This cluster of Internet Mathematics Excursions highlights different aspects of students’ understanding and use of patterns as they analyze relationships and make predictions, as discussed in the Algebra Standard. In this cluster of activities, students use interactive math applets to learn about repeating and growing patterns. In the first part, students use an interactive square-pattern grid to create, describe, and analyze repeating patterns based on a two-square pattern unit. In the second part, repeating patterns with pattern units of three, four, and five squares are investigated. In Part 3, students use an interactive cube-sequencing applet to analyze repeating patterns of colored cubes. In Part 4, growing patterns of colored cubes are created, described, and analyzed, and compared to repeating patterns.
Individual Lessons
Lesson 1 - Two-Square Repeating Patterns
In this activity, students analyze how repeating patterns are generated. Using the interactive computer applet, students create, compare, and contrast pattern units of two squares and predict how patterns with different colors will appear when repeated in a grid and check their predictions.
Lesson 2 - Multiple-Square Repeating Patterns
In this activity, students create and analyze repeating patterns using pattern units of three, four, and five squares. They
predict how patterns with different numbers of squares will appear when repeated in a grid, and check their predictions. Students investigate similarities and
differences between the rows, columns, and diagonal patterns created with each pattern unit.
Lesson 3 - Different Representations
In this activity, students create patterns using connecting cubes and describe various patterns they find in different sequences of cubes. Students explore and describe connecting patterns, and extend their patterns using a sequence of sounds and shapes. Students investigate various ways to interpret the same sequence of cubes by exploring ways to describe patterns translating from one representation to another.
Lesson 4 - Repeating and Growing Patterns
In this activity, students create and explore more complex patterns such as "growing patterns" which have related but different
relationships to "repeating patterns". Students form generalizations, analyze, and describe growing patterns using connecting-cubes, and explore what happens when growing patterns "double" or "split."
