kitchen table math, the sequel: help desk: scientific notation

## Sunday, February 3, 2013

### help desk: scientific notation

I'm looking at the Common Core math standards, and I see the first mention of scientific notation in Grade 8.

Does that sound right to you all?

Is there any reason to teach scientific notation earlier (or later)?

(I don't have an opinion -- I'm asking.)
Perform operations with numbers expressed in scientific notation,including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
Common Core State Standards for Mathematics

Jo in OKC said...

There are a significant number of students who don't take Grade 8 math. They take Algebra I instead.

So, to me, it's too late.

When are exponents covered? You can't do scientific notation until the students have mastered exponents.

ChemProf said...

I'd agree it is late. If they get pH anywhere in middle school science, they need scientific notation to understand it. I'd have guessed fifth or sixth grade, where they really get into decimals (but that may be wishful thinking on my part).

Anonymous said...

"There are a significant number of students who don't take Grade 8 math. They take Algebra I instead."

These students might cover the Grade 8 math in 7th grade, however.

But, yeah, you can't do scientific notation until you've learned exponents. This site:

suggests that Common Core gets to exponents in 8th grade along with scientific notation.

-Mark Roulo

Jo in OKC said...

OK. So do they still learn multiplication of whole numbers in 3rd grade? Because seriously, after they learn multiplication in 3rd grade it takes until 8th grade before they show exponents?

When do they cover area of a circle? (Normally expressed as pi*r^2) What about area of a square?

I get the deep versus wide thing, but that's a lot of time in there.

Crimson Wife said...

The Singapore Math series has it in the 7th grade book. Area of a circle is in the 6th grade book and area of a square is in the 4th grade book.

Glen said...

I'm teaching it to my own kids at the same time as algebra I and beginning programming. The exact age and grade aren't relevant, in my opinion. What matters is whether the student is ready for algebra. In my mind, these three should be taught together.requisites. I teach scientific notation in the serious exponents lesson in algebra and begin making use of them in beginning programming, which requires abstract expressions, functions, numerical data in scientific notation, etc. I don't see much advantage to presenting scientific notation earlier than these other two. I'd rather spend the time on other preparations for algebra, establish a solid foundation, then proceed with all three together.

Glen said...

"together.requisites" should read "together as corequisites"

Catherine Johnson said...

Thanks, everyone!

gasstationwithoutpumps said...

Computer floating-point notation should be taught at about the same time, so that students learn that 1.5E9 means 1.5*10^9, not 1.5*e^9 (as I had one grad student believe).

ChemProf said...

Agreed. I can't tell you how many students didn't know that the "E" (or "EE") button on their calculators existed, and were typing in 5x10^-5 instead of 5E-5 every time. Plus there is a peculiar error where they somehow introduce a factor of 10 when they type it in. I don't know how it happens, exactly, but I've seen the results.

Glen said...

Also agreed and, in fact, that's what I meant when I said that beginning programming is a corequisite. I teach the long, formal form (6.02 x 10^23) of course for reading and formal writing (or school assignments, if the teacher insists), but when doing our own work, even with paper and pencil, we always use the abbreviated "e" notation: 6.02e23.

(And there's an engineering notation, too, where you make the exponent a multiple of three. I teach it for recognition but don't use it, because these days SI prefixes (micro-, nano-, pico-, etc.) have mostly supplanted engineering notation.)

Scientific notation itself is an abbreviation; it is perfectly in the spirit of the notation to further abbreviate it.

Jen said...

I'd agree 6th/7th grade math is when you introduce and then master exponents. IF this is done well, introducing scientific notation in 8th grade math (at whatever age each of these classes are taken, of course).

Once you have exponents, scientific notation is just a small add-on. It's a case where adding it in too early is likely to confuse kids -- they don't think of it as exponents, but as some weird thing all its own.

I was subbing 8th gr science at a private school and I'd guess 1/3 of the kids sort of freaked out at the sight of scientific notation on the worksheet the teacher had left, "I don't remember how to do this!"

Once they were asked what 10^3 was, they knew -- and when I asked what's that multiplied by... Oh! Right! I can do that!

It's a concept that too early exposure seems to muddle rather than accelerate.

gasstationwithoutpumps said...

Engineering notation on calculators is what allows quick and easy conversion to giga- mega- kilo- milli- micro- nano- pico- prefixes. It is very, very easy to be off by a factor of 10 (or even 100) if you do the conversion in your head from scientific notation.

For EEs, capacitors are always done in powers of 10^6 (F, µF, pF, but not mF or nF).

Anonymous said...

Exponents are included in the sixth grade under 6.EE.A.1 and 6.EE.A.2c, which is expressions and equations. It can also be referred to as a power, so its first introduction is with the powers of ten under 5.NBT.A.2, the numbers and operations strand. Powers or exponents of 10 are the foundation for scientific notation, making the time of introduction more surprising.
However, there is an accelerated seventh grade course, which does include the eighth grade material and is meant as preparation for eighth grade algebra. I admit that the structure is hard to figure out but everything is taught at the correct grade level or close to it, except for the apparent separation of prealgebra into two years. Here's a hint: exponents are classified under expressions and equations, not the number system. Arithmetic operations are under operations and algebraic thinking for grades K-5.