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I’m going to post my question about 5.NF.2 in a separate post, as I realized later it was kind of a separate question.
Forgive me if this seems like a silly question, but the language of 5.NF.2 includes mixed numbers, right? I was discussing this with a colleague the other day and noticed that 5.NF.2 just says “fractions” but it follows 5.NF.1 (and is the application of the skills in 5.NF.1), so it would make sense to think that 5.NF.2 includes word problems with mixed numbers. The example in the G3-5 Fraction progression doc (page 11) does not have mixed numbers, so I am not sure what to do.
Any insight would be much appreciated.My short answer (at least how we’ve interpreted it in our district here in Florida) is no.
Our district is thinking that students will need to be able to read a z-score table. For right now, we’re going to try starting the unit with just working on the percentages for 1, 2, and 3 standard deviations from the mean, i.e. knowing the 68%/95%/99.7% rule. You can still do a lot with just those numbers.
Then, for the last part of the standard with other areas under the curve, we thought that made more sense to do once students have worked with the easier percentages first. Although we teach students to use a graphing calc to find the percentages, the syntax can sometimes be tricky. So we thought a z-score table was the way to go. At this point, students will calculate the standardized z-score and then look it up in a table.
That’s what we’re going to try. Hope that helps.Hey thanks for your quick reply. Some teachers are working on units aligned to CCSS over the summer and your speedy reply helps alot.
An update on the sums & differences story.
A few days after we talked about the graph of y = x^3 +c (which, if c is negative covers both factoring), I was working with a student on some factoring questions. The student came to x^3 – 125. In the air above his paper he moved his finger in the shape of the cubic parent function (as if tracing it in his mind). Excited by this, I asked him to explain.
He said, “Well, the graph of y = x^3 -125 would have a negative y-intercept down here and its x-intercept would be over here at positive 5. That means that the first factor has to be (x-5).” I asked him to explain if it worked for y=x^3+125 as well, and he explained that it did because the root is at -5 which makes the factor in x^3+125 be x+5.
I was so excited by this connection that the student made! I told him that he was really making some good connections and understanding and that he should share his explanation with the class. For this shy kid who usually is middle-of-pack gradewise, that was a real boost to his confidence. He explained it well in class. When someone asked if it worked for things like 8x^3 – 125, I suggested that everyone think about it and explore that on their own. We discussed that one briefly another day.
Had to share that story. I love those kinds of connections.Thanks for the replies! I had to move up to high school at the semester break, and I jumped straight into Algebra II.
When we got to this identity, we discussed it. We even explored the graph of y = x^3 + c. Since the kids already did some with roots in the fall, they were able to make some great connections with the structure and the graph.
y = x^3+c has only 1 real solution (aka x-intercept)
And we know it factors as (x+c)(x^2-x+c^2). Since we only see one x-intercept, it makes sense that the second factor is a quadratic with non-real roots. That’s part of the reason why we know the factoring pattern is as simplified as it can be.
It was a great conversation. Hooray for structure!Thanks for taking the time to reply. I do appreciate it very much. My sincerest apologies for misquoting outcomes and events in my post.
