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I was reviewing an item that was “aligned” to MACC.7.NS.3 and it read something like this:
One liquid is at -8 degrees Celsius and a second liquid is at 14 degrees Celsius. What is their difference in degrees?
a) -22
b) 6
c) -6
d) 22
Before i establish my position, a couple of things. 1) Is 7.NS.3 a “catch all” standard in NS or is it a stand alone standard? 2) Should one consider 7.NS.1 when developing items for 7.NS.3?
What is the correct answer and why?So, I’m with you that this seems like a kind of weak item to assess 7.NS.3…
As far as your questions, I don’t think any standard stands alone, and I also don’t think that 7.NS.3 is a catch all standard either. 7.NS.1-2 ask for some very specific understandings. In 7.NS.1 we are describing situations that make 0, understanding p + q on a number line and interpreting sums by describing contexts, understanding subtraction as additive inverse and representing on a number line, and applying properties of operations to add and subtract. In 7.NS.2 we apply the distributive property to rational products and interpret products and quotients by describing contexts, and deal with the -(p/q) subtlety. Then we apply properties of operations to multiply and divide and finally convert rational numbers to decimals.
In all of that we still haven’t gotten to what 7.NS.3 asks for, which is solving real-world and mathematical problems using any of the operations and probably combinations of them and using all sorts of rational numbers. I’m not sure the focus of 7.NS.1-2 is problem solving like it is in 7.NS.3.
For your second question, I would say yes. All of these standards fall under the same cluster heading and I would imagine that as the students solve problems in 7.NS.3, they will draw on the understandings that came out of the rest of the standards in this cluster.
So, it looks like there are 2 correct answers since differences can be positive or negative. I might take (a) or (d) depending on how the student justifies their choice. Of course, I don’t think I would use this without revising the prompt…
I agree the problem is weak, and I agree with Alexei’s analysis of 7.NS.A.1 and 7.EE.B.3. I would only add that grouping standards into cluster headings, which carry important meaning on their own, has the effect that you sometimes see an overlap in the meaning between two standards. So, the cluster 7.NS.A is about operations with rational numbers, and that includes problem solving, whereas 7.EE.B is about problem solving, and that includes working with rational numbers.
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