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That’s because they fixed the item. I’m going to act like it’s because of my post 🙂
I’m glad things are being cleaned up.I’ve taken this to mean that students should be able to find the area of anything by composing and decomposing. If we start giving a formula for everything, it’s going to turn into a memorization task and the conceptual understanding will be lost. Outside of formulas for rectangles and triangles/parallelograms (justified through decomposition/composition), I think other formulas would be more distracting than helpful at this level.
I think it is worth pointing out that in Grade 6, all of this terminology will be new to students. The confusion that teachers/parents may have with the change in terminology won’t be similarly experienced by students.
I think that the terms as defined in the progressions will make matters less confusing for students. In traditional teachings of ratios, rates are defined to have different units. Then you do all of the same math that you did with ratios. So why separate them and create more words to memorize? It creates a perception that it’s totally new thing, when it is not.
One new thing done with rates in the traditional approach is finding the unit rate. But why didn’t we do that when the units are the same? We can and should, but then we’d need a new term, maybe unit ratios? So we’d have ratios, unit ratios, rates, unit rates, numerical rates, and I suppose we’d also need numerical ratios to refer to the numerical part of a unit ratio. Yikes. Is that really better than not distinguishing like/different units with different terminology, allowing us to only need the three terms ratios, rates, and unit rates?
Also, if it is “common sense” for unit price to be an example of unit rate, then define unit price as the numerical part of the rate 5 dollars per pound. Then it is an example of a unit rate!
I posted a few days ago about discrepancies between language in progressions and language seen from PARCC assessments. Well, here is something similar.
The RP progression doc states that in high school and beyond, students will write rates using derived units, something like a/b units/units (using fractions). Essentially, they will move away from the wordier version of a/b units for every 1 unit and write them in a more concise manner. This makes sense in conjunction with your statement about dimensional analysis. So, how is the following Grade 6 Smarter Balanced question fair?
Item #25 on page 27)I would expect students to be using ratio tables, double number lines, or other ratio reasoning to convert units, not working with derived units. This seems like an inappropriate assessment question.
Am I missing something here?Ok, so a ratio is a comparison of two numbers. It is not a number itself. If I’m a student, I think I can handle that. So what happens when I read the following on a Grade 6 PARCC practice test item….
….The ratio of the sales tax to the amount of a purchase is a fixed number in Town Q. The table shows the sales tax for a purchase of $1,200….
I suppose what they are actually referring to is the value of that ratio. This will confuse students if they have been writing every ratio as a:b or a to b. I understand this is not a problem with Common Core Standards. Rather, whoever wrote this at Pearson did a poor job.
Something similar will happen with the words rate and unit rate that the progressions define, yet it is claimed that the concepts can be presented to students however one wants (I don’t see how this is true when 6.RP.2 specifically refers to the unit rate a/b associated with a ratio a:b). I agree that you can get at these concepts using various language, but students will get confused come testing time if the language used in a question from PARCC or Smarter Balanced differs from the language in their book. I’ve seen a few items that use unit rate in a way that is more along the lines of a/b units to 1 unit, rather than as the value a/b.
For now, this won’t cause an issue for most students as they won’t have textbooks using the language from the progression docs. However for students using Eureka and students that will eventually use the Illustrative Mathematics curriculum (I assume it will define rate and unit rate as in the progressions), how will they be able to handle the change in language on assessments?
It seems to me as though testing consortia need to avoid the words rate and unit rate. But is it really that simple? Any thoughts?That makes sense.
I hope other teachers and administrators aren’t lost on this idea. I can envision a “why are you wasting time covering this standard, it won’t be assessed” scenario. I see a similar situation with rational functions, where graphing won’t be assessed. However, it would be logical to teach some graphing so that students would have that tool to check the rational expression operations and equation solving that will be assessed.
Thanks for your reply.
Yes, that’s where I first went for clarification. Overall, F.BF.4abcd is fine coverage of inverses. My question is about the thinking behind separating F.BF.4a apart from the rest. Maybe my problem stems more with the progression doc stating that formal notation and language are not important at this stage. My thinking is that if we don’t at least call this thing an inverse, then what are the students actually going to get out of this? Students wouldn’t be doing much more than was done in standard A.CED.4.
