Mathematics - Term 4 - Week 3

Patterns are sequences that follow a specific rule. They can be numerical, geometric, or even in everyday life. For example, in a numerical pattern like 2, 4, 6, 8, the rule is to add 2 each time. Identifying patterns helps us predict future numbers in the sequence and is a foundational skill in algebra. We can also create patterns using shapes, colors, or sounds, which can be represented visually.

Consider the pattern: 5, 10, 15, 20. Here, the rule is to add 5. If we continue this pattern, the next numbers would be 25, 30, and so on. To express this algebraically, we can use the formula n = 5x, where x is the position in the sequence (1 for 5, 2 for 10, etc.). This shows how patterns can be represented using algebraic expressions.

Now it's your turn! Create a numerical pattern starting from 3 and adding 4 each time. Write down the first five numbers in your pattern. After that, try to express your pattern using an algebraic expression. Discuss your patterns with a partner and see if you can identify the rule together. This collaborative effort will help reinforce your understanding of how patterns work.

Complete the following problems on your own: 1. Identify the next two numbers in the pattern: 12, 15, 18, __, __. 2. Write an algebraic expression for the pattern: 7, 14, 21, __, __. 3. Create a shape pattern using triangles and squares, and describe the rule. Remember to show your working clearly and check your answers with a classmate.

• 14
• 16
• 20
• 18

Answer: 16

The pattern adds 4 each time, so 12 + 4 = 16.

• 1, 2, 3, 4
• 5, 10, 15, 20
• 2, 4, 6, 8
• All of the above

Answer: All of the above

All options show a consistent rule in their sequences.

Answer: n = 3x

The pattern adds 3 each time, so the expression is 3 times the position.

• Add 1
• Add 2
• Add 3
• Add 4

Answer: Add 2

The pattern increases by 2 each time.

Answer: 40, 50

The pattern adds 10 each time.

• 2, 4, 6, 8
• 1, 3, 5, 7
• 5, 10, 15, 20
• 10, 20, 30, 40

Answer: 2, 4, 6, 8

The expression doubles the position value.

Answer: 70

The pattern decreases by 10 each time.

• 10
• 12
• 15
• 16

Answer: 13

The sequence is 1, 4, 7, 10, 13.