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Math Curmudgeon @mathcurmudgeon.bsky.social · 20/09/2026

For example, the cards in play might be A. The triangle is acute. B. None of the medians is perpendicular to a side. C. All sides have integer lengths. The next player wants to play "Side lengths are 6-8-10". Is that consistent?

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Math Curmudgeon @mathcurmudgeon.bsky.social · 20/09/2026

It's a geometry review game. Players have cards with either an image or a statement about a triangle or polygon. In turn, each player must lay down a card that doesn't contradict anything in the middle. You have the four cards at the bottom. Which one is consistent with the three already played?

Center cards:
Area is less than 70
The shape is a pentagon.

Player on the left has played
"The shape is regular"

The next player must choose between
The measures of all interior angles are integers
Adjacent angles add to 180
Angle Bisectors pass through the opposite vertex.
Exterior angles are 30

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Math Curmudgeon @mathcurmudgeon.bsky.social · 15/07/2026

I'm not a middle school teacher, so please leave some feedback on difficulty and any suggestions for more cards. Thanks! 2/3

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Math Curmudgeon @mathcurmudgeon.bsky.social · 15/07/2026

Play-Testers wanted! "N is a Number" is a CONSISTENCY variation for Middle School. Each player lays down a card that is consistent with the previously played cards. You can find rules and card sets at the link. #iteachmath #mathstoday bit.ly/TheConsisten... 1/3

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Math Curmudgeon @mathcurmudgeon.bsky.social · 21/04/2026

CONSISTENCY is a Geometry game for Geometry students. Each player lays down a card that is consistent with the previously played cards. You can find rules and card sets at the link (google drive link). #iteachmath #MathToday #MathsToday #Geometry drive.google.com/drive/folder...

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Math Curmudgeon @mathcurmudgeon.bsky.social · 22/03/2026

Because 5 points create 3 overlapping triangles, 6 create 4 such, etc. Each triangle's angles add to 180. Thus, (n-2)*180.

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Math Curmudgeon @mathcurmudgeon.bsky.social · 22/03/2026

I'd like to read the article. On the other hand ... Alternatively, view purchase options below: Purchase 24 hour online access to view and download content. Article - $37.50

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Math Curmudgeon @mathcurmudgeon.bsky.social · 13/03/2026

#mathstoday #iteachmath Geometry students played CONSISTENCY with the polygons set. Lots of fun had by all. It's a Geometry game. Each player lays down a card that is consistent with the previously played cards. If you'd like to play-test it: drive.google.com/drive/folder...

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Math Curmudgeon @mathcurmudgeon.bsky.social · 10/03/2026

If you're interested, get the files from the Google Drive. They're ready to print and cut. (or print, laminate, and cut) Let us know how it goes for you!

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Math Curmudgeon @mathcurmudgeon.bsky.social · 07/02/2026

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

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

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Math Curmudgeon @mathcurmudgeon.bsky.social · 07/02/2026

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

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.

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.

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Math Curmudgeon @mathcurmudgeon.bsky.social · 05/11/2025

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

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

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Math Curmudgeon @mathcurmudgeon.bsky.social · 20/09/2025

Simple Fahrenheit to Centigrade conversions on a calculator. Life should be more simple. #Calculators #PEMDAS #GEDMAS

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Math Curmudgeon @mathcurmudgeon.bsky.social · 17/05/2025

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

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

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Math Curmudgeon @mathcurmudgeon.bsky.social · 17/05/2025

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.

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Math Curmudgeon @mathcurmudgeon.bsky.social · 17/05/2025

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.

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Math Curmudgeon @mathcurmudgeon.bsky.social · 17/05/2025

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?

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Math Curmudgeon @mathcurmudgeon.bsky.social · 08/05/2025

Rational Functions, factoring review, operations with algebraic fractions ... all wrapped up into one set of problems, with code-breaking. It's like butttaaah. #algebra2 #mathstoday

Rational Functions Cipher Puzzle v2
Simplify each expression; match to the answers on the other side.

1. (5x+15)/(x^2-x-20)*(2x-10)/(10x^2+50x+60)
2. 4/(x-5)-(4x+7)/((x+2)(x-5))
3. (4x^3+12x^2)/(x^2+5x)÷(2x^4+10x^3+12x^2)/(x^3+5x^2-4x-20)
4. 3/(x+2)+1/(x+4)
5. 4/(3(x+4))-(x+2)/(x+4)(x+1) +2/(3(x+1))
6. (x^4-x^2)/(x+5)*(x^2+3x-10)/(x^4-5x^2+4)

Matching.
A. 1/(x^2-3x-10)
B. 2(x-2)/x
C. 2(2x+7)/(x^2+6x+8)
D. 1/(x^2+6x+8)
E. x^2/(x+2)
F. (x+2)/(x^2+5x+4)

From the other side, list the answers to create the key to a Vigenére Cipher.

Vigenére KEY: ___ ___ ___ ___ ___ ___

Use the coding / decoding tools at http://rumkin.com/tools/cipher to decode the following instructions.

For each of the rational functions that follow, write in order (leaving off negative signs)
AIOV AE KA IQQI; FHBPLI WO MGYXHRT CSH XSF TTX13

f(x)=(2(x-25)(x+24))/((x-2)(x+24))
f(x)=(21x-315)/(x+18)
f(x)=(17x^2+340x-748)/(x^2-3x+2)
f(x)=(16x-400)/(x+17)
f(x)=(32(x-14)(x-8))/(2(x-8)(x+25))
f(x)=(6x^2+240x+2250)/(x^2+23x+120)
f(x)=(24(x^2+4x-12))/(x^2+8x+12)

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Math Curmudgeon @mathcurmudgeon.bsky.social · 05/05/2025

#NewTeacherAdvice Small whiteboards, cheap markers (~ $0.10 each) are well worth the math department investment.

view of classroom table with white boards, markers, and a rational functions simplification problem written on a white board.

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Math Curmudgeon @mathcurmudgeon.bsky.social · 03/05/2025

Anti-intellectualism is a feature of the population as a whole. Some of us are trying to fight that, but it can be exhausting when you are dealing with every type of person and student.

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Math Curmudgeon @mathcurmudgeon.bsky.social · 09/04/2025

#MTBoS #Iteachmath It's time for the occasional reminder of the day in 2021 when I did a Google Image search for "Math Icons". I was looking for images to use on a website menu ... symbols, math class cartoons, and such. Here's a partial screenshot. IYKYK

google image results for "math icons"
Includes a picture of Sam.

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Math Curmudgeon @mathcurmudgeon.bsky.social · 08/04/2025

Something has changed about the decor in the White House but I just seem to put my finger on it … maybe there’s a bit more orange and gilt?

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Math Curmudgeon @mathcurmudgeon.bsky.social · 04/04/2025

If you’re going to criticize and/or ridicule the 86 yo president for typos, you should probably run spell check on your own article before publishing. “allowed”

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Math Curmudgeon @mathcurmudgeon.bsky.social · 29/03/2025

And you kids said there was never going to be a use for negative numbers in the real world!

Adam Kitzinger tweet says that he now has negative four security clearances after Tulsi Gabbard posts that his clearance has been revoked again.

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Math Curmudgeon @mathcurmudgeon.bsky.social · 21/03/2025

If anyone is interested, here's a quick mock-up of how that might work ... www.desmos.com/calculator/k...

DESMOS screenshot (follow the link in the post) showing how to get points on a curve to translate along with the curve.

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Math Curmudgeon @mathcurmudgeon.bsky.social · 14/03/2025

Love this visual of the proof of the angle sum theorems in Precalculus. I do it every year and it never fails to amaze. Horizontally: Green=yellow-pink cos(A+B) = cosAcosB-sinAsinB Vertically: Yellow = green + pink sin(A+B) = sinAcosB + sinBcosA #iteachmath #MathsToday

Right triangle in a rectangle to show why the angle sum formulas in trigonometry work.

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Math Curmudgeon @mathcurmudgeon.bsky.social · 13/02/2025

In #MathsToday. The box announces that Cologuard finds 92% of colon cancers. Later in the ad, we're told false positives can occur & this slide flashes on the screen. If you receive a positive result, what are the chances that you do have colon cancer?

Cologuard advertisement.
Banner says "In a clinical study, 13% of people without cancer received a positive result (false positive) and 8% of people with cancer received a negative result (false negative)

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Math Curmudgeon @mathcurmudgeon.bsky.social · 13/02/2025

This is my favorite review activity for "Writing Equations of Lines"

Math problem
A rule from geometry says that three points determine a circle.
• Make a triangle with the three points.
• Find the midpoints of the three sides
• Find the slopes of the three sides.
• Determine the slopes of the perpendicular lines.
• Draw the perpendicular bisectors of the three sides.
• The three bisectors meet at the center of a circle.
• The points are A( 20, –18 ); B( 8, 18 ); C( –16, –6 )

Verify that the distances from center to each vertex are the same.

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Math Curmudgeon @mathcurmudgeon.bsky.social · 12/02/2025

Also, another parabola shows up when you track the vertex in y=ax^2 + bx + c when you vary b, but hold a,c constant.

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Math Curmudgeon @mathcurmudgeon.bsky.social · 10/02/2025

I had a professor named Tartaglia in college years ago. A friend asked him about "his" most recent book on ballistics. Took ProfT a while to figure out that we were messing with him because he actually wrote our calc text book & it had a section on ballistics. It was funnier at the time.

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Math Curmudgeon @mathcurmudgeon.bsky.social · 10/02/2025

Four more for today.

$Disrespectful bear cub for adding fractions incorectly$ Disappointed puppy for misusing the distributive property.

Evil raccoon enjoys your mistake with radicals (surds, if you're British)

Math unicorn has its feelings hurt when you screw up your square root operations: r(4) + r(6) = r(10)

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Math Curmudgeon @mathcurmudgeon.bsky.social · 10/02/2025

Should we start a petition to rename the Bald Eagle as the Superb Owl?

Bald Eagle taking off from the corn field on my drive in to work the other day.

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Math Curmudgeon @mathcurmudgeon.bsky.social · 07/02/2025

2.5g/c * 30,000,000 pennies 2.5(3e7) = 7.5e7 grams = 7.5e4 kilograms = 75 metric tons ~ 75 long tons * 2200 = 165,000 pounds 82.5 short tons at 14 tons each, you'd need about 6 large dump trucls. AI, of course, is wrong as usual.

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Math Curmudgeon @mathcurmudgeon.bsky.social · 07/02/2025

I feel this needs more exposure ...

Cartoon: Ozymandius statue but the face on the head is Elon Musk, and the inscription reads "so much mighy wow ... mega(?) rich how money"

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Math Curmudgeon @mathcurmudgeon.bsky.social · 07/02/2025

Time trolls trump today, Musk at the #ResoluteDesk. Which is the greater fool? #TimeMagazine

Time magazine cover with elon musk behind the resolute desk.

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Math Curmudgeon @mathcurmudgeon.bsky.social · 04/02/2025

This executive order has such strong "Nero commanding his army to fight Neptune" energy.

Drawing of "Nero commanding his army to stab the sea (Fight Neptune).

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