As I posted before, this is my first year teaching sequences in Algebra 1. The new Oklahoma math standards (OAS) include this standard:
A1.A.3.5 Recognize that arithmetic sequences are linear using equations, tables, graphs, and verbal descriptions. Use the pattern, find the next term.
I succeeded in using equations and graphs with my students. I didn't have them make tables. And, I should have included verbal descriptions. I definitely have some room for improvement for next year.
I did exceed the standard by having students write a rule for the sequence that allowed them to find any term in the sequence.
My students were a bit confused at first when it came to how to graph the sequence on the coordinate plane. Many students thought that our first point should be graphed on the y-axis. Now that I think about it, having students make a table with "Term" and "Value" as the two columns would have taken care of this because it would have turned the sequence into a set of ordered pairs. I will definitely add a table to these notes for next year!
We examined the graphed points to find the slope of the line. This value went in front of x. Then, we used the slope to determine where the line would cross the y-axis. This gave us the rest of our rule.
After doing a couple of these together, many of my students were working ahead without any prompting from me.
My students would probably have been perfectly happy to make graphs in order to find the rule, but I decided to show them a method of finding the rule that doesn't require making a 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.
Almost all of my students ended up using this method on their quiz. So, I guess my students found it useful.
The files for this lesson are on my school computer. I will upload them as soon as I get back from Spring Break!