Cycloids

I recall seeing cycloids mentioned briefly in a high school textbook long ago, though it is typically ignored today. But Harold Jacobs devotes a chapter to the cycloid in Mathematics: A Human Endeavor, a textbook I wish my high school … Continue reading

Gallery

Mathematical Gems


Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49
post image

Gallery

Constructing a unit circle


Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

In trigonometry, mastering the unit circle is a precondition for success. Loaded up with angles, sines, cosines, and tangents, it looks at first like a mess. But it can be built up in a careful orderly manner. The circle is … Continue reading

QOTD 10/16


Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Which of the following lists all the positive factors of 8? [poll id="11"] Which of the following is an equivalent simplified expression for ? [poll id="12"] [poll id="13"] … Continue reading

QOTD 10/15


Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

On the first day of school, Mr. Vilani gave his third-grade students 5 new words to spell. On each day of school after that, he gave the students 3 new words to spell. In the first 20 days of school, … Continue reading

QOTD 10/14


Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Two enterprising college students decide to start a business. They will make up and deliver helium balloon bouquets for special occasions. It will cost them $39.99 to buy a machine to fill the balloons with helium. They estimate that it … Continue reading

Class X Academy

I've been working on a summer program with Morghan Williams of YPP of Michigan, Thom Hickey with Bright Futures and Lynn Malinoff, the director of 21st Century Community Learning Centers at Eastern Michigan University. My role is thinking about the … Continue reading

Taylor series with desmos


Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

We are looking at how to introduce Taylor series, and we wanted to start with approximations to and Seems like a good application for a graphing utility. We had the students start by looking at a polynomial like It takes … Continue reading

Good things to know for the AP calculus test


Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Definitions: A critical point of a function is any point where the derivative is zero, or is not differentiable. Statements: The average value of the function on the interval is The average slope (or rate of change) of the function … Continue reading

The Rule of Adrick


Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Here are some common mistakes in calculus class:

I overheard a student explain one of these fallacies by saying "that's not how math works." In other words, these are not established truths or rules that we can apply when solving problems. The justification in a mathematical argument must be something we know preserves truth. I began applying this in class, by challenging students directly "what rule did you use to justify that step?" In honor of my student's concise evisceration of faulty reasoning, I propose the...

Rule of Adrick: If you cannot justify your reasoning with a known method, then your answer is most likely wrong.

Example usage: "You divided both sides by zero, so by the Rule of Adrick, your answer is not correct."

Note: Rarely, at least some of the rules list above work anyway because you got lucky. When does that happen?

I asked my students to volunteer similar examples. Here are some other non-rules they came up with:

  1. Applying the Pythagorean theorem to an obtuse triangle.
  2. Given , how many critical points are there? Thought it was

Inverse functions


Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 47

Warning: preg_replace(): The /e modifier is no longer supported, use preg_replace_callback instead in /home/cherry/www/education/wp-content/plugins/latex/latex.php on line 49

Inverse functions can be a challenge to think about. Tinkering with examples via a graphing utility is a good way to build comfort. You can begin with desmos.com. Let's try a fairly simple, but sufficiently interesting example: Launch desmos.com. Enter … Continue reading