From Patterns to Algebra

Today my grade 9s worked on solidifying their understanding of linear patterns, equations and graphs.

We started off today with each group getting a pattern rule (equation). They needed to use the 1 inch square tiles to build figure 0, figure 1, figure 2, figure 3, figure 4 of their pattern. Some needed to use 2 colours to represent positives and negatives.

The next step was to disassemble each figure, one at a time, and recreate it in a stack on a graph. We have 1 inch grid chart paper which is beautiful, because each square tiles fits one grid space. We line up figure 0, then put a dot at the top LEFT (along the vertical axis). Next we line up figure 1 tiles in a stack beside figure 0, and pu a dot at the top left. We keep going and noticed a pretty regular pattern.

Each group then took the tiles off their pages, and connected the dots to make their graphs complete. We repeated the process with another pattern rule or two all on the same grid. I planned ahead to make graphs that are interesting to compare, and that would bring forth a lot of vocabulary and concepts. We put all of the papers up on the whiteboards and did a group consolidation. Here’s a gallery of what we looked at. Some groups had asked for some spicy challenges!

We explored slope, steepness, parallel, positive vs negative, we looked at y intercepts, what the equation looked like if there was no “b” value (passed through the origin), or if the b values of 2 lines were the same, that’s their intersection point. We found other intersections, some by estimating. We showed what it means for a point of intersection to satisfy both linear equations. Some groups showed really good rise and run. We had some groups working on fractional slopes and non-linear patterns too by the end of the class. I hope this helps connect some of the patterning and graphing we’ve been working on this week. Tomorrow we will explore some more with desmos.