Mathematics - Term 2 - Week 7

Patterns are sequences that follow a specific rule. For example, in the sequence 2, 4, 6, 8, we can see that each number increases by 2. Patterns can be numerical, geometric, or even in words. Recognizing these patterns helps us predict what comes next and is foundational for understanding algebra.

Algebra involves using symbols and letters to represent numbers in equations. For instance, in the equation x + 3 = 7, 'x' represents an unknown number. Our goal is to find the value of 'x' that makes the equation true. This concept is crucial for solving real-world problems.

Consider the pattern: 5, 10, 15, 20. This pattern increases by 5 each time. To find the next number, we add 5 to 20, resulting in 25. We can express this pattern using the formula n = 5n, where n is the position in the sequence.

Let's solve the equation x + 4 = 12. To isolate x, we subtract 4 from both sides: x + 4 - 4 = 12 - 4, which simplifies to x = 8. Thus, the value of x that satisfies the equation is 8.

Now, let's create a number pattern together. Start with the number 3 and increase by 4. Write down the first five numbers in this pattern. Students should write: 3, 7, 11, 15, 19. Discuss how they arrived at their answers and the rule they used.

Let's solve the equation y - 5 = 10 together. Ask students to explain their steps as they add 5 to both sides. The solution should be y = 15. Encourage them to show their working clearly on the board.

Students will create their own number pattern starting from 1 and increasing by 3. They should write down the first six numbers and explain the rule they used. After that, they will share their patterns with a partner.

Provide students with the equation z + 6 = 20. They should solve for z by subtracting 6 from both sides. The expected answer is z = 14. Students will write down their steps and check their work with a peer.

• 10
• 12
• 14
• 16

Answer: 10

The pattern increases by 2 each time, so after 8 comes 10.

• x = 7
• x = 5
• x = 17
• x = 12

Answer: x = 7

To solve for x, subtract 5 from both sides, resulting in x = 7.

Answer: 10, 13, 16, 19

The pattern starts at 10 and adds 3 each time.

• y = 10
• y = 4
• y = 7
• y = 3

Answer: y = 10

Adding 3 to both sides gives y = 10.

Answer: 9

The pattern increases by 2 each time.

• 5
• 7
• 9
• 11

Answer: 7

Subtracting 2 from 9 gives x = 7.

Answer: z = 8

Subtracting 4 from 12 results in z = 8.

• 1, 2, 3, 4
• 5, 10, 15, 20
• 2, 4, 6, 8
• 3, 6, 9, 12

Answer: 5, 10, 15, 20

This pattern increases by 5 each time.