1. Think “Relevant ==> Simple ==> Intricate.” 2. Visualize “mastery blocks.” 3. Generate comprehensive examples. 4. Assessment. 5. End with lead to next topic.

1. Keitaro Matsuoka (keitaro@hackinginstructor.com)
Course Design Best Practices
1. Think “Relevant Simple Intricate.”
2. Visualize “mastery blocks.”
3. Generate comprehensive examples.
4. Assessment.
5. End with lead to next topic.

2. 2
Welcome Message Example
Each instructor should post a welcome message and a short bio to the Student Lounge. The Student Lounge is an area for students to share personal information, discuss issues not related to the course, share opinions, and just chat. During the first week, the Student Lounge will be a busy forum. Students are sharing information and welcoming each other to the course.
In addition to a general welcome, explain to the students in your initial post how to use the Student Lounge. It's an area for them to relax and communicate on a friendly basis one to another.
Here's an example of the kind of posting that sets the right tone for the class:
or
Welcome to Winter Quarter 2014.
I am Elle O’Keeffe, your Career Services instructor, and together we will make this a successful quarter.
I hope everyone had/is having/will have a great Holiday Season. My daughter and I certainly did.
About me:
I have
 a BA in English Literature
 an MA in Liberal Studies
 a graduate certificate in English
 an MBA with concentrations in HR and General Management
I am currently working on my PhD in English: Texts and Technology
I have been learning Chinese (Mandarin) since January 2010.
I started learning French a few months ago--so much easier than Chinese.
I read nonstop. Here are a few of my favorites:
Sarah's Key
The Secret Life of Bees

3. 3
Drive
To Kill a Mockingbird
The Lovely Bones
Freakonomics
The list could go on and on...
Zoe is my 74 pound four-legged baby.
I am excited to work with you this quarter. Please watch for announcements and emails from me which will include info about:
 Learning Goals
 Concepts
 Live Session Opportunities
 Technical Tips and Tricks
 Due dates
If you have a question or concern, contact me. If you do not know the procedure for something, contact me. If you need to brainstorm, contact me.
Elle.okeeffe@rasmussen.edu
Skype: Elle_RCO
Best,
Elle O’Keeffe
Notice that this sets me up as a person with plenty of education and varied interests. Also, note anyone with a dog, anyone who loves languages, anyone who speaks French or Chinese, anyone who loves to read, now has something in common with me. Finally, note I have provided multiple ways to reach me. This sends the message that I WANT to be contacted, and not just in an emergency. Finally, please note that the images break up the chunks of text.
On the other hand is the example below:
Hello, I am your instructor, Professor Smith, please post your introduction to this area along with responding to other learners' post. Thank you.
This example could benefit from a dose of warmth and engagement on the part of the instructor. To avoid this mistake, ask yourself:

4. 4
· Did I share my degrees and industry background? Is the intro/bio written in my voice? Is there info in this message that allows students to connect with me, picture me, see commonalities between them and me?
Best Practice: Make sure you double-back to the Student Lounge the first week or so, specially looking for new students who've joined the class late.

5. 5
Course Introduction Example
Welcome to Calculus II!
Have you watched Toy Story? It is a series of movies about toys who pretend to be lifeless when humans are not around, but who come to life when Andy (the little boy who owns them) leaves his room. The movies focus on Woody, who is a cowboy doll and his comrade Buzz Lightyear, an astronaut action figure who is named after Apollo 11 astronaut Buzz Aldrin. Buzz's favorite catchphrase is "To infinity ... and beyond!"
You may be wondering how Toy Story has anything to do with Calculus II. Well, the two main topics of Calculus II are integration (which is about finding the area under the curve) and infinite series. You learned about integration in Calculus I. An infinite series is a sum of numbers that goes on forever. In Calculus II, we extend the integrations further and also learn about the series that go "to infinity… and beyond!"
This course will also cover some advanced topics and techniques applied by NASA engineers who build rockets (see, it is actual rocket science!).
You know you can learn calculus. If you are taking this course, you have passed a course in Calculus I. So congratulations, and let's get ready to take off!

6. 6
Lecture “Block” Examples
Week Title: Module 09 - Inverse, Exponential, and Logarithm Functions Part 2
Page Title: Logarithmic Functions
Logarithmic Functions
The exponential function answers the question, "what is the number if it is raised to a power?" A logarithmic (or log) function answers the question, "what is the power that the number was raised to?"
The logarithmic expression, logc x (read "the log base c of x") has a base c and argument x. See the Illustration below to get an idea of what log functions look like.
Illustration
What is x in the following equations?
푙표푔381=푥
3푥=81, so 푥=4.
푙표푔2푥=−5
2−5=푥, so 푥= 132.
Natural and Common Logs
A logarithm's base can be any positive number (not 1). There are two bases that you will encounter most often. They are Base 10 and Base e.
A log of base 10 is called a common log. Typically, if the base is not specified in a log expression, it is understood to be 10. For example, log100=2, since 102 = 100.
A log with base e is called the natural log. It is so common that it has its own notation: ln x (natural log of x). So ln푥=푙표푔푒푥.
Graphs of Logarithms
All log graphs have essentially the same shape with a few important characteristics. Here is a graph of 푓(푥)=푙표푔2푥.
Characteristics:
1. There are no negative x values.
2. The y-axis is the vertical asymptote.
3. The graph contains the point (1, 0). Try plotting different log functions to verify this.
2112343211

7. 7
Logarithmic Properties
Logarithmic functions possess three major properties. You should be aware of these properties to help you expand and compact log expressions.
1. Property 1: log푎+log푏=log(푎∙푏). This means that the log of a product is equal to the sum of the logs. Example: 푙표푔 25+log2=푙표푔 50=log2∙25
2. Property 2: log푎−log푏=log 푎 푏 . This means that the difference of two logs with the same base is equal to their quotient (division). Example: log 푥−log푦=푙표푔 푥 푦
3. Property 3: log푥푎=푎log푥. Example: 푙표푔352=2×푙표푔35. The exponent jumps to the front as a multiplier.
Just remember these logs have nothing to do with the trees!
Week Title: Module 09 - Inverse, Exponential, and Logarithm Functions Part 2
Page Title: Growth and Decay Problems
Exponential Growth and Decay
In reality, it is difficult to truly experience exponential growth, at least over a long period of time. The reason is that exponential growth typically results in really big, unrealistic numbers quickly. For this reason, most exponential growth problems are about three major kinds: continuously compounded interest (seen in the previous module), exponential growth, and exponential decay. We go over the latter two here.
A common formula for all exponential growth and decay is 푃(푡)=푁푒푘푡, where P is a function of time t, and N is the original quantity, and k is the rate of change.
Exponential Growth
If a quantity increases at a rate which is proportional to the size of the quantity itself, it exhibits exponential growth.
Illustration
A crime scene investigator (CSI) in Miami collects evidence from a corpse. He notes nine bacterial colonies at 8 a.m. Monday morning. On Tuesday afternoon at 4 p.m., he notices that the colonies have grown to 113. Assuming that the growth is exponential, how many colonies will he have on Friday afternoon at 5 p.m. when he needs to present the evidence to the jury?

8. 8
The time between 8 a.m. Monday to 4 p.m. Tuesday is 32 hours. Plugging in this information to the growth formula, you get:
9 푒푘×32=113 푒32푘= 1139
Take the natural log of both sides: ln (푒32푘)=ln( 1139) 32푘=ln ( 1139) 푘= ln113932≈0.079
Put back the k value into the formula:
9 푒0.079×105=36034
About 36034 colonies will be present on Friday at 5 p.m.
To do the calculation in Excel, type in:
=9*EXP(0.079*105)
Exponential Decay and Half-Life
Half-Life is the amount of time it takes for a quantity to decay exponentially to become half of its original quantity.
Illustration
Assume that 800 g of Carbon 14 (also known as radiocarbon, which exists in all living plants and animals) are initially present. Only 400 g remained after 2.5 years. How much will remain after 4 years?
Plug in the information into the formula:
800 푒푘×2.5=400 푒2.5푘= 400800= 12 푘= ln122.5≈−0.277
Using Excel (=800*EXP(-0.277*4)), you see that about 264 g remain.

9. 9
Calculations Example
xi xi - ( xi - )2
29 39.6 -10.6 112.36
31 39.6 -8.6 73.96
35 39.6 -4.6 21.16
39 39.6 -0.6 0.36
39 39.6 -0.6 0.36
40 39.6 0.4 0.16
43 39.6 3.4 11.56
44 39.6 4.4 19.36
44 39.6 4.4 19.36
52 39.6 12.4 153.76
Sum: 412.4
s2 = 45.8222
Mean 39.6 s = 6.76921
Standard
Deviation 6.769211
Variance 45.82222
To calculate the standard deviation and variance:
1) List all the data values .
2) Select the cell for the output.
3) Use the STDEV or VAR function, as shown below.
To calculate the variance manually:
1) List all the data values.
2) List the mean of all values.
3) Take the difference between the two.
4) Square the differences.
5) Sum the squares of the differences.
6) Divide by (n - 1), which is 9 in this case.
7) Take the square root of the variance to get the standard deviation.
You notice that manual calculations and Excel calculations, say for
variance, match.

10. 10
Fun and Interactive Discussion Example
Week Title: Module 08 - Inverse, Exponential, and Logarithm Functions Part 1
Page Title: Module 08 Discussion - Cryptography
Page Type: Discussion Forum
Assume you are a spy. You need to send an encrypted message to MI6. Your task is to use a one-to-one function to encode your message using the table below.
A
B
C
D
E
F
G
H
I
J
K
L
M
1
2
3
4
5
6
7
8
9
10
11
12
13
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
14
15
16
17
18
19
20
21
22
23
24
25
26
You decide to use a one-to-one function, 푓(푥)=3푥+1, to encode the message. Agents at MI6 will use its inverse function to decode the message.
To exchange the message "BE VERY CAREFUL", you will send:
7
16
67
16
55
76
10
4
55
16
19
64
37
because B corresponds to 2 and 푓(2)=7. E corresponds to 5 and 푓(5)=16. Agents at MI6 will use the inverse function 푓−1(푥)= 13 푥− 13 to decode your message. For example, 푓−1(7)= 2, which corresponds to B.
Your mission, should you choose to accept it, is to:
1) define your own one-to-one function (initial post), and
2) send an encoded message back to MI6 (initial post), and
3) decode your fellow agent's message to you (response post to another student).
This assignment will self-destruct in 5 seconds!
Please make your initial post by midweek, and respond to at least one other student's post by the end of the week. Please check the Course Calendar for specific due dates.

11. 11
Reflection (dev math) Discussion Example
Reflection Discussion – Week 1 Expectations
For this discussion, please take a few minutes to reflect on your impressions and expectations for this class.
Any feelings/impressions are acceptable (as long as they are honest). Do not feel you need to be bubbly and positive (there is no expectation that you are excited and thrilled to be taking a math class). Since this class is partly online, we will rely on the discussion boards to discuss (and hopefully alleviate) apprehensions, fears, excitement and hopes you may have with the class. Please use the reply post to encourage and assist your fellow classmates.