subtraction (K.OA)

[Tad Watanabe]

Bill,

I know that the draft progression on OA (K-5) has been out for some times now, but I have a question.

On p. 9 of Progression, there is a chart of addition/subtraction situations with 4 types shaded in as Kindergarten subtypes.  Those four does not include Put Together/Take Apart Addend Unknown situation.  However, in the standard, the cluster heading includes the statement, “understand subtraction as taking apart and taking from.”  So, shouldn’t Put Together/Take Apart Addend Unknown be a Kindergarten subtype?  Otherwise, I am not sure what it means for children to understand subtraction as taking apart.

[Bill McCallum]

I guess you could model subtraction with a set of objects without it being a word problem per se. For example, you could ask students to count 5 blocks, take away 2, and then count the ones left over, and describe this as “5 take away 2 leaves 3”. The difference between this and a word problem is that you are not asking the student to read (or hear) about a situation and then represent it with a subtraction problem.

[Tad Watanabe]

Bill,

Perhaps my question wasn’t clear.

As you know, a word problem of the type, put together/take apart with addend unknown is like this one:

There are 8 children in the play ground.  If 3 of them are boys, how many are girls?

According to the standards, I think this type of problem is to be discussed in K – I am interpreting that is what it means to understand subtraction as take apart.  However, the progression document says this type is not to be included in K.  As I interpreting the standards correctly?

[Bill McCallum]

Tad, I don’t see “understand subtraction as take apart” as being necessarily tied to word problems. It’s just an understanding you want students to have, which could be demonstrated with manipulatives, and need not arise in word problems at all. Applying your skills and understandings in a word problem is harder than just possessing the skills and understandings, and there’s something to be said for having word problems draw mostly on skills and understandings that have been secured in earlier grades.

That said, the progressions document is, in the end, not the standards, but some professional judgement about the standards by the authors of the document. So I guess I would say that although the standards don’t require take apart word problems in K, neither do they forbid them, and the progressions document is simply offering advice on this point.

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