Homework With Meaning!

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These two homework problems may seem too easy for a 5th grade student, but on examination of the thinking displayed, it is clear that a deep understanding of important concepts, like place value, are well understood by this student.

The first problem was quickly identified as a "subtraction" problem, but it was solved using simple addition. This young mathematician added up from 267 to 323 on an open number line. This is kind of like what folks did in the good old days before cash registers had built in electronic calculators. They would count back the change using landmarks along the way. This student also used landmarks (easily recognized and "easy to work with numbers"), as she first "jumped from 267 to 270. This allowed her to easily add on to 270 in order to get to 300. From 300, the jump to 323 was a piece of cake. Finally, all of the jumps were totalled, and the distance between $267 and $323 was found correctly.

Also of note are the sentence restating the prompt (question) and the matching equation, These also signify a real sense of math understanding.

On the second problem, the student added from left to right, and to me that is great! Adding the largest place values first makes it less likely to make a mistake of great magnitude. Using the traditional algorithm makes it more likely to make a mistake in the larger place values, and that's a real drawback to sticking with traditional algorithmic thinking, unless you REALLY understand the method well.