3 From words to algebra to words
One of the difficult ideas in word problems is about translating the words into algebra and algebra into words. There are two parts to the next activity. The first part gives your students the opportunity to practise matching words and algebraic expressions and vice versa in an enjoyable way. The second part asks the students to make their own word problems from some algebraic equations.
Activity 2: Words and algebra
Part A: Flash cards
Make flash cards in two different colours (or with different shading, as in Figure 3). Leave one side of the flash card plain so that the students can write on that side. On the green cards, write an arithmetic statement in English (or the language of instruction followed in your school). On the orange cards, write the corresponding statement using mathematical symbols and operations. Make the cards relevant to the kinds of work that your students are engaged with. This could be trigonometry, circles or any other aspect of mathematics – see the examples in Figure 3.
|5 more than x||5 less than x||x less than 5||5 times x|
|x + 5||x – 5||5 – x||5x|
|Quotient of 5 and x||Quotient of x and 5||5 by x||x by 5|
|Sum of 5 and x||Difference between 5 and x||Product of 5 and x||5 raised to x|
|5 + x||½5 – x½||5x||5x|
|x raised to 5||5 squared||5 more than 5 times x||Ratio of 5 and 5 more than x|
|x5||52||5x + 5||5/(x + 5)|
FootnotesFigure 3 Words and algebra flashcards.
If you have 30 students in your class, you will need 15 pairs of cards.
Randomly distribute the cards to the students. Tell your students to find the student who has the card that completes your pair.
Part B: Writing own word problems
Modify the following equations to make them relevant to your class and write them on the blackboard:
- y = 3x
- x + y = 150
- 3x – y = 22
- 2x + 3y = 88
- A = 16p
- 32 = x(y + 2)
Tell your students the following:
- For each equation, write as many context-based word problems as you can. For example, for the equation y = 3x you could write ‘Kavita’s feet are three times as long as her baby brother’s’.
- Which equations did your students find writing word problems for the most difficult? Why do you think this was?
- For each equation, which one of your word problems was most realistic? Why? Can you try to make the other word problems more realistic?
At the end of the activity, ask your students to select the most interesting word problems for each equation and display them on the classroom wall.
You may also want to have a look at the key resource ‘’.
Case Study 2: Mrs Chakrakodi reflects on using Activity 2
My students had enjoyed using Activity 1 and their confidence was growing, but they still had difficulties writing down the algebra for ideas such as ‘She still had Rs. 150’ in the problem that we did together. Therefore, I decided to use the cards from Activity 2 and made up some more.
There were 64 students in my class, so I formed 32 pairs so that everyone had a partner. I took the students outside to the playground so they would have space to find each other. There was a lot of noise while they moved about trying to find their pair, but it was over quickly. Once they had all paired up, I got them to sit down and work together on two context-based word problems equivalent to the algebra on their cards, which they wrote on the back of their cards. Each pair then joined another pair and gave one another their context-based word problems to write the mathematical phrase in their mother tongue and then to write the algebra. When the students disagreed about anything, we discussed the ideas as a class and then I asked for some ‘really good’ word problems to share with the class.
Everyone seemed to get a lot out of using this idea. They had people to ask if they were not sure and they all heard and worked with lots of examples connecting algebra with words and with contexts.
For Part B, I asked the students to continue to work in the groups of four that they had formed earlier and to write at least four problems for each equation. When each group had come up with something for at least four equations, I stopped their working. At this point some of the groups had finished all the problems and I realised perhaps I should have had some more problems for the more mathematically confident students.
Then I used the follow-up questions in a class discussion. Asking ‘Which was most difficult and why?’ meant that the students had to think about their thinking – that is called ‘metacognition’, I think. Asking them to take this overview also meant I became more aware of what they found difficult and therefore where more practice would be needed; for this class it was using brackets. The question about whether they were realistic or not was also useful, I felt. They had to think about what they could model with this level of mathematics and saw why word problems can be unrealistic at times.
Pause for thought