Math Curmudgeon

It’s better to differentiate by classroom than by desk, but not everyone understands that.

I like when n is a fraction, like 3/8. It makes more of a chrysanthemum than a daisy.

The triangle is equiangular. The triangle is acute. The triangle is obtuse. The triangle is a right triangle. The triangle is equilateral. The triangle is isosceles. The triangle is scalene. The triangle is a 45-45-90 triangle. The triangle is a 30-60-90 triangle.

The shape is regular. A median is perpendicular to a side. None of the medians is perpendicular to a side. Only one angle bisector is perpendicular to a side. Two of the angle bisectors are perpendicular to sides. One side is also an altitude. Only one altitude intersects a side. An altitude intersects a side at its midpoint. All the altitudes intersect sides at their midpoint.

The perimeter is 50 cm. The perimeter is 99 cm. The perimeter is not less than 50 cm. The perimeter is not less than 100 cm. The perimeter is not greater than 50 cm. The perimeter is not greater than 100 cm. All sides have integer lengths. Two sides have integer lengths. All sides have integer lengths.

Sides are Pythagorean triples. Side lengths are 6, 8, & 10 Side lengths are 8, 15, 17 Side lengths are 7, 24, & 25 Side lengths are 13, 14, 15 Side lengths are 10, 20, √300 Side lengths are 20, 20, 20√2 Side lengths are 17, 17, 17 Side lengths are 14, 14, 20

Some more cards. I've got more pages of cards but these should give you a good sense of the game.

Consistency! Consistency! is designed for students who are about halfway through a typical Geometry course. It’s excellent for review and revision because it promotes discussion and argument. GAME PLAY A Round of Play: - The cards are dealt counter-clockwise and any remaining cards are set face down to form a draw pile. Each player gets the number of cards as in the table. - The player to the dealer’s right begins the round by placing any card face-up in the middle of the table. - Each player in turn lays down a card (face-up) that is consistent with all cards already in play: For example: A middle card has the image at right. The next card could be “cos⁡〖A=1/2〗 ” or “one exterior angle is 120° ” but not “Side lengths are Pythagorean triples.” - A player who cannot lay down a consistent card draws 1card and play moves to the right. - Players can bluff and lay down a card that is inconsistent with one or more of the cards already played. Anyone can challenge a card at any time. Allow 30 seconds or so for players to decide whether to challenge.

End of the Round: • The round ends in one of two ways 1. A player lays down a consistent card and no one else around the table can do so, then that player wins the round. Example: 5 people (A, B, C, D, E) are playing and C plays a consistent card. If none of the players D, E, A, and B can play a card in turn, then C has “played the last consistent card” and wins the round. In a two-player game, the second player must pass twice. 2. If a player in their turn lays down their last card (and it’s consistent!), they immediately win the round. • The player that wins the round receives 1 point for each card in play and sets these cards aside. Gloating and performing a TikTok dance are optional. • The dealer’s role moves counter-clockwise. • The rest of the cards are combined, shuffled, and a new round is dealt. Challenges: • If a player lays down an inconsistent card, then anyone can challenge the card by describing how it is inconsistent. It is important to remove inconsistent cards because further play is impossible. • Penalties depend on when the challenge is made: o In the 30 seconds: If the challenge is upheld, the “offender” takes back the inconsistent card and draws four more. If the challenge fails, the challenger draws two cards. o Later in the round: the bluffer takes back the inconsistent card and draws only two more cards (if the challenge fails, the challenger draws just one card). Teacher Notes: • We played several rounds in class before implementing the challenge penalties in order to encourage challenges and discussions. • With the challenges, the goal is to encourage the development of the paragraph proof. As students get used to the game, insist on more complete explanations in a more logical order. • Instead of calling “UNO” when down to their last card, players call “EUCLID”.

Two exterior angles add to 270° One exterior angle is 135° All exterior angles are 120° One exterior angle is acute. This triangle has two acute angles. The measures of all angles are integers. sin𝐴 is a rational fraction. tan𝐶 is a rational fraction. sin𝐵 is a rational fraction.

Area is an integer Area is 100 𝑐𝑚2 Area is less than 70 𝑐𝑚2 Area is less than 40 𝑐𝑚2 Area is greater than 100 𝑐𝑚2 Area is greater than 20 𝑐𝑚2 No side is longer than 20 cm. No side is shorter than 20 cm. One side of this triangle is twice as long as another side.

It's a Geometry game that @unsolvedmre.bsky.social had tossed into the ether. I tweaked it some, set it aside for a couple years, and tweaked it some more. Here are the instructions, and some of the cards.

What do you think?
Playable?
Enjoyable? (For your students, ...)
#ITeachMath

It's a concentration camp.
I'm sure they've got a use for that part, too.

*BOOP*

"should advocate for"

This sounds like you don't think Democrats should take advocate for, legitimately take credit for, and defend good legislation that helped Americans ... and that Republicans who voted aginst it but took credit for its benefits should reap some reward for trying to kill it.

F*** That.

Why not?
It happened under his watch.

I doubt “The Man Formerly Known as Prince But Not That Prince” will ever testify.

If you’re willing to do such a thing, then “failing victims” is not an incentive to confess.

Yeah, but ...
Someone's gotta do it and no one's beating down the door of the school to take over.

WODB graphs of parabolas with lines: tangent, intersecting two pts, not intersecting, parabola (a=-1) WODB leaf types: jagged edge, smooth edge, simple compound

Numbers: 3, 27, 123, 31 Numbers: 9, 16, 25, 43 Numbers: 121, 16, 9, 73 Superheroes: Batman, Batgirl, Wolverine, Green Lantern

Scientists: Newton, Einstein, Marie Curie, Darwin

Parabolas in different quadrants, different x-intercepts, different values of a. Chemicals: Li, O, C, He Algebra: y=4x+3, y=-4x+5, y=0.25x+5, y=4x-5

details in alt text.

"Which one doesn't belong?" display in a school hallway.

all of the display

I like that we can do this with math and other subjects, even the headline!

5/9x(70-32)=21.111

5/9(70-32)=0.014619883

Simple Fahrenheit to Centigrade conversions on a calculator.

Life should be more simple.
#Calculators
#PEMDAS
#GEDMAS

Hope they don't try that in Vermont.

Desmos activity dashboard lets the teacher see where each kid is and what they’ve entered. Also has pacing and other tools.

I like it for exploration. If you can find an activity, it’s great. Making one from scratch is time consuming.

Here’s a teacher-built one:
student.desmos.com/join/h7ufmq

Reading some of the other replies, I think I may have gone about slightly differently. I found (a1+an), which gave me the middle term and the value of n. Took a few minutes to back up and realize the final answer.

Nice one!

At the point where the derivative equals the slope between the two end points. IVT in Real World!

285 14.8518109 4100 14.8519014 1777 28.5009300 4961 28.5010049 2075 57.7293104 4997 57.7293283 4703 175.8511277 2170 175.8511567 4848 296.0611490 828 296.0612136 4859 305.1067136 661 305.1068079

5000, epsilon<0.0001
Done for now.

285 14.8518109
4100 14.8519014

1777 28.5009300
4961 28.5010049

2075 57.7293104
4997 57.7293283

4703 175.8511277
2170 175.8511567

4848 296.0611490
828 296.0612136

4859 305.1067136
661 305.1068079

413 48.43071
295 48.43082

732 99.16957
912 99.17009

156 232.95813
1191 232.95874

Nothing within 0.0001 up to the first 1500.

413 48.43071 295 48.43082 732 99.16957 912 99.17009 156 232.95813 1191 232.95874

Up to the 1500th triangle and none are within 0.0001
413 48.43071
295 48.43082

732 99.16957
912 99.17009

156 232.95813
1191 232.95874

I'm beginning to think that, maybe, subtracting irrational numbers isn't going to be near 0.

Not yet.

Nerd-sniped myself this morning:

I found myself wondering if the hypotenuse of one of the triangles ever lined up *exactly* with the leg of another, and if so, which one?

Things my students said today:
"A corner of your cheese landed on my chair." & Massive giggle fit. To her sister: "Take your earpod out of your ear, young lady." More giggles. Drops calc on own foot: "My foot. It's been attacked." Whole class loses it.
#mathstoday
#iteachmath
#YeahItsAlmostSummer

Cake Day in Calculus If you teach calculus, you probably can't look at one of these without seeing a volume of rotation. I presented this as a problem to my ca...

squarerootofnegativeoneteachmath.blogspot.com/2011/04/cake...

But … is there a Bundt cake of revolution?

Volumes by revolution

I began by placing the vertex on the x-axis, which happens at x^2+2x+1.

If we add a positive constant to that, the graph rises and roots are imaginary. Thus, the expression must be >1

I can't believe we have a Pope from Illinois. People from Chicago usually hate the Cardinals.