Laib.” Catalina glanced towards the door, perhaps plotting her exit. “Yeah, I don’t know what you’re talking about, Ms. “Well, we want something that’s going to color in all the points on the inside, too.” “So how does that help me color in the face.” “Yeah, so if you put it a value of for and for, you land here on the far right edge. let’s color in your cat! So the red outline of his face is because every point along that rim is a solution to your equation.” “And everyone else in my class has shapes colored in by now.” “It’s still going to take us forever,” Catalina lamented. I smiled - perhaps smugly, because Catalina responded with, “you’re so sneaky, Ms. “Oh, okay, so my middle of my oval was the and. It’s like she’s diagramming a mathematical sentence. I want it to the middle.”Ĭatalina had never studied equations for circles or ellipses in class, but she was starting to figure out how how the parts of the equation work. “Oh, that makes sense, because it moves side to side, along the x-axis. It didn’t take long for Catalina to discover that a value of 0 centered her new ellipse. What happens when you change the value? Can you get it to be centered along. You can continue with whichever cat you prefer.” We’ll save your work, and make a second version. I saved her work, and then shared it to another tab. “But it’s due on Friday! Please! I can’t start over!” “I think you’re going to like what we’re about to do…” I saw the muscles around Catalina’s eyebrows tense. “Well, I have some good news: the mathematical equations might be easier to figure out when it’s centered, because you’ll notice some connections. “Yeah, it made it easier for me to draw, because I could make it mirror image.” “Yes! And it’s symmetrical across that line.” “Okay, you see how in your drawing the cat’s face is centered? Along this line… do you remember what it’s called?” your cat, you have to figure out an entirely new equation. “It sounds like every time you go to add something to. “But because the cat’s head isn’t where it should be, like in my drawing, none of the whiskers really make sense.” She looked up at me with big, saucer eyes. So I figured out the slope of the lines using slope triangles and, you now, rise over run.” Yes! There was so much from here! I had her show me how she determined the linear equations to use. “I had already drawn my cat on paper.” Catalina pointed again to her sketch. “Okay, and then how did you come up with the whiskers?” “I just replaced the h and the k and the a and the b with numbers.” She pointed to the paper with the assignment. How did you come up with the equation for the ellipse?” I asked her. “Okay, let’s start slow and then go fast. “Okay, but I have a lot to do, and I don’t know how to do the mouth at all!” She pointed to the parabola of its tiny feline lips. For all of his asymmetries, this cat represented a lot of mathematical prowess. Its ears floated just North and East of its wide, oval face. She offered an apologetic smile.Ĭatalina had created a lopsided cat. Then she opened her chromebook slowly, turning it to face me. Reviewing Catalina’s WorkĬatalina pulled out her initial sketch that she had made on grid paper. We cheerfully arranged to meet later that day. “…that you could help me with my Desmos art project? It’s due soon and it’s really hard.” “Do you think…” she paused, and then started again with lowered voice. She had an impressively high growth score on last year’s state test. She now advocates for support when she’s feeling confused. I’ve known her for years, and I’m enormously proud of her mathematical journey. “Aww, I miss working with you, too!” I gushed. Laib!!! I miss working with you!” Last year, she was in a section of 7th grade that I co-taught, and I saw her in a small group for part of the school year. Nora had been wrestling with her feelings around the transition from our little K-8 school to the town’s only high school, and so she was working on a nostalgic rendition of the PBS Kids logo, a fixture of her youth. Sebastian had designed a Puerto Rican flag to honor his heritage. Within a few days, graphs were shaping into true artwork.

(Outline a set of points, and the Desmos graphing calculator will shade the interior!) Then, after students had mucked about with inequalities for a few days, she introduced the polygon tool as an inefficient way to color in areas. The next day, she taught them how to create a custom color. She gave them formulas to help create unfamiliar figures, like circles and ellipses. and then breadcrumbed different techniques over the course of the week. The classroom teacher had given some loose constraints - use at least 8 linear equations, use at least 4 inequalities, use at least 4 horizontal lines, etc. It is a glorious capstone to their K-8 math experience at our school. In the last week of two of school, the 8th graders worked on Desmos art projects.

Desmos desmos polar graphing art