At the beginning of the decimal unit, we included a variety of addition and subtraction problems on the warm-up for practice.

One day we had an addition problem, one that we were using to ensure that students knew how to “carry” when the sum in one column was a double digit number. The standard way to solve decimal addition is to line up the decimals, then to add from right to left. “Riley” chose to solve the addition problem a different way. He split each number into it’s whole number and fraction parts. He added up the fraction parts first, then added up the whole parts. Then he added the two results together to get his final answer.

If the problem was 12.37+4.86, he first added together 0.37 and 0.86 to get 1.23. Then he added together 12+4 to get 16. Finally he added 16+1.23 to get his final answer of 17.23.

It was a unique way to solve the problem. It isn’t the most efficient way to solve the problem and it opens up more opportunities for error, but it was fascinating to see how he view the problem and how to solve it.

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An interesting example of the way he put that together. One of the things we know from research is that we tend to wipe out students’ intuition in mathematics, so I appreciate that you let this student solve it the way that he did. The questions for mathematicians would be whether it was the most efficient way to solve that. Perhaps a question such as “Do you think you could solve that problem in less steps?” might have encouraged him towards a more standard algorithm.

That is an interesting way that “riley” solved it. It totally works, just wouldn’t be our thought of it. I feel like if he is comfortable with solving it that way, to allow him to because he understands. But maybe once he has mastered that, showing him another way for him to practice to see if he gets the same as before but maybe in a faster way. So mastering another method, showing him its the same both ways, and that he was much faster he might be intrigued by it. But again, that would have been neat to see just because that isn’t what we would typically do, but if students are struggling, it could be something you show others as well, to maybe make more since of decimals.