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Scientific Notation: Conclusion

For the standards, I don’t have to take scientific notation very far. They don’t need to be able to do arithmetic with them, they just need to be able to understand them: convert to them, from them, and compare them.

Those last two, in my informal evaluations during the classes, were gimmes. Incidental learning that they acquired in the process of the other stuff. I’d ask them about it, in an offhand way, and get not only correct responses, but “no duh, that’s a stupid question” commentary. From kids the specialize in evasion tactics, that’s as clear an indication that you can get that they’ve internalized it.

The one thing they did struggle with is the conversion from decimal to scientific notation. The problem was understanding how and why the mantissa (what they call the decimal part) is formed.

So, I gave them an exercise:

Write down a non-zero digit. Follow it with a decimal point, and 2-4 more digits.

Is the number greater than 10? Less than one?

Could it be? Give an example, or explain why it’s impossible.

Given my kid’s abhorrence of having to explain anything, they spent a lot of time trying to come up with examples. Their partners gleefully pointed out how wrong they were. Eventually, the explanations filtered out.

After that, it was a piece of cake:

The practice exercises were to reinforce the powers of 10/decimal relationship. The rules (especially decimal placement) came from the exercise they’d just done.

And, in complete contradiction to the arguments in my previous post, I gave them numbers from real world bits of trivia.

There are two things to fix with this lesson:

  • The layout of the worksheet: The kids wanted to skip over the rules part. I think a portrait layout would make the order I wanted things done in a bit clearer.
  • The wording of the “The decimal goes” prompt. The previous two prompts made them think about decimal movement, and their initial inclination was to write “left or right depending on the sign of the exponent” rather than “after the first non zero digit” (or, in their own words, “between the first two numbers that aren’t zeros”)

{ 4 } Comments

  1. Therm L'Eye | February 8, 2008 at 9:04 am | Permalink

    > The previous two prompts made them think about decimal movement, and their initial inclination was
    > to write “left or right depending on the sign of the exponent”

    For the record, this was my initial reaction as well (in fact, I assumed it was organized the way it was precisely to emphasize the point). It didn’t occur to me to think differently until your comment below.

  2. Mr K. | February 8, 2008 at 10:17 am | Permalink

    Ayup – the fault wasn’t theirs. I need to find a better setup without having to explicitly tell them.

    In a lot of ways, that’s the secret to good teaching (in math, at least): figuring out how to make them think of something without actually telling them what to think.

  3. teonna | September 2, 2009 at 4:55 am | Permalink

    how far is the sun away from earth

  4. Molly Kate | September 15, 2011 at 4:27 pm | Permalink

    Thank you so much for your postings on scientific notation. I used 2 of your worksheets and it helped tremendously. A few students did mention that 23.14159 is not “correct” scientific notation since 23 is not between 1 and 10 and thus tried to get out of completing the worksheet on this fact alone. I also appreciated your earlier comment and did alter the fill in the blanks per your suggestion. If you’re interested in seeing how I adapted your idea with dy/dan’s check out http://mathemagicalmolly.wordpress.com/. Thanks again for sharing!!!