#ANNMath
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marktrushkowsky.bsky.social
Super excited about the new instructional routine I recently learned that develops data literacy, spatial reasoning, estimation skills, and a conceptual understanding of part-to-whole relationships - Paper Plate Circle Graphs!

adultnumeracynetwork.org/Instructiona...

#ANNMath #MTBOS #ITeachMath
June 7, 2026 at 7:02 PM
triangleyou.bsky.social
A Desmos doodle inspired by the question: How many triangles are in a triangle made of triangles? (Visit the graph to see it do its thing.)

www.desmos.com/calculator/o...

#ANNMath #MTBoS #ITeachMath
Counting Triangles
www.desmos.com
November 26, 2024 at 12:58 AM
marktrushkowsky.bsky.social
His words also make a compelling argument for what math and math teaching & learning should be like.
#ANNMath #MTBoS #ITeachMath
markharris.bsky.social Mark Harris @markharris.bsky.social · Nov 15
Some inspiring words on cinema in the streaming era from the Pope.

Yes, THAT Pope.
The logic of algorithms tends to repeat what “works,” but art opens up what is possible. Not everything has to be immediate or predictable. Defend slowness when it serves a purpose, silence when it speaks and difference when evocative. Beauty is not just a means of escape; it is above all an invocation. When cinema is authentic, it does not merely console, but challenges. It articulates the questions that dwell within us, and sometimes, even provokes tears that we did not know we needed to express.
November 15, 2025 at 6:47 PM
marktrushkowsky.bsky.social
1/7
I've been making #slowrevealgraph sequences to help make sense of what is going on.

Here's one that looks at the number of deportations each year within the past four presidential administrations.
bit.ly/icedeportati...

#ANNMath #ITeachMath #MTBoS
Numberless bar graph - first image from a slow reveal graph sequence Graph titled: Deportations of People Arrested Within the United States. Final image from a slow reveal graph sequence
January 23, 2026 at 8:27 PM
marktrushkowsky.bsky.social
Have any baked good shouted "Fraction Talk about me!" louder than these gorgeous cookies from Brooklyn baker Lauren Dozier (instagram.com/lauren_dozier)? What fractions do you see? #ITeachMath #ANNMath
A plate of at least 8, square cookies, each divided into 4 colors (yellow, red, green, and blue). The center is a small yellow square, standing on its corner. Each side of that square is bordered by the hypotenuse of 4 blue right triangles. Each blue triangle is reflected across one of its legs with an identical red triangles. The space between the hypotenuses of the red triangles is filled with a green isosceles triangle. The remaining corners of the square are completed with 4 squares of the same color, either yellow or blue.
December 9, 2024 at 3:31 PM
marktrushkowsky.bsky.social
I am enjoying this #OpenMiddle problem, created by
Sarah Lonberg-Lew (We think - Is this one out there already?).

So far I've got 15 solutions & have 5 different digits for the sum.

Standard rules: use the numbers 1-9, no more than once each. One number per box. #ANNMath #MTBos #ITeachMath
Three fractions with single-digit numerators and denominators, being added, resulting in a single-digit sum. Each digit is represented in the picture by an empty box.
February 15, 2024 at 8:25 PM
marktrushkowsky.bsky.social
1/n

Got to do Countries In Our Closet data activity from @terc-stem.bsky.social EMPower book, Many Points Make A Point.

Step 1: Create a graph showing the countries where our clothing was made.

What do you notice? What do you wonder?

#ANNMath #MTBoS #ITeachMath #statisticalliteracy #data
A graph with columns of post-its stacked over various country names. Honduras - 5 post-its China - 6 Thailand - 4 Vietnam - 7 Jordan - 1 India - 3 Pakistan - 1 Bangladesh - 3 Madagascar - 1 Mauritius - 1 Cambodia - 1 Korea - 1 USA - 4 Sri Lanka - 4 Indonesia - 2 Mexico - 2 Guatemala - 1 Germany - 2 Nicaragua - 1
June 7, 2026 at 6:57 PM
marktrushkowsky.bsky.social
6/7

This one compares the number of DHS officers in the state of Minnesota to the number of police officers in the largest Minneapolis/St. Paul metro area police forces.

bit.ly/DHSinMNvsTCM...

#slowrevealgraph #ANNMath #ITeachMath #MTBoS
Numberless circle graph/pictograph. First image in a slow reveal graph sequence. Circle Graph/Pictograph comparing Department of Homeland Security Forces in Minnesota to the Ten Largest Twin Cities Metro Police Forces. Final image from a slow reveal graph sequence
January 23, 2026 at 8:27 PM
marktrushkowsky.bsky.social
4/7

This one is a map graph that looks at what percentage of people arrested by ICE in each state had no criminal record.

bit.ly/arrestedwith...

#slowrevealgraph #ANNMath #ITeachMath #MTBoS
Numberless map graph. First image in a slow reveal graph sequence. Map graph titled: Share of people arrested by ICE with no criminal record. Final image from a slow reveal graph sequence
January 23, 2026 at 8:27 PM
marktrushkowsky.bsky.social
Writing the alt text for the table made me think more about how it works as a multiplication table!

If 1000 is in the 8 row, than I know I need 125 at the top of that column. Sequence of odds is 2x+1, so when y is 125, x is 62. So I think 1000 is in the 8 row (4th row) and 62nd column!
#ANNMath
November 13, 2025 at 7:25 PM
marktrushkowsky.bsky.social
3/7

This one looks at the number of ICE arrests that have been people with violent convictions, people with other past convictions, people with pending criminal charges, and people with no criminal charges.

bit.ly/ICEarrestsby...

#slowrevealgraph #ANNMath #ITeachMath #MTBoS
Numberless area graph. First image in a slow reveal graph sequence. Area Graph titled: Daily ICE arrests nationwide. Final image from a slow reveal graph sequence
January 23, 2026 at 8:27 PM
marktrushkowsky.bsky.social
2/7
This one looks at the the number of Immigration and Customs Enforcement (ICE) arrests that happened at prisons/jails and the number that have happened in communities, between 2024 and 2025.
bit.ly/icearrestsby...

#slowrevealgraph #ANNMath #ITeachMath #MTBoS
Numberless line graph. First image in a slow reveal graph sequence. Graph titled: Daily ICE arrests nationwide. Final image from a slow reveal graph sequence
January 23, 2026 at 8:27 PM
marktrushkowsky.bsky.social
Last May’s Community of Math Instructors (CAMI) monthly teachers’ circle meeting started with some attention for some fairly simply-structured figures.

#ANNMath #CAMImath
#MTBoS #ITeachMath

nyccami.org/attention-an...
Two shapes. On the left, an area of 41 squares. One way to describe them is in 9 vertical columns, with 1 square, 3 squares, 5 squares, 7 squares, 9 squares, then 7, 5, 3, and 1. The figure on the right can be described as a similar figure, rotated 45 degrees, except the columns would be arranged 1, 3, 5, 7, 9, 11, 9, 7, 5, 3, 1.
September 30, 2025 at 1:23 AM
marktrushkowsky.bsky.social
Learned a new word today.

Last week I led some folks in an exploration of probability w/ a game of roller derby, where you roll 2 dice and look at the sum. Looking at our results—w/ its messy but triangular distribution & that tower of 7s—I’m calling it a Punktlandung.

#ANNMath #MTBoS #ITeachMath
A hand-drawn tally chart tracking the sums of rolling two dice from 2 to 12. The tallies form a rough, messy triangular distribution, with a massive column for the number 7 that tower over the rest of the numbers, shooting completely out of the top of the grid.
June 8, 2026 at 4:22 AM
marktrushkowsky.bsky.social
Thank you, @triangleyou.bsky.social for sharing this task they got from @howiehua.bsky.social!

What patterns do you notice in the table?
Will 1000 appear? If so, where?

I'm not quite there yet, but I'm having such fun, in the spirit in which I received it, I invite others to play!
#ANNMath
A table of numbers. Consecutive odd numbers across the top. Reading left to right: 1, 3, 5, 7... The left column is made up of powers of 2 going down. Reading: 1, 2, 4, 8,... The table can be completed by multiplying the odd numbers across the top by the powers of 2.
November 13, 2025 at 7:14 PM
marktrushkowsky.bsky.social
Phyllotaxis spirals in the leaves and buds of some hollyhock.

#ANNMath #plantmath #rehumanizingmathematics
#MTBoS
An aerial view of a hollyhock plant, in which you can see new leaves growing at an angle from the previous one in a way that allows them to “fill in the space.” An aerial view of another hollyhock plant, in which you can see new leaves growing at an angle from the previous one in a way that allows them to “fill in the space.” An aerial view of another hollyhock plant, in which you can see new leaves growing at an angle from the previous one in a way that allows them to “fill in the space.” An aerial view of the buds of hollyhock plant, in which you can see new buds growing at an angle from the previous one in a way that allows them to “fill in the space.”
June 18, 2026 at 2:07 AM
marktrushkowsky.bsky.social
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
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.
April 18, 2026 at 6:03 PM
adultnumeracy.bsky.social
We had our first Adult Numeracy Network Instructional Routine Club today! Teachers from AZ, FL, GA, MA, MN, and PA came together to do explore fraction talks.

For more information, check out adultnumeracynetwork.org

#ANNMath #AdultEd #MTBoS #ITeachMath
marktrushkowsky.bsky.social Mark Trushkowsky @marktrushkowsky.bsky.social · Feb 19
We did a fraction talk at @adultnumeracy.bsky.social Instructional Routine Club today.

#ANNMath #Iteachmath #MTBoS
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.
February 19, 2026 at 2:14 AM
adultnumeracy.bsky.social
Barcelona is Made of Math.

This article is a virtual tour of the Spanish city where mathematics, art, and exploration meet. #ANNMath #rehumanizingmath #AdultEdu
Barcelona Is Made of Math (Gift Article)
A virtual tour of the architecture in a city where mathematics and exploration meet.
www.nytimes.com
October 2, 2025 at 10:00 PM
marktrushkowsky.bsky.social
5/7

This one looks at the estimated population of undocumented immigrants by state.

bit.ly/undocumented...

#slowrevealgraph #ANNMath #ITeachMath #MTBoS
Numberless map graph. First image in a slow reveal graph sequence. Graph titled: Estimated US undocumented population by state (2022) Final image from a slow reveal graph sequence
January 23, 2026 at 8:27 PM
marktrushkowsky.bsky.social
We did a fraction talk at @adultnumeracy.bsky.social Instructional Routine Club today.

#ANNMath #Iteachmath #MTBoS
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.
February 19, 2026 at 2:10 AM
marktrushkowsky.bsky.social
7/7

This one looks at % of ICE arrests in NYC, Jan-Oct 2025, comparing targets who had criminal convictions versus those with pending criminal charges, and those with only civil immigration violations (no criminal charges).

bit.ly/icearrestsin...

#slowrevealgraph #ANNMath #ITeachMath #MTBoS
Numberless area graph. First image in a slow reveal graph sequence. Area graph titled: Share of Arrests Each Week By Criminality Final image from a slow reveal graph sequence Numberless stacked bar graph. First image in a slow reveal graph sequence. Stacked bar graph titled: Immigration Arrests in NYC Focus Far More on People Without Criminal Convictions or Charges Compared to U.S. Overall. Final image from a slow reveal graph sequence
January 23, 2026 at 8:27 PM
marktrushkowsky.bsky.social
I started making equations using only the shapes to show different relationships between the pieces.

#ANNMath #Iteachmath #MTBoS
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
February 19, 2026 at 2:10 AM
marktrushkowsky.bsky.social
Like I said, I'm not quite there yet, but I wanted to share my work so far because I feel like there must be so many different ways to approach this, and I'm curious what others do. #ANNMath
A messy ZOOM whiteboard of thinking visualized, exploring the patterns in the table, making and testing conjectures and partially answering the question. The work generally moves from top to bottom. The culmination thus far is the 1000 does appear in the 8 row (not 8th row). The final sentence is "Upwards and onwards to a generalization to figure out the column!"
November 13, 2025 at 7:14 PM
marktrushkowsky.bsky.social
I decided to create similar figures to have more to explore to look for patterns.

I used the second figure from the launch (11 squares high and 11 squares wide as opposed to 9) and “filled in the corners.”

#ANNMath #MTBoS
The area of the blue is 11 + 9 + 9 + 7 + 7 + 5 + 5 + 3 + 3 + 1 + 1 = 61 squares The area of the corners (orange) is 10 + 10 + 8 + 8 + 6 + 6 + 4 + 4 + 2 + 2 = 60 squares Again, the area of the blue is a little more than half the area of the entire square, and the area of the orange is a little less.
September 30, 2025 at 1:33 AM