Mathematics - Term 4 - Week 3

Patterns are sequences that follow a specific rule or formula. In mathematics, we often encounter numerical patterns, such as arithmetic sequences where each term increases by a constant value. For example, the sequence 2, 4, 6, 8 follows the rule of adding 2. Recognizing these patterns helps us predict future terms and lays the groundwork for algebraic thinking.

Algebraic expressions are combinations of numbers, variables, and operations. For instance, the expression 3x + 5 represents a pattern where the value of x can change, affecting the overall value of the expression. Understanding how to manipulate these expressions is crucial for solving equations and inequalities.

Consider the pattern 5, 10, 15, 20. To find the next term, we observe that each term increases by 5. Therefore, the next term is 20 + 5 = 25. This illustrates how recognizing the rule of a pattern allows us to extend it.

Let's simplify the expression 4x + 3x - 2. First, we combine like terms: 4x + 3x = 7x. So, the simplified expression is 7x - 2. This example shows how to work with algebraic expressions by combining similar components.

Now, let's practice identifying patterns together. Look at the sequence: 1, 3, 5, 7. What is the rule? Students should recognize that this is an increasing pattern where each term adds 2. Ask students to predict the next three terms and share their reasoning.

Let's work on simplifying the expression 2a + 4b - 3a + 7b. First, we combine like terms: (2a - 3a) + (4b + 7b) = -1a + 11b. Have students practice similar expressions in pairs, discussing their thought processes as they simplify.

Now it's your turn! Solve the following problems independently: 1) What is the next term in the pattern 10, 20, 30? 2) Simplify the expression 5x + 2y - 3x + y. Write your answers and show your working clearly. After completing the problems, we will review them as a class.

• 10
• 12
• 14
• 16

Answer: 10

The pattern increases by 2 each time, so the next term is 8 + 2 = 10.

• 5 + 3
• x - 7
• 12
• 4 * 5

Answer: x - 7

An algebraic expression contains variables, and 'x - 7' includes the variable x.

Answer: 8y - 4

Combine like terms: 6y + 2y = 8y, so the expression simplifies to 8y - 4.

• Add 1
• Add 2
• Add 3
• Add 4

Answer: Add 3

Each term increases by 3, which defines the rule of the pattern.

Answer: 25

This pattern consists of perfect squares: 1^2, 2^2, 3^2, 4^2, so the next is 5^2 = 25.

• 3x + 4y
• 3xy
• 7xy
• x + y

Answer: 3x + 4y

The expression 3x + 4y correctly represents the sum of 3 times x and 4 times y.

Answer: 13

Substituting x with 2 gives 5(2) + 3 = 10 + 3 = 13.

• 5a + 5
• 9a + 5
• 5a - 5
• 7a + 5

Answer: 5a + 5

Combining like terms gives (7a - 2a) + 5 = 5a + 5.