So – Patterning. I’m thinking a lot about this skill and how to make it meaningful for my mathematicians. I’m thinking a lot about its connection to algebra and how to set my grade 2’s & 3’s up for success and start them on the road to algebraic thinking.
I put them to work on Monday. I put baskets of math manipulatives out and told them to go make patterns. As predicted, they made a bunch of repeating patterns. They were quite proud of them in fact. On Tuesday, we talked about growing patterns. They weren’t really showing an understanding of reading the pattern left to right, so we had a bit of a chat about that on Wednesday when we talked about shrinking patterns and about how the direction matters. As seems to happen often this year, they were amazed by this knowledge. I think it will stick! Here is one of the examples I built to show them that direction matters:
Today, Thursday, I asked everyone to actually put their pattern on a number line. We have done a lot of work with number lines this year, and with the 100 chart. I feel like it is really paying off! I started with some guided inquiry. What, I asked, would my pattern look like on a number line?
Together we constructed a few:
Then I sent them to make some patterns of their own, and map them on number lines. I didn’t hand them the paper until they had their patterns made and could talk to me about how the pattern was growing and shrinking (by ones, by 3’s, etc. Actually, no “etcetera” because everyone either did ones or threes, like our example. I’m not worried though because tomorrow I can tell them they are too good to stick with ones and threes and they need to choose something else!)
I know it might not be right to have favourites, but this is my favourite conversation:
First, there was this:
The child who made this pattern was insistent that it was a growing and shrinking pattern. His partners were not convinced. In fact, they were downright mad because he was so sure and they couldn’t see it. I couldn’t see it either, to be honest. I wanted so badly to tell him that this was not going to work! But Cathy Fosnot’s voice echoed in my head, “Productive struggle…productive struggle…” so I handed him the strip of paper and a marker, and walked away. A few minutes later, I returned to this:
He’d figured out on his own that to make a number line his “special stones” needed to be laid out in a straight line. He was also able to finally show us that the green stones aren’t actually part of the pattern. They just mark the end/beginning of each set of clear stones. As soon as it was straight, he could help his partners see his thinking – he could explain it so much more easily. He’d made it through the struggle and came out successful on the other side. (He did write in the numbers and finish the number line – I didn’t get a picture though.)
Two others made this pattern. (I’ll add the picture later!)
When we chatted about it, they told me that they knew 22 should come next, but didn’t have enough special stones. This was a huge piece of info for me! I thought they’d just been rote counting, but are perhaps ready to make a line without having to build the concrete pattern first.
I am, however, left with one question: How does one put a repeating pattern on a number line? ABABABA patterns, or ABCABCABC patterns – can they be put on a number line?
*update* Today I challenged everyone to try something besides 1 & 3.
They tried 2, 4, 5 & 10.