Mathematics - Term 4 - Week 3

Patterns are sequences 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. We can also create patterns using shapes, like alternating circles and squares. Recognizing these patterns helps us predict what comes next and forms the basis for algebraic thinking.

Let's look at the pattern 5, 10, 15, 20. Here, each number increases by 5. To find the next number, we add 5 to 20, which gives us 25. Now, if we were to express this pattern algebraically, we could say that the nth term of this pattern can be represented as 5n, where n is the position in the sequence (1, 2, 3, ...).

Now it's your turn! Create a number pattern that starts at 3 and increases by 4. Write down the first five terms of your pattern. After that, think about how you could express this pattern using an algebraic expression. Share your pattern with a partner and discuss how you arrived at your answer.

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: 1, 3, 5, 7, __. 3. Create a shape pattern using triangles and squares, and describe the rule you used.

• 28
• 24
• 30
• 35

Answer: 28

The pattern increases by 7 each time, so 21 + 7 = 28.

• 1, 2, 3, 4
• 2, 4, 6, 8
• 5, 10, 15, 20, 25
• All of the above

Answer: All of the above

All listed sequences follow a specific rule and are patterns.

Answer: 4n

The pattern increases by 4, so the nth term can be expressed as 4n.

• 12
• 15
• 18
• 21

Answer: 15

The pattern increases by 3, so the 5th term is 3 + 3 + 3 + 3 + 3 = 15.

Answer: Circle, Square, Circle, Square, ...

The pattern alternates between a circle and a square.

• Add 5
• Add 10
• Add 15
• Subtract 10

Answer: Add 10

Each number in the pattern increases by 10.

Answer: 13

The pattern increases by 3, so 10 + 3 = 13.

• 5n
• n + 5
• 5 + n
• n - 5

Answer: 5n

The pattern can be expressed as 5 times the position in the sequence.