Question 1: Perform the division 123 ÷ 4 using the Formal Method. Show each step clearly.

Answer: 30 remainder 3

Question 2: Divide 456 by 7 using the Formal Method. Write down the steps and the final quotient.

Answer: 65 remainder 1

Question 3: Calculate 987 ÷ 3 with the Formal Method, showing all steps.

Answer: 329

Question 4: A student performs 144 ÷ 12 but makes a mistake in the subtraction step. Identify and correct the error.

Answer: Incorrect subtraction, should be 12 - 4 = 8, not 2. Fix the subtraction to proceed correctly.

Question 5: In dividing 562 by 9, a student mistakenly places the first quotient digit as 5 instead of 6. Explain why this is incorrect and provide the correct quotient.

Answer: The first digit should be 6 because 9 × 6 = 54, which is the largest multiple less than 56. The incorrect digit 5 underestimates the quotient.

Question 6: Using the Formal Method, divide 789 by 6. Show all steps and comment on any common mistake students might make.

Answer: 131 remainder 3

Question 7: A student incorrectly subtracts 13 instead of 12 during the division of 144 ÷ 12. How does this mistake affect the final answer? Explain.

Answer: Subtracting 13 instead of 12 leads to an incorrect intermediate value, causing the quotient to be underestimated by 1.

Question 8: Construct a division problem where the student’s mistake in the subtraction step causes an incorrect quotient. Explain the error.

Answer: Example: dividing 250 by 5, mistakenly subtracting 6 instead of 5 at some step, leading to an incorrect quotient.

Question 9: Solve 135 ÷ 5 using the Formal Method. Then, identify and correct a common mistake students make at the subtraction step.

Answer: 27 with no remainder; mistake: subtracting 4 instead of 5 at some step, which leads to an incorrect quotient.

Question 10: A word problem: A factory produces 648 units of a product each day. If each shipment contains 9 units, how many shipments are needed? Use the Formal Method to find the answer and show your steps.

Answer: 72 shipments

Question 11: Challenge: Divide 1001 by 13 using the Formal Method. Show all steps and explain any difficulties students might encounter with the subtraction or multiplication steps.

Answer: 77 remainder 2

Question 12: In dividing 1234 by 6, a student incorrectly estimates the first quotient digit as 2 instead of 2. Explain how this impacts the subsequent steps and the final answer.

Answer: Incorrect initial quotient digit leads to misplaced subtraction multiples, resulting in an incorrect quotient and possible confusion in subsequent steps.