No worries. And agreed that I am not sure what that item is assessing when graphing tech is in play.

which 2025 exam? I'm not seeing an alg 2 exam with a graph for question 4.

Progress is good! I wonder if they will ever switch over to something like TikZ for graphics.

Wild. I'm looking at a lot of Regents exams these days and now I won't be able to un-see this.

wat? am I going to be sad if I ask for more detail here, Dan?

Oooo, whereas for the inverse I'm flipping the axes to reflect (pun intended) the change of input<-->output.

And many perspectives does good math thinking make!

A fair point that I'll enjoy pondering. I was thinking last week about the exp & log relationship & getting annoyed when 'inverses' in a context are graphed on the same axes when, which I think is related to this.
& thanks for chatting about this! I appreciate you taking the time to engage, Carl.

similar in my mind, for celsius to fahrenheit I wouldn't swap the C and the F. one version takes C inputs to F outputs, the inverse takes F inputs to C outputs

for abstract cases I'm with you. here t and v are defined in the context, so 'swapping' them doesn't make sense in my head. I can see doing something like t(v) = [expression with v], but not swapping. It's more v is now the independent, t the dependent.

Coming back to this as I think it's where we diverge. I'm with you on 'an inverse reverses the inputs & outputs of a function'. And I see t = (60-v)/2.25 as the inverse of v = 60-2.25t. time-->volume vs volume-->time. does that match your thinking? or is this the split?

When it comes to inverse functions, the expectations are modest, requiring only that students solve equations of the form f (x)=c. The point is to provide an informal sense of determining the input when the output is known. Much of this work can be done with specific values of c. Eventually, some generality is warranted. For example, if f(x)=2*x^3, then solving f(x)= c leads to x = (c/2)^(1/3), which is the general formula for finding an input from a specific output, c, for this function, f. At this point, students need neither the notation nor the formal language of inverse functions, but only the idea of “going backwards” from output to input. This can be interpreted for a table and graph of the function under examination. Correspondences between equations giving specific values of the functions, table entries, and points on the graph can be noted (MP.1). And although not required in the standard, it is reasonable to include, for comparison, a few examples where the input cannot be uniquely determined from the output. For example, if g(x) = x^2, then g(x)= 5 has two solutions, x = +/- sqrt{5}.

I know a lot of the focus of that section is on the idea of inverses while trying to not get bogged down in notation. By the CCSS Progressions, "The point is to provide an informal sense of determining the input when the output is known." p245

Curious what you would change. Notation or something deeper?

Sending you love, friend. Thank you for sharing some of his story. A generous and curious man passed those traits onto his kiddo.

K8 reposted something of yours and I was delighted to see your name pop up!

I used to always start on the last page that had no name for the same reason.

Mine loves the Ranger's Apprentice series. I'll look into Method for Magic!

saaaame

*If A is true and B is true, what else could be true!?

Great point. Aligned with "riding in the wagon."

I'm wondering if the language is mimicking horse riding lingo more than car lingo. Horse, motorcycle, and bike passengers can't be totally passive the way car passengers can (well, a small child could be given proper buckles). Super curious about the other languages take!

K-pop Demon Hunters explained by a Korean teacher 😈🧑‍🏫 YouTube video by Talk To Me In Korean

I also just got looped in. Listening to the sound track on repeat. Pondering how to get tiger/magpie merch. I love the language/culture breakdowns, like this one: youtu.be/qCmpU3ssip8

That sounds sub-optimal. Mostly I'm just using light rail to go to/from the airport when I'm in Seattle, so I'd not noticed that quirk.

You can get an ORCA card and it works on all of these. I'm not sure on how the end-to-end fare works these days, though.

I love his work! magical.

Iran Join Rick as he explores the most surprising and fascinating land he's ever visited: Iran. In a one-hour, ground-breaking travel special on public television, you'll discover the splendid monuments of...

In the spring of 2008, I feared America was on the verge of war with Iran — and, believing that it’s good style to get to know people before you bomb them, I made “Rick Steves’ Iran,” a one-hour special that could (and would) only debut on PBS. Sadly, this special has become pertinent again today.

The majority of my taste in humor is thanks to Mel Brooks movies. Cannot wait.

I think a 4. Slightly worse that "mid".

Semi-related: In college I ran into one of my maths professor post final and he cheerily said that I did <Scottish accent>"Amazingly satisfactorily."</Scottish accent>
I'd no idea what that meant until I got my grades (it was positive).

I avoided putting the final total anywhere on the paper to make it easier for students to dig in and discuss with one another with out the letter-status so front and center. (I also didn't post the grades till the end of the day so kiddos didn't come to class having already looked)

wontons (pork and vegetable filled, fried)

"Allowing other people who are not you to decide what matters to you."
37 minute video. Worth it.