Mark Trushkowsky
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marktrushkowsky.bsky.social
Mark Trushkowsky
@marktrushkowsky.bsky.social
130 followers 160 following 62 posts
math, teaching, adult education, numeracy, music, movies, gardening, play, beauty
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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
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
The Northern Lights (Minneapolis, MN)
Red and green aurora lights Red and green aurora lights Red and green aurora lights Red and green aurora lights
November 12, 2025 at 8:14 PM
marktrushkowsky.bsky.social
I’m not sure if this is exactly what you mean, but I think Rough Draft Math by @mandymathed.bsky.social has a lot to say about risk taking.
November 6, 2025 at 11:58 PM
marktrushkowsky.bsky.social
Next I tried it with Fig. 13. I created a grid in the center of each square unit to see if it would that have the same area as the figure we can build with the corners from Figure 11, removing the center, and pushing the corners together.
A grid drawn over figure 13 resulting in an area of 60 sq units, which is the same area as the rearranged figure created with the corners of Figure 11.
September 30, 2025 at 1:52 AM
marktrushkowsky.bsky.social
Another pattern emerged when I started playing around with creating a grid in the center of each sq unit

The area of the blue figure is 61 sq units.

I noticed the grid by itself had an area of 40 sq units. It also looked a lot like the figure we got we we added corners to our original figure
Figure 11 (area of 60 squares units). A grid made from connecting the center points of Figure 11. The grid by itself, and area of 40 square units The grid and the figure created from the corners of Figure 9, both with an area of 40 square units
September 30, 2025 at 1:45 AM
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
marktrushkowsky.bsky.social
I wondered what would happen if we “finished” the square by filling in the corners.

Looking at just the green area, I rearranged the pieces to look similar to the original figure. The figure felt similar, but like an “even” version.

#ANNMath #CAMImath
#MTBoS
On the left, a blue figure with an area of 41 square units, arranged in centered columns 1, 3, 5, 7, 9, 7, 5, 3, 1. On the right, the same figure, imbedded in a 9x9 square, with the same 41 squares in blue, plus 40 green squares (10 in each corner, arranged as stairs 4, 3, 2, 1) The blue figure removed and the green squares rearranged into columns with heights of 2, 4, 6, 8, 8, 6, 4, 2
September 30, 2025 at 1:25 AM
marktrushkowsky.bsky.social
Crop art nurtures through inspiration, and humor.
The quote: “All flourishing is mutual” from Braiding Sweetgrass by Robin Wall Kimmerer, above two hands filled with seeds, all created using seeds. A black and white image of a person made of beans, planting a single red bean, above the word PERSIST, written with red beans. “We may encounter many defeats, but we must not be defeated.” Maya Angelou Three kittens peering directly at you, between the words, “ARE YOU POOPING?”
August 31, 2025 at 4:23 AM
marktrushkowsky.bsky.social
More crop art.
A portrait of a goat, created from seeds (natural colors) A furry portrait of a prairie rodent, created from seeds Olive Trees with Yellow Sky by Vincent Van Gogh, created from seeds A portrait of a rooster, created from seeds (dyed/painted)
August 31, 2025 at 4:04 AM