One of the more difficult things we expect students to learn is how to solve word problems — and many adults find them challenging as well. Yet problem solving is an essential mathematical skill because this is typically where students encounter the application of mathematics to situations and “real-world” problems.
Sometimes school word problems can feel artificial or forced. Part of the reason is that we have to limit the complexity and “realness” of a situation so that the mathematics remains within what students currently know and understand. The problem needs to be manageable enough for students to practise the particular mathematical ideas they are learning.
There are a couple of strategies I suggest to help students become more successful problem solvers.
A key part of solving a word problem is translating the words into mathematics.
That means students should be able to mark up the actual problem they are working on: circle what they are being asked to find, cross out unnecessary information, underline important quantities, label units and unknowns, write mathematical symbols, draw arrows, sketch diagrams, and write partial expressions or equations directly beside the words they are translating.
It is not realistic to expect students to hold all of that information in their heads while also trying to generate mathematical expressions or equations and solve them.
In real-world problem solving, we routinely make annotations, notes, sketches, and calculations directly on the documents and information we are working with. Encourage students to let the problem sheet become a working document. Doing so reduces how much they need to juggle mentally and allows them to focus on one piece of the problem at a time.
Whenever practical, provide students with word problems on a sheet they are allowed — and encouraged — to write on.
One activity I strongly encourage secondary teachers to try is having students collectively develop a Math ↔ English Translator.
There is an important warning: English phrases do not always translate into mathematics in a simple one-to-one way. A word or phrase may suggest a possible operation or mathematical relationship, but students still need to consider the context and the quantities involved.
For example, “more than” often suggests addition, but students must still determine which quantity is being added to which when they write the actual expression or equation. There are checks students can use to determine whether their translation makes sense.
A way I used to do this was to have students take out a sheet of notebook paper, turn it landscape, and fold it twice to create four equal vertical columns. Each column was headed with one of the four operations: +, −, ×, ÷.
If you prefer, you can use the premade Math–English Translation Page available here — or simply look at it as an example and have students make and “own” their own.
The important part is that the page should not be considered finished after the activity.
Have students keep it as a running, growing, working reference and add to it whenever new mathematical language appears in class or in word problems. Consider allowing students to use it on quizzes and tests, or create a classroom wall of mathematical expressions and language that everyone can refer to.
The goal is not to memorize a list of keywords.
The goal is to become better at asking:
What am I being asked to find?
What quantities and are involved?
How are those quantities related (what relationships or operations)?
Then students can begin translating the language into mathematics.
Examples coming soon
Let’s Count On Math™
Find the Counting. Find the Meaning.
