Dear Claire,
I stumbled (re-stumbled?) upon Fawn’s post about the first two days. Sprinkled with her usual wit and ornery charm, the visual pattern process struck me, especially since we’re hitting that hard next week as we “create equations and inequalities and apply them to solve problems.”
(You might recognize that language from the pacing guide you wrote.)
Anyway, we started with Visual Pattern #2:
The projector was on the fritz (#RealTeacherProbs), so I drew the four steps on the board.
“Look over here. Pencils down, fold your hands. This is step one. [pause] This is step two. [pause] This is step three, [pause] and this is step four. [pause] On your yellow paper, please draw me step five. Go.”
After one round of the “talk to your neighbor song,” I drew playing cards (read: popsicle sticks) and asked students to describe their drawing to me as I drew it.
“Okay, draw five squares and then four squares.”
“No, like… the four squares are connected.”
“No! Just… look at step four and draw that first.”
I smirked, “I can’t see step four. Describe it to me.”
“Ugh! The four squares are going vertically.”
“Okay, now connect them to the bottom row.”
“No! Mr. Vaudrey! Connect them to the last one!”
“Dude, Mr. Vaudrey is trolling hard right now.”
Jayla couldn’t take it any more. “Okay! Listen and do exactly as I say!” She stands up.
I put on my best hurt puppy face. “But… I have been doing exactly as you say.”
Jayla holds up a hand. “Shh! Draw the line of five squares horizontally, touching each other. Then, from the last square on the right, draw four squares vertically, all connected.”
“There! Was that so hard?” Jayla drops back into her seat.
Although the class was loud this whole time, I submit that every student was … maybe not engaged, but invested in the problem. The discussion of which squares go where also helped the rest of the class access the problem. We spent maybe seven minutes describing in great detail how the squares were arranged.
Visual Patterns are an example of doing fewer problems, but making them count.
The whole class understands the structure, so when I ask them to fill in the table, and describe how they found steps 10 and 27, they can describe their reasoning.
- Step 10 has 18 squares because step five has 9 squares and I timesed it by two.
- Step 10 has 19 squares because it’s increasing by two and I just counted.
- Step 10 has 19 squares because it has a row of 10 squares on the bottom, then nine squares going up vertically from the last one.
- Step 10 has 21 squares because I increased by two each ti–wait.
- Step 10 has 19 squares because it’s like two rows of 10, but minus one.
For each of these answers—right or wrong—I erased what I had written and re-wrote what the student said. Understandably, students who were confident in their answer were upset when the teacher wrote a different answer on the board.
I share Fawn’s love of student struggle. If I were featured in the next Avengers film, I’d be a super-villain who gains power off of the furrowed brows of teenagers.
~Matt “For anyone who doubts my excitement at returning to the classroom, this is the fourth blog post in a day and a half” Vaudrey