Create and analyze rectangular patterns

Create and analyze rectangular patterns

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


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


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.

Teacher Tips

  • Same shape, different measures

    Ask the students how to measure the area and perimeter of a square. Discuss what "area" measures versus what "perimeter" measures.

  • Four square foresight

    Predict the size of the next square in the pattern. What does this pattern represent? What would be the size of the nth square?

Student activity

Follow the steps below to guide your students through this lesson plan.

Note teachers: Please download the student activity handouts located in the sidebar under Software and Materials Needed, for additional details about the main activities for this lesson plan.

  • Step 1: Create the patterns easily by just looking at the patterns drawn here.
  • Step 2: Quantify the information.
  • Step 3: Analyze the rate of growth.
  • Step 4: Make predictions.
  • Step 5: Add some geometry.
  • Step 6: Create your own three-stage design.


  • Observe students as they work through the lesson.
  • Evaluate the work on the student handout.
  • Evaluate completed assignments.
  • Evaluate students as they explain the patterns they created to other students.