Illustrate the quotient by using the given concept of division. Sketch any new pieces that are necessary to show regrouping.

`396\div132`, using the measurement (subtractive) concept

To illustrate the quotient of \(396 \div 132\) using the measurement (subtractive) concept of division, follow these steps:

### Concept Overview:
In the measurement (or subtractive) division concept, you repeatedly subtract the divisor from the dividend until what remains is less than the divisor. The number of times you subtract gives you the quotient.

### Steps:
1. **Start with the total amount (396)**: This is your dividend, and it represents the quantity you want to divide.
  
2. **Subtract the divisor (132)** from 396**: 
   - First subtraction: \(396 - 132 = 264\)
   - Second subtraction: \(264 - 132 = 132\)
   - Third subtraction: \(132 - 132 = 0\)

3. **Count the number of subtractions**: 
   - You subtracted 132 three times, so the quotient is \(3\).

### Sketch to Illustrate:
Imagine that you have a number line or a series of blocks representing the number 396. Each block or segment represents 132 units.

- **First block**: Represents 132, leaving 264 after the subtraction.
- **Second block**: Represents another 132, leaving 132 after the subtraction.
- **Third block**: Represents the final 132, leaving 0 after the subtraction.

Here's how you can visualize it:

- **Initial value**: 396 (a full line or set of blocks)
- **After 1st subtraction**: 264 remaining (one block/segment removed)
- **After 2nd subtraction**: 132 remaining (another block/segment removed)
- **After 3rd subtraction**: 0 remaining (final block/segment removed)

The number of blocks you removed (which is 3) is your quotient.

Would you like a more detailed explanation or any sketches?

Explore how to illustrate the quotient of 396 divided by 132 using the measurement (subtractive) concept of division. Follow a step-by-step explanation with examples and sketches to understand the process visually. Suitable for students in Grades 4-6.

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