[nvitale]

It not working the way I expected:
On the “Tools” page/tab, under K-8 Standards by domain….

If I click on most of the Domain names, they link to a document that has all of the standards across grade levels for the given Domain (“standards by domain”, as expected)

If I click on Number and Operations – Fractions, it links to the full progressions document for the domain, not the list of standards in the domain (which is what I was looking for).

Thanks for looking into it.

[nvitale]

Thank you Cathy, for your reply!
I do understand that line of reasoning, and it is basically how I began thinking about this. The concept of equality of sums of equal expressions which you and the Algebra Progressions expressed so well is fairly accessible, and is an extension of the reasoning used in solving one-variable equations. I also think the point made about “realizing that a solution to a system of equations must be a solution of all the equations in the system simultaneously” gets to an important point. There is something about the assumption of equality of the equations for the solution set (not equivalence) that makes this reasoning hold water.
What I’m grappling with here is that the resulting system has the same solution as the original system, but the equations are not equivalent (as you would find if you just scale one or both of the original equations, or otherwise manipulate each equation algebraically, but separately) – and the graph would look different (although still cross at the solution point). Another way of thinking about his is that the solution sets of the new equations in the system have the same intersection, but each individual equation’s solution set does not have to be identical to any of the solution sets of the original equations. I’m seeing that this is a result of our assumption of equality is for a special case (for the solution) – our resulting equations are equal (and therefore sum-able or substitute-able) at the solution values, but otherwise are NOT equivalent – interesting!
Still not sure how a students would “prove” this, what proof might look like. I still feel like I’m missing something about this standard – just reading it has made me re-think what I think I know about systems of equations…
Maybe I will post this in the general forum, I would love to hear your further thoughts and thoughts from others.

[Author]

Posts