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In the Huffington Post, Jason Zimba is quoted as saying “The number line is not an appropriate model for place value”. His comment is part of an interview pertaining to that atrocious viral response to a “Common Core” math problem. I’m sure you’ve all seen it on Facebook by now.
But what I’m wondering is why Zimba disparages the actual problem rather than the widespread misunderstanding of its purpose (Common Core teaches models AS WELL AS methods, right?).
We’re supposed to use the number line to model lots of operations, like operations on fractions (Hung-Hsi Wu, anyone?)
Why is the number line “an inappropriate model for place value”? What exactly is wrong with the problem? Can you give an example of a better problem or task that addresses the same standards?
I can’t speak for Jason, but I can give you my thoughts on this problem. There are two concepts at play in this problem: one is the understanding of subtraction as a missing addend problem. That is, understanding 427 – 316 as the number you add to 315 to get 427. The number line is a good model for visualizing this. The other concept is using the base 10 system in subtraction. That is, understanding 427 as 4 hundreds 2 tens and 7 ones, 316 as 3 hundreds, 1 ten, and 6 ones, and subtracting hundreds from hundreds, tens from tens, and ones from ones. I agree with Jason that the number line is not a good model for this understanding. The precise relationship between 100s, 10s and 1s is not so easy to see on the number line, because you can’t really accurately depict a one on a scale which also includes hundreds. The ones and the tens can get confused; indeed, that seems to be exactly the problem Jack was having (although it’s a little hard to figure out which marks are Jack’s and which marks are the student doing the problem). Also, the method presented might be misconstrued as suggesting you have to go in order: first subtract the hundreds, then the tens, then the ones, which really misses the point. I don’t think the problem is completely bad, but I do think it’s a little off key. I’d be inclined to use a number line for something like 23-8, where you can easily see the intermediate numbers 10 and 20. For a 3 digit subtraction I’d want to use base ten blocks, or just the verbal decomposition described above.
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