# Toon Town and Math

My youngest son is, as he will proudly tell you, “five and three-quarters” years old. The son of two math geeks, and the younger brother of two more, he is unsurprisingly also a math kid. Of all my boys, I think he is the one with the strongest mental math skills.

He likes to play Toon Town. He has recently earned a “whole cream pie” gag, which does 36 points of damage. He’s home sick today. He has been figuring out how much total damage various numbers of cream pies can do. He just came and told me, “Tomorrow, I’m going to tell my teacher that I know how much 6 x 36 is!” I asked him how much it was, and he correctly answered 216. A few minutes later he told me that he knew how much 9 x 36 was, and again gave the correct answer. Who knew how much computation Toon Town could inspire?! I asked if he knew how much 10 x 36 was. He again answered correctly, but hesitated just long enough that I knew he was adding another 36 to his previous result, rather than using the usual trick for multiplying by ten.

I pointed out that the easy way to multiply a number by 10 is to just add a zero to the end. He replied, “Yes, but I do it the old-fashioned way!”

Meanwhile, his mental math is so strong that he has little interest in the standard pencil-and-paper methods. He missed the lesson on “borrowing” yesterday, having vomited just before math time. So I showed him at home. He was willing to listen, because he knew that it was what he had missed at school, but he doesn’t like the method. He much prefers what he considers to be more intuitive mental math methods. For example, to compute 34 – 16, he will do 34 – 20 = 14 and then add 4 since he subtracted 4 too much originally, to get the answer of 18. I know that the “fix” is to give him numbers large enough that he can’t do the subtraction using his mental math methods, but for the moment I’m just enjoying watching the little gears turn. ๐

548-382 = 548-400 +18

Is there a fix? Borrowing just might be inferior.

Jonathan

Borrowing *is* inferior for smallish numbers, particularly if you don’t have pencil and paper handy, and it’s great that he can intuitively see how to do it a better way. But… suppose one had to calculate something like 13210430003 – 7894382499. In the absence of a calculator that can hold those numbers, I’m guessing paper and pencil borrowing is the “best” way to go on this one, hence perhaps still worth teaching. ๐ I don’t care to change the way he does the ones he can do in his head (and his teacher would probably go with me on that) but I do think that eventually it’s worth knowing the borrowing algorithm (and of course why it works!)

5,210,430,003 + 105,617,501 = 5,316,047,504

(I had to count commas, the rest of my work is above). For some of us, borrowing is too much of a hassle ๐

But you are correct. They taught me to borrow. I know how to borrow. I just avoid doing it.

Certainly, if I am attacking something mentally, I use your son’s algorithm, or what I just showed you, far more frequently than borrowing. So I am half teasing, and half enjoying the cleverness you shared!

Jonathan

You said:

I pointed out that the easy way to multiply a number by 10 is to just add a zero to the end. He replied, โYes, but I do it the old-fashioned way!โ

I love this!

Mathmom, I can’t believe you are talking about a 5yo here. I’ve worked with 3rd and 4th graders (8-10 year olds) who have trouble with the train of thought that your E is using at only 5. Very impressive!

Ok, jd, I’m impressed. I don’t think my 5yo is at that point yet (neither am I, but that doesn’t mean anything), but it’s interesting to see that you prefer the “mental math” method even for large, messy numbers.

Mama G, I’ve worked with kids older than 4th grade who still have trouble with mental math techniques like this. It’s one reason I went on a mini-rampage against the overuse of calculators in our school’s math program, and I did convince the principal/math teacher to change that! We are doing more explicit mental math teaching now, and the practice and training does help. With my little guy, it probably helps that writing is still an effort for him, so he has a built-in incentive to do it “in my brain” as he would say, rather than on paper.

Your numbers looked big, but it’s only a slight adjustment to what your son is already doing.

he makes 34 – 16 into 34 – 20 + 4

I make 123 – 88 into 123 – 100 + 12

Doing it for almost 40 years, I can handle bigger numbers. But the technique is almost the same.

Honestly, he could end up carrying for the rest of his life, no great loss. But he has his hands around the numbers, he is in control, and that will allow him to focus on concepts (because the skill side will come easy). Lots of upside potential there.

Jonathan