Recognising Patterns

Recognising Patterns

Patterns are sequences or arrangements that follow a specific rule or formula. They can be found in numbers, shapes, colours, and even sounds. Recognising patterns is an essential skill in mathematics and plays a crucial role in teaching young learners. In this section, you will learn how to identify different types of patterns and how they can be used in various contexts.

Types of Patterns

There are several types of patterns that you can recognise:

• Number Patterns: These patterns consist of a sequence of numbers that follow a specific rule. For example, the sequence 2, 4, 6, 8 is a number pattern where each number increases by 2.
• Shape Patterns: These patterns involve a sequence of shapes that repeat or follow a specific arrangement. For example, a pattern of circles, squares, circles, squares is a shape pattern.
• Colour Patterns: These patterns involve a sequence of colours that repeat or follow a specific arrangement. For example, red, blue, red, blue is a colour pattern.

Identifying Number Patterns

To identify number patterns, look for a rule that explains how the numbers change from one to the next. Here are some common types of number patterns:

Arithmetic Patterns

An arithmetic pattern is a sequence of numbers where the difference between consecutive terms is constant. This difference is known as the common difference.

For example, consider the sequence 5, 10, 15, 20:

• The first term is 5.
• The second term is 10.
• The third term is 15.
• The fourth term is 20.

To find the common difference, subtract the first term from the second term:

10 - 5 = 5

Now, check the difference between the subsequent terms:

15 - 10 = 5

20 - 15 = 5

Since the difference is the same, this is an arithmetic pattern with a common difference of 5.

Geometric Patterns

A geometric pattern is a sequence of numbers where each term is found by multiplying the previous term by a constant. This constant is known as the common ratio.

For example, consider the sequence 3, 6, 12, 24:

• The first term is 3.
• The second term is 6.
• The third term is 12.
• The fourth term is 24.

To find the common ratio, divide the second term by the first term:

6 / 3 = 2

Now, check the ratio between the subsequent terms:

12 / 6 = 2

24 / 12 = 2

Since the ratio is the same, this is a geometric pattern with a common ratio of 2.

Recognising Patterns in Shapes

Shape patterns can be recognised by observing how shapes are arranged or repeated. Here are some examples:

Repeating Shapes

A simple shape pattern can be created by repeating shapes in a specific order. For example, consider the pattern triangle, square, triangle, square:

• The first shape is a triangle.
• The second shape is a square.
• The third shape is a triangle.
• The fourth shape is a square.

This pattern alternates between a triangle and a square. To extend this pattern, you would continue the sequence as triangle, square, triangle, square.

Growing Shapes

Another type of shape pattern is a growing pattern, where shapes increase in size or number. For example:

• One circle
• Two circles
• Three circles

This pattern grows by adding one more circle each time. To extend the pattern, you would continue with four circles.

Recognising Patterns in Colour

Colour patterns can be identified by observing how colours are arranged or repeated. For example, consider the pattern red, yellow, red, yellow:

• The first colour is red.
• The second colour is yellow.
• The third colour is red.
• The fourth colour is yellow.

This pattern alternates between red and yellow. To extend this pattern, you would continue with red, yellow, red, yellow.

Using Patterns in Teaching

Recognising patterns is an essential skill for young learners. Teachers can use patterns to develop critical thinking and problem-solving skills. Here are some ways to incorporate patterns into teaching:

• Games: Use games that involve identifying and creating patterns. For example, have students create their own shape patterns using blocks.
• Art Activities: Incorporate patterns into art projects. Students can create patterns using colours, shapes, or lines.
• Storytelling: Use stories that involve patterns. For example, tell a story about animals that follow a pattern in their behaviour.

Common Mistakes in Recognising Patterns

Summary

• Patterns are sequences that follow specific rules.
• There are different types of patterns, including number patterns, shape patterns, and colour patterns.
• Arithmetic patterns have a constant difference, while geometric patterns have a constant ratio.
• Shape patterns can be repeating or growing.
• Recognising patterns is important for developing critical thinking skills in young learners.

Check your understanding

1. What is the common difference in the arithmetic pattern 4, 7, 10, 13?
2. Identify the common ratio in the geometric pattern 2, 6, 18, 54.
3. Describe a shape pattern that grows by adding one more shape each time.
4. How can patterns be used in teaching young learners?