How do I teach long division?

Teaching long division involves breaking down the process into manageable steps and using clear explanations and plenty of practice. Here’s a structured approach:

1. Building a Foundation: Division Vocabulary

Before diving into the algorithm, ensure the student understands the terminology.

Dividend: The number being divided (the larger number inside the division bracket).
Divisor: The number you are dividing by (the number outside the division bracket).
Quotient: The answer to the division problem (written above the dividend).
Remainder: The amount left over when the divisor doesn't divide the dividend evenly.

2. Introducing the Long Division Layout

Familiarize the student with the standard long division setup. For example, to divide 938 by 4:

      ______
  4 | 938

3. Demonstrating with Examples

Work through examples, clearly explaining each step. Use the acronym DMSB (Divide, Multiply, Subtract, Bring Down) as a memory aid:

Example: Dividing 938 by 4

Divide: How many times does 4 go into 9? Answer: 2. Write the 2 above the 9.
```
     2____
 4 | 938
```
Multiply: Multiply the divisor (4) by the quotient digit (2). 4 x 2 = 8. Write the 8 below the 9.
```
     2____
 4 | 938
     8
```
Subtract: Subtract 8 from 9. 9 - 8 = 1. Write the 1 below the 8.
```
     2____
 4 | 938
     8
     1
```
Bring Down: Bring down the next digit from the dividend (3) next to the 1.
```
     2____
 4 | 938
     8
     13
```

Repeat steps 1-4 with the new number (13).

Divide: How many times does 4 go into 13? Answer: 3. Write the 3 above the 3 in 938.
```
     23___
 4 | 938
     8
     13
```
Multiply: Multiply 4 by 3. 4 x 3 = 12. Write the 12 below the 13.
```
     23___
 4 | 938
     8
     13
     12
```

Subtract: Subtract 12 from 13. 13 - 12 = 1.

Bring Down: Bring down the last digit (8).

Repeat steps 1-4 with the new number (18).

Divide: How many times does 4 go into 18? Answer: 4. Write the 4 above the 8 in 938.
```
      234_
  4 | 938
      8
      13
      12
       18
```

Multiply: Multiply 4 by 4. 4 x 4 = 16. Write the 16 below the 18.

Subtract: Subtract 16 from 18. 18 - 16 = 2

Since there are no more digits to bring down, the remainder is 2. Therefore, 938 ÷ 4 = 234 R 2.

4. Practice Without Bringing Down Zeros (Early Practice)

Start with problems where the divisor goes into each digit of the dividend without needing to bring down a zero immediately. This helps solidify the DMSB steps. Example: 639 / 3

5. Teach Bringing Down

Introduce problems where you need to bring down a zero because the divisor doesn’t go into the current digit. Emphasize that you only bring down one digit at a time.

6. Explain Problems with Remainders

Explain what a remainder represents and how to express it in the answer.

Key Teaching Tips:

Start Simple: Begin with easier problems and gradually increase the difficulty.
Visual Aids: Use visual aids like manipulatives or diagrams to illustrate the process.
Repetition and Practice: Consistent practice is crucial for mastering long division.
Real-World Connections: Relate long division to real-world scenarios to make it more engaging.
Patience: Long division can be challenging, so be patient and encouraging.