Constructing Word Problems

One of the best ways to learn solving of word problems is to try and construct simple word problems. Writing a Math Word Problem is similar to a recipe and can be described as below. This summarises all the ideas that we have touched upon in the previous chapters.

Arithmetic Operation

The first step is to decide the kind of Arithmetic operation, algorithms & computations that we want children to practice and learn. For example, we may decide on Subtraction.

At the higher grade levels, students can be given word problems which have a combination of arithmetic operations.

A typical problem could be the cost of purchasing items with a given price and also calculating the balance that the shopkeeper would have to return, when we pay a certain amount of money. This would be a combination of multiplication & subtraction.

Number System, Algorithm &amp; Computation levels

Next, we have to decide the type of number system to use along with the algorithms and computations that they should be learning. For example, we may decide that the problem should have mixed fractions and the procedure may be of converting both mixed fractions into improper fractions and then converting the answer back to mixed fractions. We may also want students to use LCM in the subtraction process. Hence the fractions have to be &lsquo;unlike&rsquo;.

Operation Metaphor

Third is to choose an appropriate arithmetic metaphor. In the above case we may choose &ldquo;Separate&rdquo; metaphor.

Life Situation & Context

Once the metaphor and the operation are chosen, we need to look for an appropriate life situation. The life situation should be a familiar one for the student, so that he can visualise the operation. In this case since fractions have to be involved, we could use the life situation of sharing an item purchased in fractional quantities into 2 unequal quantities.

While selecting life situations, we need to be careful to ensure that they do not reinforce traditional gender biases. Encourage word problems which also deal with the lives of girls in village areas involving cooking, cleaning etc. so as to remove a perception that math problems are only about areas which are mostly dominated by boys.

For the above problem we could think of purchasing a certain quantity of sugar and sharing a part of it with another person. The problem could also ask for the remaining quantity of sugar. Choosing the above automatically decides that weight units need to be used. The obvious unit is Kg.

Also since we are dealing with purchase of sugar, the whole number part of the mixed fraction may only be a single digit number.

Language/ Math Vocabulary

Then we have to write the word problem using simple daily used language so that students would not have any difficulty in understanding it.

Along with daily language, we also need to use specific and appropriate math vocabulary. The words which can be used for the remaining quantity of sugar are left, rest, balance etc. In the case of the above problem, we may use the term left. An example could be as given below.

"Ram's mother purchases 4 ⅔ kgs of sugar from a shop for their family as well as her sister's family. That was the balance amount of sugar available in the shop on that day. Her sister wants 2 ⅘ kgs out of it. How much sugar will be left for Ram's family?"

The various aspects covered in the problem can be summarised as below.

Students need to be told that a real-life situation would use whole numbers instead of fractions. But we are modifying the situation so that we can practice fraction operations.

All the different elements can be mixed and matched appropriately to create interesting math stories which will also test various competencies that the students need to learn.

Chapter 15.6 gives the various components of a math story in a graphic form.