As usual, the unit starts off with a divider. You can read about these dividers here.
This summer, I plan to play around and try to re-design our dividers to take up less paper so I can put the individual section headers on the same sheet of paper. You can see one of the section headers on the right.
Here are our SBG skills for the unit:
This unit was definitely of the short and sweet variety!
We began by talking about the different types of sequences. Oklahoma standards only mention arithmetic and geometry sequences. I decided to include a category called "Neither" as well. This let me expose my students to the Fibonacci sequence!
I modified an activity from last year's Algebra 2 unit on Sequences and Series to make this Arithmetic, Geometric, or Neither? classifying activity. My original plan was to make this a color-coding activity, but I ended up giving up on that idea!
For next year, I think I would like to tweak it a bit and add some Fibonacci sequences into this activity! Maybe I should add Fibonacci as a separate type of sequence for my students to learn.
I used this activity from Mathspad (subscription required) as a quick quiz review.
Next, we focused our attention on arithmetic sequences.
For each sequence, students had to create a graph. They used this graph to find the slope and determine what the y-intercept of the function would be.
In the future, I will give students a table to fill out. I think this will ease the stress of going straight from sequence to graph.
I first learned about the DINO method for finding the nth term of an arithmetic sequence from the Miss Brookes Maths blog. A google search led me to this free worksheet and poster set from Numero Maths.
I think I will get rid of the DiNO part of this next year because it seems too much like a trick.
I created this practice sheet. Students were given a sequence. They had to write a rule and use that rule to find the 15th term, 50th term, and 100th term.
Note to self: Title this as "Arithmetic Sequences" next year. It looks too much like the one you made for geometric sequences!
I loved how we derived the formula for arithmetic sequences by noticing that it made a linear function. It flowed so nicely in class due to the fact that we had spent so much time focusing on linear functions earlier in the year.
Geometric sequences are my students' only real exposure to exponential functions in Algebra 1. So, I just broke down and gave my students the formula for finding the rule for a geometric sequence. It doesn't feel right, but I couldn't really think of how else to go about it. If you have an idea for fixing this, please share it in the comments!
Practice sheet for writing rules for geometric sequences and finding the 8th and 10th terms. See how similar it looks to the one for arithmetic sequences? Definitely going to title these for next year!
After working with finding rules and terms, I decided I still needed my students to wrap their minds around how the graph of a geometric sequence differed from the graphs we had previously made for arithmetic sequences.