Unravelling word problems

Swarna Krishnan

When I was seven years old, I was afraid of mathematics, especially the word problems. I used to worry about the steps the teacher expected us to write for the word problems more than the algorithm or answer. I was instructed to look for key words to identify the basic operations like ‘total for addition’, ‘remaining/left for subtraction’, etc. So, even when I was given problems like “Ram had 342 pencils and Shyam bought 171 sharpeners. How many pencils are there totally?” I ended up adding both numbers as I was conditioned to add numbers if the word ‘total’ was present in the problem.

Now as a teacher myself, when I see a word problem like this, I realize that I never utilized most of my skills, especially my reading and comprehension skills. I also now see that most students are so stressed about the steps to be written and the operation to be used that they fail to realize that simply reading and understanding the problem will help them actually solve it. Perhaps one reason that students fail to realize this is the nature of the word problems we give them. The word problems are either not related to life or are extremely bizzare like the one I mentioned above. Why will anyone have 342 pencils or buy 171 sharpners?

I didn’t want my students to experience any confusion while dealing with word problems. I also wanted to build their comprehension skills while doing word problems. So, when I began to teach primary math, I decided to use real life situations my students could relate to. Here is an example. When I was teaching them addition word problems, I introduced them to the ABC Family Restaurant, where they could order lunch for that day. I prepared a menu with the list of items available and their price and displayed it in my online class.

ABC -Family Restaurant

Idly – Rs 20

Tea – Rs 15

Coffee – Rs 10

Plain Dosa – Rs 35

Onion Dosa – Rs 40

Vangi Bath – Rs 55

Chicken Manchurian – Rs 80

Mutton – Rs 45

Lassi – Rs 25

Vanilla Ice cream – Rs 60

Lemon Juice – Rs 25

Chilly Chicken – Rs 90

I then gave them the problem –
You are going to ABC Restaurant. You have Rs 500 in your purse. You can order any item, any number of times.
• Calculate the amount to be paid.Predict whether you will be able to pay for the food.

Here are some of the answers given by my students.

  • “Akka, I want 3 idlis and 1 coffee. I have to pay 70 rupees. I have money to pay.”
  • “Akka I want to order 29coffeesfor my friends. It will cost me Rs. 290and so I can pay.”
  • “Akka I want 2 idlis, 1 vangi bath for me, 2 onion dosas for my sister,2 muttons and 1 chicken manchurian for my parents. We also want 2 lassis. Akka, mutton is cheaper here, that’s why I ordered 2 for my mother and father. I have to pay Rs 395. I have the money to pay. ”

I was really happy with most of the answers, butI wanted to test them further. So I gave a challenging order, “I have Rs 500 in my purse. I want 3 vangi baths, 3 vanilla icecreams, 2 lemon juices, 4 chilly chickens.” I asked them to calculate the amount and predict whether I would be able to pay for this order.
“Akka you have to pay Rs 755.You can’t pay.”

Then I told them, “I have only Rs 500 and I want to eat something from my order. What all can I get from my order with the money I have?”

They came up with many solutions like ordering 1 chilly chicken instead of 4 without changing the rest of the order or ordering 2 vangi baths,2 vanilla ice creams,1 lemon juice,2 chilly chickens.These solutions were very interesting and exciting.

At the same time, I was also bombarded with questions like
• Why was the extra amount not charged (GST)?
• Why were the chutneys and sambars not assigned any price?
• Why was the chicken costlier than mutton?

I answered a few of their questions and countered them with some of my own“Are we right in adding two or more food items?”

While most of them agreed to it, some of them gave hilarious reasons which made me laugh out loud.
a) “All are eatables.”
b) “They belong to the same restaurant.”
c) “All are tasty.”

Finally one student said, “Akka we are not adding different items, we are adding the price of different items. So we are correct.”

I was brimming with joy, not just at the last answer, but for all the answers my students had given. I felt happy that they had understood the basic idea behind addition, which is nothing but counting of similar items. I could also see that they could relate ordering food in the restaurant with addition.

My lesson was a shift from normal pedagogy and I was able to assess my students skills like observations, problem solving and reasoning, mental math, decision-making, logical thinking, imaginative, etc. It was an interactive class where most students wholeheartedly participated and entertained the class with their orders and answers, even the shy and quiet ones. In this class, I didn’t stress on writing the statements for the word problems. My objective was to test and track their conceptual understanding of addition and their application in real life situations. I can proudly say that I successfully triggered all the right responses. I also made sure that my students weren’t doing calculations based on key words in the word problems. This also paved the way for future lessons on addition with larger numbers, multiplication, fractions, percentage, subtraction, etc.

As I was ending my class, one boy asked, “Akka give me the menu for one more restaurant, I will place my order.”

While he didn’t get anything he ordered, his request made me grin, as the word problems were no longer problems of words but solutions for real life situations.

The author is an enthusiastic teacher and content developer, who believes in the continuous process of new and practical ways of teaching. She can be reached at [email protected].

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