# Teaching how to read and translate word problems

High school students have a lot of trouble understanding word problems, and I don't know how to help them.

It's been too long since I've had trouble understanding usual word problems, so when I read the problem I automatically know what to do and how to do it. This, however, makes for terrible pedagogy.

What are good strategies to help them develop skill at solving these exercises?

• What type of word problems are there? i.e., what class is it? Do you think this question (about high school students) is distinct enough from MESE 5885 (about sixth graders) to warrant separate posts? Or do we just need a detailed answer about classifying and teaching word problems? (See my comment at the linked question for some places to start...) – Benjamin Dickman Dec 4 '14 at 6:55
• @BenjaminDickman The variety of problems they can tackle is much bigger. They can deal with geometry word problems, algebra, functions. It's not simple arithmetic word problems. Furthermore, they are held to higher standards: They are expected to write solutions rather than merely equations. Also, it's not just first year high school students (but they certainly need more help). – Mark Fantini Dec 4 '14 at 7:15
• If there is such a variety, then maybe you can include some specific ones to guide responses? Geometry, algebra, functions, across all four years of high school... this yields a fairly broad range. – Benjamin Dickman Dec 4 '14 at 8:00
• High school lasts three years here. They have most difficulty with algebra, I'll focus on that. – Mark Fantini Dec 4 '14 at 8:35

I feel your angst, word problems are a consistent weakness across most grade/subject levels. Learning to decode and solve word problems is a learned skill and so it needs to be practiced. However, just giving students 50 word problems and telling them to solve them for homework wont help anyone. I'd suggest to focus on each of the following items individually, guiding students at first and then slowly letting them try on their own. Once they begin to pick them up, you can start having them combine the different techniques, again with guidance at first and gradual release.

• decoding "buzz words" (sum, difference, product, each, etc.)
• underline/highlight important words/numbers
• crossing out extraneous information
• draw a picture! (one of the most helpful skills in life)
• translating sentences into equations/expressions
• underline/highlight what the final question of the word problem is
• reading word problems (it sounds trivial, but many of my students have trouble even finishing reading certain word problems)
• make a plan (outline steps of what you need to do, sentence by sentence)
• make a table (for certain problems, this can really help visualize what is going on)
• smart solving (if you just spent the previous week calculating slope, there is a good chance the word problem today will have something to do with slope)
• working backwards (asking yourself "What do I know? What do I need to know? How can I know it?", one of the most difficult practices for students to develop)

Another area I would focus on, which is not necessarily used in the process of solving a WP, is the aspect of explaining an answer. If a student can explain their answer with words it proves a certain level of understanding. One idea is to give them a word problem, let them read through it, then present them with the work of someone else and see if they can explain what this other person did to solve the problem. In a similar vein, you can give them a worked through solution and have THEM write the word problem. This gives them a chance to be creative and also practice working backwards. I hope this helps!

The answer provided by celeriko seems like it hits all of the main points. However, I have found in my experience teaching word problems with students that a few additional strategies are most effective for struggling students.

1. Rewriting the important mathematical "givens" in a problem. By having students rewrite these ideas, they're taking possession of these parts of the problem, and begin dissecting the problem from a "word problem" to a "regular problem". It is also helpful for them to have these pieces easily accessible and to not have to dig back into the paragraph of the word problem to use them. Writing things down is also helpful for students who are struggling because it gives them something to do. A common complaint I have heard from students is not knowing how to get started. This gives them something to start doing.
2. Decoding "buzz words" as celeriko mentions is key. There are other less common buzz words that I think are even more helpful than the ones listed in this other answer. Some of these other are:

• IS: This is usually translated into the mathematical symbol $=$ but is also used very often in common English grammar, so it is often glossed over.
• OF: Similar to IS, it needs to be emphasized in mathematics as multiplication.
• PER: Division, or fractions, with the word or words prior belonging to the numerator and the word(s) after belonging to the denominator.
• PERCENT: I discuss this with PER and break down the word into its two roots. PER meaning division, and CENT standing for 100. There are plenty of examples you can use to connect CENT to 100, such as cent or century.
• THAN: This is an interesting one since it doesn't actually stand for any operation, but when paired with LESS, like "$5$ less than $9$" actually commutes the order of the elements when translating the word problem into a mathematical expression.
3. Creating a dialog and discussing problems with students in class is also important. This promotes a common method that many mathematicians use to solve their own problem, which is creating a dialog with themselves (I believe Polya mentioned this, but I could be wrong). In having these discussions, hopefully your students can glean from you some of your thought processes, and you may also discover how you actually think about these problems to enable you to break them down for your students.

• great suggestion for the buzzwords, very often these give my students problems ! – celeriko Dec 6 '14 at 3:10
• Excellent answers already but just to add a behaviour that you can model. Have the students choose a typical problem and solve it on the board and give as much of your internal dialogue as you can: make the strategy that you are following explicit. – Timonides Dec 8 '14 at 8:38

Have you tried doing the reverse. Show them the solution and ask them to form a word problem (based on the solution). It would show you how students parse (break down) word problems in their minds.

Start easy for example: x + 2 = 8 form a word problem using slices of pizza. The way the children form sentences will show you the words they use to define a problem.

It would also allow you to reword some problems using words that the children use, since it looks more of a language problem than a math problem.

Don't be strict in the child's sentence construction, the point is you want an insight into their minds of how they form, break down, and express math word problems in their heads. You will probably see word problems looking like conversations instead of properly structured math word problems.

Once you have a common ground you can later show them what a properly structured word problem looks like - with emphasis on buzzwords as suggested by Andrew Sanfratello - allowing you to compare buzzwords to the words your students use.