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Discussion Board (DB) Assessments

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Discussion Board (DB) Forum Requirements

Great Students,
Greetings to everyone.
To ensure a safe learning environment for everyone and a high academic standard for teaching and learning, I ask everyone to please follow these requirements.

(1.) Please review the Rules of Netiquette.

(2.) Each post should be unique and substantive. Please be creative.
(a.) The post should be on-topic as asked in the Discussion assessment.
(b.) There are several concepts/topics discussed each week as listed in the Pacing Guides. When applicable, post on a different concept/topic that has not been posted by someone else, provided it is a topic/concept listed for that week.
(c.) Review all previous posts from your colleagues and my comments to their posts/responses as applicable, before you submit your own post.
(d.) Unless stated otherwise, all DB posts besides DB 1 are applied problems. We want our students to see the meaning of what they are learning. We want them to relate their learning to real-world applications.
In that regard, please post an application of the topic/concept.
Review your textbook (eText), solve an applied problem, check the solution at the back of the textbook or in the Solution Manual to ensure you got it correct.
Then, submit your post by writing the applied problem completely, solving it by showing all work, and interpreting your solution (Write – Solve – Interpret).
Please see the DB Samples for examples of substantive posts.
(e.) As specified in the DB Samples, please write:
(i.) Topic
(ii.) Concept (The concept is a part of the topic.)
(iii.) Applied Problem (Please note that all word problems are not applied problems. To help you in this regard, the applied problems shall be provided for you.)
(iv.) Solution
(v.) Interpretation/Conclusion/Decision (whichever is applicable)
(vi.) Reference

(3.) (a.) The initial post is typically due on Thursday each week by 11:59 pm EDT.
(b.) Please make only one initial post. In other words, only one thread per student is allowed.
(c.) Multiple posts/threads are not allowed and will not be graded.
(d.) Re-posts are allowed and may be needed based on my comments to your initial post.
(e.) If you need to do a re-post, please post it as a response to my comments or as a response to your first post as applicable. But, please do not create a new thread.
(f.) I am not required to comment on every post. However, if I make any comment to your post, please make sure you address that comment as applicable.
(g.) If you do not understand my comments, please contact me via email and/or attend the Live Sessions/Student Engagement Hours. Typically, I do not go back-and-forth with a student (responding more than one time to a student) in DB forums. Hence, it is highly recommended you contact me via email if you have any question regarding my comments.
(h.) If any of your colleagues or I make any comment to your initial post, please do not edit/modify that post after we write the comments. Rather, respond to the comments as applicable.

(4.) (a.) The initial response (response to an initial post) is typically due on Saturday each week by 11:59 pm EDT.
(b.) In your response, please mention the first name of your colleague.
(c.) At least one response (one or more responses) to an initial post of your colleagues is required.
(d.) Please write a substantive response.
A substantive response is the response that provides constructive criticism, alternative approach that gives the same correct output, additional helpful information that will improve the post, and the correction of any incorrect step and/or output among others.
How would you improve the initial post?
Did you find any errors in the initial post? If you do, please correct the error. Teach your colleague about the error, and explain to him/her how to fix it.
What new knowledge can your colleague acquire from you based on your response?
Can you solve the initial post using an alternative approach that will give the same correct output?
What real-world examples/applications can you provide based on the initial post? Discuss/Explain. Do not just state/mention. Cite your sources accordingly.
Did your colleague learn anything meaningful from you based on your response to the initial post?
Please focus on the initial post. Do not deviate from the concept/topic in the initial post. Do not bring up your own unrelated topic/concept.
Teach/Show your colleague something new and meaningful based on the initial post.
Please see the DB Samples for examples of substantive responses.

(5.) (a.) Any attachment should be inserted directly (not attached). Any attachment whose content is not entirely seen directly in the Canvas editor will not be graded.
This implies that no one should click your attachment to see it. Insert it directly so everyone can clearly see it. Please see (b.) below.
(b.) For all Math work (symbols, formulas, equations, fractions, radicals and exponents among others); please use the Insert Math Equation icon.

Equation Editor: Part 1

Equation Editor: Part 2

(c.) Alternatively, if your handwriting is legible; you can write your post/response on paper, take clear pictures of the entire work and insert directly in the Canvas editor.
Do not attach as a file. Insert directly in the editor as a picture.
Use the Snipping Tool or the Snip & Sketch on your computer to take clear screenshots and trim off excess space/irrelevant information, then insert the screenshots directly in the Canvas editor.

(6.) (a.) For DB 2 through DB 9 assessment, written and/or video submissions are acceptable.
For DB 1 and DB 10 assessment, written submission is required.

(b.) Written Submission:
Use an acceptable font and a font size of 14pt in all your writings.
Using the Times New Roman font and a font size of 14pt is recommended.

(c.) Video Submission:
(I.) Closed-captionining of your video is required.
(II.) Please insert the video directly in the Canvas editor. Do not post an attachment.

(d.) Written and/or Video Submissions:
(I.) Make sure your post and response are well-formatted (visually appealing), nice background/lighting, etc.
(II.) Use only ordered lists. Enclose numbers/numerals/alphabets in the ordered lists in parenthesis. Alternatively, you may make them bold. This is necessary to show that they are ordered lists.
(III.) Avoid unordered lists. In other words, avoid bullets.
(IV.) Use appropriate spacing in your work.
(V.) Insert any diagrams/visuals directly in the Canvas editor. Label them accordingly. If they are not to scale, please write a note in that regard as applicable.
(VI.) If you need to include any link in your post or response, please paste the direct address of that link.

(7.) Please proof-read your writings for mechanical accuracy errors.
Any use of "i" attracts deduction of points.
Multiple mechanical accuracy errors will lead to deduction of points.
I understand that this is not an English class. However, you are expected to write well.

(8.) Sources must be cited accordingly.
You may use the APA (American Psychological Association) style, MLA (Modern Language Association) style, or the Chicago Manual of Style.

(9.) Please review the Sample Discussion Post and Response.

Should you have any questions, please let me know.
Thank you.

Samuel Chukwuemeka
Working together for success



Discussion Board (DB) Samples

Sample 1:
Example Post
Topic: Linear Functions

Concept: Slope

Word Problem/Application:
In January 2004, the price of a gallon of milk was $3.30 per gallon.
In January 2015, the price was $3.76 per gallon.
Calculate the average rate of change in the price of a gallon of milk from 2004 to 2015.
Interpret your solution.
(Source: United States Department of Labor).

Solution:
The average rate of change is also known as the slope.
From the information, we see that the input is the year and the output is the price of a gallon of milk.

Student: How did you know? Teacher: What variable depends on what variable? Does the price of milk depend on the year, or does the year depend on the price of milk?
Student: The price of milk depends on the year.
Teacher: That is correct. This means that the price of milk is the ...
Student: Dependent variable also known as the output or the $y-value$
Teacher: That is correct. The year is the ...
Student: Independent variable also known as the input or the $x-value$
Teacher: Correct. Another reason is the based on the wording of the question: it asked for the average rate of change in the "price" based on the "year"
This means the changes in the output based on the changes in the input.
That describes the slope.


$ Point\:1 = (2004, 3.30) \\[3ex] x_1 = 2004 \\[3ex] y_1 = 3.30 \\[3ex] Point\:2 = (2015, 3.76) \\[3ex] x_2 = 2015 \\[3ex] y_2 = 3.76 \\[3ex] m = \dfrac{y_2 - y_1}{x_2 - x_1} \\[5ex] = \dfrac{3.76 - 3.30}{2015 - 2004} \\[5ex] = \dfrac{0.46}{11} \\[5ex] = 0.041818182 \\[3ex] $ Interpretation/Conclusion/Decision:
The average rate of change in the price of a gallon of milk from 2004 to 2015 is about $0.0418 per year.
This means that there was an increase of about $0.04 (4 cents) in the price of a gallon of milk per year from 2004 to 2015

Reference:
Chukwuemeka, Samuel (2018). Word Problems on Linear Functions. Retrieved May 12, 2023, from https://precalculus.appspot.com/RelationsFunctions/relations-functions.html

Example Response
Samuel, you did well in your work.
We can check your interpretation to ensure it is correct.

Check the Interpretation
Use the exact (not approximate) values of the slope.

$ 2004:\:\:Price = \$3.30 \\[3ex] 2005:\:\:Price \approx 3.30 + 0.041818182 = 3.341818182 \\[3ex] 2006:\:\:Price \approx 3.341818182 + 0.041818182 = 3.38363636 \\[3ex] 2007:\:\:Price \approx 3.38363636 + 0.041818182 = 3.42545454 \\[3ex] 2008:\:\:Price \approx 3.42545454 + 0.041818182 = 3.46727272 \\[3ex] 2009:\:\:Price \approx 3.46727272 + 0.041818182 = 3.5090909 \\[3ex] 2010:\:\:Price \approx 3.5090909 + 0.041818182 = 3.55090908 \\[3ex] 2011:\:\:Price \approx 3.55090908 + 0.041818182 = 3.59272726 \\[3ex] 2012:\:\:Price \approx 3.59272726 + 0.041818182 = 3.63454544 \\[3ex] 2013:\:\:Price \approx 3.63454544 + 0.041818182 = 3.67636362 \\[3ex] 2014:\:\:Price \approx 3.67636362 + 0.041818182 = 3.7181818 \\[3ex] 2015:\:\:Price \approx 3.7181818 + 0.041818182 = \$3.75999998 \approx \$3.76 $





Sample 2:
Example Post
Topic: Application of Linear Systems

Concept: Mixology

Word Problem/Application:
Timothy likes to drink.
However, he does not like strong drinks.
During his birthday party, he received several alcoholic drinks as gifts.
One of the gifts was a vodka containing 40% alcohol by volume (40% ABV).
He wants a 5-liter solution containing 16% alcohol. So, he mixes the wine with the vodka.
How many liters of each drink (wine and vodka) should he mix?

Solution:
Let the volume of the 10% alcohol wine be x
Let the volume of the 40% alcohol vodka be y
Volume of the mixture = x + y

Volume: x + y = 5 ...eqn.(1)

Concentration: 10% of x + 40% of y = 16% of the mixture
0.1x + 0.4y = 0.16(5)
0.1x + 0.4y = 0.8 ...eqn.(2)
x + 4y = 8 ...modified eqn.(2)

So, the two equations are:

$ x + y = 5 ...eqn.(1) \\[3ex] x + 4y = 8 ...eqn.(2) \\[5ex] \underline{Elimination-by-Subtraction\;\;Method} \\[3ex] To\;\;find\;\;y,\;\;eliminate\;\;x \\[3ex] eqn.(2) - eqn.(1) \implies \\[3ex] (x + 4y) - (x + y) = 8 - 5 \\[3ex] x + 4y - x - y = 3 \\[3ex] 3y = 3 \\[3ex] y = \dfrac{3}{3} \\[5ex] y = 1 \\[3ex] y = 1\;liter \\[5ex] \underline{Elimination-by-Addition\;\;Method} \\[3ex] To\;\;find\;\;x,\;\;eliminate\;\;y \\[3ex] -4 * eqn.(1) + eqn.(2) \implies \\[3ex] -4(x + y) + (x + 4y) = -4(5) + 8 \\[3ex] -4x - 4y + x + 4y = -20 + 8 \\[3ex] -3x = -12 \\[3ex] x = \dfrac{-12}{-3} \\[5ex] x = 4 \\[3ex] x = 4\;liters \\[3ex] $ Interpretation/Conclusion/Decision:
Timothy should mix 4 liters of the 10% alcohol wine with 1 liter of the 40% alcohol vodka to obtain 5 liters of the 16% alcohol solution.

Reference:
Chukwuemeka, Samuel (2023). Applications of Two By Two Linear Systems. Retrieved May 16, 2023, from https://precalculus.appspot.com/LinearSystems/wordProblems2by2.html

Example Response
Samuel, your work was thorough. The steps are detailed. The interpretation is clear.
Another method that could be used to solve this application is the Substitution Method.

$ \underline{Substitution\;\;Method} \\[3ex] From\;\;eqn.(1) \\[3ex] x = 5 - y ...eqn.(3) \\[3ex] Substitute\;\;(5 - y)\;\;for\;\;x\;\;in\;\;eqn.(2) \\[3ex] (5 - y) + 4y = 8 \\[3ex] 5 - y + 4y = 8 \\[3ex] 3y = 8 - 5 \\[3ex] 3y = 3 \\[3ex] y = \dfrac{3}{3} \\[5ex] y = 1\;liter \\[3ex] Substitute\;\;1\;\;for\;\;y\;\;in\;\;eqn.(3) \\[3ex] x = 5 - 1 \\[3ex] x = 4\;liters $



Discussion Board (DB) Rubric

Discussion Board Rubric
Criteria Ratings Points
Post 50 to > 40.0 pts
Proficient
Post is substantive, on-topic, and submitted on time.
40 to > 25.0 pts
Fair
Post is substantive, and on-topic, but not submitted on time; and/or Post is not substantive and on-topic, but submitted on time.
25 to > 0 pts
Novice
No post was submitted; and/or Post is not substantive; and/or Post is partly substantive but not submitted on time; and/or Post is off-topic.
50 pts
Response 30 to > 24.0 pts
Proficient
Response is substantive.
24 to > 15.0 pts
Fair
Response is not substantive.
15 to > 0 pts
Novice
No response was submitted; and/or Response is not substantive.
30 pts
Requirements 20 to > 16.0 pts
Proficient
All DB requirements were followed; or Some DB Requirements were followed.
16 to > 10.0 pts
Fair
Some DB Requirements were followed.
10 to > 0 pts
Novice
Some DB Requirements were followed; or No DB Requirement was followed.
20 pts
Total Points: 100

Canvas Course Rubric:
DB Rubric



Week 1 Discussion

Post:
May you please review and address?
Number your responses to these questions accordingly.
In other words, your answers should be an ordered list just as the questions is an ordered list.

(1.) Write a brief introduction of yourself.
Include whatever information you want us to know about you.

(2.) Click the Modules link located in the Left Hand Side in the canvas course.
Review all the information in the Getting Started module.
How many items/sections are listed in that module?

(3.) Click the course navigation links on the course website.
Review all the information.
(a.) Besides the Projects, how many links were provided?
(b.) How many projects were listed?
(c.) How many projects are you required to do?

(4.) (a.) Do you have access to a working computer (laptop/desktop only; not a smartphone, not a tablet, not an iPad, not a Chromebook) with Internet connection to complete the course successfully?
A Chromebook may be used to complete MyLab Math (MLM) assignments.
However, you may not use a Chromebook to complete the project.

(b.) What internet browsers are allowed?

(5.) Have you reviewed the course syllabus?  
If Yes, do you understand it?
If No, please review it before you continue.

(6.) After reviewing the section on the course website: About Online Classes: Taking MTH 161 with Mr. C
(a.) Are you ready for this online class?
(b.) How many MyLab Math (MLM) questions are you required to attempt daily?
(c.) There is a diagram that lists the Learning Aids (indicated by two red braces) for some questions on MLM.
How many Learning Aids are on that diagram?

(7.) Have you registered for the MLM assignments?
If Yes, have you attempted any question on an assignment?
If No, please stop now. Go and register now. Attempt at least one question before you continue. 

(8.) Have you reviewed the Discussion Board (DB) Forum requirements?
If Yes, do you understand it?
If No, please review before you continue.

(9.) Have you reviewed the Discussion Board (DB) Post and Response samples?
If Yes, do you understand them?
If No, please review before continuation.

(10.) Have you reviewed the Discussion Board rubric?
If Yes, do you understand it?
If No, please review it before you continue.

(11.) (a.) How many types of graded assessments are there for this course?
(b.) What is the weight of each type of assessment?
(c.) Do you know how your MLM grades are calculated?
(d.) Do you know how to calculate your current course grade?
(e.) Do you know how to calculate your final course grade?

(12.) (a.) Have you reviewed the Welcome announcement?
If No, please review it before continuation.
(b.) If Yes, what are the days and times for the Live Sessions/Student Engagement Hours?
(c.) If the day and time is not convenient for you, and you need verbal explanations, what should you do? 

(13.) (a.) How many tutoring opportunities are available for you?
(b.) Please list them.

(14.) The Tentative Class Schedule on the course syllabus is also known as the Pacing Guide on the course website.
(a.) What page number(s) on the course syllabus did you find it?
(b.) What is the initial due date of the project draft?
(c.) What is the initial due date of the project?
(d.) What is the final due date of the project draft?
(e.) What is the final due date of the project?
(f.) What is the final due date of all MLM assignments?

(15.) Do you understand that:
(a.) This course will require a lot of your time.
(b.) You will do a lot of work on your own in this course.

(16.) (a.) Have you reviewed the Frequently Asked Questions (FAQs)?
If No, please review before you continue.
If Yes, do you understand it?
(b.) Can you think of any question that you would like to be addressed/answered?
If Yes, please state so.
If No, please state so.
(More questions will be updated as needed, as we progress through the course.)

Response:
May you please review and address?
Provide numbered responses to these questions.

(1.) Review the brief introduction of your colleague.
Based on the introduction, say something nice to your colleague.

(2.) Review the entire post of your colleague.
Advise your colleague on how to successfully complete the course. Please be specific.



Week 2 Discussion

Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Samples)
(c.) Discussion Assessment Rubric

(d.) Applied Problems for DB 2
Please Note: one question per student.
No two students may do the same question.
You may do a similar question on MLM.
You may not copy any of the MLM Learning Aids.

Section 2.1:
Questions: Pages 61 — 63
Odd-Numbered Answers: AN5 — AN6
Numbers:
(107.) — (119.)
(129.)
(132.)

Section 2.2:
Questions: Pages 69 — 70
Odd-Numbered Answers: AN6
Numbers:
(32.) — (37.)
(47.) — (50.)
(60.)

Section 2.3:
Questions: Pages 84 — 85
Odd-Numbered Answers: AN6 — AN7
Numbers:
(79.) — (82.)
(105.)
(106.)

Section 2.4:
Questions: Pages 95 — 98
Odd-Numbered Answers: AN7 — AN8
Numbers:
(51.) — (64.)
(79.)

Section 2.5:
Questions: Pages 110 — 111
Odd-Numbered Answers: AN9 — AN10
Numbers:
(85.) — (88.)
(99.) — (100.)
(103.)

(1.) Please post:
Discuss a real-world application of any of the concepts/topics assigned last week or this week.

(2.) Please respond to the initial post of any of your colleagues.



Week 3 Discussion

Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Samples)
(c.) Discussion Assessment Rubric

(d.) Applied Problems for DB 3
Please Note: one question per student.
No two students may do the same question.
You may do a similar question on MLM.
You may not copy any of the MLM Learning Aids.

Section 2.6:
Questions: Pages 114 — 116
Odd-Numbered Answers: AN10
Numbers:
(11.) — (14.)
(18.) — (19.)
(22.) — (27.)
(29.)

Section 3.1:
Questions: Pages 132 — 134
Odd-Numbered Answers: AN12 — AN13
Numbers: (37.) — (54.)

Section 3.2:
Questions: Pages 140 — 142
Odd-Numbered Answers: AN13 — AN14
Numbers: (17.) — (22.)

(1.) Please post:
Discuss a real-world application of any of the concepts/topics assigned this week.

(2.) Please respond to the initial post of any of your colleagues.



Week 4 Discussion

Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Samples)
(c.) Discussion Assessment Rubric

(d.) Applied Problems for DB 4
Please Note: one question per student.
No two students may do the same question.
You may do a similar question on MLM.
You may not copy any of the MLM Learning Aids.

Section 3.3:
Questions: Pages 154 — 155
Odd-Numbered Answers: AN14 — AN16
Numbers: (85.) — (94.)

Section 3.4:
Questions: Pages 161 — 164
Odd-Numbered Answers: AN16
Numbers: (3.) — (21.)

Section 3.5:
Questions: Page 168
Odd-Numbered Answers: AN17
Numbers: (33.) — (38.)

(1.) Please post:
Discuss a real-world application of any of the concepts/topics assigned this week.

(2.) Please respond to the initial post of any of your colleagues.



Week 5 Discussion

Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Samples)
(c.) Discussion Assessment Rubric

(d.) Applied Problems for DB 5
Please Note: one question per student.
No two students may do the same question.
You may do a similar question on MLM.
You may not copy any of the MLM Learning Aids.

Section 4.1:
Questions: N/A
Odd-Numbered Answers: AN18 — AN19
Numbers: N/A

Section 4.2:
Questions: Pages 196 — 197
Odd-Numbered Answers: AN19 — AN22
Numbers:
(43.) — (46.)
(48.)
(53.)
(59.)

(1.) Please post:
Discuss a real-world application of any of the concepts/topics assigned this week.

(2.) Please respond to the initial post of any of your colleagues.



Week 6 Discussion

Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Samples)
(c.) Discussion Assessment Rubric

(d.) Applied Problems for DB 6
Please Note: one question per student.
No two students may do the same question.
You may do a similar question on MLM.
You may not copy any of the MLM Learning Aids.

Section 4.3:
Questions: Page 207
Odd-Numbered Answers: AN22
Numbers: (57.) — (59.)

Section 4.4:
Questions: Pages 221 — 222
Odd-Numbered Answers: AN26 — AN27
Numbers: (55.) — (66.)

(1.) Please post:
Discuss a real-world application of any of the concepts/topics assigned this week.

(2.) Please respond to the initial post of any of your colleagues.



Week 7 Discussion

Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Samples)
(c.) Discussion Assessment Rubric

(d.) Applied Problems for DB 7
Please Note: one question per student.
No two students may do the same question.
You may do a similar question on MLM.
You may not copy any of the MLM Learning Aids.

Section 4.5:
Questions: Page 230
Odd-Numbered Answers: AN27
Numbers: (71.) — (74.)

Section 4.6:
Questions: Page 244
Odd-Numbered Answers: AN28
Numbers: (115.) and (116.)

Section 4.7:
Questions: N/A
Odd-Numbered Answers: AN28 — AN29
Numbers: N/A

Review Exercises:
Questions: Page 255
Answers: AN31
Numbers: (50.) and (51.)

(1.) Please post:
Discuss a real-world application of any of the concepts/topics assigned this week.

(2.) Please respond to the initial post of any of your colleagues.



Week 8 Discussion

Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Samples)
(c.) Discussion Assessment Rubric

(d.) Applied Problems for DB 8
Please Note: one question per student.
No two students may do the same question.
You may do a similar question on MLM.
You may not copy any of the MLM Learning Aids.

Section 5.1:
Questions: Pages 265 — 266
Odd-Numbered Answers: AN32
Numbers: (59.) — (70.)

Section 5.2:
Questions: Pages 277 — 278
Odd-Numbered Answers: AN35
Numbers: (89.) — (96.)

(1.) Please post:
Discuss a real-world application of any of the concepts/topics assigned this week.

(2.) Please respond to the initial post of any of your colleagues.



Week 9 Discussion

Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Samples)
(c.) Discussion Assessment Rubric

(d.) Applied Problems for DB 9
Please Note: one question per student.
No two students may do the same question.
You may do a similar question on MLM.
You may not copy any of the MLM Learning Aids.

Section 5.3:
Questions: Pages 293 — 294
Odd-Numbered Answers: AN36
Numbers: (107.) — (122.)

Section 5.4:
Questions: Pages 306 — 309
Odd-Numbered Answers: AN38
Numbers:
(119.) — (136.)
(142.)
(150.)

Section 5.5:
Questions: N/A
Odd-Numbered Answers: AN38 — AN39
Numbers: N/A

Section 5.6:
Questions: Pages 323 — 324
Odd-Numbered Answers: AN39
Numbers: (97.) — (100.)

Section 11.2:
Questions: Pages 746 — 748
Odd-Numbered Answers: AN85 — AN86
Numbers:
(79.) — (88.)
(101.)

(1.) Please post:
Discuss a real-world application of any of the concepts/topics assigned this week or next week.

(2.) Please respond to the initial post of any of your colleagues.



Week 10 Discussion

Please review:
(a.) Discussion Board (DB) Forum Requirements
(b.) Discussion Post and Response (Samples)
(c.) Discussion Assessment Rubric

(1.) Please post:
Write a one-page summary (minimum of 250 words) of what you learned in the class.
Please review your writings.
Give specific examples.

(2.) Please respond to the initial post of any of your colleagues.