Learning how to solve a math problem in different ways has many benefits.
1. It helps students understand the underlying principles of a math topic.
2. It leads students to think about which approach is the fastest or most efficient way to solve a math problem.
3. It also leads students to understand that math questions can be posed in a variety of ways just like math problems can be solved in a variety of ways.
Let us begin with the third benefit. Some students can solve a math problem when it is presented in one way. When the same idea is presented in a different way, they are completely lost. Not only would this be a nightmare on the day of state assessments, this misunderstanding undermines the entire point of a math lesson.
This chart shows the different ways that multiplication can be presented. Many students just know of multiplication as being represented as "groups". Each example shows multiplication in a different context. It is important for students to understand the different ways that a math topic can be presented. It is also just as important for students to know that a math problem can be solve in a number of ways.
I can remember walking past a student that had not memorized his multiplication facts. He drew tiny circles on the corner of his paper to find the answer to a math problem. This leads to point two on our list. Using multiple approaches to solve a math problem helps students determine which one is the most efficient as well as fastest. There is a place for drawing tiny circles to determine the answer to a problem. Using this method is not the most efficient because it takes so much time. Showing how to solve the same math problem in multiple ways helps the student determine the best approach to solve a math problem.
Use the four box or two box approach. The math problem is written in the center of the page. The larger box can be divided into two or four parts. Each part can show a different way to solve the math problem.
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