Partial Quotients · Two-Digit Divisors

Teaching Notes

To divide by a two-digit number, subtract multiples of the divisor and add the partial quotients. Every problem on this worksheet has a remainder of 0.

Before You Begin

• Multiplication and subtraction with two-digit numbers

Teaching Steps for Parents and Teachers

1. Check 12 × 10 = 120, then calculate 156 − 120 = 36.
2. For the remaining 36, check 12 × 3 = 36.
3. Since 36 − 36 = 0, add the partial quotients 10 and 3 to get 13.
4. Check with 12 × 13 = 156.

Worked Examples

156 ÷ 12 = 10 + 3 = 13

1. 156 − 120 = 36 and 36 − 36 = 0. Since 120 = 12 × 10 and 36 = 12 × 3, add the partial quotients: 10 + 3 = 13.

Answer: 13

Common Mistakes and How to Help

Adding the remaining amount directly to the quotient

The remaining 36 contains 12 a total of 3 times. Add 3 to the quotient, not 36.

Correcting the answer without explaining why

Distinguish the partial quotient from the amount subtracted. At each step, check that the divisor times the partial quotient equals the amount subtracted. Have the student start again at the first incorrect step.

Questions to Check Understanding

• Can you check the answer using 12 × 13 = 156?
• What does each number in the worked example represent in the original problem?
• Can you use the same method when the numbers change?

Practice Advice

Work through the example together and have the student explain why the answer is 13. Ask the student to explain the first two problems aloud, then solve the next three independently. Review the intermediate steps as well as the final answers. If an error repeats, return to the difficult teaching step before assigning more problems.

Next Practice

• Choose New Numbers for more practice with the same conditions. Ask the student to explain the reasoning as well as give the answer.
• If the student cannot explain the method independently, use smaller numbers to explore the same relationship first.