She's well-educated, experienced, so she's just lying about it. The question for me is what she expected Klein's reaction to be. Did she not expect to be countered? Or did she expect the counter would occur but figured it would be good to just get this out there to sow uncertainty (two-sides, etc.)?
OR difference of squares
(15-3)(15+3)=225-9=225-10+1=216
Can we do estimates? Round down 12 to 10, round up 18 to 20. So about 200.
In computer programming, there's a rich debate about operator overloading, which is the same thing. E.g., the + operator means both addition (4+5=9) and concatenation ("4"+"5"="45"). C++ was criticized for allowing programmers to add meaning to existing symbols and Java took this out. 3/3
It helps to admit to Ss that it can be confusing, rather than making them feel stupid when they get confused by it.
Good notation reduces cognitive load so the reader can focus on the concepts. Multiple meanings for the same notation has a cognitive cost (and an occassional serendipitous win). 2/3
So many thoughts!
1. Agree 100% that invented notation for temporary use is a mistake.
2. The inverse/mult-inverse notation is genuinely problematic but, it's not going to be changed so just alert Ss to the strangeness and move on. Kansas City isn't in Kansas, there's 2 Washingtons, etc. 1/3
12 = 2*6
18 = 3*6
12*18 = (2*3)*6*6=6^3=216
Will the admission go on the same show as the original, incorrect, footage? Or will the lie end up with much more viewership than the truth?
Apparently she’s been released. It’s all horrifying and inexcusable. evanstonnow.com/skokie-woman...
I was unable to find it funny. If we lived in a just world it’s exactly what should happen. I’ve seen these kinds of announcements in a school I worked at, and it’s stomach-churning.
I appreciate the sentiment, but I can’t find humor.
But it suggests we could assume a value, say the angle of the big sq, and compute the soln showing that the assumed value doesn't appear in our answer. I'll try this next.
3/3
The real work, presumably done by the problem poser, is to prove that the unspecified value does not alter the answer.
That's why I felt a little dirty solving it this way!
2/3
It's "cheap" bc it uses a non-math theorem: If a trusted source (e.g., AMC, @catrionaagg.bsky.social , etc.) poses a question, there exists a unique answer and we may take any value we like for any unspecified values, so long as it is consistent with the givens. 1/3
Diagram with large square rotated until its left edge is vertical.
Here's a cheap way: The prob is underspecified - we can't determine the orientation of the big SQ. Let bottom rt of the bottom pink sq be (0,0). We know (0,4) lies on SQ. Rotate SQ c.w. until a vertex is at (0,4). This satisfies the givens. The angle is 45. Cheap, but correct (I think!).
+1 on @averypickford.bsky.social 's idea. Stats is motivating and real-world connected. Use simulations (physical and apps) instead of computation. Use/teach spreadsheets whenever you can bc it's such a useful skill. Have them collect data themselves. For PR, call it data science if you can!
I’m no lawyer, but it seems to me that while the Capitol police have some immunity in doing their job, Sheehy does not and should be arrested and sued into oblivion.
This case is horrifying. The man had deferred action, was on a full path to a green card, is a college grad magna cum laude, and ICE arrested him randomly while looking for someone else:
“What do we do?” said one ICE officer, to which another replied “We’re going to take him with us anyway.”
P.S. The sum/product formula is easy to prove using (x+r1)(x+r2), and yields a quick corollary that if we have real coeffs (1) the sum is real, which means a+bi pairs with c-bi and (2) the product is real, which for these pairs only works if a = c, that is, conjugates.
3/2 😉
I posted about using sum/product of roots, which still seems more useful and elegant to me. But this last idea (shifting by 3) is very cool.
My strong preference would be to have developed x^2-(r1+r2)x+r1r2 in prior work. Then we get b=-[(-3+i) + (-3-i)] and c=(-3+i)*(-3-i) both of which are easy to compute: b=6 and c=10.
x^2+6x+10
2/2
IF the goal is to practice algegraic manipulation, then I'd multiply (x-(-3+i))(x-(-3-i)), trying to use each root as a block, rather than expanding and multiplying trinomials. HOWEVER, ..... (1/2)
401,000 people moving state to state in fear of having legal documents invalidated (KS), jail time for using restrooms (FL, UT), loss of access to adult care (dozens) or youth care (dozens even in D-led states), & the message from “opposition” is still largely “you’re making too big a deal of this.”
Way below, tbh.
Thx. Your link says something quite different: the %age of the stock of "large homes" owned by Boomers (empty nesters) vs Millenials (not GenZ) in 2022 when GenZ were younger, and says nothing about second homes.
My quick research: GenZ 27.1% own homes; GenZ is 14-29. Boomers 17% own a 2nd home.
I understand the concern, but is this statement factually accurate? Can you post a link to the information this is based on? Has it changed in 2026?
Graph showing people's estimates of probability for various phrases.
What does "likely" mean, in terms of probability? This article looks at the question - I think it would make a great class exercise, where students give their own answers, and then read the article. #iTeachMath #MTBOS
www.thetimes.com/uk/science/a...
BREAKING
Former ICE agent:
On my first day training new cadets, I received secretive orders to teach them to violate the Constitution by entering homes without a judicial warrant.
Wow! Nice (quick) work!
Understand. Could you slip problem #1 into an assignment, and then slip #2 into a later assignment? I.e., fold it into your work rather than take time?
1. Our system of time measurement, with 60 minutes in an hour and 60 seconds in a minute originated with the ancient Sumerians in the 3rd millennium BC. They used a base 60 (rather than base 10) system, and this also explains why we define one “degree” as 1/360 of a circle. a. Sometimes people give a time as 1.5 hour. How many hours, minutes and seconds is this? Write your answer as HH:MM:SS. b. Suppose a video is 0.2 hours. How many minutes and seconds is this? c. Suppose some strange instructions for a cake specify baking for 2.23 hours. How many hours, minutes, and seconds is this? If it is not an exact number of seconds, include decimals on the SS value. d. A movie is 95 minutes and 34 seconds. Give the length of the movie in HH:MM:SS form, and then give the length in hours, using decimals as needed. 2. We have written angle measures in decimal format (e.g, 32.5 degrees). However, there are occasions (often in navigation) where angle measures are written in degree:minute:second format. There are 60 minutes in a degree and 60 seconds in a minute. For example, an angle of 33.5 degrees might be written in DD:MM:SS form as 33:30:00. a. Write 1.5 degrees in this format. Write 0.2 degrees in this format. b. Suppose an angle is 63.25 degrees. Write this in DD:MM:SS format. c. Suppose an angle is 40 degrees, 10 minutes, and 15 seconds. Write this as a single value in degrees, using decimals as needed.
Here's an option: Use something like this as part of a homework or a group work assignment. The goal is to avoid making DMS sound weird and something you have to be taught. Rather, it's just an idea that you can certainly figure out. Avoid "teaching" it.
