Mathematics - Term 1 - Week 9

Patterns are sequences that follow a specific rule. They can be numerical, geometric, or even verbal. For example, the sequence 2, 4, 6, 8 is a numerical pattern where each number increases by 2. Recognizing patterns helps us predict future numbers in the sequence and is foundational for algebraic thinking.

Algebraic expressions use letters to represent numbers. For instance, in the expression 3x + 2, 'x' can stand for any number. This allows us to express patterns in a more general form. If we know that the pattern increases by 3, we can write it as 3n, where 'n' is the position in the sequence.

Consider the pattern 5, 10, 15, 20. This pattern increases by 5 each time. We can express this as 5n, where n represents the term number (1, 2, 3, ...). For example, when n = 3, 5n = 15, which is the third term in the pattern.

Let's create an expression for the pattern 1, 4, 7, 10. Here, the pattern increases by 3. We can express this as 3n - 2. For n = 1, 3(1) - 2 = 1; for n = 2, 3(2) - 2 = 4, and so on. This shows how algebra can represent patterns.

Let's work together to identify the pattern in the sequence 12, 15, 18, 21. What is the rule? (Answer: The pattern increases by 3.) Now, can we write an algebraic expression for this pattern? (Answer: 3n + 9, where n starts at 1.)

Now, let's solve the expression 2x + 5 for x = 4. What do we get? (Answer: 2(4) + 5 = 8 + 5 = 13.) Let's discuss how we arrived at this answer and ensure everyone understands the steps.

Solve the following problems independently: 1) Identify the pattern in the sequence 3, 6, 9, 12 and write an algebraic expression. 2) Evaluate the expression 4y - 3 for y = 5. 3) Create a pattern that increases by 7 and write its algebraic expression.

After completing the problems, review your answers. If you made mistakes, write down what went wrong and how you can correct it. Discuss your findings with a partner to reinforce your understanding.

• 10
• 12
• 14
• 16

Answer: 10

The pattern increases by 2 each time.

• 5n
• n + 5
• 3n + 2
• 5n - 5

Answer: 5n

The pattern increases by 5, so it can be expressed as 5n.

Answer: 2n - 1

This expression represents the odd numbers starting from 1.

• 10
• 8
• 6
• 12

Answer: 10

Substituting x = 3 gives 2(3) + 4 = 6 + 4 = 10.

Answer: Increases by 7.

Each number increases by 7.

• 20
• 24
• 22
• 18

Answer: 20

The pattern increases by 4, so the 5th term is 4 + 4(4) = 20.

Answer: 8

Substituting y = 2 gives 3(2) + 2 = 6 + 2 = 8.

• A random list of numbers
• A sequence of even numbers
• A single number
• A list of colors

Answer: A sequence of even numbers

A pattern follows a specific rule, like even numbers increasing by 2.