Creating and Extending Patterns

Creating and Extending Patterns

Patterns are sequences or arrangements that follow a specific rule. They are important in mathematics because they help learners recognise relationships and predict future elements. In this lesson, you will learn how to create and extend patterns using various methods.

Understanding Patterns

Before creating or extending patterns, it is essential to understand what a pattern is. A pattern can be made of numbers, shapes, colours, or sounds. For example, the sequence of numbers 2, 4, 6, 8 is a numerical pattern where each number increases by 2.

Types of Patterns

There are two main types of patterns:

• Repetitive Patterns: These patterns repeat a certain sequence. For example, the pattern red, blue, red, blue is repetitive.
• Growing Patterns: These patterns change in a way that increases or decreases. For example, the pattern 1, 2, 4, 7 increases by 1, then 2, then 3.

Creating Patterns

To create a pattern, you need to decide on the elements and the rule that governs the sequence. Here are steps to create a simple numeric pattern:

1. Choose a starting number. For example, let’s start with 3.
2. Decide on a rule. We will add 5 to each number.
3. Write the first few elements of the pattern:

3 (starting number)
3 + 5 = 8
8 + 5 = 13
13 + 5 = 18
Pattern: 3, 8, 13, 18

Extending Patterns

Extending a pattern involves continuing it based on the established rule. Let’s extend the pattern we created earlier:

1. Start with the last number in the established pattern, which is 18.
2. Use the same rule (adding 5):

18 + 5 = 23
23 + 5 = 28
Pattern extended: 3, 8, 13, 18, 23, 28

Examples of Creating and Extending Patterns

Example 1: Numeric Pattern

Let’s create a new numeric pattern starting from 10 and adding 3:

1. 10 (starting number)
2. 10 + 3 = 13
3. 13 + 3 = 16
4. 16 + 3 = 19

The pattern is 10, 13, 16, 19. Now, let’s extend it:

19 + 3 = 22
22 + 3 = 25
Extended pattern: 10, 13, 16, 19, 22, 25

Example 2: Shape Pattern

Now, let’s create a shape pattern. Consider a pattern of circles and squares:

1. Start with a circle.
2. Next, add a square.
3. Continue alternating:

Circle, Square, Circle, Square
Next: Circle, Square

The pattern is Circle, Square, Circle, Square. To extend it:

Circle, Square, Circle, Square, Circle, Square

Common Mistakes

Using Patterns in Teaching

When teaching patterns to young learners, it is beneficial to use visual aids and physical objects. For example, using blocks or beads can help children see and manipulate patterns. Encourage them to create their own patterns using different colours or shapes.

Activities for Learners

Here are some activities you can use to help learners understand patterns:

• Pattern Creation: Give learners a set of objects (e.g., buttons, blocks) and ask them to create their own patterns.
• Pattern Extension: Provide a pattern and ask learners to extend it. For example, if the pattern is 1, 2, 3, 4, ask them what comes next.
• Pattern Identification: Show learners different patterns and ask them to identify whether they are repetitive or growing.

Conclusion

Creating and extending patterns is a fundamental skill in mathematics that helps learners develop logical thinking and problem-solving skills. By understanding different types of patterns and how to manipulate them, learners can apply these concepts in various mathematical contexts.

Check your understanding

• What is the difference between a repetitive pattern and a growing pattern?
• Create a numeric pattern starting from 5 and adding 4. What are the first five numbers?
• Extend the pattern 2, 4, 6, 8 by using the same rule.
• How can you use physical objects to teach patterns to young learners?