I couldn't take any more of those damn Face-ing Math worksheets. My students and I were both tired of PowerPoint presentations. There was no way I was about to fill my cabinets with more posters. Pair those feelings with a restless group of 8th graders who know their ticket has been punched to the high school. Testing was over. No finals to give.
Yep, the end of the school year was fast approaching and I needed something that my students and I could get interested in without running the class off the rails of sanity.
Enter: Mr. Sierpinski and the Triangle of Doom.
Yep, the end of the school year was fast approaching and I needed something that my students and I could get interested in without running the class off the rails of sanity.
Enter: Mr. Sierpinski and the Triangle of Doom.
The instructions were simple:
OK class, your job is to create a Sierpinski Triangle. Using a clean sheet of paper, a pencil, and a ruler, you need to create each iteration with precision. There may not be any folds or holes in your paper when you are finished. You will leave your paper here at the end of class... NO TAKING IT HOME! I must caution you, however, to be very patient with this. It isn't as easy as it looks.
"Yeah, whatever Stevens, that's what you always say," proclaims Amber, ready to take on the challenge.
Sure, Amber. You wait. Here is what you will need:
-- Paper (up in the front of the room)
-- Patience
-- A ruler with a straight edge!
-- PATIENCE
-- A very sharp pencil
-- PATIENCE!!!
You will be graded on the precision of your triangle along the following guidelines:
-- 8" Equilateral Triangle
-- 4" Equilateral Triangle
-- 2" Equilateral Triangles
-- 1" Equilateral Triangles
-- 1/2" Equilateral Triangles
-- 1/4" Equilateral Triangles
Any questions?
Nope. After all, it's just a silly triangle. Students grabbed a ruler, the one sheet of clean paper, and a handful of confidence. I mean really, how long should it take to draw a triangle?
OK class, your job is to create a Sierpinski Triangle. Using a clean sheet of paper, a pencil, and a ruler, you need to create each iteration with precision. There may not be any folds or holes in your paper when you are finished. You will leave your paper here at the end of class... NO TAKING IT HOME! I must caution you, however, to be very patient with this. It isn't as easy as it looks.
"Yeah, whatever Stevens, that's what you always say," proclaims Amber, ready to take on the challenge.
Sure, Amber. You wait. Here is what you will need:
-- Paper (up in the front of the room)
-- Patience
-- A ruler with a straight edge!
-- PATIENCE
-- A very sharp pencil
-- PATIENCE!!!
You will be graded on the precision of your triangle along the following guidelines:
-- 8" Equilateral Triangle
-- 4" Equilateral Triangle
-- 2" Equilateral Triangles
-- 1" Equilateral Triangles
-- 1/2" Equilateral Triangles
-- 1/4" Equilateral Triangles
Any questions?
Nope. After all, it's just a silly triangle. Students grabbed a ruler, the one sheet of clean paper, and a handful of confidence. I mean really, how long should it take to draw a triangle?
The class quickly realized the need for precision and measurement. What was supposed to be an 8" equilateral triangle took a lot more time and patience than initially expected. Especially for the GATE students and high performers, this was humbling. It's just a triangle... How hard can it be?
Sure enough, all students cleared the first hurdle and thought they were onto the next one. Next up was the 4" triangle and, if the measurements are sound from the 8", this shouldn't have been too tough.
Sure enough, all students cleared the first hurdle and thought they were onto the next one. Next up was the 4" triangle and, if the measurements are sound from the 8", this shouldn't have been too tough.
Quickly, the measurements students had made for their 8" triangle were coming into play with the 4" triangle, proving that they were slightly off. Even a 1/64th of an inch difference can make a noticeable slant in the triangle. ARGH!
Oh yeah, you'll need an eraser, too.
Starting over was incredibly common, which was great for students to see. It wasn't "the smart kids" flying through the challenge; it was the low-to-middle students who were persevering.
Once the 8" & 4" were precise, students got into the 2" triangles and mistakes were shining through.
Oh yeah, you'll need an eraser, too.
Starting over was incredibly common, which was great for students to see. It wasn't "the smart kids" flying through the challenge; it was the low-to-middle students who were persevering.
Once the 8" & 4" were precise, students got into the 2" triangles and mistakes were shining through.
To be expected, there was a high amount of frustration during this entire process. We had built a culture in our classroom all year where it was OK to get frustrated, OK to be stuck, and OK to ask for help. We really needed that culture for this project because kids who have never struggled in math were struggling mightily.
And they were furious that they couldn't take it home.
And they were furious that they couldn't take it home.
Something pretty amazing started happening as the students were given a safe space to struggle. While many of them would typically plow through a problem set, a project, or a challenge without asking for help until the very end, the overwhelming majority of the class let down their guard and were constantly checking in against the rubric.
Stevens, am I good?
*goes back, draws a line*
How about now?
*goes back, draws a bisector*
...repeat
Better yet, they were checking in with their peers and lifting each other up to get through this common goal: draw a triangle.
By day 3, I had become unnecessary, other than to hand out new sheets of scratch paper. Students walked into class, grabbed their triangle, ruler, pencil, a ton of patience, and got to work, then checked to make sure their table group was looking good.
For 5 school days, we worked on drawing triangles, but it was so much more than that. Seeing the look of accomplishment on their faces for "conquering" Mr. Sierpinski after all they had been through was rewarding for them and for me.
If you have some time at the end of the school year, a stack of scratch paper, and a lot of patience, it's worth trying out.
Stevens, am I good?
*goes back, draws a line*
How about now?
*goes back, draws a bisector*
...repeat
Better yet, they were checking in with their peers and lifting each other up to get through this common goal: draw a triangle.
By day 3, I had become unnecessary, other than to hand out new sheets of scratch paper. Students walked into class, grabbed their triangle, ruler, pencil, a ton of patience, and got to work, then checked to make sure their table group was looking good.
For 5 school days, we worked on drawing triangles, but it was so much more than that. Seeing the look of accomplishment on their faces for "conquering" Mr. Sierpinski after all they had been through was rewarding for them and for me.
If you have some time at the end of the school year, a stack of scratch paper, and a lot of patience, it's worth trying out.
Happy "Sierpinski Shenanigans" Fishing
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