Create and analyze rectangular patterns

In this lesson, students analyze and create rectangular patterns of squares. They identify stages of a pattern by coloring squares. They analyze rates of growth and create a three-stage rectangular design.

Objectives

Students will identify geometric patterns, their growth rates, and formulas, by analyzing and creating three-stage rectangular designs.

Learning outcomes

Students will do the following:

Organize information in a table.
Identify number patterns.
Write formulas and graph the relationships among numbers.
Examine growth rates.
Add and multiply polynomials (for students in algebra).
Use formulas to make predictions and create their own three-stage rectangular designs.

Lesson procedure

Introduction

In this activity, you will learn about geometric patterns by analyzing rectangular patterns of squares. First, you will identify three stages of a pattern by coloring squares in a Microsoft Office Excel grid and quantifying the information in a table. Next, you will analyze the rates of growth in the three stages of the pattern, graph the formula or the points for each stage, and make predictions about other stages based on your findings. Finally, you will create your own three-stage rectangular design, quantify the information in tables, find the formulas or graph the points for three stages of your design, and share your pattern with other students.

Note: This activity can be adapted by eliminating the challenge to find the formula (the first alternative of the third activity under Step 3). Students can still graph and see the rate of growth using only the data points.