Having explored the “From Patterns to Algebra” work by Ruth Beatty and Catherine Bruce at a few PD days this semester, I thought it would serve as a good place to jump off from in my grade 9 course. Most students were exposed to some patterning in elementary school, so I thought there might be some level of comfort in starting with something familiar.
DAY 2 – Visual Patterns with Multiplicative Rules
The students really like working vertically so I wanted to start with a warm up that let them use the whiteboards. We looked at 2 ratio questions from previous EQAO assessments.
The students struggled with the first question. Working vertically really allows you to constantly assess the students. It really let me see some misconceptions. I was shown recently how to use a ratio table by another teacher. I have used this strategy in my 2P class so I showed the students how to solve the question using the table.
Most employed this strategy to solve the second ratio question and were successful.
We began to look at patterns that contained an initial value of 0.
Next, I had students graph the first pattern. I really didn’t provide much instruction on how to graph, etc. I was interested to see how much they knew.
I only had one group do a bar graph (I was actually expecting more…).
When I taught the 10 applied spiralled course, the consolidation piece for me was the most important. I think it’s critical to bring the class together and discuss what the students findings were and what the goal of the activity was.
We filled out this sheet as a class.
We talked about the rule, completing a table of values and graphing. We graphed the trend line and used a dashed line to show that the data was discrete. We also discussed that it was direct, as the trend line passed through the origin.
In addition, I showed students how to calculate the multiplier from the graph and using the table of values.
Little do they know they are calculating slope. How convenient the notation for slope is m. They just think m is for multiplier. No one should ask this year why we use the letter m for slope.
Students completed 2 additional patterns for homework. They graphed, calculated the multiplier from the graph and created the rule.
Day 3 – Patterns with an Initial Value other than Zero
As with day 2, we started with some EQAO questions for warm up. I chose another ratio question just to make sure they would nail it. They did! During the travel time between classes I had the question on the Smart Board. I had left the room to grab some cubilinks and when I returned everyone was already at the white boards working. The bell hadn’t even rang yet! Love it!
This lesson followed a similar structure to the one above. We looked at patterns that had tiles at position 0. We constructed a pattern that I had put on the Smart Board using two colours of cubilinks.
Students were then given a rule card. They had to construct the pattern in their group. Once complete, they had to circulate the class and determine the rule for each of the other tables. They recorded these on a sheet and we took them up as a class.
We filled out a similar sheet for consolidating these patterns.
We discussed how the graphs were similar and how they were different. Introduced some new terminology (partial variation, initial value, constant, y-intercept). Students began transitioning from writing the pattern rules as words to more of an equation like T = 2n + 3.
Students completed 4 patterns for homework similar to day 2.
Day 4 – Patterns with the Same Initial Value but Different Multiplier
We worked through some Solve Me Mobiles. They are a great way to practice equations and solve linear systems (secretly).
We started by discussing these 2 questions from Patterns to Algebra.
Students were really good at this. They already were hinting at how the multiplier changes the steepness/slope of the trend line.
Next, we built the pattern below. Discussed how to find position 0 and which part of the rule told us position 0.
Students then built and graphed three patterns.
We looked at the trend lines and how they were the same and how they were different. Some great work here for the first week of the semester!
Students discussed and wrote answers to the following questions.
No homework as it was Friday.
This week went great! Students are really engaged and seem to be understanding it really well. I think there is some familiarity with patterning so it was a comfortable topic to start with. Next week we are going to shift gears and do some measurement and scatter plot activities.