- #1

EM_Guy

- 217

- 49

(40+7) x (60 + 2)

40 x 60 + 40 x 2 + 7 x 60 + 7 x 2

2400 + 80 + 420 + 14

2480 + 434

2914

Consider a rectangle with dimensions 47 units by 62 units. The rectangle can be subdivided into four smaller rectangles: 40 x 60, 40 x 2, 7 x 60, 7 x 2.

So when kids multiply two digit numbers together, they don't need to split up partial products and carry. Such an algorithm works, but is not very intuitive and doesn't get the concept of the multiplication operation across to the average elementary age kid. Instead, kids can find partial products, and then add them together. This also has a geometric interpretation as I just demonstrated.

How about division?

3000 / 62

Well, 62 goes into 3000 at least 10 times, so we write down 10.

10 x 62 = 620. 3000-620 = 2380 remainder.

62 goes into 2380 at least 10 times, so we write down another 10.

10 x 62 = 620. 2380-620 = 1760 remainder.

62 goes into 1760 at least 20 times, so we write down 20.

20 x 62 = 1240. 1760-1240 = 520 remainder.

62 goes into 520 at least 8 times, so we write down 8.

8 x 62 = 496. 520-496 = 24 remainder.

So, 10 + 10 + 20 + 8 is 48. The answer is 48 R24, or 48 + 24/62 = 48 + 12/31.

Again, this is a more intuitive way to perform division. The traditional algorithm for performing long division I think is a lot less intuitive. Most people, especially kids, don't understand why each step in the traditional algorithm works. So they are really learning simply how to follow a procedure. There is value to practicing standard operating procedures; however, mathematical education should focus on teaching concepts and helping children develop intuition. Kids should learn the structure of numbers and the concepts of operations performed on those numbers. Geometric interpretations are also useful to help kids make sense of what they are doing.

Common Core gets very political, and I'm sure that there are all kinds of political arguments that can be made for or against Common Core. But for the moment, I think that the Common Core methods of performing arithmetic have a lot of merit.

Any thoughts about this?