Model Magic: Visualizing Division with Two-digit Divisors
Using models to understand division with two-digit divisors offers a visual approach to a concept that can sometimes seem abstract. Models, such as base-ten blocks, number lines, or area models, can provide a tangible representation of the division process. Let's explore how to use models to divide by two-digit numbers.
Dividing Using Two-digit Numbers with Models
Base-Ten Blocks Model
Example 1:
Divide \(84\) by \(12\).
Solution Process:
Imagine you have \(84\) base-ten blocks. Group these blocks into sets of \(12\). Count how many groups you can form.
Answer:
You can form \(7\) groups. So, \(84 \div 12 = 7\).
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Area Model
Example 2:
Divide \(96\) by \(16\).
Solution Process:
Draw a rectangle to represent \(96\). Divide this rectangle into columns, each representing \(16\). Count how many columns you can form.
Answer:
You can form \(6\) columns. So, \(96 \div 16 = 6\).
Models provide a hands-on and visual approach to understanding division with two-digit divisors. They break down the process into manageable chunks and offer a clear representation of how numbers are divided. Whether you’re using base-ten blocks, area models, or any other visual tool, the key is to group, count, and understand the division process step by step. With practice, these models can become invaluable tools in your mathematical toolkit, helping you visualize and solve division problems with ease!
Practice Questions:
1. Using a model of your choice, divide \(72\) by \(12\).
2. Divide \(110\) by \(22\) using an area model.
3. Using base-ten blocks, divide \(140\) by \(14\).
4. Divide \(180\) by \(20\) using a number line model.
5. Using an area model, divide \(88\) by \(11\).
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Answers:
1. \(6\)
2. \(5\)
3. \(10\)
4. \(9\)
5. \(8\)
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