Create and extend number patterns, including multiples, factors, prime numbers, and other rules like "multiply by 2 and add 1" and "divide by 2 and add 2".

Here are the solutions to the number pattern questions:

1. Create a pattern that includes:

• a) Multiples Pattern: $6, 12, 18, 24, 30, \dots$ What is the rule? Add 6 to the previous term.

• b) Factors Pattern: $1, 2, 3, 4, 6, 8, 12, 24$ What is the rule? List the factors of 24 in ascending order.

2. Extend the following pattern.

• a) Tip: prime numbers are special numbers that can only be divided by themselves and 1. $2, 3, 5, 7, 11, \boxed{\textbf{13}}, \boxed{\textbf{17}}, \boxed{\textbf{19}}$

• b) Rule: multiply by 2 and add 1. $1, 3, 7, 15, \boxed{\textbf{31}}, \boxed{\textbf{63}}, \boxed{\textbf{127}}$