it possible for an input to have more than one output?
Is it possible for a WNMU student to have more than one Student ID?
Is it possible for an American to have more than one SSN (Social Security Number)?
Is it possible for a student to make more than one grade on the same test?

This leads us to these concepts:
Function
One-to-one Function (Injective Function)
Onto Function (Surjective Function)
Bijective Function

Questions for Thought: Second Set
Determine if these scenarios represent a relation, function, one-to-one function, onto function, surjective function.
Write all that is applicable.
(1.) A WNMU student has only one Student ID.
(2.) A WNMU student has more than one Student ID.
(3.) Two WNMU Students have the same grade on a Math quiz.
(4.) A WNMU student has two different grades on a Math quiz.
(5.) Every WNMU student was born by a woman.
Welcome to Functions.

Alright, let's recall the five ways of representing relations and functions.
Let us express the relationship as a Table.

Function: Number of Cheeseburgers and Weight

Number of cheeseburgers, c	Weight, w (pounds)
1	3
2	6
3	9
4	12

Based on the table:
When I ate a cheeseburger, I gained 3 pounds.
When I ate two cheeseburgers, I gained 6 pounds.
When I ate three cheeseburgers, I gained 9 pounds.
When I ate four cheeseburgers, I gained 12 pounds.

Questions for Thought: Third Set
This implies that:
For every 1 cheeseburger I ate (unit increase in the input), how does that affect my weight (the output)?

(1.) What concept was asked in Question (5.)?
(2.) Is the value of that concept: positive, negative, or zero?
(3.) Can you give examples/scenarios of a negative slope?
(Hint: the output decreases for every unit increase in the input)
(4.) Can you give examples/scenarios of a zero slope?
(Hint: the output remains the same for every unit increase in the input.)

Welcome to Linear Functions

May you please:
(1.) Review the Overview and Objectives.
(2.) Review the Readings/Assessments.
(3.) Complete the assessments initially due this week.
(4.) Participate in the Week 8 Discussion.
(5.) Attend the Live Sessions/Office Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 9: Introductory Statistics

Great Students,

Greetings to everyone.
Welcome to Module 9.

In Modules 1 – 6, we discussed several topics in Geometry.
In Modules 7 and 8, we discussed several topics in Algebra.
In this module, we shall study an important branch of Mathematics: Statistics.
Specifically, we shall discuss the basic terms in Introductory Statistics.
Then, we shall discuss Data Collection.
Recall that in Algebra, we discussed the concept of Variables.
In Introductory Statistics, we shall extend that concept and introduce new terms to classify data.

Questions for Thought:
(1.) Did you register for this course?

Of course...Mr. C, what kind of question is that?
Why do I have access to the Canvas course if I did not register for it?
Typical of Nigerians...answering questions with questions 😊

Are you familiar with any of these?
Name:
Date of Birth:
Age:
Address:
...among others
Did you provide any of these when you enrolled at WNMU?
If the answer is Yes, then all the information you provided is known as Data.
Have you ever wondered: what does WNMU do with these data?

(2.) Some of you are on social media platforms: YouTube, Facebook, Twitter, TikTok, Instagram and Snapchat among others.
You gave these platforms your data when you registered for their services.
Have you asked yourself: what do these platforms do with my data?

(3.) In your daily conversation/interaction/communication with people, have you discussed: race, gender, color, age, religion, temperature, height, weight, number of people, number of something, etc.?
If you have, you have probably discussed data.

Statistics is all about data:
Data Collection: How do you collect data?
Data Organization: What do you do with the data?
Is it not better to organize it before you use it?
Data Presentation: What are the several tools you can use to present the data to make it meaningful?
How do we present the data in a way that makes meaning for everyone?
Data Analysis: How do we analyze the data?
What evidence/information/results can we get by analyzing the data?
How do we use the results of the analysis?
Data Interpretation: After analyzing the data, how can we use our results to make the right decision and the right conclusion?

Welcome to Introductory Statistics

May you please:
(1.) Review the Overview and Objectives.
(2.) Review the Readings/Assessments.
(3.) Complete the assessments initially due this week.
(4.) Participate in the Week 9 Discussion.
(5.) Attend the Live Sessions/Office Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 10: Introductory Statistics

Great Students,

Greetings to everyone.
Welcome to Module 10.

Welcome to Spring Break

May you please:
(1.) Complete all outstanding assignments.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 11: Introductory Statistics

Great Students,

Greetings to everyone.
Welcome to Module 11.

In Module 9, we began our study on Introductory Statistics.
We also discussed Data Collection.
After collecting data, we organize the data in classes.
After organizing data, we use several data presentation tools to present the data.
Statistics has several data presentation tools including: line graph, bar chart (bar graph), Pareto chart, pie chart (circle graph), histogram, pictogram (pictograph), dotplot, stem-and-leaf plot (stemplot), box-and-whisker plot (boxplot) and scatter plot (scatter diagram) among others.
Given that we have different types of variables and data sets, what tool is best suited for representing a specific data?
What are the merits and demerits of using each tool?

Next, we shall extend our discussion by using one of the tools (scatter diagram) to show the relationship between two variables.
A relationship between two variables implies that there is an association between the two variables.

Do you agree or disagree?
It is okay to disagree. You just have to support your disagreement with facts. 😊

That association may or may not be causal.
So, we note these terms: relationship, association, causation
For example:
Old Age and Osteoarthritis
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2818253/
Osteoarthritis is a multi-factorial condition for which aging is the major risk factor. (Anderson, A.S., & Loeser, R.F.; 2010, February)
Arthritis is associated with old age.
However, does old age cause arthritis?

This leads us to the topic of Correlation and Regression, which is not covered entirely in this course.
However, some courses in Statistics and Psychology discuss it in detail.

Welcome to Data Presentation

May you please:
(1.) Review the Overview and Objectives.
(2.) Review the Readings/Assessments.
(3.) Complete the assessments initially due this week.
(4.) Participate in the Week 11 Discussion.
(5.) Attend the Live Sessions/Office Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 12: Descriptive Statistics: Data Analysis

Great Students,

Greetings to everyone.
Welcome to Module 12.

In Module 11, we discussed Data Presentation.
We used several data presentation tools including dot plot, stem plot, boxplot, histogram, pictogram, bar chart, and pie chart among others to present data.
After presenting data, what should we do?
Well, you probably said it right...Analyze the data.
Data Analysis is done for the two types of Statistics: Descriptive Statistics and Inferential Statistics.
For this module, we shall only be concerned with the analysis of the descriptive statistics of data.
These include the:
(1.) Measures of Center (Measures of Central Tendency)
(2.) Measures of Spread (Measures of Variability or the Measures of Variation)
(3.) Measures of Position (Measures of Location)
(4.) Measures of Shape

For this announcement, let us focus on the Measures of Center.
Let me begin with a story. 😊
It was on a Saturday
A family of the Dad, Mom, Daughter, Son
The two children are in middle school.
The Dad and Mom were reviewing the notes of their children
The children were reading books.
All of them were in the living room at home.


Dad: Elijah
Son: Yes, Dad
Dad: Esther
Daughter: Yes, Dad
Dad: A philanthropist wanted to buy shoes for the motherless and fatherless children at an orphanage.
There were 300 children at the orphanage.
He arrived at the orphanage and asked for a shoe size.
What shoe size should the director recommend?
Son: He asked for just a shoe size...
Rather than shoe sizes?
Dad: Yes. Do you not think it is cumbersome to ask for the shoe sizes of 300 children?
Son: But, if he really wanted to help, why would he not help "all" of them?
Typically, all of them would not have the same shoe size.
So, why not just make everyone happy by providing each one with the shoe that fits him/her?
Dad: I understand.
But, let's assume he just wanted a shoe size.
What shoe size should the director give?
Son: But, Dad; why would he want to do that?
Dad: Answering questions with questions...typical of a Nigerian
Just answer my question or say you do not know the answer.
Rather than answering it with a question
Son: I have your gene, Dad ☺
Dad: Whatever...
But, I want you to think about it... while I ask your sister
Esther, what shoe size would the director recommend?
Daughter: I think Elijah made a point.
Why would the philanthropist choose to buy shoes of only one size?
One size certainly does not fit all.

Mom: Listen my children.
Your Dad is indirectly asking you about what you learned in school last week.
He wants you to see the connection/application of what you learned.
Daughter: Okay, Mom. I get it.
The director can measure the shoe sizes of the 300 children.
Find the sum.
And divide by 300
That is known as the Mean or Average
Dad: Correct! Proud of you, Daddy's girl! ☺
Son: The second way would be the arrange all those measured shoe sizes in order ...
Preferably in ascending order
Because it is an even sample size, there would be two sizes in the middle.
So, find the average of those two sizes.
That measure is the Median
Mom: Perfect! Mummy's boy! ☺
But, why would you arrange the sizes in ascending order?
What about descending order?
Would it not give the same result?
Daughter: Mom, guess what? ☺

... click to finish reading the story.

Welcome to Descriptive Statistics: Data Analysis

May you please:
(1.) Review the Overview and Objectives.
(2.) Review the Readings/Assessments.
(3.) Complete the assessments initially due this week.
(4.) Participate in the Week 12 Discussion.
(5.) Attend the Live Sessions/Office Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 13: Probability

Great Students,

Greetings to everyone.
Welcome to Module 13.

In Module 12, we discussed the Data Analysis section of Descriptive Statistics.
In this module, we shall discuss Probability.
The applications of probability span across several disciplines.
You shall note them as you review the resources provided for you this week.
For this course announcement, let us focus on one important application: the application of probability in Biology.
This application is a life decision: Marriage.

Student: Mr. C, I thought we are studying Math.
You are a Math Faculty, right?
When did you become a Marriage Counselor?
Teacher: My dear, we want to relate a Mathematics application to Biology.
It is known as interdisciplinary connection.
It is an application that is very important, yet is often omitted/skipped when discussing the topic of probability.
Please note that I am not telling you what to do.
It is just an advice based on what we are studying.
Student: So, what is the application?
Teacher: Let's see 😊

Probability in Biology
People who inherit one sickle cell gene and one normal gene have sickle cell trait (SCT).
People with SCT usually do not have any of the symptoms of sickle cell disease (SCD), but they can pass the trait on to their children.
[What is Sickle Cell Trait? (https://www.cdc.gov/ncbddd/sicklecell/traits.html)]
Sickle cell disease (SCD) is a group of inherited red blood cell disorders.
Red blood cells contain hemoglobin, a protein that carries oxygen.
Healthy red blood cells are round, and they move through small blood vessels to carry oxygen to all parts of the body.
In someone who has SCD, the hemoglobin is abnormal, which causes the red blood cells to become hard and sticky and look like a C-shaped farm tool called a sickle.
The sickle cells die early, which causes a constant shortage of red blood cells.
Also, when they travel through small blood vessels, they get stuck and clog the blood flow.
This can cause pain and other serious complications (health problems) such as infection, acute chest syndrome and stroke.
[What is Sickle Cell Disease? (https://www.cdc.gov/ncbddd/sicklecell/facts.html)]



A man and a woman wants to marry.
Both have the sickle cell trait (SCT).
They do not know about Probability in Biology, but they saw this diagram on the CDC’s website.
They know you took a Statistics class with Mr. C and that you might help explain the diagram.

(a.) Using a Tree Diagram and/or a Punnett Square, explain the diagram to the man and his fiancée.
Include the concept of Probability in your explanations. Assume they intend to have four children.

(b.) Should they get married or not? Advise them.
(To see my advice, please review the Applications of Probability)

Welcome to Probability

May you please:
(1.) Review the Overview and Objectives.
(2.) Review the Readings/Assessments.
(3.) Complete the assessments initially due this week.
(4.) Participate in the Week 13 Discussion.
(5.) Attend the Live Sessions/Office Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 14: Combinatorics

Great Students,

Greetings to everyone.
Welcome to Module 14.

In Module 13, we discussed the topic of Probability.
In this module, we shall discuss an extension and application of probability: Combinatorics.
Combinatorics is the mathematics of counting.
It is the branch of mathematics that deals with the counting of finite items, and the arrangement of finite items with or without regard to the order of arrangement.

Have you ever wondered why:
(1.) Your student ID is combination of a letter and eight numbers.
If all the United States adults attended WNMU and if there is no restriction on the letter or the number, would there be a unique student ID for everyone?

(2.) The social security number (SSN) is a 9-digit number.
If the population of the United States is the same as the population of China or India, do you think a 9-digit number would work?

(3.) Affirmative Action is sometimes referred to as Positive Discrimination.
Fifteen applicants (Nine men and Six women) applied for four open positions in a company.
How many ways can the positions be filled if at least one woman is given a position?

All these questions and more are answered in Combinatorics.
Guess what? Let's review this Student-Teacher scenario.
What are your thoughts?
It's okay if you do not agree with me. Educators do not always agree. 😊

Teacher: You know what I'm thinking?
Student: What are you thinking, Mr. C?
Teacher: In my elementary schools days in Nigeria ...
in those days that we acted up.
Student: Of course, I know you acted up.
Teacher: Excuse me...how did you know?
But anyway... 😊
Our teacher gave us options:
Spanking or
Doing some extensive writing on several pages of an exercise book
Writing something like this: ...
"I am sorry Auntie, I will not do it again."
Student: You called your teacher, Auntie?
Is she your Aunt?
Teacher: No, she is not.
But, we called our teachers Uncles and Aunties...back in those days.
And we had to write each sentence very well so that it will not cross the lines in the pages of the book
That punishment improved our writing...punishment that also taught us to write
Because if any sentence crossed the line (either the line above or the line below), we had to write it again.
I am thinking of a good punishment that would improve Math skills...
Student: And what is the punishment?
Teacher: List all the permutations of the word, SAMUEL
Student: The number of permutations will be 6! = 720 ways.
Teacher: I did not ask for the number of permutations.
I asked to list all the permutations.
Yes, the number of permutations can act as a check to ensure you listed all of them.
Student: Mr. C, would you really give a child this kind of punishment?
To write 720 permutations?
SAMUEL
SAMULE
SAMLEU
SAMLUE
...
That is a lot of work.
Teacher: I would not ask an adult to list all the permutations.
But, would I tell a child to do it? Yes, I would.
Student: Why would you do that, Mr. C?
That is child abuse.
Teacher: Excuse me, my dear.
That is more beneficial that allowing the child to play video games for an hour.
Children are very intelligent.
They are energetic.
They love to explore.
You need to give them a lot of work so they do not waste their potentials.
Well, let's continue...

Welcome to Combinatorics

May you please:
(1.) Review the Overview and Objectives.
(2.) Review the Readings/Assessments.
(3.) Complete the assessments initially due this week.
(4.) Participate in the Week 14 Discussion.
(5.) Attend the Live Sessions/Office Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success

Welcome to Week 15: Congruency and Similarity with Constructions

Great Students,

Greetings to everyone.
Welcome to Module 15.

In Modules 13 and 14, we discussed the topics of Probability and Combinatorics.
In this module, we shall head back to Geometry.
Specifically, we shall discuss the topics of Congruency and Similarity.
What are congruent figures?
What are similar figures?
Compare and Contrast: Congruency and Similarity.
How can we determine if two triangles are congruent?
How can we determine if two triangles are similar?
What Triangle Theorems apply to congruent triangles?
What Triangle Theorems apply to similar triangles?
What theorems apply to similar figures?
Let us briefly discuss an application of similar triangles.

It is a bright sunny day.
Person A is a man.
He is standing next to a very tall tree.
He can see his shadow and the shadow of the tree.
He knows his height.
He knows the length of his shadow.
He knows the length of the shadow of the tree.
How can he determine the height of the tree?

Welcome to Congruency and Similarity with Constructions

May you please:
(1.) Review the Overview and Objectives.
(2.) Review the Readings/Assessments.
(3.) Complete the assessments initially due this week.
(4.) Participate in the Week 15 Discussion.
(5.) Attend the Live Sessions/Office Hours for this week.

Should you have any questions, please ask. I am here to help.
Thank you.

Samuel Chukwuemeka
Working together for success