Numberless Word Problems

Purpose of Word Problems

Word problems are the first step towards building the skill of problem-solving & modelling real-life situations with math. This involved training in conceptual thinking.

One of the best ways for this in the classroom is "discussions" and "role modelling" real life situations to identify the math embedded in them.

But we saw in the chapter on "Teaching Word Problems" that, possibly due to inadequate teaching, that students forget the real-life connection of the word problem and focus only on the numbers in the word problems.

1. There is not much discussion of the problem. The focus is on using the numbers in the problem and getting an answer.

2. Many a time students do not even bother if the numerical answer makes any sense.

3. Because of this focus on numbers, they miss out that the problem they are doing today is similar to the one they did the previous day. Each problem is different since the numbers are different!

4. Many also have this notion that "all" the numbers in a word problem need to be used!

Numberless Word Problems

A numberless problem is the same word problem with all numbers removed. It is an effort to shift the focus of word problems to discussions rather than mere computations.

The real challenge for teachers is to raise relevant questions with students & facilitate the student discussion. The discussions should bring out all the important aspects about the problem, the real life situation, the math metaphor, the arithmetic operation, the numbers involved and the computational skills involved.

Using a Numberless Problem

Let us take the following problem. "Ram bought 5 kg of rice from the shop. On the way the handle of the bag broke and 1 kg of rice fell on the road. How much of rice ultimately Ram brought home?"

Let us rewrite the above problem as a numberless problem. " Ram bought some rice from the shop in a bag. On the way the handle of the bag broke and some rice fell on the road. Ram brought the remaining rice home."

What can be the questions that can be discussed?

1. Can you visualise completely what happened?

   1. What could be the reasons for such an event to happen?

   2. What kind of a shop do you think Ram bought the rice from?

2. What do you think is the unit of measurement which would be used?

3. What are the magnitudes of the numbers likely to be used in this problem?

4. What do you think we need to find out in this problem?

5. What "life situation" or "math metaphor" the problem illustrate?

6. What operation would you use to solve the problem?

Since the approach is radically different from a traditional word problems and focuses on facilitating student discussions, it would take time, effort & introspection.