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Engineering notation, math, 10y/o xposted


LMD
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Cross posted from general. Dd will be 10 soon, is loving working through beast academy amongst other things. Not really too advanced but she's bright and intuitively understands maths. Lately she says she wants to be an engineer.

 

Has anyone taught engineering to their young kids in elementary or middle school? How? Do you have any good resource suggestions?

 

Dh thinks it would be good to introduce in late elementary alongside decimals, percentages etc. so I'm looking for interesting books on the subject.

 

 

Thanks!

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By Engineering Notation you mean writing 2.456x10^5 for 245600?

 

You can teach it after the concept and use of place value is fluent, the application of multiplication is smooth and once exponents are understood.

Once your kid understands why 10^3 = 1000, 10^2 = 100, 10^1 = 10 and 10^0 = 1, then you can introduce it. It is just another way to make sense of place value and how it effects numbers.

 

And yes, decimals are just more place value.

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Cross posted from general. Dd will be 10 soon, is loving working through beast academy amongst other things. Not really too advanced but she's bright and intuitively understands maths. Lately she says she wants to be an engineer.

 

Has anyone taught engineering to their young kids in elementary or middle school? How? Do you have any good resource suggestions?

 

Dh thinks it would be good to introduce in late elementary alongside decimals, percentages etc. so I'm looking for interesting books on the subject.

 

 

Thanks!

 

Scientific notation should be taught in 6th grade. That's when they learn decimals.

 

I taught my eight-year-old using an abacus.

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Thanks Gil, yes that's what I mean.  She is pretty fluent in all those concepts.  Thanks for your explanation, that helps me see what I need to do.  We need to do a little more work on decimals and percents before I plan to introduce it, but I don't think she'll struggle with the concept.  It's more that I'm not sure exactly how to best introduce it.  Looking for a little hand-holding!  I'm pretty good with maths myself, but I never encountered this.  Which is why it was DH's suggestion!

 

Binip, that's exactly what my DH says, teach it along side decimals.  How did you teach it with an abacus?  *intrigued*  I'd love to hear details if you have the time.

 

In my general ed. thread ElizabethB mentions that they teach it in Dolciani's pre-A.  I'm currently looking at sourcing one of those...

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Thanks Gil, yes that's what I mean.  She is pretty fluent in all those concepts.  Thanks for your explanation, that helps me see what I need to do.  We need to do a little more work on decimals and percents before I plan to introduce it, but I don't think she'll struggle with the concept.

Question for you: Why do you think that she needs to work on percents before being introduced to Engineering Notation? What have percents (which are an application of fractions to the decimal number system) got to do with engineering notation (which is simply another method of writing numbers in the decimal system?) It's more that I'm not sure exactly how to best introduce it.  Looking for a little hand-holding!  I'm pretty good with maths myself, but I never encountered this.  Which is why it was DH's suggestion! First make sure that you understand that there is no "concept" to Engineering Notation. It is a shorthand for numbers in base 10.

 

There is no "concept" outside of "This is short hand for writing numbers that are extremely large or extremely small and the only reason Engineers and Scientist use it is to prevent extremely large or small numbers from being misread." <--That is it. That is the "concept" of Engineering notation, there isn't anything else to it. It is LITERALLY just one more way to express numbers in base-ten.

 

If she understands place value and that place value allows us to write a number (ie 2579) that stands for a quantity that can be expressed as

  • Words in the English language (two thousand, five hundred seventy-nine)
  • As the SUM of each digits value within the decimal system. (2000 + 500 + 70 + 9)
  • As the PRODUCT of an integer and a multiple of ten 2*1000 + 5*100 + 7*10 + 9*1)
  • As the POWERS of ten scaled by an integer value  2*10^3 = 2000 and 5*10^2 = 500, and  7*10^1 = 70 and 9*10^0 (because 10^0 = 1)

Then that is the whole story. She is ready for Engineering Notation because for EN you only need to understand place value. You can introduce it now, give her a couple of problems each day and as she gets more and more into decimal fractions you can show her that the powers work both ways because .1 = 10^(-1), .01=10^(-2), and .001=10^(-3) and so on and so forth. Don't make it hard when it isn't.

 

As you see, through out the K-6 mathematics schema, we are inching our way toward teaching order of operations, but in reverse (addition-->multiplication --> exponents.) The place value system is powerful because it allows us to simply write 4 symbols: 2579 and understand that quantity based on knowing place value.

 

In fact, the ONLY reason we express 2579 in writing as "2579" and not one of the above expressions most of the time is because its shorter and tells us the EXACT SAME INFORMATION. The only reason we use a comma between every three digits is because its easier and helps us to not make mistakes. Its a convention of the written language. A grammar rule, just like beginning a sentence with a capital letter or putting a period at the end of one.

 

If you don't think she'll struggle with the explanation I just gave then I would just show it to her today. I wouldn't expect her to do it correctly every time after this, but if you give her a number to express in each of the ways above, everyday then I expect her to have it down cold by May. Because once she understands place value and can identify the powers of ten in the decimal system up to 1,000 it is a matter of practicing the grammar of math and learning to quickly and fluently apply the convention.

 

It doesn't have to be mastered all at once. Just show her. By showing it to her, then you can  demystify that little slice of base-ten math for her.

 

Binip, that's exactly what my DH says, teach it along side decimals.  How did you teach it with an abacus?  *intrigued*  I'd love to hear details if you have the time.

 

In my general ed. thread ElizabethB mentions that they teach it in Dolciani's pre-A.  I'm currently looking at sourcing one of those...

 

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We need to do a little more work on decimals and percents before I plan to introduce it, but I don't think she'll struggle with the concept.

 

As long as she knows her place value well, you can introduce the concept in your daily life.

 

Look at Table 13.3 in link. That's how my boy's public school elementary school math text covers it. Can't remember which grade level but I guess 3rd grade. What I remembered was at lower elementary, kilo, mega, micro and milli were covered.

 

https://books.google.com/books?id=G4BVGFiVKG0C&pg=PA764&lpg=PA764&dq=prefix+nano+micro+mega+kilo+elementary&source=bl&ots=bqJF-VlXc7&sig=ANq4XStiqKvd23kolbGUNSccFwI&hl=en&sa=X&ei=TyA1VeOgMIL1oASn_oC4Ag&ved=0CCEQ6AEwAg#v=onepage&q&f=false

 

For example they learn 1000g is 1kg so kilo is 1000 of a unit of measure. Also 1000mm is 1m so milli is 1/1000 of a unit of measure.

 

I think micro and mega was actually in my kids public school English book under vocabulary words for prefixes :)

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