Partial Quotients · One-Digit Divisors

Teaching Notes

Subtract multiples of the divisor in steps, then add the partial quotients. Every problem on this worksheet has a remainder of 0.

Before You Begin

• The relationship between multiplication and division; subtraction

Teaching Steps for Parents and Teachers

1. Check 4 × 20 = 80, then calculate 84 − 80 = 4.
2. For the remaining 4, check 4 × 1 = 4.
3. Since 4 − 4 = 0, add the partial quotients 20 and 1 to get 21.
4. Check with 4 × 21 = 84.

Worked Examples

84 ÷ 4 = 20 + 1 = 21

1. 84 − 80 = 4 and 4 − 4 = 0. Since 80 = 4 × 20 and 4 = 4 × 1, add the partial quotients: 20 + 1 = 21.

Answer: 21

Common Mistakes and How to Help

Adding the subtracted amounts instead of the partial quotients

Connect the subtracted amounts 80 and 4 to the partial quotients 20 and 1 using 4 × 20 and 4 × 1.

Correcting the answer without explaining why

The amounts subtracted are 80 and 4. Add the partial quotients 20 and 1 instead. Have the student start again at the first incorrect step.

Questions to Check Understanding

• Does multiplying the quotient 21 by 4 give the original dividend?
• 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 21. 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.