MathsTeacherDopers, advice sought on 11yo keen to learn logarithms

In My Humble Opinion
1

My partner’s 11yo boy (ie half way through 5th grade) has determined for reasons unknown that he wants to learn logs, and that I’m the guy to teach him. I was pretty good at maths at school but that was over 30 years ago; I don’t suppose I’ve used trig more than a handful of times since, and never logs.

I believe he’d be due to come across this stuff in school in about 1 year’s time. My half-baked plan was to start with basic algebra, bring in Pythagoras, basic trig, then on to logs.

So I wander into a large bookstore to see what’s around these days for advanced primary school kids interested in maths, and all I can see are what amounts to a bunch of comic books. Every one is illustrated with happenin’ dudes on skateboards and spiky hair sayin’ rad things and making stupid jokes. They were transparently trying to engage the enthusiasm of bored kids in a classroom and I suspect that would put him off faster than anything. Also they are all strictly based on the goverment-mandated curriculum, so for instance every book’s chapter on algebra is also on patterns (ie what number is missing from this sequence …) which is of no use to this project, it seems to me.

I was looking for something more straightforward, that just lays down the necessary concepts and techniques that need to be mastered before progressing to the next stage, presumably with some worksheets to make sure the good stuff is bedded down before moving on. Naturally I’ll need to be a chapter or so ahead of him all along :smiley:

I guess what I’m after is not just a recommendation on an exact book for me to brush up from, but also comment on my approach, and indeed any reallife experiences in this line. Thanks to anyone with help to offer!

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Perhaps I’ve been over-specific in my title; I didn’t really mean to restrict this thread to teachers only! Any interested layperson will do.

I really need help here, this is moving fast - I’ve already had to bluff my way through the first lesson last night.

Any mod reading this, would you be so kind as to change the thread title to the new ones I’ve used for this post? Thanks so much, in advance!

3

Can’t say that this will help you much - but I see that you haven’t gotten any other answers. General support only.

My dad did office calculations for the Los Angeles County Department of Public Works, Survey Section - back before there were computers or calculators. So I helped him by looking up 7 place (?) logs in a book, used for precise surveying adjustments.

As you pretty much know, logs are the other side of the coin from exponents. I imagine the first lesson or two (?) will be to check your child’s understanding of exponents. Easiest with whole number exponents, of course. Then, the idea that adding exponents is the same as multiplying numbers. (2^4) * (2^3) = 2^(4+3) = 2^7.

Then, the idea of partial number exponents. If we have 2^3 and 2^4, why not 2^3.5? We have 10^0 = 1, and 10^1 = 10, so for numbers between 1 and 10, we can come up with the decimal exponents so that 10^x = number. (Don’t know how much algebra you need to pull this off.) Can tabulate these decimal exponents, values of x.

What’s the logarithm of 20? See how 20 = 10 * 2, and how logarithms add. The logarithm of 10 is 1, and the logarithm of 2 (base 10) is, ah, 0.xxx something. So, the logarithm of 20 is 1.xxx.

We want to multiply 244 by 323 without actually doing any multiplication. We instead add the logarithms of 244 and 323, then find out what number has the logarithm of the sum.

We can do this with log tables and an adding machine (my dad could do remarkable things with just an adding machine) or we can mark up the logarithms on sliding rulers and, viola!, we have that ancient tool of geekdom, the sliderule.

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Don’t know if this is any help, but maybe this will be more of a refresher for you. I, er, learned it at my daddy’s knee, myself.

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Thanks for the reply. I think I’m going to have to dial back a bit on logs temselves, reviewing what he has to do to get there I think it’s a bit over-ambitious just yet. I’ll concentrate on algebra and other basic maths, and throw in some trig. I’ve already run Pythagoras past him.

Also I’ve found some more books that fit in with his syllabus but aren’t so comic-booky.

5

Here are some links that explain logarithms at a level a bright 11-year-old would probably be able to understand:

http://mathforum.org/library/drmath/view/55521.html

http://www.shodor.org/unchem/math/logs/

http://www.brynmawr.edu/nsf/tutorial/ss/sslog.html

http://www.phon.ucl.ac.uk/cgi-bin/wtutor?tutorial=t-log

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That last site is exactly what I was after. That is totally awesome. Thanks so much, that’ll help me and him!

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Well, by the exponent addition rule you just mentioned, 2^3.5 = 2^3 * 2^0.5 = 8 * sqrt(2)

Make sure he understands why sqrt and ^0.5 are equivalent.