Elementary school math specialist here, in NYS (but not NYC). I also write textbooks, including a lot of math ones. So this is sort of my bailiwick.
A few points, mainly to do with context. Which, as many people have correctly noted, is a lot of what’s missing here.
First, this question is very much a Common Core question. The CC, as you all probably know, is a set of standards much more than a curriculum, but it does occasionally allude to specific methods. This is one of those times. From Grade 1 “Operations and Algebraic Thinking,” standard C.6, “Add and subtract within 20…Use strategies such as…decomposing a number leading to ten (e.g. 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9)…” That’s exactly the process used in the question.
You may think that this is a rather silly thing to require kids to do–isn’t just getting the answer all that counts? Well, we do want kids to commit these basic facts to memory. But we have had a tendency in the past to jump the gun on this, allowing kids to memorize before they understand. In my career I have seen any number of kids who have learned these facts by heart. Many of them did that instead of having strategies based on the relationships between the numbers. Many–not all–of these kids do well in first and second grade math based on this ability to memorize. Many–not all–of them noticeably fall off in fourth, fifth, sixth grade, when there’s too much to memorize and the kids with the deep understanding begin to shine. So, from where I sit, posters like even sven and Ivory Tower Denizen are exactly right–these are important strategies which should be taught explicitly.
The question asks kids not to find the answer to 15 - 8, but to analyze the process. Again, you may or may not find this helpful; in my experience, it is *very *helpful for nearly all kids. Yes, it’s kind of meta. Yes, it may be different from how you learned it. Yes, it helps kids understand math in a deeper and more thoughtful way. It should be noted that this is the trend in other disciplines as well. Kids are no longer asked to read a passage and simply answer “What was Mr. Brewer’s opinion of pigeons?” Rather, they are increasingly asked to identify the line that gives Mr. Brewer’s opinion, or the form of argument that Mr. Brewer is using when he gives his opinion…and this at younger ages than used to be the case.
Back to the question. We can always quibble about the wording, but once you have looked at the Common Core standard it should be clear that there is only one accurate answer to the question: 15 - 5 - 2. Not only does that answer accurately reflect what’s happening in the pictures (we start with 15, we cross out 5 to get down to 10, then we cross out two more to get down to eight), but the others don’t work. 10 - 2 does not show “how to make a ten”; it only shows what happens after you have made the ten. 15 - 5 does not “solve 15 - 7”; it only shows how to get down to that ten. And 10 - 5 - 2 does not give the correct answer of 8.
Because I do this professionally, the answer is obvious to me…which does not mean it will be obvious to you. I am an expert in “Common Core math for first graders,” the way you may be an expert on football plays or cryptic crosswords or medical diagnoses, depending on your job and your hobby; I wouldn’t expect to “see” what you see in your areas any more than I would expect you to see what I see in mine. (Until you learn the “code,” cryptic crosswords are just about completely bewildering, for example.) So I can’t stress enough what several people said above: we have trouble with this question only because we’re not used to it. If you had sat through instruction in this method, you would have done a variety of problems that looked just like this one, along with a bunch of other related ones, and it would be easy to pick out the correct answer. This is a perfectly fair question for a first grader who has learned this method.
[For the record, though, two things. First: the problem is poorly set up. It looks like the two answer choices on the left go with Step 1 and the two on the right go with Step 2. That threw a few posters, and reasonably so. Also: these kinds of strategy questions don’t lend themselves terribly well to a multiple choice format, which also adds a bit to the apparent clunkiness of the question. If you really want to know if kids can use this method, better to actually observe them using it, but that’s not all that efficient.]
One more thing–I am surprised to hear that this question is being used on a pretest. Nothing wrong with pretests, for all the reasons said above. But this question, as some posters point out, is so heavily based on learning a specific method that it’s hard to imagine most kids getting it right; plenty of very strong math thinkers will miss this question at the start of first grade, since they didn’t learn this particular language in kindergarten. Obviously, if it *is *being used that way, then it’s being used that way. I wouldn’t do it myself, and there’s a good chance it isn’t supposed to be used like that, and I don’t suppose you’ll get good information out of it. But if it’s used after the unit on subtraction, it is going to be informative indeed.