Word Problem Solving

Tricks for Solving Word Problems

The math worksheets on this section of the site deal with simple word problems appropriate for primary grades. The simple addition word problems can be introduced very early, in first or second grade depending on student aptitude. Follow those worksheets up with the subtraction word problems once subtraction concept are covered, and then proceed with multiplication and division word problems in the same fashion.

Word problems are often a source of anxiety for students because we tend to introduce math operations in the abstract. Students struggle to apply even elementary operations to word problems unless they have been taught consistently to think about math operations in their day to day routines. Talking with kids regularly about ‘how many more do you need’ or ‘how many do you have left over’ or other seemingly simple questions when asked regularly can build that basic number sense that helps enormously when word problems and applied math start to show up.

There are many tricks for solving word problems that can bridge the gap, and they can be helpful tools if students are either struggling with where to start with a problem or just need a way to check their thinking on a particular problem.

Make sure your student reads the entire problem first. It is very easy to start reading a word problem and think after the first sentence or two that ‘I know what they’re asking for…’ and then have the problem take an entirely different turn. Overcoming this early solution bias can be difficult, and it is much better to develop the habit of making a complete pass over the problem before deciding on a path to the solution.

There are particular words that seem to show up in word problems for different operations that can tip you off to what might be the correct operation to apply. These key words aren’t a sure-fire way to know what to do with a problem, but they can be a useful starting point.

For example, phrases like ‘combined,’ ‘total,’ ‘together’ or ‘sum’ are very often signals that the problem is going to involve addition.

Subtraction word problems very often use words such as ‘difference,’ ‘less,’ or ‘decrease’ in their wording. Word problems for younger kids will also use verbs like ‘gave’ or ‘shared’ as a stand-in for subtraction.

The key phrases to watch out for multiplication word problems include obvious ones like ‘times’ and ‘product,’ but also be on the look out for ‘for each’ and ‘every.’

Learning when to apply division in a word problem can be tricky, especially for younger kids who haven’t fully developed a concept of what division can be used for… But that’s exactly why division word problems can be so useful! If you see words like ‘per’ or ‘among’ in the word problem text, your division radar should be sounding off loud and clear. Pay attention to ‘shared among’ and make sure students don’t confuse this phrasing with a subtraction word problem. That’s a clear example of when paying attention to the language is very important.

Draw a Picture!

One key bit of advice, especially for basic word problems, is to encourage students to draw a picture. Most early grade school word problems are basic counting exercises, where you’re dealing with quantities or sets that are fairly small. If students can draw a picture of the problem (even using simple representations like squares or circles for the units discussed in the problem), then it can help them visualize exactly what’s occurring.

Another useful visualization strategy is to use manipulatives. Paper clips, checkers or other handy objects can stand in place of the problem’s subject, and this provides an opportunity to work up other simple examples with different numbers.