Would you Rather...

Introduction

Imagine your favorite uncle gives you $100 for your birthday. You decide you want to start saving your money (good idea), so you need to choose a type of savings account to invest your birthday money in.

Would you rather invest your money in an account where you….

Option A: receive $100 increase every MONTH for the next 10 years...

OR

Option B: double your money ONCE a year for the next 10 years?

**Do NOT solve this problem. Take 10 seconds to make your initial decision. We will revisit your choice later on in the webquest.

Task

Throughout this webquest you will explore different types of sequences, mainly arithmetic and geometric sequences. You will define, make conjectures, and problem solve using visuals, graphs, tables, and words. At the end of this webquest you will create your own sequence and represent it in multiple ways.

Process

Let’s Explore: You will be given an image.
1. Take a few minutes of quiet THINK time to make some observations about the image. What do you notice? What do you wonder?
2. Click on this DESMOS link to view the image. Follow the directions on the following slides of the activity to complete your brainstorm.

Let’s Research: Use the resources in the "Credits" tab to learn about arithmetic and geometric sequences in order to complete this graphic organizer (a paper copy will be provided by teacher).

Consider these questions as you explore:
1. What are their definitions?
2. What are the differences between arithmetic and geometric sequences?
3. Can I find an example?
4. Can the sequence be represented by a formula?

Let’s Play: Next, you will complete some practice problems in order to deepen your understanding of sequences represented in multiple ways (tables, graphs, words, formula). Click on this Quizizz LINK to access the problems. You will have unlimited attempts in order to score a 70% or higher.

Let’s Solve: Now that you have a better understanding of sequences, please go back to the Intro question and solve it. Click on this link to view the problem. Your teacher will give you a paper copy to work on.

Let’s Create: Now it is your turn to write a real life scenario that defines either an arithmetic or geometric sequence. Then you will represent your scenario in three other ways (visual, graph, formula) as described in this document (CLICK ME). Your teacher will provide you with this storyboard template for you to complete your final task.

Evaluation

Storyboard Rubric

0

5

10

Sequence

student's sequence is NOT defined by an arithmetic or geometric pattern

N/A

student's sequence does represent the definition of an arithmetic or geometric pattern

Story

incomplete and/or missing

student attempts to write a real-world scenario, however, it contains mathematical errors

student successfully uses a sequence to describe, in detail, an accurate real-life portrayal of an arithmetic or geometric situation

Rule

incomplete and/or missing

student attempts to write an equation for their sequence, however, the rule contains mathematical errors

student successfully writes an equation representing their sequence using appropriate notation

Graph

incomplete and/or missing

student attempts to graph their sequence on a coordinate plane, however, their graph contains mathematical errors

student successfully graphs their sequence on a coordinate plane and uses an appropriate scale and labels on the axes

Visual

incomplete and/or missing

student attempts to create a visual representation for their sequence, however, it contains errors

student successfully creates a visual representation for their sequence showing its pattern

Conclusion

Great job exploring arithmetic and geometric sequences. Did you know there are other types of sequences? Use the strategies you have practiced throughout this webquest in order to put your skills to the test! Can you identify the rule of another visual pattern? Click on this document to view the challenge.

Credits

Videos

Arithmetic Video (writing a rule):

https://www.youtube.com/watch?v=T1ZBizIL5Lw

Geometric Video (writing a rule):

https://www.youtube.com/watch?v=4NT9E-wbJMg

Arithmetic & Geometric Video (graphing the sequence):

https://www.youtube.com/watch?v=jU6JTdhHVuI

Visual Pattern Video:

https://www.youtube.com/watch?v=Ywomf4-5Puo

Arithmetic Video (real world application):

https://www.youtube.com/watch?v=zxQPCLa9UhI