Mathematics - Term 4 - Week 3

Patterns are sequences that follow a specific rule or formula. In mathematics, we often encounter numerical patterns, such as even and odd numbers, or patterns that increase or decrease by a certain amount. For example, the sequence 2, 4, 6, 8 is a pattern where each number increases by 2. Recognizing these patterns helps us predict future numbers in the sequence and form algebraic expressions.

Consider the pattern: 5, 10, 15, 20. This pattern increases by 5 each time. We can express this pattern using an algebraic expression: n = 5x, where n is the number in the sequence and x is the position in the sequence (1, 2, 3, ...). For instance, when x = 3, n = 5 * 3 = 15. This shows how algebra can help us understand and describe patterns.

Let's work together to create a pattern. Start with the number 3 and increase by 4 each time. Write down the first five numbers in this pattern. After that, let's form an algebraic expression for this pattern. The sequence will be: 3, 7, 11, 15, 19. The algebraic expression can be written as n = 4x - 1. Discuss with your partner how you arrived at this expression and the significance of each part.

Now it's your turn to practice independently. Solve the following problems: 1) Identify the next two numbers in the pattern: 12, 15, 18, 21. 2) Write an algebraic expression for the pattern: 1, 4, 7, 10. 3) Create your own pattern starting from 10 and decreasing by 3 each time. Write down the first five numbers and the corresponding algebraic expression. Be sure to show your working clearly!

• 10
• 12
• 14
• 16

Answer: 10

The pattern increases by 2 each time, so after 8, the next number is 10.

• n = 5x
• n = 4x
• n = 3x + 2
• n = 2x + 3

Answer: n = 5x

The pattern increases by 5, so the expression is n = 5x, where x is the position in the sequence.

Answer: 7, 10, 13

Starting at 7 and adding 3 gives us 10, then adding 3 again gives us 13.

Answer: n = 2x - 1

This pattern increases by 2, starting from 1, which can be expressed as n = 2x - 1.

• 2
• 0
• 3
• 1

Answer: 2

The pattern decreases by 2 each time, so after 4, the next number is 2.

• 3, 6, 9
• 10, 8, 6
• 1, 2, 3
• 5, 10, 15

Answer: 10, 8, 6

This sequence decreases by 2 each time, indicating a decreasing pattern.

Answer: 4, 3, 2, 1

Starting from 4 and subtracting 1 gives us the sequence 4, 3, 2, 1.

Answer: n = 5x

This pattern increases by 5, so the expression is n = 5x, where x is the position in the sequence.