## How do we solve a word problem?

**Monica Kochar**

During the teacher training sessions that I conduct, whenever I ask the teachers to tell me an area they struggle with to teach the students, invariably the answer is, “Solving word problems”. Their query is – “Is there a method to this madness that works with most problems?”

So I thought about this, did some research, and found a really simple tool which helps solve almost all linear equations in one variable. I have shared this with teachers and found it quite popular with them. I wish I had known this when I was teaching; it would have saved many hours of struggle!

Here I will discuss two problems, leave one with a hint and then fi nally summarize the method in short steps. I hope you fi nd this useful for your students. This is applicable for classes 7 and 8.

#### Problem 1 – Related to age

Problems related to age is one area where a standard method would help a lot of students. So this is how they can go about solving this problem…!

Raghu’s father is 24 years older than him. After 10 years, the father’s age is double that of Raghu. How old are they now?

**Step 1: Underline the important information**

This is by far the most important step! Which information is important? Usually students should notice how many people are mentioned in the question and how their ages are linked. They should also see if it is a past-present or present-future or any other combination query. The important information relates to the number of people, timeline, and relationships.

**Step 2: Choose the unknown ‘x’**

“Which is the unknown?” This is the question that echoes in the classroom of all good teachers. What do we have to fi nd? What will we take as ‘x’? If there are two unknowns, which would you take as ‘x’? This is another question that makes the students decipher information accurately.

**Step 3: Tool box!**

Now here is help for students to learn to organize information in the form of a grid! Ours will be a 2 x 2 grid for we have 2 people in our question and a present-future combination.

Now write the good old ‘x’ where it belongs in the problem. Let Raghu’s age be ‘x’ so that is where we place our ‘x’.

**Step 4: How to fill the tool box**

Find the value to put into all the other boxes in terms of ‘x’ using the information given. Note that ‘age future’ should be calculated according to the ‘age present’ and not according to the connections given! This is very important. So here we go!

**Step 5: Form the equation**

Which components of the boxes will be used to make the equation? Choose them based on the information in the problem!

**Step 6: Find ‘x’ and then the answer!**

The value of x is 14. Is that the fi nal answer…No!

**Answer:** Raghu’s age is 14 years. Father’s age is 14+24 = 38 years

Let’s take another problem:

#### Problem 2 – Related to speed, distance, and time

Two planes, which are 2000 miles apart, fl y toward each other. Their speeds differ by 60 miles per hour.

They pass each other after 5 hours. Find their speeds.

**Mark the key info**

__Two planes__, which are__2000 miles apart__, fly__toward each other__. Their__speeds differ by 60__miles per hour. They pass each other after__. Find their speeds.__**Choose ‘x’**

Two planes, which are 2000 miles apart, fl y toward each other. Their speeds differ by 60 miles per hour. They pass each other after 5 hours.__Find their speeds__.**The tool box**

This will be a 3×2 grid for we have speed, distance, time on one hand and 2 planes on the other. So the tool box will look like this:

**Fill the toolbox**

Since we have to find the speeds of the planes, let ‘x’ be the speed of one of the planes.

Fill in the remaining information using ‘x’ and what is given in the problem. This is what we get:

**Form the equation**

The relationship between distances gives the equation.

**Find ‘x’ and then the answer**

Value of x is 170.

** Answer:** Hence the speed of the slower plane is 170 km/hour and the speed of the faster plane is 170+60 = 230 km/hour

#### Try yourself

Why don’t you try one? Here is a problem and an empty box for you to fill!

Rs. 14,000 has been divided and put into two accounts. One account pays 3% interest, while the other pays 4% interest. At the end of one interest period, the total interest earned was Rs. 500. How much was invested in each account?

This will be a 3×2 grid as shown below:

The answer is Rs. 6000 and Rs. 8000.

**Finally – The 5 steps for solving a linear equation are:**

- Mark the key info
- Choose ‘x’
- Draw the toolbox and input ’x’
- Fill up the tool box
- Form the equation
- Find ‘x’ and then the answer

Try problems from your textbook and… enjoy!

The author has been a teacher for 19 years and is on a sabbatical from ‘schooling’. She is now a freelance math curriculum developer and is experimenting with strategies to make math accessible to all. She can be reached at reachmonica@gmail.com and has a blog titled http://humanemaths.blogspot.in.

Math is almost always looked at in isolation and in an abstract way by all and generally evokes negative feelings in many children. This new column proposes to change all that and get teachers to help their students love math and also see it in connection with other areas of knowledge. Less procedural and more creative and conceptual thinking will lead to a more focused ‘happy math class’ is what we hope.

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