Mon - June 14, 2004
King's X From the Math Monster by Sandra Dodd
Article about unschoolers and "doing the
times
tables."
<http://sandradodd.com/timestables>
<http://sandradodd.com/timestables>
Posted at 08:39 AM Read More
Sun - June 13, 2004
Multiplying by Eleven
Just some ideas of ways to play around with
multiplying by 11. Memorizing the "tricks" is not the important thing - it is
the underlying understanding of why the tricks work that will
last.
It's easy to figure out 11 times any number up to 9 -- 11X2=22, 11X3=33, 11X4=44, up to 11X9=99.
For 11 times 10 or higher, here's a handy trick:
For 11 times a two-digit number take the first digit, place it to the left and then place the second digit on the right. Insert the sum of those two digits in the center. It works from 11x10 = 110 and up as long as the sum of the two digits is less than 10:
Examples:
11 x 11 = 1 2 1 (1 + 1 = 2)
11 x 12 = 1 3 2 (1 + 2 = 3)
11 x 13 = 1 4 3 (1 + 3 = 4)
11 x 14 = 1 5 4 (1 + 4 = 5)
and so on.
If the sum of the 2 digits is 10 or up, there is an extra step. You still put the left digit on the left and the right digit on the right and then find the sum. If it is 10 or more then just put the right number (of the sum) in the center. Increase the left digit by one.
Examples:
11 X 19 --- put the 1 on the left, the 9 on the right. The sum of 1 and 9 is 10, so put the 0 in the middle and then increase the left digit by 1 to get 209.
11 X 29 -- put the 2 on the left, the 9 on the right. The sum of 2 and 9 is 11, so put a 1 in the center and increase the left digit by 1 to get 319.
11 X 48 -- put the 4 on the left, the 8 on the right. The sum of 4 plus 8 is 12, so put the 2 in the center and increase the 4 to a 5 to get 528.
Some people might find it is fun to figure out why these little "tricks" work.
11 times anything is really 1 times it plus 10 times it (11 is 1 plus 10).
1 times something is easy - it is that thing.
10 times something is easy - it is that thing with a zero on the right.
So = 11 times 4 is 1x4 plus 10x4 or 4+40=44.
11 X 9 is 1x9 plus 10x9 or 9 + 90 = 99.
Two-digit numbers work the same way:
11 x 41 is 1x41 plus 10x41 or 41 + 410 = 451.
11 x 39 is 1x39 plus 10x39 or 39 + 390. Notice how when you line these up like this:
It's easy to figure out 11 times any number up to 9 -- 11X2=22, 11X3=33, 11X4=44, up to 11X9=99.
For 11 times 10 or higher, here's a handy trick:
For 11 times a two-digit number take the first digit, place it to the left and then place the second digit on the right. Insert the sum of those two digits in the center. It works from 11x10 = 110 and up as long as the sum of the two digits is less than 10:
Examples:
11 x 11 = 1 2 1 (1 + 1 = 2)
11 x 12 = 1 3 2 (1 + 2 = 3)
11 x 13 = 1 4 3 (1 + 3 = 4)
11 x 14 = 1 5 4 (1 + 4 = 5)
and so on.
If the sum of the 2 digits is 10 or up, there is an extra step. You still put the left digit on the left and the right digit on the right and then find the sum. If it is 10 or more then just put the right number (of the sum) in the center. Increase the left digit by one.
Examples:
11 X 19 --- put the 1 on the left, the 9 on the right. The sum of 1 and 9 is 10, so put the 0 in the middle and then increase the left digit by 1 to get 209.
11 X 29 -- put the 2 on the left, the 9 on the right. The sum of 2 and 9 is 11, so put a 1 in the center and increase the left digit by 1 to get 319.
11 X 48 -- put the 4 on the left, the 8 on the right. The sum of 4 plus 8 is 12, so put the 2 in the center and increase the 4 to a 5 to get 528.
Some people might find it is fun to figure out why these little "tricks" work.
11 times anything is really 1 times it plus 10 times it (11 is 1 plus 10).
1 times something is easy - it is that thing.
10 times something is easy - it is that thing with a zero on the right.
So = 11 times 4 is 1x4 plus 10x4 or 4+40=44.
11 X 9 is 1x9 plus 10x9 or 9 + 90 = 99.
Two-digit numbers work the same way:
11 x 41 is 1x41 plus 10x41 or 41 + 410 = 451.
11 x 39 is 1x39 plus 10x39 or 39 + 390. Notice how when you line these up like this:
39
+ 390
429
then when you add you're really just
putting the 9 on the right, adding the 3 and the 9 and getting 12 and then
putting the 2 in the middle and adding the 1 to 3 to get 4 on the left. This is
the "trick."
Posted at 10:17 PM Read More
7 X 8
For some reason, this is the multiplication
fact that almost everybody has trouble remembering. So - here is a little quick
way to remember it. Just count: 5, 6, 7, 8. Why does that remind you of how to
multiply 7 X 8?
Because 56 is 7X8 -- 5, 6, 7, 8.
Because 56 is 7X8 -- 5, 6, 7, 8.
Posted at 06:26 PM Read More
Wed - January 21, 2004
Finger Multiplication
Hold your hands up in front of you, palms forward
.
Your thumbs are each a "6",
Your pointer fingers are each a "7"
Middle fingers are each an "8"
Ring fingers are each a "9"
Pinky fingers are each a "10"
Okay - now hands are in front of you, palms forward, fingers upward.
Let's multiply 7X8:
Put the pointer finger of left hand (7) touching the middle finger of right hand (8).
Now count the two fingers that are touching plus one finger below that on the left and two fingers below that on the right.
Countiing the two touching fingers and the ones below them you have five "lower" fingers.
On the top, above the touching fingers, you have 3 on the left and 2 on the right.
So - to multiply 7X8 you have your 7 finger and your 8 finger touching and then you add up all the lower fingers (counting the touching ones) and that is 5. (That is how many "tens" the answer will have.)
Then you multiply the top ones and that is 2X3 is 6.
To multiply 7X7 you touch your 7 fingers together and you get:
4 under and 3x3 on top - 49
yep
cool
I fooled with trying to write equations for how it works - never manged to do it.
if you put the two thumbs together - that is 6X6....
but you only have two lower fingers - so that's only 20.
only a "2" I mean.
but when you mulitply the top fingers it is 4X4 which is 16.
gmta
so you add the 16 to the 20 that you get from the 2 thumbs.
that makes 36
so - the lower fingers are really "tens"
and the upper fingers are "ones"
Your thumbs are each a "6",
Your pointer fingers are each a "7"
Middle fingers are each an "8"
Ring fingers are each a "9"
Pinky fingers are each a "10"
Okay - now hands are in front of you, palms forward, fingers upward.
Let's multiply 7X8:
Put the pointer finger of left hand (7) touching the middle finger of right hand (8).
Now count the two fingers that are touching plus one finger below that on the left and two fingers below that on the right.
Countiing the two touching fingers and the ones below them you have five "lower" fingers.
On the top, above the touching fingers, you have 3 on the left and 2 on the right.
So - to multiply 7X8 you have your 7 finger and your 8 finger touching and then you add up all the lower fingers (counting the touching ones) and that is 5. (That is how many "tens" the answer will have.)
Then you multiply the top ones and that is 2X3 is 6.
To multiply 7X7 you touch your 7 fingers together and you get:
4 under and 3x3 on top - 49
yep
cool
I fooled with trying to write equations for how it works - never manged to do it.
if you put the two thumbs together - that is 6X6....
but you only have two lower fingers - so that's only 20.
only a "2" I mean.
but when you mulitply the top fingers it is 4X4 which is 16.
gmta
so you add the 16 to the 20 that you get from the 2 thumbs.
that makes 36
so - the lower fingers are really "tens"
and the upper fingers are "ones"
Posted at 12:31 AM Read More
Tue - January 13, 2004
BUZZ
A game that is based on multiples - once you
understand how to play it, you can make up your own
versions.
Doing "twos" with three people - persons A, B, and C, on all multiples
of two, say "Buzz" instead of the number. (No fun with two people, of
course <G>).
A: 1
B: Buzz
C: 3
A: Buzz
B: 5
C: Buzz
A: 7
B: Buzz
C: 9
A: Buzz
B: 11
C: Buzz
With only two people you can do multiples of three:
A: 1
B: 2
A: Buzz
B: 4
A: 5
B: Buzz
A: 7
B: 8
A: Buzz
B: 10
A: 11
B: Buzz
A: 13
B: 14
Try combining "Bizz" and "Buzz" -- Do "bizz" on multiples of three and
"buzz" on multiples of two. Say "Bizz Buzz" when it is both a multiple
of two and three.
Do it with other multiples - remember fives are pretty easy - so do
twos, then fives, then threes and then combinations.
A good car game.
Doing "twos" with three people - persons A, B, and C, on all multiples
of two, say "Buzz" instead of the number. (No fun with two people, of
course <G>).
A: 1
B: Buzz
C: 3
A: Buzz
B: 5
C: Buzz
A: 7
B: Buzz
C: 9
A: Buzz
B: 11
C: Buzz
With only two people you can do multiples of three:
A: 1
B: 2
A: Buzz
B: 4
A: 5
B: Buzz
A: 7
B: 8
A: Buzz
B: 10
A: 11
B: Buzz
A: 13
B: 14
Try combining "Bizz" and "Buzz" -- Do "bizz" on multiples of three and
"buzz" on multiples of two. Say "Bizz Buzz" when it is both a multiple
of two and three.
Do it with other multiples - remember fives are pretty easy - so do
twos, then fives, then threes and then combinations.
A good car game.
Posted at 11:23 PM Read More
Thu - November 20, 2003
Quick Multiplication Trick
Use a grid to multiply quickly and develop a good understanding of the properties of multiplication.
Example: To multiply 4 X 3, draw a grid with 4 lines in one direction and 3 lines in the other direction and put dots at all the intersection points. Count the dots for the answer.
This method helps kids understand visually that multiplying is just addition and also shows visually that 4 X 3 is the same as 3 X 4 - the commutative law of multiplication.
Posted at 01:11 PM Read More
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Published On: Jun 14, 2004 08:54 AM
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Published On: Jun 14, 2004 08:54 AM