Long Division, Jigsaw Patterns

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Long Division: Play the Game & Have a Conversation (e.g., 2018/9) Of course, with understanding, one can enjoy the convenience of a calculator. But let's dive into the world of long division and make it a fun experience. Imagine teaching long division as a number game in small groups! It's an engaging activity that's full of patterns and opportunities for reviewing addition, subtraction, and multiplication. With this design and enough number pieces, you can play the game on a table or on a wall (using the model with nail holes). It "forces" the user to align the numbers (place values), which is essential in long division. 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, you may need more zero's and decimal points. There are other ways to organize the process of long division, but this approach makes it easy to visualize. The Long Division Algorithm is the most loved and hated part of school mathematics. But presented in a meaningful way, it's a really pretty and illuminating experience for students. Two big ideas behind the Division Algorithm/Theorem are: we take as many multiples of the divisor as possible, and when dividing any integer by another nonzero integer N, there are at most {0, 1, ..., N - 1} intermediate remainders. Let's explain using an example. You have $9418 to give away evenly to 35 people. You can keep the leftover or break it down further. Everybody gets as much as possible in the first round in thousands, which is zero in this case. Find the leftover and move on to the next largest sum possible in hundreds, which is $200 in this round. Find the leftover and move on to tens. Everyone gets $60 in this round. Find the leftover and move on to ones. Everyone gets $9 in this round. You can keep the $3 left or move on to dimes or cents... 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... https://en.wikipedia.org/wiki/Long_division