Mathematics - Term 4 - Week 3

Patterns are sequences or arrangements that follow a specific rule. They can be found in numbers, shapes, and even in everyday life. For example, the sequence 2, 4, 6, 8 is a pattern where each number increases by 2. Recognizing these patterns helps us predict future numbers in the sequence and lays the groundwork for algebraic thinking.

Algebra involves using symbols and letters to represent numbers in equations and expressions. For instance, if we let 'n' represent a number, the expression 'n + 3' indicates that we are adding 3 to that number. Understanding how to manipulate these expressions is crucial for solving mathematical problems.

Consider the pattern: 5, 10, 15, 20. Here, we can see that each number increases by 5. If we were to continue this pattern, the next number would be 25. We can express this pattern using the formula n = 5k, where k is a whole number starting from 1.

Let's solve the expression 2n + 4 when n = 3. First, we substitute 3 for n: 2(3) + 4. This simplifies to 6 + 4, which equals 10. Thus, when n is 3, the expression evaluates to 10.

Now, let's work together on identifying the pattern in the sequence: 1, 4, 7, 10. What is the rule? Students should notice that each number increases by 3. Ask them to predict the next two numbers in the sequence and explain their reasoning.

Let's evaluate the expression 3x - 2 when x = 5. First, substitute 5 for x: 3(5) - 2. This simplifies to 15 - 2, which equals 13. Have students practice with different values of x and share their results.

Students will complete a worksheet where they identify the rule in various number sequences and predict the next three numbers. Encourage them to write down their reasoning for each answer.

Students will solve a set of algebraic expressions such as 4y + 5 when y = 2, and 7z - 3 when z = 4. They should show their working clearly and check their answers with a partner.

• 15
• 18
• 21
• 24

Answer: 15

The pattern increases by 3 each time, so 12 + 3 = 15.

Answer: Add 3.

Each number increases by 3.

• 20
• 22
• 24
• 26

Answer: 22

Substituting x = 4 gives 5(4) + 2 = 20 + 2 = 22.

Answer: 8

Substituting n = 6 gives 2(6) - 4 = 12 - 4 = 8.

• 50
• 60
• 70
• 80

Answer: 50

The pattern increases by 10 each time.

Answer: Add 2.

Each number increases by 2.

• 5
• 6
• 7
• 8

Answer: 7

Substituting y = 2 gives 3(2) + 1 = 6 + 1 = 7.

Answer: 4n, where n is the position in the sequence.

Each term is 4 times the position number.