Colleen
Werner
IPSWICH HIGH,
IPSWICH,
MA

Algebra II :
Unit #1 - Sequences and Series :
Lesson #10

Objective:
SWBAT use sequences and series to model financial scenarios.

1 Modeling Activity -
80 minutes

Before students get back into the groups assigned in the previous period, I take a few minutes to hold a whole-group discussion about their progress so far. I make sure every group is clear on the expectations for a complete problem solving demo, which must be submitted at the beginning of the next class period. The demo should include a clear explanation of their problem-solving technique. [MP3] The posters submitted will go on the wall and any videos created by students will be played in class the following day.

Students then spend 80 minutes completing their problem-solving demonstration [MP1]. As they continue their work, I meet with each group to make sure they are on track. I offer more hints on day two than I did on day one, because I want to make sure they are able to complete the project and come up with a meaningful demonstration of their problem solving ability. During this time I also encourage the higher-ability groups to select the more challenging problems to present.

resources

Problem Solving Demo Rubric.doc

https://betterlesson.com/lesson/resource/2764801/problem-solving-demo-rubric
Interest Cards.docx

https://betterlesson.com/lesson/resource/2781750/interest-cards
2 Exit Ticket and Assignment -
10 minutes

To complete the exit ticket, students must calculate the balance on two different interest-bearing accounts: one in which regular deposits are made and one in which a one-time deposit is made. This allows me to determine whether students have learned to differentiate among money problems that are modeled as sequences and those that are modeled as geometric series.

The homework, saving money problems, is a collection of mixed financial problems - some are best modeled as sequences and others as series. [MP4] I publish the answers to this assignment on Edmodo so that students will know whether they understand this material before tomorrow's assessment.

resources

Exit Ticket Money Problems.doc

https://betterlesson.com/lesson/resource/2764803/exit-ticket-money-problems
Saving money problems.doc

https://betterlesson.com/lesson/resource/2764802/saving-money-problems
Using Common Sense to Check Answers

Real World Applications

Students often come to my classroom feeling that they will be more successful at "word problems" if they turn their common sense OFF. I think this comes from the experience of doing many of the classic word problems we do in math in which you have to suspend disbelief in order to get the job done. Here are some examples

- A projectile is fired directly upwards. In the absence of wind and air resistance, how high will it go?
- A paddock is built alongside of a river...

IN any case, it seems to take some prodding on my part for my students to turn their common sense back ON. For all the problems about money it is essential that they do so. Students come to class with a lot of understanding about money and interest so they can get much better answers to financial questions if they apply their common sense.

In the exit ticket for this lesson, I ask students to calculate the balance on two different accounts - one in which they deposit a single sum and watch it grow and the other that receives deposits every month. Students get turned around about which one should be treated as a geometric sequence and which one as a series. By applying common sense to the situation and calculating the balance WITHOUT interest, they can easily check their answers. A check of this kind could look like this:

*My answer is $1,424. I deposited $200 each month for 4 years. Is this a reasonable answer? My balance would have to be at least $96,000 because $200 * 12 * 4 = $96,000. I must have made an error.*

I ask my students to explain in writing whether their answer passes a common sense check to encourage this type of thinking.