I would use algorithms but my teacher says no algorithms =[

So im using tidy numbers - 19 x 21 = 20 x 21 -1 x 21=420-21=399 = ]

Okay algorithms are fine but we have to work it out mentally and we can't figure it straight away...
My teacher wants us to use strategies

Hi;

Here are my ideas :

1. I don't know if this counts as algorithms, but knowing the squares of numbers under 20 could be very helpful (like   
   Anakin had said), especially in the Pythagorean Theorem. Say you memorized 19², then immediately you may tell that   
   19x38 is 722 (19^2=361, 361*2=722)
2.Thing like 33*27 equals to (11*3)*(3*9)=11*81=891 Rearranging factors.
3. In addition, try to match up numbers that makes a multiple of 10 (like tidy numbers, you said)
4. For a multiplication of 11: (say 11x44) first write down the left-most digit, (i.e. the 4) then write down the sums of adjacent numbers starting from the left-most digit. (e.g., thousand+ hundreds, hundreds+tens, tens+ones)and stop after calculating the tens digit and the ones digit. If any of the sums exceeds 9, add 1 to the previous sum. So now we have 48_
Finally, write down the ones digit. so 44*11 =484 in the same way, 11x34=374, 11x345=3795, 11x765=8415. This may be confusing, and useless but just interesting to point out (and the fact is that you probably know this already).
5. At the last, I say, practise will make anyone better and faster at almost anything. If you practise enough times, you can just tell the anwser without pondering. Just practise and you might find some neat strategies of arithmetic

Last edited by iamfriendly (2010-04-14 08:56:59)