Mathematics - Term 3 - Week 5

Patterns are sequences that follow a specific rule. They can be numerical, geometric, or even in everyday life. For example, the sequence 2, 4, 6, 8 follows a pattern where each number increases by 2. Recognizing these patterns helps us predict what comes next and is foundational for algebra. In algebra, we often use letters to represent numbers in patterns, allowing us to express rules more generally.

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 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 describe patterns succinctly.

Let's work together on the pattern: 3, 6, 9, __. What is the next number? First, we notice that each number increases by 3. Therefore, the next number is 12. Now, let's express this pattern algebraically: n = 3x. If x = 4 (the fourth position), then n = 3 * 4 = 12. Try to find the next number in the pattern: 1, 4, 7, __.

Now it's your turn! Create a numerical pattern that increases by 4. Write down the first five numbers in your pattern and express it using an algebraic expression. After that, solve the following problems: 1) What is the 6th number in your pattern? 2) If your pattern starts at 10, what is the 10th number? Show your working clearly.

• 10
• 12
• 14
• 16

Answer: 10

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

• n = 5x
• n = x + 5
• n = 10x
• n = 15 - x

Answer: n = 5x

The pattern increases by 5, so the expression n = 5x correctly represents it.

Answer: 15

The pattern increases by 3, so the 5th number is 15.

• 15
• 20
• 25
• 30

Answer: 20

The pattern is 10, 15, 20, so the 3rd number is 20.

Answer: n = 2x - 1

This expression represents the odd numbers starting from 1.

• 35
• 40
• 45
• 50

Answer: 40

The pattern increases by 10, so the next number is 40.

Answer: 24

The pattern increases by 4, so the 6th number is 24.

• 1, 2, 3, 4
• 2, 4, 6, 8
• 5, 10, 15, 20
• 1, 3, 5, 7, 10

Answer: 1, 3, 5, 7, 10

This sequence does not follow a consistent rule as it jumps to 10.