13 x 7 = 28...maybe??

For this week's post, I watched this video on YouTube. It's an Abbott and Costello clip illustrating how 13 x 7 = 28...or does it?? Here's the video:




This video, is very interesting. It shows us as educators how some students may rationalize the process of multiplication. There are several different techniques that can be used to determine a product of a multiplication problem. Several approaches are demonstrated in this video.

Students learn techniques for all things we teach, particularly mathematics, in different ways. This video shows us that while some students may understand key concepts and have basic understanding, they may be missing key components in the steps they take to solve problems. In this video, it looks as though single digit multiplication is understood, however when adding a second digit, it gets treated like single digit multiplication which is not correct.

In the film, this is how the standard algorithm is presented

13
x 7
______
21 (7x3)
+ 7 (7x1)
__________
28

However, the correct way to perform this algorithm is:

2
13
x 7
_________
91 (7x3=21; carry the 2; 7x1=7 then add the carry number of 2. 7+2=9. That number goes in the tens space. The solution is 13 x 7 = 91)

Here we see that by not correctly understanding where to place the numbers, how to carry, or failure to comprehend the significance of the face value of numbers, you will get the wrong solution.

Understanding and recognizing where students are struggling and tracing it back to what specific part they don't understand, teachers will be able to better correct habits and get students on track. Without digging in and investigating where the errors occur, teachers will only see wrong answers, and students will be frustrated and discouraged because in their mind, they are correct.

One thing that I liked about this video is that it showed the group of 3 men working together to try to teach and learn from each other and come up with the correct solution. This is collaborative learning. They had a real life problem that needed a solution. They worked together to develop a series of algorithms to rationalize their findings. In a classroom setting, we would have them reach an agreement and develop a system that would lead to the correct solution and group understanding.

This video below shows another way to teach children how to multiply with double digit numbers. I've never seen this approach before and I find it interesting.