Posted: Jan 06, 2021 7:45 am
Hi ST,
One thing that you and your kid may find interesting involves simple arithmetic, especially since he is 7.
I'm not sure when I learned my math multiplication tables but I assume that he can divide by 7, with a known remainder (knowing the multiplication table for 7 is very helpful, of course).
I do not mean to under-estimate the abilities of your son, but for now, let's let him tell a friend (perhaps an older friend who can "appreciate" what he is doing) that he can multiply two 3 digit numbers in his head and write down the answer, left-to-right. Have the friend suggest one 3 digit number and your son will "arbitrarily" fill in the other number for multiplication as being 143.
Since 143 = 1001/7, then abc*143 is simply abcabc/7. So all he has to do is concatenate the number upon itself and divide by 7.
Example: The friend gives the number 432. So 432*143 = 61776. And 432432/7 = 61776. With a little practice, this may become almost second nature, and it may amaze his friends.
When he is older, he may want to tell people that he can multiply two 9 digit numbers in his head and write the answer from left to right. If there is a group of people, I find that asking members of the group to provide a random digit (9 times) tends to suppress any pretense. Then he will multiply this number by 142857143 (as "made up" by him).
Since 142857143 = 1000000001/7, then abcdefghi*142857143 = abcdefghiabcdefghi/7. Again, all he has to do is concatenate the number upon itself and divide by 7.
Example: The group gives the number 361214813. So 361214813*142857143 = 361214813361214813/7 = 51,602,116,194,459,259.
Of course, about 2% of the fun is having people briefly think that you are a human calculator, and 98% of the fun is telling them how it works a short time later (which I always do). I also use this to try to stay mentally sharp (yeah right, impossible for me) by, on occasion, making up a few 9 digit numbers and doing the calculations.
Some things to consider:
Note: I learned this from a book by Martin Gardner, which my dad gave me when I was 12 or so. Gardner also gives the problem of 1443 times a 2 digit number, since 1443 = 10101/7, but I never use this (I simply don't like it as much as the 3 and 9 digit problems). Ex: 1443*96 = 969696/7 = 138528.
One thing that you and your kid may find interesting involves simple arithmetic, especially since he is 7.
I'm not sure when I learned my math multiplication tables but I assume that he can divide by 7, with a known remainder (knowing the multiplication table for 7 is very helpful, of course).
I do not mean to under-estimate the abilities of your son, but for now, let's let him tell a friend (perhaps an older friend who can "appreciate" what he is doing) that he can multiply two 3 digit numbers in his head and write down the answer, left-to-right. Have the friend suggest one 3 digit number and your son will "arbitrarily" fill in the other number for multiplication as being 143.
Since 143 = 1001/7, then abc*143 is simply abcabc/7. So all he has to do is concatenate the number upon itself and divide by 7.
Example: The friend gives the number 432. So 432*143 = 61776. And 432432/7 = 61776. With a little practice, this may become almost second nature, and it may amaze his friends.
When he is older, he may want to tell people that he can multiply two 9 digit numbers in his head and write the answer from left to right. If there is a group of people, I find that asking members of the group to provide a random digit (9 times) tends to suppress any pretense. Then he will multiply this number by 142857143 (as "made up" by him).
Since 142857143 = 1000000001/7, then abcdefghi*142857143 = abcdefghiabcdefghi/7. Again, all he has to do is concatenate the number upon itself and divide by 7.
Example: The group gives the number 361214813. So 361214813*142857143 = 361214813361214813/7 = 51,602,116,194,459,259.
Of course, about 2% of the fun is having people briefly think that you are a human calculator, and 98% of the fun is telling them how it works a short time later (which I always do). I also use this to try to stay mentally sharp (yeah right, impossible for me) by, on occasion, making up a few 9 digit numbers and doing the calculations.
Some things to consider:
- If the number that the person(s) gives is divisible by 7, then there will be repeating digits in the result. Example: In the 3 digit case, the person suggests 847. 847*143 = 121121 so you say something like "Wow, isn't that interesting" (before you tell them your method).
- If you make a mistake, you can usually discover it since the final two digits will most likely not be divisible by 7. In which case, you say something like "Wow, this is a hard one, let me re-calculate".
- Of course, you can only do this once with 143 and 142857143 as the given second multiplicand, which helps lead to the fun of telling your audience how it works if they ask you to do it again.
- Verifying the results of the 9 digit calculation became a lot easier after the calculators that are now common on computers became able to provide the requisite number of digits.
Note: I learned this from a book by Martin Gardner, which my dad gave me when I was 12 or so. Gardner also gives the problem of 1443 times a 2 digit number, since 1443 = 10101/7, but I never use this (I simply don't like it as much as the 3 and 9 digit problems). Ex: 1443*96 = 969696/7 = 138528.