# Write an equation of each horizontal tangent line to the curve

If either argument is NaN, then the result is NaN. If the first argument is positive zero and the second argument is positive, or the first argument is positive and finite and the second argument is positive infinity, then the result is positive zero. ## Alan Schoen geometry

Which one would be the most difficult for a student to solve? Of course, only other people can be the judge of whether I know something worth teaching! Equations that can trigger arithmetic Part of the problem with trying to make generalizations about how kids will tend to struggle or succeed in solving equations is that there are MANY ways to successfully solve an equation.

So I want to play with the idea that it can be helpful to think of an equation as having triggers that can activate various strategies that a kid might potentially use for an equation.

Here are just a few: Just treat it like an arithmetic problem — what minus 12 is 9?

## Open-Channel Flow

I want to be clear about two things. Second, I think that arithmetic is generally something that students have had a lot of experience in, compared to algebra. Not all arithmetic is equal One of my favorite things in math education thought is CGI.

Here is an excerpt from a wiki article I wrote on CGI: Their earliest work identified a taxonomy of addition and subtraction word problem types. Different arithmetic word problems trigger different strategies, even when they use the same numbers. And they have a systematic way of thinking about it! Attempts to give kids alternate ways of seeing the operations are hard precisely because the operations are built so snugly on these paradigmatic actions.

This determines which strategies get triggered by various subtraction problems, even without contexts, and even when they contain the exact same numbers.

## Phi and Pentagons

You can also de-trigger arithmetic by tossing in more variables, but here some subtlety is needed: In particular, the metaphor of undoing or unwinding i.

Here are a couple that might make for good other case studies, if this becomes a series of posts: I think the dominant approach is to classify problems by surface-level complexity and to vary everything else, in the hopes that kids will get exposure and practice with all these different types of problems.

My point is that there is no organized, principled, systematic way that we have of thinking about the various different problem types of equations, so we just typically put them all in a blender and then present them to students all at once.

And then we spot-check the difficulties for months and months.The slope of a line in the plane containing the x and y axes is generally represented by the letter m, and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.

This is described by the following equation: = . (The Greek letter delta, Δ, is commonly used in mathematics to mean "difference" or "change".). C# Helper contains tips, tricks, and example programs for C# programmers.

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Hoek,Brown Underground Excavation in Rock - Ebook download as PDF File .pdf), Text File .txt) or read book online. Parametric Equations in the Graphing Calculator. We can graph the set of parametric equations above by using a graphing calculator. First change the MODE from FUNCTION to PARAMETRIC, and enter the equations for X and Y in “Y =”.. For the WINDOW, you can put in the min and max values for \(t\), and also the min and max values for \(x\) and \(y\) if you want to.

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