Mathematics - Term 1 - Week 9

Patterns are sequences that follow a specific rule. For example, in the sequence 2, 4, 6, 8, the pattern is that each number increases by 2. Identifying patterns helps us predict future numbers in the sequence. Patterns can be numerical, geometric, or even in shapes and colors. Recognizing these patterns is a foundational skill in algebra.

Algebra involves using symbols and letters to represent numbers in equations. For instance, in the equation x + 3 = 7, x represents an unknown number. Solving for x means finding the value that makes the equation true. Algebra allows us to express relationships and solve problems systematically.

Consider the pattern 5, 10, 15, 20. To find the next number, we observe that each number increases by 5. Therefore, the next number is 25. We can express this pattern with the formula n = 5x, where x is the position in the sequence (1, 2, 3, ...).

Let's solve the equation 2x + 4 = 12. First, we subtract 4 from both sides to get 2x = 8. Next, we divide both sides by 2, resulting in x = 4. This means that when x is 4, the equation holds true.

Now, let's work together on identifying patterns. Look at the sequence 3, 6, 9, 12. What is the rule? (Answer: Each number increases by 3). What would the next two numbers be? (Answer: 15, 18). Discuss how you arrived at your answer with your partner.

Let's solve the equation 3y - 5 = 16 together. Start by adding 5 to both sides to get 3y = 21. Then, divide by 3 to find y. What is the value of y? (Answer: y = 7). Share your steps with the class.

Complete the following sequences by identifying the pattern: 1) 4, 8, 12, __, __. 2) 10, 20, 30, __, __. Write down the rule you used to find the next numbers.

Solve the following equations on your own: 1) 5x + 2 = 17. 2) 4z - 3 = 9. Show your working clearly and be prepared to discuss your methods with the class.

• 28
• 24
• 30
• 35

Answer: 28

The pattern increases by 7 each time.

• 2
• 4
• 3
• 5

Answer: 4

Subtract 6 from both sides to get 2x = 8, then divide by 2.

Answer: The pattern increases by 2 each time.

Each number is 2 more than the previous number.

Answer: x = 3

Add 9 to both sides, then divide by 3.

• Add 2
• Multiply by 2
• Subtract 2
• Divide by 2

Answer: Multiply by 2

Each number is double the previous number.

• 5
• 10
• 15
• 20

Answer: 5

Divide both sides by 5 to find y.

Answer: 50

The pattern increases by 10 each time.

Answer: z = 4

Subtract 4 from both sides, then divide by 2.