# Multiple Representations of Patterns

I have all my classes doing a Visual Pattern from Fawn as a warm up once a week. With my Algebra 1 students I decided to extend the assignment to create posters showing how the patterns relate to the table, words, graph, and general formula.

I did a similar assignment last year for exponential growth and decay when we got to that section, but I figured I should start with linear patterns. When we do the project again for exponential patterns hopefully the connections will be even stronger.

The process:

The warm up was a simple linear pattern from Visual Patterns.

I always have them fill in a table and attempt to come up with a rule. After they did this, I asked one student to share the results with the whole class using the projector. While she was explaining I had another student plot the table points on a graph on the board.

We had a quick discussion on where the pattern “up 2” showed up in the four representations (drawn pattern, table, algebraic expression, graph) and had presenting students mark the 2s on the examples. Then I asked where the plus one in the rule came from. The student at the front said it was the one red star in every pattern. The one drawing said: “Oh, if I extend this back, its right here!” (pointing to the y-intercept). I asked them to find it in the table. (It wasn’t there….So add it! Where would to show up?)

I then handed each student a new pattern and asked them to make a table, graph, rule, and color code the connections between the representations. When they were confident, I had them make post sized versions to hang around the room.

A few examples:

Things I noticed: Some students drew in a Stage 0. I asked why, and for the most part these students thought of stage 0 as taking away the pattern part of stage 1. I asked the others why they didn’t draw a stage 0. The response was generally, “Is there a Stage 0? I see the start value here in 1…” I want to dig deeper into this difference.

Note On Slope: We haven’t talked slope yet. Students saw the pattern as change in number of squares or dots exclusively since n was going by 1s, and I didn’t push them on it yet although I did start those discussions one on one with the students as they worked. My plan is to give them Step 1, 3, and 6 of a pattern and ask them to come up with a rule. As well as to introduce slope/rate of change with a similar task (and non-integer changes) and have the discussion on rates of changes of 1.5 vs 3/2; and where those show up in the different representations. Then have them go back and update the current posters and with creating new examples with differing x changes as well. I’m not sure if I should have done this during this task, waited to do a connection of representations until we had already talked about this, or if this do it now and revisit is best.  The students have definitely benefited from looking at the different representations, and there ability to come up with pattern rules has been improved but part of me is still worrying I should have done the Step 1,3,6 thing at the same time…maybe giving that to my students who needed more of a challenge for their original poster and then had a class discussion about how they were the same/different.