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

Number Word Problems 1 – How to Solve Number Problems Mentally

This is the first part of the Solving Number Problems Series for Grade 6-8 students, a-sub series of the Math Word Problem Solving Series.

Some of you probably need paper and pencil to solve number problems. You will be surprised that if you think harder and work backward, you can actually solve these problems in your head. Consider the following examples.

Example 1

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

Explanation and Solution

First, one number is 1 more than the other. That means that if we subtract 1 from the larger number the two numbers will be equal. That’s our first clue.

Second, if we subtract 1 from the larger number, then we should also subtract 1 from the sum (Can you see why?). That makes the sum 46. Now, since the two numbers are equal, we can divide 46 by 2. That gives us 23 which is the smaller number. Now, since the other number is 1 larger than 23, then it is 24.

Answers: 23 and 24 » Read more

Proof that Out of 6 Persons Either 3 are Friends or 3 are Strangers

Did you know that out of 6 people, either 3 are friends or 3 are strangers? Three are friends in the question means mutual friends: A and B are friends, B and C are friends, and A and C are friends.  Three are strangers also mean that out of three persons, none of whom know each other.

In the mathematical proof below, we represent the individuals by vertices and the relationships by edges. As we can see, we can form triangles. In the triangles below, a green edge connecting two vertices means that the persons represented by two vertices are friends and a red edge connecting two vertices means that the persons represented by two vertices are strangers. A triangle formed by edges of the same color represents three mutual friends or three mutual strangers. We highlight this relationship by filling the interior of the triangle with the appropriate color. » Read more

1 2 3 4 5 9