possible edits

[lhwalker]

Pg 11, second paragraph …”this content be included only in optional courses.”  It is not immediately clear what “this content” is.  Page 15 first paragraph “turns on” could mean “leads to” or “depends on.”  Pg 15 3rd paragraph unclear to me:  “A symbolic proof has the advantage that the analogous proof showing…?”

[Bill McCallum]

Thanks for these!

[Cathy Kessel]

For p. 15, paragraph 3, see how this edit works for you (I’ve included the preceding paragraph):

To prove that a linear function grows by equal differences over equal intervals,F-LE.1b students draw on the understanding developed in Grade 8 that the ratio of the rise and run for any two distinct points on a line is the same (see the Expressions and Equations Progression).   An interval can be seen as determining two points on the line whose $x$-coordinates occur at the boundaries of the intervals. The equal intervals can be seen as the runs for two pairs of points. Because these runs have equal length and the ratio of rise to run is the same for any pair of distinct points, the consequence that the corresponding rises are the same. These rises are the growth of the function over each interval.

In the process of this proof, students note the correspondence between rise and run on a graph and symbolic expressions for differences of inputs and outputs (MP.1). Using such expressions has the advantage that the analogous proof showing that exponential functions grow by equal factors over equal intervals begins in an analogous way with expressions for differences of inputs and outputs.

[THenry]

First, I’d like to say that the progressions documents have been wonderful for guiding instruction.  Even the more general high school documents provide helpful insights for instruction including important connections, powerful example questions, clarity on points to emphasize and equally important, those to deempohasize.

Here are a few small errors I’ve found in the Functions progression:

pg. 7, in the example in the margin, b) says f(3)=f(3), perhaps the intention was to say f(3)=f(-3) ?
pg.11, in the note after the first paragraph I believe it is a mistake in repetitions when it says “Composition and composition of functions…”
pg.18, in the last paragraph I think the word and can be omitted where it says “the tangent and function is not often…”
A minor point on pg. 5, there is reference to the “red triangle” in the image, but there is only one red line.  The triangle referred to is likely clear to readers, but could simply be shaded to make the document complete/correct.

Thank you to all who have invested time in creating these documents!

[Cathy Kessel]

On behalf of multiple people, you’re welcome! I think it makes everyone happy if you’re finding the documents helpful.

Re p. 7: correct, it’s f(–3). (And note that the task comes from Illustrative Mathematics so you can comment on it at the task page.)

Re p. 11: That definitely was an non-optimal sentence—one needed to read “composition” and “composition of a function and its inverse” as two topics joined by “and”. Here’s the rewrite.

Note: Inverse of a function and composition of a function with its inverse are among the plus standards. The following discussion describes in detail what is required for students to grasp these securely. Because of the subtleties and pitfalls involved, it is strongly recommended that these topics be included only in optional  courses.

Re p. 18: Agreed.

 

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