Week 2 Discussion — Flip It, Avoid It, or Draw It? — Traditional alternative (no AI)

Instructors: publish this instead of the adaptive version if you prefer, and unpublish or delete the adaptive one.

Hook

Two people can solve the same inequality in different ways and both be right. One divides by a negative and flips the sign; another rearranges so the x term stays positive and never flips at all. And when a real rule says "within" or "more than," someone has to decide whether the edge counts. This week you learned enough to argue about those choices, not only follow them.

Your discussion question — choose Option A or Option B; they carry the same weight and the same rubric, and you say which you picked.

Option A: A study partner says: "I never use the flip rule. In −2x + 1 < 9 I add 2x to both sides and subtract 9 instead, so x never ends up with a negative number in front of it." Is avoiding the flip a better habit than learning the flip rule, a worse one, or merely different? Test the study partner's method on −2x + 1 < 9 or on −3x > 9, and argue which approach you would teach a friend and why.

Option B: Pick a real "within" or "more than" rule from your life, your job, or your community — a budget ceiling, a thermostat setting, a delivery radius, a time window, a tolerance on a measurement. Write it as a linear inequality or an absolute-value inequality, solve it, and write the answer in interval notation. Then argue whether the bracket-or-parenthesis choice at the edge actually matters in that situation: would including the endpoint change any real decision?

There is no single right answer here. Some people find the flip rule cleaner, others find rearranging safer, and a delivery radius, a pay range, or a thermostat can each be argued in more than one direction at the edge. Pick the one you actually care about, and show us your reasoning.

Expectations

Activity format: one initial post followed by two substantive peer replies. Plan on about 45 minutes across the two deadlines; your instructor sets both due dates in Canvas.

Your initial post — by the first due date (early in the module week):

• Say which option you chose.
• Show the algebra step by step, and check your result by substituting a value inside your answer and testing the endpoint.
• Use at least two of this week's terms (linear inequality, flip rule, interval notation, infinity, absolute value, absolute-value inequality, union) correctly.
• Take a clear position and give a reason for it.
• Length: roughly 150–250 words if written. You may instead record your post as audio or video (about two minutes) and attach a transcript; both forms are scored by the same rubric.

Your replies — by the second due date (the end of the module week):

• Reply substantively to at least two classmates.
• A substantive reply does more than agree: test the poster's answer with a value of your own, point out a check they skipped, or argue the other side of their edge decision. "Nice point!" on its own does not count.

What a strong post looks like:

I chose Option B. My apartment search needs a place within 2 miles of campus, which sits at mile marker 10, so |m − 10| ≤ 2. That gives 8 ≤ m ≤ 12, written [8, 12]. I tested m = 9: |9 − 10| = 1, and 1 ≤ 2. The brackets matter here, because an apartment at exactly marker 12 is still a 2-mile trip, and I would not want to rule it out. "Within" is the middle, an AND, so one interval is right.

Notice how it writes the rule as algebra, shows the check, names the AND, and defends the edge choice with a real decision. That is the bar.

Participation rubric

This discussion is worth 10 points. The three criteria below look at your initial post and your peer replies.

Post early if you can — the best threads happen when people have time to reply before the second due date.

Built with The Course Maker · samples.thecoursemaker.com