what we know about patterning at grades 5&6

Posted on: October 31st, 2014 by jnovakowski

On Thursday morning, I visited Gillian Ewart’s grades 5&6 class at McNeely to work with the students around sharing their learning with technology. The class has moved on to investigating patterns. I explained that I had just been in a Kindergarten class where the students had been learning about repeating patterns. I asked Gillian’s students to explain to me what they meant by patterns. Students mentioned the terms input/output, expressions and “plus-ing numbers” with an example of a pattern rule of “starting at 2 plus 4″ with the number sequence of 2, 6, 10, 14, 18… and were able to use the terms increasing and decreasing patterns.

The students knew about t-charts and terms and what “n” stood for in an expression so I wrote the expression 2n + 1 on the whiteboard and asked the students to represent that expression using materials.

The different representations the students created reflected the materials they used. Some students wanted to replicate a t-chart and label the terms of their patterns, often using the materials to do so, like the photo on the right below.

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The photo on the left above shows how one student showed the “plus one” in each term but turning over the two-sided counter to show the yellow side. After sharing his example, we introduced the term constant. A growing vocabulary of mathematics language is associated with this topic of study.

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The students took a gallery walk around the class to see how other students represented the expression and thinking about “how is this the same as my representation? how is it different?” Next, the students were asked to think of an expression that they wanted to represent, choose their materials and represent the first four or five terms. Some students chose whiteboards or paper to create t-charts to solve for their expressions to support them as they built their representations. The students then took a photo with their iPads, labelled the photo using the Skitch app and then explained their pattern using ShowMe, submitting their screencasts to the class account.

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Some examples of their screencasts follow. These were their first attempts at orally sharing their understanding around number patterns and we asked the students to include as much of the specific math vocabulary as they could. We are considering these screencasts “first drafts” as most of the students just focused one part of a bigger explanation about their patterns. (please note that the sd38blogs platform is having difficulties with links to videos or embedding videos…here are the URLs for now until we get things sorted out)

http://www.showme.com/sh/?h=9nIZow4

http://www.showme.com/sh/?h=24I61w0

http://www.showme.com/sh/?h=z7KHnXc

For many students at this age, they become self-conscious sharing their thinking in large group discussions. Today we noticed the students were comfortable during the gallery walk where their models spoke for themselves and that the students are growing more comfortable recording their voices on the iPads. As a follow-up, some students will share their screencasts using the projector in the class and there will be another gallery walk where students need to figure out their classmates’ expressions, as expressed in their representations.

~Janice

 

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