Draw an Area Model then Solve using the Standard Algorithm

Area models are a useful way to solve a variety of mathematical problems, from basic addition and subtraction to more complex problems involving fractions and decimals. The area model consists of a rectangle divided into smaller rectangles, each of which represents a number. This visual representation helps students to better understand the problem and make the necessary calculations. With a few simple steps, students can use the area model to solve problems and understand the concepts behind them.

How to Draw an Area Model

Drawing an area model is simple. First, draw a rectangle with the two numbers you are trying to add or subtract. Then, draw a vertical line down the right side of the rectangle and label the two sections. For example, if you are adding 15 and 12, the left side of the rectangle should be labeled “15” and the right side should be labeled “12”. Next, divide each side into smaller rectangles, each representing a single digit. For example, each side of the rectangle would be further divided into one rectangle for the “tens” place, one for the “ones” place, and so on. Finally, label the small rectangles accordingly.

Solve using the Standard Algorithm

Once the area model is drawn, you can use the standard algorithm to solve the problem. First, add the numbers in the ones place. In the example of 15 + 12, the ones place would be 5 + 2 = 7. Then, add the numbers in the tens place. In the example of 15 plus 12, the tens place would be 1 + 1 = 2. Finally, add the two numbers together to get the answer. So, 15 + 12 = 27.

Using Area Models to Solve Other Problems

Area models can also be used to solve other problems, such as multiplying and dividing fractions. To multiply fractions, draw a rectangle with the two fractions side by side. Label the rectangles with the numerator and denominator of each fraction. Then, divide the rectangles into smaller rectangles, representing the individual digits of the numerator and denominator. To solve the problem, multiply the numerators and denominators separately, then add them together. To divide fractions, draw a rectangle with the numerator of the first fraction at the top and the denominator of the second fraction at the bottom. Then, divide the rectangles into smaller rectangles, representing the individual digits of the numerator and denominator. To solve the problem, divide the numerator of the first fraction by the denominator of the second fraction.

Using the Area Model to Check Your Work

The area model can also be used to check your work. Once the problem has been solved, draw a new rectangle and divide it into smaller rectangles that represent the answer. Make sure that each rectangle is labeled correctly and that the number of rectangles matches the number of digits in the answer. For example, if the answer is 27, the rectangle should be divided into two rectangles labeled “2” and “7”. If the answer is correct, the numbers in the rectangles should match the numbers in the original problem.

The area model is a useful tool for solving a variety of mathematical problems. It can be used to add, subtract, multiply, and divide fractions and decimals. With a few simple steps, students can draw an area model, use the standard algorithm to solve the problem, and use the area model to check their work. With practice and patience, students can quickly become proficient in using area models to solve a variety of mathematical problems.