Table of Contents

Pattern and Symmetry Level 3

Introduction

Have you ever noticed how some designs repeat, or how certain shapes look the same even when flipped or turned? Patterns and symmetry are all around us, and understanding them can be fun and useful! In this article, we will dive into the exciting world of patterns and symmetry, helping you to identify and create beautiful designs through math.

Definition and Concept

Patterns are sequences or designs that repeat in a predictable manner. They can be made up of numbers, shapes, colors, or even sounds. Symmetry, on the other hand, refers to a balance or similarity between two halves of a shape or design. A shape is symmetrical if you can divide it into two identical parts.

Relevance:

  • Mathematics: Understanding patterns and symmetry is essential for geometry and art.
  • Real-world applications: Patterns and symmetry are used in nature, architecture, and everyday design.

Historical Context or Origin​

Patterns and symmetry have been studied for centuries. Ancient civilizations, such as the Egyptians and Greeks, used symmetrical designs in their art and architecture. The famous mathematician Euclid wrote about symmetry in his works, laying the foundation for geometry as we know it today.

Understanding the Problem

To explore patterns and symmetry, we will look at how to identify and create them. Let’s start by understanding how to recognize patterns in shapes and designs:

  • Look for repeating elements (like colors, shapes, or sizes).
  • Identify the sequence of the pattern (for example, circle, square, circle, square).

Methods to Solve the Problem with different types of problems​

Method 1: Identifying Patterns

  • Observe a sequence of shapes and note the repeating elements.
  • Write down the pattern rule (e.g., “Every third shape is a triangle”).

    • Example:
    Identify the pattern in the sequence: triangle, square, triangle, square. The rule is: “Triangle, Square” repeats.

    Method 2: Creating Patterns

  • Choose a starting shape or color.
  • Decide on a rule for repetition (e.g., every second shape is a different color).
  • Draw or build your pattern based on the rule.

    • Example:
    Create a pattern using red circles and blue squares: Red, Blue, Red, Blue.

    Exceptions and Special Cases​

  • Non-repeating Patterns: Patterns can sometimes be complex and not repeat regularly, like in fractals.
  • Asymmetrical Shapes: Some shapes, like a star, may not have symmetry but can still be part of a pattern.

    • Step-by-Step Practice​

    Problem 1: Identify the next shape in the pattern: Circle, Triangle, Circle, Triangle, ___.

    Solution: The next shape is a Circle because the pattern alternates between Circle and Triangle.

    Problem 2: Create a pattern using three colors: Red, Green, Blue.

    Solution: A possible pattern could be: Red, Green, Blue, Red, Green, Blue.

    Examples and Variations

    Easy Example:

    • Identify the pattern: 1, 2, 1, 2, __.
    • Solution: The next number is 1.

    Moderate Example:

    • Identify the pattern: A, B, A, B, A, __.
    • Solution: The next letter is B.

    Advanced Example:

    • Identify the pattern: 2, 4, 6, 8, __.
    • Solution: The next number is 10.

    Interactive Quiz with Feedback System​

    You do not have access to this page.

    If you are not a subscriber, please click here to subscribe.
    OR

    Common Mistakes and Pitfalls

    • Missing the repeating element in a pattern.
    • Forgetting the rule when creating a pattern.
    • Assuming all patterns are numerical when they can also be visual or auditory.

    Tips and Tricks for Efficiency

    • When identifying patterns, write down the elements to visualize the sequence.
    • Practice creating patterns with everyday objects to strengthen your understanding.
    • Use colors and shapes to make patterns more engaging and memorable.

    Real life application

    • Art and Design: Artists use patterns and symmetry to create visually appealing works.
    • Nature: Many plants and animals exhibit patterns, like stripes on a zebra or the spirals of a shell.
    • Architecture: Buildings often incorporate symmetrical designs for aesthetic balance.

    FAQ's

    A pattern is a repeated sequence of elements, such as shapes, colors, or numbers.
    Symmetry is when two halves of a shape or design are identical or balanced.
    Yes! Patterns are everywhere in nature, like in leaves, flowers, and animal markings.
    Start with a shape or color and decide on a rule for repetition. Then, draw or arrange the elements based on that rule.
    Understanding patterns helps us make predictions, solve problems, and appreciate the beauty in art and nature.

    Conclusion

    Exploring patterns and symmetry is not only a fun activity but also a foundational skill in mathematics. By recognizing and creating patterns, you enhance your problem-solving abilities and appreciation for the world around you.

    References and Further Exploration

    • Khan Academy: Interactive lessons on patterns and symmetry.
    • Book: Math in Nature by David A. Adler.

    Like? Share it with your friends

    Facebook
    Twitter
    LinkedIn

    Filter

    • Category

    • Levels

    • Subject