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. Recognizing patterns helps us predict future numbers in the sequence. Patterns can be numerical, geometric, or even algebraic, and they form the foundation for algebraic thinking.

Algebra involves using symbols and letters to represent numbers in equations and expressions. For instance, in the expression 3x + 5, 'x' is a variable that can represent any number. Understanding how to manipulate these expressions is crucial for solving equations and understanding relationships between quantities.

Consider the pattern 5, 10, 15, 20. The rule is to add 5 each time. If we want to find the 6th term, we can continue the pattern: 20 + 5 = 25. Therefore, the 6th term is 25.

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

Let's work together on the sequence 1, 4, 9, 16. What do you notice about these numbers? They are perfect squares: 1^2, 2^2, 3^2, 4^2. What would the next number be? It would be 5^2, which is 25. Now, try to identify the next two numbers in the sequence.

Now, let's solve the equation 3y - 7 = 5. Start by adding 7 to both sides to get 3y = 12. Then, divide by 3 to find y. What is the value of y? Work through it step by step and share your answer.

Complete the following problems on your own: 1) Identify the next two terms in the pattern 2, 5, 10, 17. 2) Solve the equation 4x + 2 = 18. Show all your working clearly. After you finish, we will review the answers together.

After completing your problems, take a moment to review any mistakes you made. What strategies can you use to correct them? Discuss with a partner how you approached the problems and what you learned from any errors.

• 15
• 18
• 21
• 24

Answer: 15

The pattern increases by 3 each time.

• 5 + 3
• x + 2
• 12 = 4y
• 7 - 2 = 5

Answer: x + 2

An algebraic expression contains variables, while the others are equations or numerical expressions.

Answer: x = 2

Add 10 to both sides to get 5x = 10, then divide by 5.

• 9
• 10
• 11
• 12

Answer: 9

The pattern increases by 2, so the 5th term is 7 + 2.

Answer: x = 4

Subtract 4 from both sides to get 2x = 8, then divide by 2.

• y = 2x + 3
• y = x^2
• y = 3/x
• y = 5

Answer: y = 2x + 3

A linear equation has a constant rate of change, represented by x to the first power.

Answer: 20, 24

The pattern increases by 4 each time.

• y = 2
• y = 3
• y = 4
• y = 5

Answer: y = 3

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