In the first one, I ask a kid to think of a four-digit number; scramble it to make a new number; subtract the smaller number from the larger; scramble the result; circle one digit (not a zero–a zero is already a circle); scramble the remaining three digits; and read me the final number. I then tell them what number they circled.
In the second one, I ask a kid to give me a number between 1 and 1000 (or 100 and 900 if I’m feeling like making it look harder). I ask a different kid for a different number in the same range. I write them like:
.784…784
x326…x___
I then fill in the blank with a final three-digit number. I ask the kid to use a calculator to get both products and add the products together. I immediately write a number down on a slip of paper and wait till the kid finishes. WHen the kid is done, she finds out that I have already written the answer down on the paper.
The third one is easiest to figure out (and I’ve not yet done it with my class of fourth graders). Before the test, I put a slip of paper taped under each chair. I ask each child to think of a number; figure out the next consecutive whole number; add the two numbers together; add nine; divide by two; and subtract the original number. I then tell them that I foretold what number they would end up with and ask each child to look under their desk to find out what number they would end up with.
Those are my only three math-geek tricks. I am finishing up my student teaching soon, and would like to know any other math-geek tricks that might impress fourth graders.
If they use calculators for anything, try this one.
Have the student take a calculator and multiply single digit numbers together until he gets an 8 or 10 digit number (whatever the display will hold), like 2 x 4 x 5 x 3 x 7 x 7 x 3 x … whatever. Now, let the student read off all the digits except one of them, in any order they want.
You tell them the number they left out.
(Note that this isn’t guaranteed to work, but will work with very high probability on someone who doesn’t know the trick)
Is it an absolute requirement of the first trick that “scrambled” means “not one digit should still be in the same place”? Because if not, I don’t see how it could possibly work (in fact, even with that requirement I still don’t grak how you do it, but I’m working on it…)
If you take any number, add up the digits and subtract the result from the original then add up the resulting digits, you’ll always get a number which is a multiple of 9. For example:
1+0+4+3+3=11
10433 - 11 = 10422
1+4+2+2 = 9
5+8=13
58-13=45
4+5 = 9
8+9+5+8+9=39
89589 - 39=89550
8+9+5+5=27
88,888,888,888,888,888. 8 * 17 = 136
88…88 - 136 = 88,888,888,888,888,752
8+8…+7+5+2 = 126 (126 is divisible by nine 1+2+6 = 9)
If the kid in question is good at doing arithmetic in their head, you can do the following trick which my father used to keep me entertained on long car rides:
Let’s say the kid is nine years old. Tell them to pick any number between 1 and 10, but don’t say it out loud.
Have them square the number
Have them add twice the number to that
Have them divide that by their number
Have them add say, errrmm, seven
Have them subtract their number.
They will have magically arrived at their age, despite the fact that you didn’t know their number!
Now, depending on how clever they are, you may need to add obfuscating steps around 4 and 5 so it isn’t so obvious how it works. As I got older, my father would add more and more steps, until I eventually figured it out.
Ooooh - I think I see it now. At the end, they tell you a THREE digit number, not a four-digit number with the circled one still stuck in its place, right?
This is way simpler than y’alls, and not so much a trick as a neat thing. Still, it’s one didn’t occur to me until I was nearly 30 years old, and I wish someone had pointed it out sooner, because I always got fuzzy remembering the upper multiples of 9 for my times tables.
Write the numbers 0-9 vertically on a piece of paper, then 9-0 next to them, also vertically. You have the multiples of 9. Also, a two digit multiple of 9 always adds up to 9 (before 99, of course) 0+9 = 9, 1+8=9, etc.- which would have saved me a whole bunch of “is it 54 or 56?” over the years!
It seems like it can only work if somehow it is guaranteed to be the case that the result of the subtraction will yield three identical digits plus a fourth which has some determinate relation to the numeral found in the other three digits’ place. But that can’t be, as far as I can tell.
Okay, here, I’ll just do the trick with you.
The rightmost digit after I scramble the three remaining is 0. So which one did I circle?
I promise to tell the truth as to whether you are right or not. I’ll post the original four, the subtraction, and so on.
Now that I’ve gone through it, I’m even more puzzled how this could possibly work. If it does work, it will be awesome.
On edit: I see now you mean read off the whole final number, not just the final digit. That makes the trick much more plausible! So, my final number was 910.
Have them think of any number that’s not 0 or 1 (the smaller the number, the easier the math, unless they have a calculator.)
Multiply the number by 9.
Add up all the digits in the number (if you got 5067 (9*563), you wind up with 18.) If the new number is more than one digit, add those digits together, and so on, until you only have a one digit number. (You will always get 9, because of that little quirk about multiplying by 9 WhyNot pointed out.)
Subtract 4 from the number (You will now have 5.)
Think of an animal that begins with that letter.
Show a picture of an elephant (that will be the most likely answer, though probably several eagles as well, so maybe an eagle riding an elephant? )
While not quite a numerical trick, you could always show them what happens when you cut a Mobius Strip in half.
To make it more dramatic, of course, you’d start out with a vertical untwisted strip of paper and get two different rings when cutting through it, and then you’d show them what happens when you do the same with a Mobius Strip. For added excitement, you could also show them what happens when you do two or three half-twists instead of one, etc. They would probably be entertained for a while.
Well if you didn’t know that, you probably don’t know this: If a multiple of nine adds up to more than nine, then add up the digits of that multiple. That will always be a multiple of nine. If you keep doing this at each step, you will always end up at 9.*
Similarly, multiples of three always add up to three in this way.
There are tricks for several other numbers as well though I can not recall them atm.
-FrL-
*“Nine, nine, nine. That crazy number nine. Take any number, you will find: It all comes back to nine.” Who knows where that comes from? Hint: There’s a James Earl Jones connection!
Umm…no, they don’t. 18 is a multiple of three, buts adds up to 9. 9 is a multiple of three and adds to…umm…9. 27 also adds up to 9. A multiple of three will always add up to 3, 6, or 9, though, if you continue adding until you get to a one digit number.
While not exactly a trick, I always liked the story of some-famous-mathematician-as-a-kid whose teacher, to keep the class quiet for an hour or so, told them to add up all the numbers from 1 to 100. And the kid was finished in about 1 minute.
See how long it takes your class to figure out how he did it
That was Gauss, I believe, and expecting ‘kids’ (probably not teenagers, or at least not older than, say 16) to figure out how he summed the series seems a bit much.
I dunno - we had that as a poster on the wall in my class in primary school (grade 5 and 6) and it didn’t take me all that long to figure it out. There’s bound to be a maths geek or two in there somewhere.
Trying to figure out how LHoD does Trick 2 would be far harder (you really need algebra to do it properly) and keep 'em tearing their hair out for much longer
So, my final number was 910.
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