# Extreme math facts: how radical do you get? (semi-JAWM)

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DS7 is very excited about multiplication. We are doing lots of multiplication problems using C-rods. Last night he snatched a book about multiplication out of my hands and hid in a corner with it for a while.

Our math program includes lots of multiplication work up to x10, but no further.

* Multiplication facts up to x12

* Squares to 30 & Cubes to 30 - inspired by Miko -

* Did you or your kids memorize further than twelves? (I knew a kid in elementary school who had them up to 15 and I thought he was a god.) Was it useful to have them memorized even though everything  above 10 can be "worked out"?

* What other math facts might be good to practice at the grammar stage?

Edited by kubiac
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After my son knew the facts through 12, we practiced them by doing mental math, which he preferred to the rote drill.

Also, the ability to quickly factor numbers into prime factors is extremely useful.

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My dad was big on the 16 times table, for computing. If he likes it anyway you could add that in.

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I totally thounderstand gut you were adding radicals into your times tables. Like what the square root of 3 times the square root of 12?

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I found that the computations that were especially useful were memorized over time simply by usage. The only thing I did find particularly useful to "just know" were the prime numbers (roughly up to 100). Again, I never sat down and memorized them, but having learned them through use made factoring much easier.

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Knowing some of the cubes could be useful too.

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Beast Academy level 3 (sorry, I don't remember which book offhand) has a fabulous method for quickly calculating square numbers that end in 5. DS8 really enjoyed having people quiz him to see how fast he could do it. It might not be useful to learn just to learn, but the mental math practice that it required was great IMO.

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I think it's useful to know the following times tables through ten:

12 (because there are 12 inches in a foot, and also 24 hours in a day)

15 (because there are 15 x 4 minutes in an hour, and we often work in quarter or half hours)

16 (because there are 16 tablespoons in a cup, 16 ounces in a pound, 16 cups in a gallon - plus, 16 is 2 to the 4th)

25 (because the largest coin in common usage in America is 25 cents)

But it's really not necessary unless you anticipate your son having to do a lot of real-world mental math involving those scenarios.

Edited by Tanaqui
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DD#1 has memorized many of the squares up through 26^2. Through usage, she recognizes some of the common cubes. I think those are very helpful to know, although I won't force the memorization on my math-hating children. Our elementary math program encourages memorization of times tables up through 12x12. I haven't pushed further.

I, too, thought your post would have to do with memorizing some really "radical" numbers, like the approximate number equivalent to the square root of 2. Or the first 20 digits of irrational numbers like e.  :laugh:

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Here are some good math facts to have memorized, especially page 1.

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Here are some good math facts to have memorized, especially page 1.

Great reference, I'm saving this!

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I have only the faintest recollection of radical being a math term! Maybe my kids will know it better.

Thanks for all the ideas and tips. I am taking notes furiously.

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Ds10 is doing up to 15 at school but I think that is because the other kids are still working on the lower ones and he needs something to do.

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DD hasn't even memorized up to 10's. We gave up on that a while ago. She uses a combination of skip-counting and making hash marks on the margin of the paper when necessary to figure the ones she doesn't have memorized.

If your DS wants to memorize them, let him! I wouldn't devote a whole lot of extra time to it on your end, though.

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My DS11 who finished AoPS intermediate algebra did not remember his 10x10 multiplication table until after he turned 8. He just add on the spot very fast. It just make him slightly slower than my DS12. This kid of mine also has no concept of time until he was 8/9 years old. My DS12 added extremely fast instead of memorizing as well until he somehow remembered them.

My parents memorized until 16x16 in 1st grade public school because of the imperial units. When I was in 1st grade, my school exercise book had the 12x12 printed on the back cover for reference as well as the conversion units from imperial to metric.

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My dd took what seemed like forever to memorize the standard ones.  In fact, until she entered grade 6 at ps this past year, I wasn't sure they were memorized.

I had already decided that we would just continue to practice on the side because if we spent our time on getting perfect recall, she's be doing multiplication memorization till the end of our days.

So - no radical multiplication for us, at least with my eldest.

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