Mathematics - Term 2 - Week 7

Patterns are sequences that follow a specific rule. In mathematics, we often look for numerical patterns where numbers increase or decrease in a predictable way. For example, the sequence 2, 4, 6, 8 follows the rule of adding 2 each time. Recognizing these patterns helps us predict future numbers in the sequence and lays the groundwork for understanding algebra.

Algebra involves using letters and symbols to represent numbers in equations and expressions. For instance, in the expression 3x + 5, 'x' represents an unknown number. Understanding how to manipulate these expressions is crucial for solving equations. We will explore how to simplify expressions and solve for 'x' using various strategies.

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 as 5n, where n is the position in the sequence (1, 2, 3, ...).

Let's solve the equation 2x + 3 = 11. First, we subtract 3 from both sides to isolate the term with 'x': 2x = 8. Next, we divide both sides by 2 to find x = 4. Thus, the solution to the equation is x = 4.

Now, let's practice extending a pattern together. The sequence is 1, 3, 5, 7. What is the next number? Students should notice that we are adding 2 each time. Therefore, the next number is 9. Can anyone explain how they arrived at that answer?

Let's solve the equation 4y - 2 = 10 together. First, we add 2 to both sides to get 4y = 12. Then, we divide by 4, resulting in y = 3. Discuss with your partner how you approached this problem and any strategies you used.

Now it's your turn! Solve the following problems independently: 1) Extend the pattern: 10, 20, 30, ___. 2) Solve the equation: 5z + 4 = 24. Show all your working clearly. After completing the problems, review your answers with a classmate and discuss any mistakes.

After completing your practice problems, take a moment to review any mistakes you made. Write down what you learned from correcting those mistakes. Understanding where you went wrong is a vital part of the learning process.

• 10
• 12
• 15
• 18

Answer: 12

The pattern increases by 3 each time.

Answer: 5

Subtract 7 from both sides to get 3x = 15, then divide by 3.

• 5 + 3
• x + 2
• 10 = 5
• 7 - 4

Answer: x + 2

An algebraic expression contains variables, like 'x'.

Answer: 32

The pattern doubles each time.

• 2
• 3
• 4
• 5

Answer: 3

Add 3 to both sides to get 6y = 18, then divide by 6.

Answer: 5

Divide both sides by 5 to find a = 5.

• 1, 2, 3
• 5, 9, 13
• 10, 14, 18
• 2, 6, 10

Answer: 10, 14, 18

Each number increases by 4.

Answer: 70

The pattern decreases by 10 each time.