My school has 3 days a year that are used as “attendance incentive days”. Basically, if a student has less than 2 absences and maintains higher then a D in all their classes they are not required to attend school these days. Today was one of those days. It was nice to have time to work with students who were behind and fill in a few conceptual holes in the process.
I have been wanting to write about How We Do Visual Patterns, so here it is. (I cycle through several openers each week; Visual Patterns, Number Talks, Mental Math, Would You Rather, and Estimation)
This process has been evolving since the beginning of the year. I started off with something very similar to Fawn’s first hour found here. And I want to lead you through where things started and where they are right now.
For the first couple weeks, every pattern was about finding the squares/circles/shapes in a particular step;
At this point, students were too focused on numbers. They wrote out tables and looked for patterns within the numbers.
In the example above, most students overlooked the shape and saw a +3, +5, +7 pattern, which is fine, but I wanted to shift their thinking towards writing rules.
So I started asking for an equation. I went through about 2 visual patterns asking: “Find an equation to solve for the number of ________ in any step”.
This was WAY too complicated, so I changed the question:
Things started falling into place at this point., Almost every student can now contribute to our discussions; a simple rewording drastically lowered the entry point for all students.
Now instead of throwing around variables students write it as they see things, which in my opinion is awesome. The picture above gives an idea of how students create a rule:
S1 (Blue): “From step 1 to step 2 you take the original pattern and add 4″
S2 (Red): “I did almost the same thing but called the pattern before the one we want to find x”
S3: (Green): “It also works if you take the step, multiply it by 4, and add after”
S4: (Green): “I did the same thing but called the step we want to find x”
This was all facilitated by the students; no joke.
So, right now here is how we do visual patterns.
- The bell rings and I let students know we are opening with a Visual Pattern.
- I pull up a stopwatch in front of students and tell ’em how long they have (2-3 minutes).
- I remind students that it is OK if they don’t reach a rule, we are more interested in the process of finding one. It is also OK if the rule doesn’t work.
- I put something like this up on the board and start the timer.
- By themselves, students create a rule; no talking during this time.
- The timer goes off and I pull up our seating chart; I have the option to randomly choose a student. I do this in front of them.
- Whoever is called on shares where they are at in the process of writing a rule; it doesn’t have to be anything fancy. Sometimes the share what they see changing, sometimes they have a rule, they used to try and opt out; that didn’t fly.
- After 3 people have been randomly chosen I open things up for discussion; sometimes it ends there, other times it goes on for 10+ minutes.
Here’s the deal: I don’t help students along or provide a “correct” rule at the end. Things have gone this way since they very first Visual Pattern. Sure there are always times where I want to step in and some days we don’t get very far into creating a rule.But, I believe that students deserve opportunities to engage in discussions and share their thinking without being critiqued.
So much of what happens in math classrooms is about the teacher; we provide correct answers, solution methods, assignments, and assessments. The focus needs to shift towards the students and their perspectives. Taking 10 minutes out of one period, once a week to provide students with this opportunity has directly impacted what my students get out of the other 240 minutes each week and created an amazing culture of patient problem solving in my classes.
Here are a couple resources for Visual Patterns
OUSD Instructional Toolkit