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Posts by Mark Trushkowsky

What do you notice? What do you wonder?

On the top row, there are two pink frogs facing right and two blue frogs facing left, with a single space between them. The frog pairs are facing towards each other. 

On the bottom, there are two blue frogs on the left, still facing left, and two pink frogs facing right, with a single space between them. The frog pairs are facing away from each other.

What do you notice? What do you wonder? On the top row, there are two pink frogs facing right and two blue frogs facing left, with a single space between them. The frog pairs are facing towards each other. On the bottom, there are two blue frogs on the left, still facing left, and two pink frogs facing right, with a single space between them. The frog pairs are facing away from each other.

Once again, a simple set-up yielded many questions and ribbit holes… ahem, rabbit holes, to explore.

Super fun Community of Adult Math Instructors (CAMI) meeting on this swapping frogs problem!

nyccami.org/ribbit/

#ANNMath #ITeachMath #MTBoS #AdultEdu

3 days ago 2 1 0 0
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"I fear some [council members] are indifferent." Have you paid someone's rent, organized a fundraiser, gone on patrol, found someone an attorney, done someone's laundry, delivered groceries, held a baby of someone sheltering in fear? "If not you may be too far removed to have good judgment."

1 month ago 326 125 3 18
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"Aside from the internment camps used to incarcerate Japanese Americans in the 1940s, such facilities have no precedent in American history..."

US Conference of Catholic Bishops statement on Trump's new mass prison camps.

Full statement at the link:

www.usccb.org/news/2026/th...

1 month ago 4296 1739 140 59
At the top is a pictorial equation: a pink triangle and small green triangle on the left side of the equals sign and a red trapezoid on the right side. 

Below are five steps, linked by arrows. Step one has all three shapes from the equation. Step two has the green triangle placed over the red trapezoid, covering a portion of it. Step three has the pink triangle place over the red trapezoid as well. A triangular piece of the pink triangle is sticking out above the area of the red trapezoid. The only part of the red trapezoid still visible is a red triangle. Step four has the pink triangular piece slide over to be above the visible triangular piece of the red trapezoid. Step five shows that the access pink triangle exactly covers the remaining red triangle. This shows that the areas of the pink triangle and the small green triangle together are equal to the area of the red trapezoid.

At the top is a pictorial equation: a pink triangle and small green triangle on the left side of the equals sign and a red trapezoid on the right side. Below are five steps, linked by arrows. Step one has all three shapes from the equation. Step two has the green triangle placed over the red trapezoid, covering a portion of it. Step three has the pink triangle place over the red trapezoid as well. A triangular piece of the pink triangle is sticking out above the area of the red trapezoid. The only part of the red trapezoid still visible is a red triangle. Step four has the pink triangular piece slide over to be above the visible triangular piece of the red trapezoid. Step five shows that the access pink triangle exactly covers the remaining red triangle. This shows that the areas of the pink triangle and the small green triangle together are equal to the area of the red trapezoid.

At Instructional Routines Club, someone commented that one of the benefits of virtual manipulatives is that you can cut/decompose them. I used that idea to represent my reasoning behind one of my equations.

#ANNMath #Iteachmath #MTBoS

2 months ago 1 0 0 0
1. One pink triangle equals 2 small green triangles
2. One red trapezoid equals 3 small green triangles
3. One red trapezoid and one small green triangle equals one large green triangle equals to pink triangles equals four small green triangles
4. One pink triangle and one small green triangle equals one red trapezoid

1. One pink triangle equals 2 small green triangles 2. One red trapezoid equals 3 small green triangles 3. One red trapezoid and one small green triangle equals one large green triangle equals to pink triangles equals four small green triangles 4. One pink triangle and one small green triangle equals one red trapezoid

I started making equations using only the shapes to show different relationships between the pieces.

#ANNMath #Iteachmath #MTBoS

2 months ago 1 0 1 0
A trapezoid divided up into 12 congruent triangles. 3 of the triangles are red, together forming a smaller trapezoid within the larger trapezoid. The remaining 9 triangles are green. 

3/12 of the triangles in the larger trapezoid are red.

A trapezoid divided up into 12 congruent triangles. 3 of the triangles are red, together forming a smaller trapezoid within the larger trapezoid. The remaining 9 triangles are green. 3/12 of the triangles in the larger trapezoid are red.

An equation. On the left side of the equal sign, a larger trapezoid is composed of three smaller orange trapezoids and 3 small triangles. On the right side are four trapezoids. Three are the same as the smaller orange ones on the left side of the equation. One of them is composed of the three small yellow triangles, arranged to show they have the same area as each orange trapezoid. 

My colleague created this representation for showing that the red trapezoid 1/4 the area of the original shape. Her goal was to get there without finding the 3/12 and then reducing. I had a similar approach, but loved how clearly her model conveyed our thinking without words.

An equation. On the left side of the equal sign, a larger trapezoid is composed of three smaller orange trapezoids and 3 small triangles. On the right side are four trapezoids. Three are the same as the smaller orange ones on the left side of the equation. One of them is composed of the three small yellow triangles, arranged to show they have the same area as each orange trapezoid. My colleague created this representation for showing that the red trapezoid 1/4 the area of the original shape. Her goal was to get there without finding the 3/12 and then reducing. I had a similar approach, but loved how clearly her model conveyed our thinking without words.

The original trapezoid rearranged as three large triangles. 
The triangle on the left is pink. The middle triangle is green. The triangle on the right is broken up into 4 smaller, congruent triangles. Three of those are red and one is green. 

The goal was to show that the red trapezoid can be seen as 3/4 of 1/3.

The original trapezoid rearranged as three large triangles. The triangle on the left is pink. The middle triangle is green. The triangle on the right is broken up into 4 smaller, congruent triangles. Three of those are red and one is green. The goal was to show that the red trapezoid can be seen as 3/4 of 1/3.

It was a virtual meeting, and some of us used Polypad to noodle with the shapes. Inspired by a colleague, I started making wordless visual representations of my reasoning.

#ANNMath #Iteachmath #MTBoS

2 months ago 1 0 1 0
Text: What fraction of this shape is red? How do you know? How else do you know?

Image: a trapezoid composed of 5 different pattern blocks. Two pink right triangles are arranged to create an equilateral triangle that can be seen as one-third of the area of the trapezoid. A large green triangle in the middle of the trapezoid has the same area as the pink. A third triangle is composed of a red trapezoid and a smaller green triangle. The red trapezoid and small green triangle together have the same area as the pink triangles and as the large green triangle.

Text: What fraction of this shape is red? How do you know? How else do you know? Image: a trapezoid composed of 5 different pattern blocks. Two pink right triangles are arranged to create an equilateral triangle that can be seen as one-third of the area of the trapezoid. A large green triangle in the middle of the trapezoid has the same area as the pink. A third triangle is composed of a red trapezoid and a smaller green triangle. The red trapezoid and small green triangle together have the same area as the pink triangles and as the large green triangle.

We did a fraction talk at @adultnumeracy.bsky.social Instructional Routine Club today.

#ANNMath #Iteachmath #MTBoS

2 months ago 2 0 1 1

of course they knew. IT WAS THEIR POLICY.

2 months ago 341 87 4 0
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What You Need to Know About the SAVE Act

The SAVE Act is bad. While lots of people are talking about the ID portion, It creates a criminal cause of action to put election workers in prison for (even accidentally) registering someone to vote without ID.
campaignlegal.org/update/what-...

2 months ago 365 224 4 0

"I'm too old for this imperial shit" - Black Skin, White Masks

2 months ago 1051 170 17 2
Sign made of plywood propped up in a telephone pole by the street. It has ‘We won’t forget what you did. Abolish ICE.’

Sign made of plywood propped up in a telephone pole by the street. It has ‘We won’t forget what you did. Abolish ICE.’

2 months ago 425 108 1 2
Plywood sign on sidewalk says, ‘3000 neighbors stolen ICE OUT everywhere’

Plywood sign on sidewalk says, ‘3000 neighbors stolen ICE OUT everywhere’

2 months ago 88 29 0 0

Hey @triangleman.bsky.social, maybe a new Math-on-a-Stick station?

2 months ago 0 0 0 0
A photo of a sidewalk with two circles. Each circle has six smaller circles inside, colored (clockwise from 3 o’clock) blue, purple, teal, red, pink, yellow. In the center of each circle is a pair of bare footprints. Between the two larger circles are the words “mirror me”

A photo of a sidewalk with two circles. Each circle has six smaller circles inside, colored (clockwise from 3 o’clock) blue, purple, teal, red, pink, yellow. In the center of each circle is a pair of bare footprints. Between the two larger circles are the words “mirror me”

This is lovely.

#sidewalkmath #rehumanizingmathematics
#mathforidentityandbelonging

2 months ago 2 0 1 0
A screenshot of a thread with the following questions:

On the water front -
Are you having enough to drink today? Do you need anything to wash and clean? Can I help replenish any tears you've shed? Are you staying fluid these days? Are your waters calm, still, deep, turbulent, rushing, frozen, evaporated...?

Through the fire -
Where is the sun for you? Are you in enough light? How can I help you stay warm? What's burning for you? Do you need any fuel? What spark are you carrying? Is your blaze to high? Do you need rekindling? What's the smoke?

From the earth -
How grounded are you feeling? What is nourishing your soil? Where are you rich? Are you getting vitamins/minerals? Can I help you stand more firmly? Are you eating your veggies? When was your last rest? Do you need to lay down?

In the air -
Have you taken a breath? What's inspiring you? Have you felt the wind/breeze? What's in your wings/sails? Can I help you stay afloat? What do you need to fly? What whisper would you like to hear?

A screenshot of a thread with the following questions: On the water front - Are you having enough to drink today? Do you need anything to wash and clean? Can I help replenish any tears you've shed? Are you staying fluid these days? Are your waters calm, still, deep, turbulent, rushing, frozen, evaporated...? Through the fire - Where is the sun for you? Are you in enough light? How can I help you stay warm? What's burning for you? Do you need any fuel? What spark are you carrying? Is your blaze to high? Do you need rekindling? What's the smoke? From the earth - How grounded are you feeling? What is nourishing your soil? Where are you rich? Are you getting vitamins/minerals? Can I help you stand more firmly? Are you eating your veggies? When was your last rest? Do you need to lay down? In the air - Have you taken a breath? What's inspiring you? Have you felt the wind/breeze? What's in your wings/sails? Can I help you stay afloat? What do you need to fly? What whisper would you like to hear?

Some friends and I were wondering if these dystopian days will bring about the end of asking each other, “how are you doing?” and it brought me back to these nurturing & sustaining questions, gifted by @teachnexttmb.bsky.social as a better way.

2 months ago 2 2 2 0

For all my non-Minnesota people, do not think for a second that Frey has anything to do with getting ICE the fuck out of Minneapolis.

2 months ago 1 0 0 0

You can't... repeal... a scientific finding. At that point it's just called lying about it.

2 months ago 12623 4468 209 113
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Prison Culture » Police “Reforms” You Should Always Oppose…

I pulled together a small list of body camera-related resources, just in case anybody is curious about how abolitionists think about them.

- Mariame Kaba wrote a blog post in 2014 about police reforms to oppose: www.usprisonculture.com/2014/12/01/p...

2 months ago 9 7 1 0
A musician playing a guitar in sugarcane that is somehow in the middle of a football field

A musician playing a guitar in sugarcane that is somehow in the middle of a football field

First shot: sugarcane

The backbone of Puerto Rico's agricultural economy since colonial times

Still used to make rum of course!

2 months ago 3611 625 35 283
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There is also the Bad Bunny Syllabus
www.badbunnysyllabus.com

I am here for all of it!! Want to read that dissertation 😍

2 months ago 7 5 0 1

What game?

2 months ago 1 0 1 0

Macbeth: SHIT

2 months ago 10076 2034 137 50

I'm hardly the first person to note this, but it's enormously instructive that our President and his followers saw the message "THE ONLY THING MORE POWERFUL THAN HATE IS LOVE" and understood it, correctly, as an attack on them

2 months ago 25045 5858 104 50

Thinking about the fact that the writing on the football was in English.

The audience for THAT message - significant.

Truly going to be thinking of the incredible brilliance & beauty of that show for a long time! 💛

2 months ago 15 3 0 0

GREATEST HALFTIME SHOW EVER!

2 months ago 0 0 0 0

Put this family up in the Governor’s Mansion and dare this administration to come get him, @governorwalz.mn.gov

Fuck this shit.

2 months ago 43 10 0 1

SCORPION: take me across the river
FROG: if I do that, you'll sting me
S: if I sting you, we'll both drown
F: ok, that makes sense
*halfway across the river*
F: so?
S: so what?
F: sting me
S: what?
F: sting me, like you promised
S: no
F: sting me so we'll both drown
S: *crying* what is happening?

2 months ago 2025 381 17 10
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“We call ourselves a civilized nation, but we lack rules and accountability around what a person claiming to be law enforcement is permitted to do to another human being. I am not afraid and I am not afraid to keep working on this problem even after ICE is gone." - Aliya Rahman

Hero.

2 months ago 4 0 0 0
WATCH: Minneapolis resident and U.S. citizen Aliya Rahman describes being detained by ICE
WATCH: Minneapolis resident and U.S. citizen Aliya Rahman describes being detained by ICE YouTube video by PBS NewsHour

The testimony of Aliya Rahman, Bangladeshi American & U.S. citizen, before Congress about her violent ICE arrest and detention.

2 months ago 2 2 1 0