# Activities

• • • ##### Subject Area

• Math: Algebra I: Sequences and Series

• ##### Author 9-12

60 Minutes

• ##### Device
• TI-30X IIB
• TI-30X IIS
• TI-34 II Explorer Plus™
• ##### Other Materials
This is Activity 12 from the EXPLORATIONS Book:
Math Investigations with the TI-30X IIS: Activities for Secondary Mathematics

The following materials are required for this activity:
• Centimeter cubes or square tiles
• Grid paper
• ##### Report an Issue

Making Sense of Shapes and Sizes

#### Activity Overview

Students develop algorithms for generating and generalizing patterns related to triangle and square geometric models.

#### Before the Activity

• See the attached PDF file for detailed instructions for this activity
• Print pages 119 - 122 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to the class.

Follow the activity procedures:

• Use square tiles or centimeter cubes to build geometric shapes found on the Student Activity pages
• Record the area and perimeter for each shape
• Notice that the cubes take on a triangular staircase shape, and that the values in the Area column represent the triangular sums of that pattern
• Use these results to write an algorithm to generate the number patterns in the Area column and the Perimeter column
• Alternatively, use an algebraic model to generalize the pattern in these tables
• #### After the Activity

Students complete the Student Activity pages and answer questions.

• Review student results
• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary