Solving Math Word Problems in Numbers Using Algebra

This is the third part of the Solving Math Word Problem Solving Series on Numbers for Grade 6 – 8 students. The first part was on solving number problems mentally by working backward. The second part discussed on solving number problems using the model method. In this post, we are going to discuss how to solve word problems using Algebra if the mental and model methods fail. We will start with simple problems and will continue to solve more complicated problems later. We will use the problems we discussed in the first two parts of this series. Note that the discussion in this post is quite detailed because it is designed for beginners particularly middle school and high school students.

Example 1 One number is 1 more than the other. Their sum is 47. What are the numbers?

Solution

First Sentence: One number is 1 more than the other.

If there are two numbers and the other one is 1 bigger than the number, then if the smaller number is 5, the other is 5 + 1 or 6. So, since we don’t know what the number is, we let the number n. This means that the larger number is n + 1» Read more

Create e-textbooks with Dbook’s New Version

Two years ago, I have mentioned a promising software called Dbook, a mathematics software developed by the Center for Research for International Cooperation in Education Develoment (CRICED) of the University of Tsukuba in Japan. Dbook lets you create interactive electronic textbooks from scanned images or those which were created in word processors and desktop publishing software. Recently, Dbook’s new version was finished, although I am not sure if the software had been released online.  However, to know the capabilities of Dbook, here are some tutorials on Youtube by Prof. Masami Isoda of CRICED.

For more information about the Dbook (older version), you may want to visit the official website.

Solving Number Problems Using Model Method

This is the second part of the Word Problem Solving Series on Numbers. In the previous post, I have shown you ways on how to solve number problems mentally by working backward. In this post, I am going to teach you how to use models, rectangles in particular, to solve the problems in the previous post. This representation is called the model method. The model method is very popular in Singapore.

Example  1

One number is 1 more than the other. Their sum is 47. What are the numbers? Solution

Let us represent numbers using rectangles. The first rectangle is the smaller number, and the second rectangle is the larger which is 1 more than the smaller. Clearly, if take away 1 from the larger number, the two numbers will be equal.

model method number problem

In addition, if we take away 1 from the larger number, then, we also have to take away 1 from the sum which gives us 46 after subtraction. Since the two rectangles have the same size, they will have to split 46 equally. This gives each large rectangle 23 each. This means that the smaller number is 23 and the larger number is 23 + 1 = 24. » Read more

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