who: J1 and J2
where: in bed
when: just before going to sleep
Another mystery process trick
I found this post Little Math Magic on JD2718's blog. We did something similar at the beginning of the year with calendars (here) and the kids really liked making a choice, doing some calculations that obscure the choice, then seeing if I can figure out their choice, so I expected that they would enjoy this, too. Computationally, it is a bit more challenging for the kids as it involves squaring 2 digit integers.
talking though 14 squared, J2 asking if we could do 10*10 + 4 *4. We talked about why that doesn't work. In fact, J1 raised the example of 11x 11. Since J2 knew that this is 121, they were able to compare with the other "algorithm" and see that 10x10 + 1x1 isn't right.
J1 said that, instead, we could do 10 * 14 + 4 * 14, which J2 then calculated. When he got to 196, he was delighted, since he did recognize that old friend. Also, he mentioned 169 was another familiar square friend: "13 squared, right?"
From 196, we keep the 6 and then square that, getting 36. We keep the 6 again. Finally, we need to multiply this result by our original number, so 14*6. J2 remembered 4*14 was 56 from an earlier calculation, so he just calculated 14x6 = 14x4 + 14x2= 56 + 28 = 84.
At the time, it felt really good to hear them helping each other work through these calculations, especially their thought process checking the possible algorithm for multiplying 2 digit numbers.
Well, now that they understand the algorithm, we still have to do it as a trick, where they don't tell me their starting number. After that, let's see if they can figure out how it works?