Sequences Algebra One

I am used to teaching sequences and series in Algebra 2 & Pre-Calculus. But four years ago when we were given the task of aligning our Algebra 1 curriculum with the Common Core - lo & behold the first unit was "Patterns" which really was all about sequences - arithmetic, geometric and other sequences (Fibonacci, etc). And they wanted us to use function notation rather than sequence notation and students were supposed to naturally discover the formulas for a term in an arithmetic sequence and geometric sequence, ha! We gave it our best shot. After teaching this unit for three years I see now that the Common Core no longer has this as their first unit and that sequences are blended into other units. We have fine-tuned it over the last 3 years and aren't going to toss it just yet. Connecticut is making their own "Algebra for All Common Core" curriculum, so we'll just wait and see what they want us to do (it will include an end of year exam for all students in the state taking Algebra 1).

It's actually kind of fun to start with patterns, it gets students thinking mathematically. I have students do some exploring with patterns in worksheet they get for homework on the first day of school. You can find that here.

Then we develop the concepts & vocabulary. And "come up with" the arithmetic formula using what they already know about the slope intercept form of linear equations (y = mx + b) from there they see they have to find the "0 term" for the equation/formula. Geometric is harder to develop, so we kind of just give it to them. We revisit both sequences when we do linear and exponential functions. Overall it's a short unit with a cool little performance task at the end.

Foldables for Sequences

I use three sets of foldables for my ISN. Remember my page numbers are all wrong, I'm going to be better about the left side even & right side odd this coming school year. Also these are my first attempts at foldables and I'm not crazy about how everything lined up. I got better at that as the year progressed. The heading for each is a link to access that foldable via box.com.

INTRODUCTION TO SEQUENCES

ARITHMETIC SEQUENCES

GEOMETRIC SEQUENCES

Those are all Left Side Learning Pages (3 in all for this unit). The Right Side Reflect pages for opposite arithmetic & geometric are:

I don't have the actual examples - just notes to myself as to what to have students do.

And we do some cool stuff with the recursive rule and our calculators (TI-83 or TI-84). You can set them to generate a sequence recursively just by kind of following the rule. Type in the first term, [enter] then type in [+] "the common difference" [enter], You will see the first & second terms on the calculator screen. Then just keep typing in [enter] to generate more terms (the 3rd, 4th, etc). Not especially efficient if you want the 50th term but it's cool to do. And we talk about this is how computers generate terms. But they can do it super fast.

And if you are interested in my performance task, it's kind of cool. I made a honeycomb model out of cardboard for students to see what the core of the table looks like. Of course that is at school so I can't post a picture yet! Honeycomb Performance Task with the exploratory task we do the day before the PT and honeycomb graph paper.