Create a flow diagram and describe it using the rule: Multiply by 2, then add 3. Also, determine the rule for an input-output diagram and write a number sentence.

You're on a roll — here are the solutions for the flow diagrams and number sentences. 2. Create your own flow diagram and describe it. Let's use the rule: Multiply by 2, then add 3. Flow Diagram: Input boxes (from top to bottom): 1, 2, 3, 4, 5, 6 First operation box: × 2 Second operation box: + 3 Output boxes (from top to bottom): 1 × 2 + 3 = 5 2 × 2 + 3 = 7 3 × 2 + 3 = 9 4 × 2 + 3 = 11 5 × 2 + 3 = 13 6 × 2 + 3 = 15 The completed output boxes are: 5, 7, 9, 11, 13, 15. Description: The rule for this flow diagram is to multiply the input number by 2, and then add 3 to the result to get the output number. 3. Determine the rule and then write a number sentence for each. a) Input-Output Diagram Step 1: Determine the rule. Let's test a rule of the form (Input × A) + B. Using the first two pairs: 9A + B = 32 6A + B = 23 Subtracting the second equation from the first: (9A + B) - (6A + B) = 32 - 23 3A = 9 A = 3 Substitute A=3 into 6A + B = 23: 6(3) + B = 23 18 + B = 23 B = 5 The rule is (Input × 3) + 5. Step 2: Fill the operation boxes. The first operation box is × 3. The second operation box is + 5. Step 3: Write the number sentences. i. 9 × 3 + 5 = 32 ii. 6 × 3 + 5 = 23 iii. 7 × 3 + 5 = 26 iv. 3 × 3 + 5 = 14 v. 4 × 3 + 5 = 17 vi. 8 × 3 + 5 = 29 b) Input-Output Diagram Step 1: Determine the rule. Let's test a rule of the form (Input × A) + B. Using the first two pairs: 7A + B = 62 5A + B = 46 Subtracting the second equation from the first: (7A + B) - (5A + B) = 62 - 46 2A = 16 A = 8 Substitute A=8 into 5A + B = 46: 5(8) + B = 46 40 + B = 46 B = 6 The rule is (Input × 8) + 6. Step 2: Fill the operation boxes. The first operation box is × 8. The second operation box is + 6. Step 3: Write the number sentences. i. 7 × 8 + 6 = 62 ii. 5 × 8 + 6 = 46 iii. 8 × 8 + 6 = 70 iv. 4 × 8 + 6 = 38 v. 9 × 8 + 6 = 78 vi. 6 × 8 + 6 = 54 What's next?