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.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
Follow the activity procedures:
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