Create Your Own Reality Series!

Create Your Own Reality Series!

Due: Thursday, Sept. 20 by the end of class

Would you like to create your own reality series? What would you do? What kinds of people or things might be involved? Maybe you could focus on seats in a theater or the distance a ball travels when it bounces. What's that? You thought this project was going to be about a television reality series? Sorry, this project focuses on arithmetic and geometric series (and sequences). In some cases, this might even be more interesting than what you find on television!

Arithmetic and geometric sequences and series arise in many situations. Here are a few examples:

Depreciation of the value of a car can be an arithmetic sequence if the value of the car depreciates by a certain dollar amount every year. The sequence becomes geometric if the value depreciates by a percentage each year.

Investments can be represented by arithmetic sequences or series if a set dollar amount is added at given intervals.

If salary increases are given at a particular percentage per year, a geometric sequence can be used. It is also interesting to calculate the distance traveled by a ball as it bounces. If a ball bounces to 80%

of its previous height, you can use this as the common ratio to evaluate the geometric series. Be sure to take into account the distance up and down between each bounce. An athlete in training might add a set distance to each workout. An arithmetic series can be used to calculate the total distance after a certain amount of time training (ex. after one month of training).

In our studies of Sequences and Series, we discussed many topics about arithmetic and geometric sequences and series. You have seen how to find the nth term, write an explicit formula and find the sum of each type of series. You learned that a geometric series can be finite or infinite and depending on the common ratio, the series might have a partial sum or it might not. Now you can use these concepts in real-life scenarios.

Main Idea: In a group of 3, choose four situations that can be represented by arithmetic or geometric sequences and series. Choose at least one situation that is arithmetic and one that is geometric. If you wish, search the Internet for real-life scenarios to help you get started. If you choose to use something you find during your research, be sure to change the numbers to make your application unique. Find something fun that you find interesting. Whether it is investment related, physics related, or something else entirely, choose what interests you most to make your own reality series!

Once you have completed the work for all four problems (requirements explained below), choose one scenario and act it out in a video.

Requirements: A well-developed Reality Series Project should have:

1. Real-life series (Choose real-life situations which use arithmetic or geometric sequences and series. You must have at least one of each type for this project.)

2. Research (Include any research you did to discover the real-life applications of sequences and series. If you created the real-life applications yourself, explain your thinking. If you used ideas from other

sources, show how you changed the terms, common difference, or common ratio to make your application unique.) 3. Diagrams or pictures (Include a diagram or picture of the situations you have chosen. Either write out the 1st several terms, or use pictures to represent what is taking place. For example, if a ball is bouncing you might want to show the distance traveled in the 1st of several bounces.) 4. Formulas (Write the formula that represents your scenario). 5. Show what you know! (Use as many of the concepts about arithmetic and geometric sequences and series as you can to describe your real-life situations. For example, show how to find the nth term of your arithmetic sequence or describe how to evaluate the 1st n terms. Discuss whether your geometric series is finite or infinite and how you know. Pretend you have only 2 terms in the sequence. Describe how you could write a rule for the nth term. Make up your own questions about your sequences and series and then answer them yourself.) 6. Includes References: Identify any external resources you used to complete the project, such as web sites, articles, books, etc.

Grading: Your work will be evaluated using the rubric provided below:

CATEGORY

4

3

2

1

Score

Conference/Concept

Problems (Written Portion)

Team met with Mrs. Collier Team met with Mrs. Collier Team met with Mrs. Collier

for a mini-conference and for a mini-conference and for a mini-conference and

has a clear picture of what has a fairly clear picture of has brainstormed their

they are trying to achieve. what they are trying to

concept, but no clear focus

Each member can

achieve. Each member has emerged for the team.

describe what they are can describe what they are Team members may

trying to do and generally trying to do overall but has describe the goals/final

how his/her work will

trouble describing how product differently.

contribute to the final

his/her work will contribute

product.

to the final product.

Real-life scenarios are presented for all 4 problems.

Real-life scenarios are

Real-life scenarios are

presented for 3 problems. presented for 2 problems.

Team met with Mrs. Collier for a mini-conference and has spent little effort on brainstorming and refining a concept. Team members are unclear on the goals and how their contributions will help them reach the goal.

Real-life scenario is presented for 1 problem.

Diagrams/Pictures

Each problem has a corresponding diagram and/or picture.

Three problems have a corresponding diagram and/or picture.

Two problems have a corresponding diagram and/or picture.

One or no problems have a corresponding diagram and/or picture.

Math Skills

Math is accurate.

Math is mostly accurate. Math is somewhat accurate. Math is not accurate.

Formulas

An accurate formula is

An accurate formula is

presented for all problems. presented for most (at

least 3) problems.

An accurate formula is

An accurate formula is

presented for most (at least presented for one or no

2) problems.

problems.

Articulation Technical Skills

Teamwork

Your problem is clearly Your problem is articulated Your problem is difficult to Your problem is impossible

articulated in your video. in your video.

understand in your video. to understand in your video.

There are no technical issues with your recording (e.g. volume level hard to hear).

There are few technical issues with your recording (e.g. volume level hard to hear).

There are several technical issues with your recording (e.g. volume level hard to hear).

Due to the technical issues with your recording, it is difficult to understand your video.

Students meet and discuss Students meet and discuss A couple of team meetings

regularly. All students

regularly. Most students are held. Most students

contribute to the

contribute to the

contribute to the discussion

discussion and all are

discussion and are listened and are listened to

listened to respectfully. All to respectfully. All team respectfully. All team

team members contribute members contribute a fair members contribute a fair

a fair share of the work. share of the work.

share of the work.

Meetings are not held AND/OR some team members do not contribute a fair share of the work.

Total: /32 (+ peer & self evaluations)

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