Mathematics - Term 1 - Week 9

Patterns are sequences that follow a specific rule. For example, the sequence 2, 4, 6, 8 shows an increasing pattern where each number is 2 more than the previous one. Patterns can also be found in shapes, colors, and even sounds. Recognizing these patterns helps us predict what comes next and is a foundational skill in algebra.

Consider the pattern: 5, 10, 15, 20. This is an arithmetic pattern where each number increases by 5. To find the next number, we add 5 to the last number: 20 + 5 = 25. Now, let's write a rule for this pattern: 'Start at 5 and add 5 for each subsequent number.'

Let's work on identifying patterns as a class. I will display the following sequence: 3, 6, 9, __. What do you think the next number is? (Students will respond with 12.) Great! Now, can anyone explain how they figured that out? (Encourage students to share their thought processes.)

Now it's your turn! Solve the following expressions: 2x + 3 when x = 4. Show your working clearly. (Students will calculate: 2(4) + 3 = 8 + 3 = 11.) Remember to write down each step you took to arrive at your answer.

• 8
• 9
• 10
• 11

Answer: 9

The pattern increases by 2 each time.

• 2, 4, 6, 8
• 1, 2, 3, 5
• 5, 10, 15, 25
• None of the above

Answer: 2, 4, 6, 8

This sequence increases by 2, showing a clear pattern.

Answer: 10

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

• Add 5
• Add 10
• Subtract 10
• Multiply by 2

Answer: Add 10

Each number increases by 10.

Answer: 16, 20

The pattern increases by 4 each time.

• n + 1
• n^2
• 2n
• n + 2

Answer: n^2

These numbers are perfect squares: 1^2, 2^2, 3^2, 4^2.

Answer: 13

Substituting y gives 5(3) - 2 = 15 - 2 = 13.

• 70
• 60
• 50
• 40

Answer: 70

The pattern decreases by 10 each time.