At a Snail's Pace

Author

Texas Instruments

Alignment

Standards Alignment

Textbook Alignment

Subject Area

Math: Algebra I: Sequences and Series

Level

9-12

Activity Time

60 Minutes

TI Calculator

TI-83 Plus Family

TI-84 Plus

TI-84 Plus Silver Edition

Other Materials

Lead pencils
Red and green colored pencils
Metric ruler
Compass
Tracing paper and graph paper

Resource Types

Lessons

Report an Issue

At a Snail's Pace

Activity Overview

In this activity, students plot a mathematical relationship that defines a spiral. They use technology to create a spiral and to plot a set of ordered pairs.

Before the Activity

Set up the calculator for data collection using the procedure described in the attached Appendix file

See the attached PDF file for detailed instructions for this activity

Print pages 101 - 108 from the attached PDF file for your class

During the Activity

Distribute the pages to the class.

Follow the Activity procedures:

Draw a square and record the coordinates of its vertices

Construct a congruent square to the left of the original square to form a rectangle

Construct a square above this rectangle with the side of the square equal to the length of longer side of the rectangle

Continue adding squares in a clockwise direction

Record the length of the sides of each square and the coordinates of its vertices

Using a compass, make a quarter circle inside the square

Repeat this step with each square

Record the coordinates of the center-points and lengths of the radii for the circles

Observe that the construction resembles a spiral

Construct a Fibonacci spiral using the calculator and the data for the center points and radii

Compare the spiral formed on the calculator with the spiral drawn on the graph paper

Observe that Fibonacci sequences can be seen in the lengths of the sides of the squares, widths of the rectangles, lengths of the rectangles, and radii of the concentric circles that form the spiral

After the Activity

Students will complete the Data Collection and Analysis page and answer questions listed on it.

Review student results:

As a class, discuss questions that appeared to be more challenging

Re-teach concepts as necessary

Download Files

Download All Files (ZIP)

Before the Activity Files

Teacher Notes Appendix PDF Teacher Notes PDF

Author

Texas Instruments

Alignment

Standards Alignment

Textbook Alignment

Subject Area

Math: Algebra I: Sequences and Series

Level

9-12

Activity Time

60 Minutes

TI Calculator

TI-83 Plus Family

TI-84 Plus

TI-84 Plus Silver Edition

Other Materials

Lead pencils
Red and green colored pencils
Metric ruler
Compass
Tracing paper and graph paper

Resource Types

Lessons

Report an Issue

iPad is a trademark of Apple Inc., registered in the U.S. and other countries.
Vernier EasyData,Vernier EasyLink and Vernier EasyTemp are registered trademarks of Vernier Science Education.

Control your cookie preferences

You can control your preferences for how we use cookies to collect and use information while you're on TI websites by adjusting the status of these categories.

Category	Description	Allow
Analytics and performance cookies	These cookies, including cookies from Google Analytics, allow us to recognize and count the number of visitors on TI sites and see how visitors navigate our sites. This helps us improve the way TI sites work (for example, by making it easier for you to find information on the site).
Advertising and marketing cookies	These cookies enable interest-based advertising on TI sites and third-party websites using information you make available to us when you interact with our sites. Interest-based ads are displayed to you based on cookies linked to your online activities, such as viewing products on our sites. We may also share this information with third parties for these purposes. These cookies help us tailor advertisements to better match your interests, manage the frequency with which you see an advertisement, and understand the effectiveness of our advertising.
Functional cookies	These cookies help identify who you are and store your activity and account information in order to deliver enhanced functionality, including a more personalized and relevant experience on our sites. If you do not allow these cookies, some or all site features and services may not function properly. If you do not allow these cookies, some or all of the site features and services may not function properly.
Social media cookies	These cookies allow identification of users and content connected to online social media, such as Facebook, Twitter and other social media platforms, and help TI improve its social media outreach.
Strictly necessary	These cookies are necessary for the operation of TI sites or to fulfill your requests (for example, to track what items you have placed into your cart on the TI.com, to access secure areas of the TI site, or to manage your configured cookie preferences).	Always On

Category

Description

Allow

Analytics and performance cookies

These cookies, including cookies from Google Analytics, allow us to recognize and count the number of visitors on TI sites and see how visitors navigate our sites. This helps us improve the way TI sites work (for example, by making it easier for you to find information on the site).

Advertising and marketing cookies

These cookies enable interest-based advertising on TI sites and third-party websites using information you make available to us when you interact with our sites. Interest-based ads are displayed to you based on cookies linked to your online activities, such as viewing products on our sites. We may also share this information with third parties for these purposes. These cookies help us tailor advertisements to better match your interests, manage the frequency with which you see an advertisement, and understand the effectiveness of our advertising.

Functional cookies

These cookies help identify who you are and store your activity and account information in order to deliver enhanced functionality, including a more personalized and relevant experience on our sites. If you do not allow these cookies, some or all site features and services may not function properly.

Social media cookies

These cookies allow identification of users and content connected to online social media, such as Facebook, Twitter and other social media platforms, and help TI improve its social media outreach.

Strictly necessary

These cookies are necessary for the operation of TI sites or to fulfill your requests (for example, to track what items you have placed into your cart on the TI.com, to access secure areas of the TI site, or to manage your configured cookie preferences).

Always On

At a Snail's Pace

At a Snail's Pace

Before the Activity Files

Control your cookie preferences

Products

Product Support

Teacher Resources

Administrator Resources

Lessons and Activities

General Information