What’s the fastest way that you could help this student?

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What’s the fastest way that you could help this student?

Thanks to Tina for the submission! Go check out her very exciting new and remarkable collaboration with some dude, Productive Struggle.

## 3 replies on “Negative Infinity”

Another student was complaining to me recently how teachers don’t like when he writes E rather than x10^. Do you think writing this in scientific notation would have helped or would the student still breeze by the negative sign?

Actually beginning to evaluate by hand helps to show both the value of the limit and why the larger exponents run the show in this case. Plug 1000 in for x:

Numerator: 5,000,000 – 12

Denominator: 1,000,000,000,000 + 5,000,000

Most will probably have enough sense of place value to realize this is pretty much the same as 5,000,000/1,000,000,000,000. May not be a slam dunk for everyone that this is close to 0.

x^2 & x^4 look pretty similar, as do 1000^2 & 1000^4, and very large or small numbers that the calculator spits out in scientific notation.

It seems like a lot of kids don’t really understand what their calculators mean when they say “E-12” or whatnot. I always hope that making kids write the exponent of 10 will help them have a little more chance to understand the meaning, but I don’t know that I have any evidence that this policy actually helps. It’s more of a case of me not knowing what else to do when I have kids who don’t know what their calculator’s display is telling them.

I think my approach here, though, would be more algebraic: “When x is really big, the highest power of x totally blows away the other powers in a sum” to get them to (5x^2)/(x^4) and then to 5/x^2 and then to “5 divided by a really big number is practically zero”. So I don’t know how much, in helping this kid, I’d focus on that kind of understanding of limits as opposed to working on getting them to understand “E-12”.

The misuse of “=” here always irritates me a bit, too. I wish I had some better idea of how to get kids to use some other symbol when they mean some other relationship.