Math = Love: Interactive Notebook Pages for Algebra 1 Sequences Unit

## Saturday, April 1, 2017

### Interactive Notebook Pages for Algebra 1 Sequences Unit

We've been done with sequences in Algebra 1 for a bit now, so that means it's time to upload our interactive notebook pages for that unit.

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.

After graphing the sequences, we discovered that geometric sequences form exponential functions.

These files are on my school computer.  I will upload them Tuesday when I get back from our three-day weekend!  Here's the link where the files will be posted.

1. I was wondering if you were going to make that language connection between "geometric sequence" and "exponential function." I love the solid connections between the visual, numerical, and symbolic expressions of what's happening.

2. Thank you for sharing all your hard work. I tried to download the files for sequences but they don't appear to all be in the folder or did you only share a few? Thanks again for the links!

3. I am also looking for the rest of the files. Thanks for the great work. I love how you've changed this from years past. I have different notes that I'm currently using.

4. I love the "Top 10 Things to Remember" chapter heading in place of clip art. Very useful. I think I'll take student nominations on what to include in the Top 10 list for each chapter... should be interesting!

Thanks again for your generosity in sharing these resources, Sarah. As an extra plus, I'm learning a lot from the changes you make to your materials from year to year.

1. You're very welcome!

5. Sarah I love your blog, you've made such a difference in my teaching. I was wondering if it would be possible to download the files from this lesson? Thanks so much!!

6. Hi Sarah,

I know you said that you will get rid of the DiNO method because it seems like a trick. What did you do differently this year?

7. I like what you said about DiNO being a trick. When I taught this as part of Integrated Math 1 this year, I emphasized that linear sequences can be written as linear functions and geometric sequences could be written as exponential functions. It meant students had to figure out the "zeroeth" term, by going back and subtracting or dividing. But I liked that they didn't have to memorize a whole different formula that they didn't really understand. Some students made the connection to (n-1) on their own, which was awesome. I'm wondering if I'm the only one that teaches it that way, or if other math teachers would think that's a valid approach?