Long Division, Jigsaw Patterns

Long Division: Play the Game & Have a Conversation (e.g., 2018/9)

Of course, with understanding, one can enjoy the convenience of a calculator.

Long division could be taught as a number game in small groups! It is fun and full of patterns and opportunities for reviewing addition, subtraction, and multiplication. With this design and enough number pieces, one can play the game on a table or on a wall (using the model with nail holes).

1. It "forces" the user to align the numbers (place values).
2. The jigsaw design allows it to go beyond the length of the initial board.

Of course, one needs a lot of numbers and some decimal points. Depending on the specific problem, one may need more zero's and decimal points. Of course, there are other ways to organize the process of long division.

####Notes

The long division algorithm is the most loved and hated part of school mathematics. Presented in a meaningful way, it is a really pretty and illuminating experience for students. There are two big ideas behind the Division Algorithm/Theorem. The first big idea is: we take as many multiples of the divisor as possible. The second big idea is: When dividing any integer by another nonzero integer N, there are, at most, {0, 1, ..., N - 1} intermediate remainders. Sooner or later, the remainder will be back!

Let's explain using an example. You have 9418 dollars. You want to give the money away evenly, as much as you can, to 35 people. You can keep the leftover or, if you like, you can further break it down.

1. Everybody gets as much as possible in the 1st round in thousands, that is, 0 in this case.

2. Find the leftover if necessary and move on to the next largest sum possible in hundreds, that is, 200 in this round.

3. Find the leftover and move on to tens. Everyone gets 60 in this round.

4. Find the leftover and move on to ones. Everyone gets 9 in this round.

5. You keep the 3 dollars left or move on to dimes or cents or ....

6. Take a look at the intermediate remainders {24, 31, 3, ...}, which will repeat if the process goes on. Please note that the meaning of the remainder changes as the process unfolds: hundred, ten, one, tenth, hundredth, thousandth, ....

####Reference

1. https://en.wikipedia.org/wiki/Long_division