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”)