Thinking about different ways to manifest micromaterials, I decided to make one that would have helped me a bunch, back when I was learning about simple linear equations.

The definition of a linear equation:

#### y = mx + b

is simple enough…but what does it really mean?

Understanding that the “m” is equal to the slope and the “b” is equal to the “y intercept” is also easy to memorize, but then we also need to know that “slope” is the rate of how quickly the line rises or falls (“rise over run” as it’s sometimes taught), and the “y intercept” is where it intersects the “y axis”…

And we’ve now got a bunch of terms to know. The understanding of what the terms mean is necessary to be able to correctly solve linear equations from lines, but would it possibly also be helpful to be able to visualize from lines to equations?

I felt like moving one step past mere visualization to actual physical creation of lines would provide an additional means of really understanding what these different equations actually mean.

## Next Steps

Being able to connect a physical motion (and visual feedback) to an equation is good, but what would be even more helpful for some learners might be to get feedback on predicted lines from equations, showing learners an equation and asking them to draw the line.

It’s an interesting question about how best to give this feedback, as well as “how close” to the actual line is “close enough” to tell the learner that they successfully predicted what the line would look like. It may be enough to just show the predicted line and the actual line, with the learner able to see themselves how close they actually got.

In addition, the ability to extend beyond just linear equations to also include quadratic and possibly even exponential equations would be nice, so I’m hoping to be able to add those in as well in the future.

Lastly, the placement of the equation isn’t ideal, since it overlaps the graph and would be better placed below the graph. This and other simple stylistic improvements are slated for version 2 of this simple micromaterial.

Everything is very open with a very clear

description of the challenges. It was really informative.

Your website is useful. Thank you for sharing!

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