A few weeks ago, I assigned this project to my Math 2 students:

It’s a unit assessment on the various patterns we’ve studied in our first month or so at school. We’ve looked at linear, exponential and power patterns, as well as a few wonky “other” patterns. While looking at these patterns, we’ve figured out how to represent them in a variety of ways: in verbal, numerical, tabular and graphical forms, as well as in equations. There are two types of “equations” we discussed: NOW-NEXT equations (which are recursive formulae) and f(x) equations.

Well, I finished grading the projects, and they turned out nicely. Overall, I think my students need to work on explaining their thinking more, but I have another 6 weeks, and then they’ll have another trimester with me or another teacher to hammer that idea into them.

Here are some of the projects.

Some posters (click to enbiggen):

And some “training manuals”:

This student even dedicated her book to me. How cute is that?

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This is something that I’ve been working on with my students. I really liked the way your students have compartmentalized their thinking into equations, verbal, graphs and equations. Clearly you taught them to approach things that way and boy does it make sense. I think this is something that I could use in my classroom.

I’ve never heard of NOW-NEXT before. Maybe I know it by another name. What is it? Can you say more? I’d appreciate and thank you.

I think NOW-NEXT equations are a myschool-ism. I had never seen them before I worked here. The idea is one of recursive thinking; what do I do to what I have now to get the next term in the sequence (or the y-value in the table)?

For example, if you have an x-y equation, y=3x + 7, it’s NOW-NEXT equation would be, NEXT=NOW + 3, starting at 7, which we abbreviate as SV=7 (starting value is 7).

Thanks for sharing your patterns project. As a high school geometry teacher, I read the instructions of your project and my mind went in a totally different direction. In my classes, I have many EL students so even a task such as classifying triangles and quadrilaterals can be a chore. My thought was to have students come up with diagram or training manual that would help the company organize it’s polygons. Perhaps the polygons could be organized first by the number of sides they have. Then, perhaps the three-sided polygons could be organized by their side or angle classifications. The quadrilaterals could maybe then be organized by trapezoids, kites, parallelograms, etc. Then parallelograms could be put into categories based on rectangles, squares, etc. I know with Common Core on the horizon, our school is looking at ways to get students to think, problem solve, discuss, and write in a way that they perhaps have not been accustomed to. Thanks for sharing!

Hi Jerrod,

Thanks for sharing your idea. I think that classifying tasks are incredibly rich, and the one you’ve outlined sounds like a good one. Though, I challenge you to see what classification systems your students come up with on their own. If you do this project, please share the results!