Carole and the Common Core

Here’s another meme criticizing the Common Core:

carolereasonable

The criticism is that the student has provided a fully correct answer and gotten dinged for not providing an estimate. This is, of course, taken as yet another illustration of why Common Core is ruining America’s future.

In other cases of Common Core outrage, the problem has been traced back to non-Common Core materials, or misapplication of standards. In this case, though, this is an accurate representation of Common Core expectations about estimation:

CCSS.MATH.CONTENT.3.OA.D.8
Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

The question appears to be from the 2012 edition of enVision Math, which includes this model:

carolereasonable2

It is clear from this model that “reasonableness” is to be interpreted as an estimate that is used to check a final answer without repeating the full calculation.

The ability to estimate is key to doing quick mental math. Prior to the calculator, most complex calculations in practical settings were done through estimation. \(3.61 \times 5.12\) is not easily done on a slide rule; \(3.5 \times 5.0\) is close enough for most applications. Personally, I use estimation all the time: When I’m shopping, for instance, I check the final bill against what I expect it to be based on rounding. I know it won’t be exact; I’m checking for reasonableness. If I buy five books at $12.95, $9.95, $3.99, $3.99, and $2.99, I expect the final bill to be a little more than $34 (after Michigan sales tax, it’s $35.90). If it’s not, there’s something wrong.

Reasonableness and estimation are key parts to developing number sense. This is hardly new to Common Core, but it certainly is a key aspect of it.

To highlight another part of the model from the book, it also states that part of being correct is making sure that you’re answering the question being asked. Outraged parents apparently want the child in the question to be lauded for getting the exact answer even though that answer is already in the question. The question is not, “What is 103 – 28?” The question is, “Is 75 a reasonable answer for this, and why?”

This isn’t picking flystuff out of pepper. This isn’t a triviality. This is a key to teaching habits that will help children in far more complex problems (like the book-buying example above): How do you estimate quickly so you can check your answer?

I’m not fond of the implication that the only way to check reasonableness is to repeat the problem with simplified numbers, but I agree with the teaching goal. One of the first things I taught my son with regards to numbers is that you should always see prices like $3.95 as $4, not as $3, because the stores are trying to trick you. And at any rate there’s an argument to be made that more nuanced kinds of reasonableness checks (Can a measurement be negative? Can candy cost $500/lb?) aren’t knowledge-appropriate for all third graders.

Regardless, I do agree with the importance of stressing to students that estimation is an integral part of efficient mathematics, as this problem does.

2 Comments

  1. David Jao

    My objection is that the problem does not state to use estimation. It simply asks without context “Is 75 pages a reasonable answer” without clearly stating that the student is expected to use estimation. Had I been given this problem with no context, I too would not have guessed that I was supposed to use estimation.

    I would accept this question as valid only if it were clearly posed in an unambiguous context in which estimation was clearly understood to be the aim of the question.

    Reply
    1. Paul Hartzer (Post author)

      It *was* provided with context, though. The book clearly defines what it means by “reasonableness”, and the test item refers back to the section of the book. There are also several other questions in the same test (http://www.webschooltools.com/Curriculum/Miller/UnitFiles/2014052759TopicTestUnit2.pdf) that reference section 2-7 and use “best estimate”, “round… to estimate”, “about how many”, and “estimate how many”. Between the model in the book, the general use of the word “reasonable”, and the other four problems on the test, there ought to be sufficient information to remind a student who has worked with this material what “reasonable” means.

      When I first saw the item, I agreed with you and the outraged parent. However, in the context of the curriculum, there ought to be no confusion.

      Reply

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