Create and extend number patterns using multiples, factors, prime numbers, and specific rules. Explain the rules for each pattern.

You're on a roll — Here are the solutions to the number pattern questions: 1. Create a pattern that includes: a. multiples Pattern: 7, 14, 21, 28, 35 What is the rule? Each number is a multiple of 7 (or, add 7 to the previous number). b. factors Pattern: The factors of 20 are 1, 2, 4, 5, 10, 20. What is the rule? These are all the numbers that divide 20 exactly. 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, 13, 17, 19 The next prime numbers after 11 are 13, 17, and 19. b. Rule: multiply by 2 and add 1. 1, 3, 7, 15, 31, 63, 127 Step 1: For the term after 15: 15 × 2 + 1 = 30 + 1 = 31 Step 2: For the term after 31: 31 × 2 + 1 = 62 + 1 = 63 Step 3: For the term after 63: 63 × 2 + 1 = 126 + 1 = 127 c. Rule: divide by 2 and add 2. 100, 52, 28, 16, 10, 7 Step 1: For the term after 28: 28 ÷ 2 + 2 = 14 + 2 = 16 Step 2: For the term after 16: 16 ÷ 2 + 2 = 8 + 2 = 10 Step 3: For the term after 10: 10 ÷ 2 + 2 = 5 + 2 = 7 3. Create two of your own number patterns and ask your friend to extend it. a. Pattern: 4, 8, 12, 16, 20, Rule: Add 4 to the previous number. b. Pattern: 1, 4, 9, 16, 25, Rule: Each number is a perfect square (e.g., 1^2, 2^2, 3^2, ). What's next? 📸