11 thoughts to “Teacher Math Lesson: The Division Algorithm”

This is ridiculous. If you really want to teach the partitioning of the number into 4 equal groups, it can be taught much faster.
1. Break 138 into its places, that is: 138 = 100 + 30 + 8
2. Take each place/piece and break into 4 equal parts:
100 can be broken into 4 groups of 25
8 can be broken into 4 groups of 2
30 can be broken into 4 groups of 7 with 2 left over
So you have 25 + 2 + 7= 34 with 2 left over.
If you want, 2 broken into 4 parts = 0.5. So: 25+2+7+0.5=34.5 DONE

This will confuse more than help. We want kids to be creative in creating their understanding. However, they need to be taught in a way that won't take them forever or easily lend to errors.

You are right: there are quicker ways to do this particular operation. I chose to divide by 4 so that the demonstration with physical materials would be quicker; because the divisor is 4, we can easily divide each place mentally, and add the pieces together, as you have done.

However, if the divisor was, say, 7, your method would be extremely difficult.
In fact, splitting 138 into 100+30+8 would hinder the child, mostly because 100 is really difficult to divide 7 ways.

The point of the algorithm is that it works with any numbers, as do all algorithms. But it's not the only way to do division. Ideally, children will learn multiple methods, including written algorithms, mental shortcuts, and so on.

Thanks for responding to my comment. So, let me try to explain my concerns. 1. I think the video presentation is too long and doesn't highlight the point. 2. Once the student has grasped the concept of division using manipulatives, what is next? I'm sure tons of research has been done to demonstrate that students don't "get" what division is doing. How does this method help them "do" division efficiently?

I think too much time is spent emphasizing how complicated division is and that the terminology of "into" is flawed. Not enough time is spent on the goal of the algorithm.. From my perspective (correct me if I am wrong) you are simply modeling division by sharing manipulatives (dividend) equally among a number of bins (divisor).

I got so distracted by all the introductory remarks that I didn't have the patience to see the simplicity of what you were doing. I thought you were emphasizing division of place values first (i.e. divide the 100's, 10's and 1's) and then dealing with the remainder. Again, what I proposed was an attempt to streamline what I thought YOU were saying. Personally, once I learned that division was sharing things equally, I understood the traditional algorithm. I understood place value..

Thanks again for your interest, and the detailed comments. I think maybe we are looking at this from two different perspectives.

The intended audience for this video is classroom teachers who are looking for ways to help children with their math.

The division algorithm is not easy for children, but can be explained in ways to make it as clear as possible. As you say, place value is the key here, as with all algorithms. That's why base 10 material is so helpful.

Once children "get" the algorithm, and truly understand how it works, they should be able to use that understanding to do division mentally or in other flexible ways and in general understand how to divide base 10 numbers into equal groups.

The base 10 materials, used with the algorithm, illustrate the process of division, with the aim ultimately of freeing students from needing to use the algorithm. But we want to get there without instilling the need to use a calculator for every question.

I did not learn blocks in Europe 30 years ago just the short long division. When my 5 grader bring his assignment with blocks I was like OMG!. Thank you sir for presenting this the right way that both of us understand! Will use your videos more.

This is ridiculous. If you really want to teach the partitioning of the number into 4 equal groups, it can be taught much faster.

1. Break 138 into its places, that is: 138 = 100 + 30 + 8

2. Take each place/piece and break into 4 equal parts:

100 can be broken into 4 groups of 25

8 can be broken into 4 groups of 2

30 can be broken into 4 groups of 7 with 2 left over

So you have 25 + 2 + 7= 34 with 2 left over.

If you want, 2 broken into 4 parts = 0.5. So: 25+2+7+0.5=34.5 DONE

This will confuse more than help. We want kids to be creative in creating their understanding. However, they need to be taught in a way that won't take them forever or easily lend to errors.

You are right: there are quicker ways to do this particular operation. I chose to divide by 4 so that the demonstration with physical materials would be quicker; because the divisor is 4, we can easily divide each place mentally, and add the pieces together, as you have done.

However, if the divisor was, say, 7, your method would be extremely difficult.

In fact, splitting 138 into 100+30+8 would hinder the child, mostly because 100 is really difficult to divide 7 ways.

The point of the algorithm is that it works with any numbers, as do all algorithms. But it's not the only way to do division. Ideally, children will learn multiple methods, including written algorithms, mental shortcuts, and so on.

Thanks for expressing your interest!

Thanks for responding to my comment. So, let me try to explain my concerns. 1. I think the video presentation is too long and doesn't highlight the point. 2. Once the student has grasped the concept of division using manipulatives, what is next? I'm sure tons of research has been done to demonstrate that students don't "get" what division is doing. How does this method help them "do" division efficiently?

I think too much time is spent emphasizing how complicated division is and that the terminology of "into" is flawed. Not enough time is spent on the goal of the algorithm.. From my perspective (correct me if I am wrong) you are simply modeling division by sharing manipulatives (dividend) equally among a number of bins (divisor).

I got so distracted by all the introductory remarks that I didn't have the patience to see the simplicity of what you were doing. I thought you were emphasizing division of place values first (i.e. divide the 100's, 10's and 1's) and then dealing with the remainder. Again, what I proposed was an attempt to streamline what I thought YOU were saying. Personally, once I learned that division was sharing things equally, I understood the traditional algorithm. I understood place value..

Thanks again for your interest, and the detailed comments. I think maybe we are looking at this from two different perspectives.

The intended audience for this video is classroom teachers who are looking for ways to help children with their math.

The division algorithm is not easy for children, but can be explained in ways to make it as clear as possible. As you say, place value is the key here, as with all algorithms. That's why base 10 material is so helpful.

Once children "get" the algorithm, and truly understand how it works, they should be able to use that understanding to do division mentally or in other flexible ways and in general understand how to divide base 10 numbers into equal groups.

The base 10 materials, used with the algorithm, illustrate the process of division, with the aim ultimately of freeing students from needing to use the algorithm. But we want to get there without instilling the need to use a calculator for every question.

You are awesome!!!!!!!!!!!!!!

I did not learn blocks in Europe 30 years ago just the short long division. When my 5 grader bring his assignment with blocks I was like OMG!. Thank you sir for presenting this the right way that both of us understand! Will use your videos more.