My grade 11 students started the year with sequences and series this year. I love starting with patterns because I find it’s intuitive for some students so it lets everyone get their feet wet. Also, if students are proficient at picking up patterns, it will help them throughout the year!
To introduce the unit, I started by asking them to create 3 pattern cue cards. I had given them a few patterns as samples at the end of the previous day’s lesson, but I had asked them to be creative and come up with any type of pattern they wanted.
Students created a varied range of patterns. About half of the cue cards created were arithmetic or geometric sequences (which was fantastic for the sorting activity we did with the cards). The other half were creative and came up with other neat ideas for their patterns. (Some samples are below of the “outside the box” patterns!)
Using the cards, I asked the students to sort the cards into at most 4 categories in their table groups. Most teams didn’t have any trouble sorting the cards into piles, although some groups needed some prodding to find the similarities between their cards. Once they had chosen categories, I asked them to create a title for each category. Here’s a sample of the categories one of my classes came up with:
I noticed a few great things happening:
- The categories the students came up with included the characteristics of the arithmetic and geometric sequences we were going to discuss during the unit. We were now able to think of examples from our cue cards of arithmetic or geometric sequences. (This was a goal of mine, since students often struggle with classifying sequences.)
- Most students created patterns that were far more creative and complex than the patterns in the sequences and series that we would be discussing (arithmetic and geometric).
- Most students intuitively could see that a pattern was a sequence (or an ordered list, separated by commas) after doing this introduction assignment.
I’ll definitely do this assignment again in the future. Next time I will likely stack the deck with more geometric and arithmetic patterns so that the categories are more likely to be the same as the way we will be classifying them throughout the unit. Not only was it great to get across the concepts, but they also got to express themselves with some really creative cards! Here’s a taste of some of the creative ones:
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