A month ago I wrote a post on First Day Lessons. Many — more than two — of you expressed interest in the lesson “Patterns Poster” for Algebra 1.

I would never redo a lesson if I didn’t think it was worthwhile, and I think this is the 7th year that I do this same lesson to start off algebra. So, if you’re still interested, this is the lesson in detail.

**Why I love this lesson**

- It’s not tied to a specific unit/concept in the algebra curriculum, so you can do it whenever.
- It’s visual.
- Entry points are low — kids can draw the next step and the next. They can count the number of items in each step. They can see how the pattern is growing.
- I suck at bulletin boards, so I decorate my classroom with students’ work. (By December, we’re looking up at the ceiling to see if we could showcase stuff up there.) These posters decorate the room quite nicely, and Back-to-School Night is just around the corner.
- Kids are coming up with the equations themselves — this is powerful stuff!
- Kids are talking with each other about their thinking.

**First hour**

- I put this pattern up on the screen:
- I ask students to sketch the 4th step in their math journal (quadrille-ruled composition notebook).
- I ask them to sketch the 13th step.
- I call on students to come up and share what they drew for steps 4 and 13.
- We complete this T-chart together.
- I ask them to write an equation for step
*n*. - I give each student this patterns_poster. They notice that they just did all the steps with me, and now they get to go through the steps again with a different pattern. We go over both sides of the paper, including the rubric.
- I put the patterns (faced down) into a container and walk around the room asking kids to reach in and take one. There are 12 different patterns (patterns_poster_patterns_A_thru_I and patterns_poster_patterns_J_K_L). I have 34 kids, so about 3 kids have the same pattern. [07/05/14: Since this post, I’ve started visualpatterns.org where there are
~~well over 100~~180 patterns available.] - They begin working.

**Second hour**

- They immediately get back to work.
- I interrupt them and say, “When I call out the pattern, raise your hand if you have that pattern, and I want you to look around the room to see who else has your same pattern because you’ll be helping each other after you work on it by yourself. Ready? Okay, raise your hand if you have pattern A…”
- I add, “So when you think you have the equation, or when you are struggling with the pattern, I’m NOT the first one you come to. I’m gonna sit at my desk and paint my nails. You need to seek each other out first for help. Got that? Good!”
- … OMG, I swear this lesson gets better and better each year. All 34 kids are working quietly on their patterns. Erica furrows her eyebrows, thinking hard. Janie kicks her backpack. Mike is talking to himself about how he sees the pattern growing. Doug is… WHAT?!! Doug is not misbehaving?! (I haven’t taught Doug before but his reputation precedes him.) He is completely into the pattern, carefully sketching the next steps.
- The talk among them begins. They scoot their chairs closer. They find each other and form small groups. A few hands go up. I respond, “Do you need help? Have you talked with your pattern-mate yet?” The hands come back down. One student, “I haven’t yet. But I just want to clarify something.”

I’m now working with Chris. He has this pattern:

His sketch of the 13th step looks like this:

At the bottom of his paper, I see he has this expression for the pattern:

Our conversation goes something like this:

Me: Okay. Show me why the “plus 4” in the expression?

Chris: Hmmmm. The equation works.

M: I didn’t say it wouldn’t work. I just want to see where “plus 4” is in your sketch. Let’s take a look at your sketch for step 13 here. How did you get “4n + 4” from the drawing?

C: ……

M: You’re right! Your expression works. That’s good, Chris! But your sketch doesn’t match up with it… Think about what I mean by that, I’ll be back.

About five minutes later, I return to Chris’s desk, “How are you doing?” He says, “The ‘plus 4’ is the 4 corners.” Yes!!!! So as I talk with him, he realizes that these two sketches jive more with “4n + 4,” and he’s able to verbalize that whatever step number you’re on, there’ll be four groups of it around the square, and the “plus 4” is for the 4 corners.

We go back to his original sketch of step 13 and come up with a general sketch.

And he is able to write an expression that would represent these sketches better:

Then I ask, “Well, are these two expressions the same?” Chris looks at me like I need a refresher course on how to distribute.

Three kids have been patiently waiting for me to help them with this pattern below. One says, “We are really struggling, Mrs. Nguyen. I know you want us to struggle and all, but how much longer?” I laugh. I start helping them look at the pattern as sets of triangles, or they can start by focusing on the horizontal toothpicks only, then look at the ones that slope upward, downward, or maybe just the toothpicks along the perimeter… I say to them, “You have a tougher pattern here! Aren’t you lucky!”

They do not get the poster paper until I approve the work on the paper. I show them a few examples from previous years. (I’ve tweaked this assignment a little, so the requirements are not always the same from year to year. I wish I left in the rubric a written explanation of how they see the pattern like you see in the paragraphs on these posters.)

They’ll get one more class period to work on this for a total of three. I don’t believe in giving kids math class time to color and make things look pretty. (Large posters of tessellations make me cringe.) I just want what’s on the rubric, but for whatever reason the girls tend to spend more time — at home — making theirs very colorful.

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