A division model, often using an area model, visually represents the process of division by breaking down the dividend into smaller, manageable parts. This method helps in understanding the relationship between the dividend, divisor, and quotient. Here's how to approach it:
Understanding the Area Model
The area model represents division by depicting the dividend as the total area of a rectangle. The divisor corresponds to one side of the rectangle, and the quotient is the length of the other side.
Steps for Using an Area Model
-
Draw a Rectangle: Begin by drawing a rectangle. This rectangle will represent the dividend you are dividing.
-
Place the Divisor: On one side of the rectangle, write the divisor. This represents the known length of one side.
-
Estimate Partial Quotients: Start dividing the dividend by the divisor by using estimates. Ask yourself, "How many times does the divisor go into the dividend?" You’re aiming to find partial quotients that, when multiplied by the divisor, won't exceed the dividend.
-
Divide and Subtract:
- Multiply the divisor by your partial quotient and put this product below the dividend.
- Subtract that product from the dividend. The remainder will be the new part to divide.
- Write the partial quotient above the rectangle on its corresponding side.
-
Continue the Process: If you still have a remainder, create a smaller section within your rectangle. The remainder now becomes a new dividend. Repeat steps 3 and 4.
-
Add Partial Quotients: Once you have completely divided, you will have a set of partial quotients. Add these partial quotients together to find the final quotient.
Example using Reference Information
Let's look at the example from the video, using a simple division like 25 ÷ 5:
- Set up: Draw a rectangle, and place '5' (the divisor) on the left side.
- First Partial Quotient: The video suggests dividing 20 by 5, which equals 4.
- Write '4' above the rectangle on the corresponding side.
- Multiply the partial quotient (4) by the divisor (5), which gives 20. Subtract 20 from 25, leaving a remainder of 5.
- Second Partial Quotient: Next, divide the remaining 5 by 5, which equals 1.
- Write '1' beside the 4 above the rectangle.
- Multiply the partial quotient (1) by the divisor (5), which equals 5. Subtract 5 from 5, leaving 0.
- Final Quotient: Add the partial quotients (4 + 1), which equals 5. Thus, 25 ÷ 5 = 5.
| Step | Calculation | Area Model Representation |
|---|---|---|
| 1. Set up the division problem | 25 ÷ 5 | Rectangle with divisor 5 on the side |
| 2. First Partial Quotient | 20 ÷ 5 = 4 | A partial area of 5x4 is removed. |
| 3. First Remainder | 25 - 20 = 5 | Remainder of 5 left to divide |
| 4. Second Partial Quotient | 5 ÷ 5 = 1 | Remaining area is 5x1. |
| 5. Final Quotient | 4 + 1 = 5 | Add the partial quotients. |
Practical Insights
- The area model method is especially helpful with larger numbers.
- It breaks down complex divisions into smaller, more manageable steps.
- This visual method aids in understanding the concept of division, making it easier for learners to grasp.
- It reinforces the relationship between division and multiplication.
By following these steps, you can use the division model effectively to solve division problems and gain a clearer understanding of the process.
