Making Arithmetic and Geometric Series Real
These past few weeks we've been working on Sequences and Series in Algebra II. We started with an activity I got from a workshop led by Justin Coffey called Hexagon Trains. This was a great introduction to arithmetic sequences and I plan on doing it again next year with little to no changes. We wrapped up arithmetic sequences by doing a cup stacking activity I got from the same workshop. Students got 6 Styrofoam cups to measure, stack, and calculate the common difference between stacked cups. This generated an explicit formula they could use to predict the amount of cups needed to stack up to a person's height. Calculations were never exact so this led to discussions as to why we might be off. Responses included things like imprecise measuring of the common difference, and the weight of stacked cups pushing down and therefore reducing the overall height. Here is a Twitter post of that activity!
We then moved on to series and looked at summing arithmetic sequences. One of the last tasks we did was calculate how many push-ups I'll do with my New Years Resolution!
I also threw in a quick activity about how to sum squared sequences. It was another fun excuse to use Legos.
I hope the students enjoy this look into how geometric series are used in the real world. I report back with any problems I ran into and/or changes I'll make next year. If you have any suggestions or want to share things you do to make sequences and series real to students, let me know in the comments! Feel free to borrow any or all of this for your classroom!
Cup stacking challenge was a success today! We used arithmetic sequences to predict how many cups would be needed to reach certain heights. Actual amounts were 64 and 68 cups which led to some great discussion on why our explicit arithmetic sequence formulas might’ve been off. pic.twitter.com/lF5ZRYZu1b— Mr. Derstein (@MrDerstein) February 23, 2018
We then moved on to series and looked at summing arithmetic sequences. One of the last tasks we did was calculate how many push-ups I'll do with my New Years Resolution!
The students used arithmetic series to figure out the total amount of push ups I’ll do this year! They also figured out how much money we’d save by putting a penny in a piggy bank each day. So 1,2,3,4...,365 pennies. It’s $667.95! pic.twitter.com/6cKKRMMlyG— Mr. Derstein (@MrDerstein) February 27, 2018
I also threw in a quick activity about how to sum squared sequences. It was another fun excuse to use Legos.
After that we moved on to geometric sequences and series. Today, we'll be looking at how much money we can save up using recurring monthly payments into a savings account generating interest. I created the worksheet below to bring everything together. We'll do the first page together and then let them work on the back page themselves.Played with some legos again today and found out how many we would need to make an 8 row square pyramid. Didn’t really need the formula for this but they did use it to find out how many cans of their favorite soda they’d need to make a 25 row pyramid. 5,525 cans! pic.twitter.com/NEwg90HTZ0— Mr. Derstein (@MrDerstein) February 28, 2018
I hope the students enjoy this look into how geometric series are used in the real world. I report back with any problems I ran into and/or changes I'll make next year. If you have any suggestions or want to share things you do to make sequences and series real to students, let me know in the comments! Feel free to borrow any or all of this for your classroom!
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