If you haven’t heard of Patterns to Algebra by Dr. Ruth Beatty and Dr. Catherine Bruce you have to check it out! It is a resource that transformed my teaching and filled in the blanks that I had always missed when teaching linear relations to my grade 9’s.

Linear relations is really one big concept: the fact that some things in life follow a linear pattern (or an almost linear pattern) and we can represent this type of relationship using a graph, table, equation, or story. The problem is, the way that I taught it (which was mostly following the general order of a textbook since I didn’t know what else to do) was teaching kids that these four representations were very different things. I did try to get them to connect the four, but the deep understanding of the inter-connectedness of it all was lacking. I can clearly remember being frustrated when my students could not understand why the first differences (when x is increasing by 1) is the same as the slope. I showed them with a graph, but I knew they couldn’t see the connections.

Fortunately I discovered Patterns to Algebra! Well, it actually discovered me. A fellow teacher had been asked to pilot the materials with her Grade 9 Applied class and I decided to try it alongside her with my Grade 9 Academics. I’m sure part of our success was the benefit we had of working together. We had the same prep and so we spent every day going through the materials we’d been given and planning what we were going to do with our students. We even did some cross-class stuff (since both our courses were running at the same time) and had our classes go see each others patterns and try to guess the “rules”.

I won’t attempt to explain the whole scope of the resource here. But basically it is a thoroughly researched, well thought-out plan for teaching linear relations through patterning. It starts off with students doing robot charts (or input/output charts, whatever you prefer) and patterns with a multiplier only. Then students do the same with a multiplier and constant. Students are writing “rules” for the tables and the patterns and with not much exposure are able to explain why Number of Tiles = Position # x 5 +2 grows faster than Number of Tiles = Position Number x 2 + 5. Eventually you lead into graphing (using the patterns) and story telling (using graphs and patterns) and it all connects together so nicely! By the end students have a clear understanding of what is really happening in a linear pattern and are able to connect that to any of the 5 representations (graph, equation, story, table, pattern). It’s so EXCITING!!!!

This resource is a grades 6-10 resource and often students remember patterning and “robot charts” from elementary school. I think that is a great thing… another connection! Kids have had so much exposure with patterning we need to be using it in high school because they understand it! That’s part of the power of this resource… it reaches ALL students. I found that my students with the most gaps were the ones that grabbed onto this and loved it. They were finally completely understanding something and doing well at it. The great part is too that as you continue to delve deeper into linear relations and analytic geometry (for grade 9 academic) you always have something concrete to refer back to. Kids never forget the patterns!

Try it… you’ll love it!!

(oh, by the way… now I barely teach first differences: it comes out when students notice that the multiplier (i.e. slope) can be looked at from comparing the position number to the number of tiles OR looking at how each pattern changes from one position number to the next. They also think it’s a “trick” for finding out the rule for an input/output chart. All I have to tell them is the vocabulary!)

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