SWBAT notice, describe, and represent patterns of regularity in the checkerboard problem.

Students will begin describing the relationships between the data and begin generalizing the patterns.

10 minutes

This is the continuation of the previous 4 lessons (checkerboard squares, squares in a row, checkerboard posters, Describing checkerboard patterns ). They are spending the class period finishing up posters which will be used as part of a culminating activity and assessment tomorrow.

Today's warmup is designed to help them notice and recognize the square number pattern in the tables for the posters they are creating. I give them two In/Out tables to complete the pattern and I ask them to create one of their own to have their math family group try. For many of them this project is the first time they have been asked to write a variable expression to represent a generalized rule for any number. Both of the tables I give them involve squaring and subtracting (n - 1)^2 and n^2-1, which is a big pattern in the posters they are creating. They saw a similar one in yesterday's warmup (Describing checkerboard patterns ) where we paid special attention to the difference the parentheses make.

34 minutes

Students will spend the remainder of the class period creating their poster in pairs or trios. They received the requirements in a previous lesson (Checkerboard poster) and I have two sample posters posted in front of the room.

I hand back the posters they started work on yesterday and encourage them to take out the handout (look for patterns in your poster) I gave them yesterday. They know they are being graded on their teamwork as well, so I go over again what kinds of ways they can contribute to their project. While only one person might be working on the poster at a time the partner can be looking for and talking about patterns that might be emerging, or helping to make decisions about how and where to show a certain element on the poster, etc. I also encourage them to take out and use their checkerboard asignment (how many squares with a table).

They are allowed to get up and get supplies as they need them (markers, rulers, pencils, erasers) or to get up and look at the sample posters.

As I circulate I am looking and listening for students who may be stuck. I am also making sure they understand and are refering to the required elements. I ask which element they are working on, how they decided to represent it and why, and where they plan to put the other elements. As I see and hear students working really collaboratively I will highlight it for the class. "This team is noticing a connection between the size of the checkerboard and the numbers in the table", "I like the way this team is really making decisions together", "This team has found a really cool way to show the 3rd required element, you should come take a look", etc. If it looks like a student is stuck on a particular element (element number 3 was trickiest for them) I tell them to focus on the other elements first and get back to it if they have time. They best way I found to explain element number 3 was that it was an explanation with a visual of how they calculated the number of a certain size square. But I also tell them they can just write an explanation in words.

The most important part for tomorrow's lesson is the title and the table so they can see the relationship between the dimensions and the data in the table.

As they finish their posters I distribute tonight's homework which is their collaborative teamwork assessment.