Strategies for Solving Word Problems

We are very experienced at helping students learn the steps to solve math problems and to gain practice and confidence in solving math problems, in both English and French! Be sure to book a tutoring session if you have a student who struggles with math problems in English or French.

Many students struggle with word problems, but here are some tips to help:

The First Step - Read the Problem

The first step when solving a word problem in math is to read the word problem. At this point, students should not even think about how they will solve the word problem, and they should just read the math word problem as though it were a story. They should make sure that they know what all of the words in the word problem mean and, if they do not, they should use a dictionary or the internet to find the word’s meaning, or if they are stuck they can ask an older sibling, a parent, a teacher, or someone else they trust to help them. We repeat, at this point, they should not even think about it having anything to do with math, they should just read it like they would read a story, and make sure that they understand all of the words in the word problem.

The Second Step - Understand the Problem in a Mathematical Sense

The second step when solving a word problem in math is to understand the word problem in a mathematical sense. They should determine what information they have, whether any of it is extra information they do not need, and figure out what the word problem asks them to find. Sometimes, it is helpful for students to make a list of information they are given, cross out any information they are given that is extra information they do not need, and make a list of information they need to find.

The Third Step - Make a Plan to Solve the Word Problem

By the time students reach the third step, they should know (from completing Step 2) what information they have and what they need to find. In the third step, they make a plan of how they will solve the word problem. Sometimes, for fairly simple word problems, the plan can be as simple as performing a mathematical operation (such as addition, subtraction, multiplication, or division). For more complex word problems, a more strategic plan to solve the problem can be made. This can involve strategies such as proportional reasoning, finding a pattern, drawing a diagram, solving a simpler problem, or even acting it out!

The Fourth Step - Solve the Word Problem

Students should now carry out the plan they made in the third step and solve the word problem. Suppose their plan was not effective for solving the word problem. In that case, they might need to revisit Step 3 and make a new plan, or they might even need to revisit Step 2 if they missed a necessary piece of information, or Step 1 if they do not understand one of the words in the word problem. This is when perseverance is needed and, if stuck, some help from a teacher, a parent, or an older sibling, for example.

The Fifth Step - Check the Answer

One awesome characteristic of math is that there is almost always a way to check your answer!

We always tell students that, usually, the students who earn the highest marks on math tests (or, actually, any tests) keep their tests for the longest time and check and double-check their work! We encourage students not to think that the students who hand their tests in very quickly know all the answers and will earn the best marks - because it is, quite often, the opposite of that!

While how the answer can be checked depends on the word problem, a few common ways that the answer can be checked are to perform the opposite operation (for example, addition and subtraction are opposite operations, so if the word problem was solved by using addition, then subtraction can be used to check that the addition was done correctly, and multiplication and division are opposite operations), to estimate the answer and check that the answer obtained is close, and to plug the answer in for the variable if variables were used in solving the word problem.

If the answer is wrong, the student should analyze why their answer is incorrect (they might need assistance). Depending on the reason for which their answer is incorrect, they might need to return to Step 4 and solve the problem again (if they made a calculation error, for example), or to Step 3 and make a new plan (if their plan was not the correct strategy), or to Step 2 (if, for example, they missed an important piece of information), or to Step 1 (if they do not understand one of the words in the problem).

After the student has checked the answer and determined that it is correct (or at least reasonable), the student should write the answer the way their teacher expects it to be written. Some teachers want complete sentences, while others are fine with just one word that states what the answer is (for example, 15 cookies).

Here is an example of Solving a Word Problem by Using these Steps

The word problem we will solve:

Mr. Sand is going on a trip to the beach. The total distance to the beach is 263 km. His car has a 60 L gas tank and can travel 640,000 m on that tank of gas. Suppose that there are two service stations available to Mr. Sand. Station A charges $1.60 per litre of gas, while Station B charges $1.70 per litre of gas. Determine the cost of the gas for his trip if he fills up at Station A versus the cost if he fills up at Station B. Which is more economical?

The First Step - Read the Problem

We read the problem and we discover that we are not sure what the word economical means. Therefore, we can look up the definition of economical online and learn that it means giving good value or service in relation to the amount of money, time, or effort spent. So, we now know that the word economical means the least money spent.

The Second Step - Understand the Problem in a Mathematical Sense

We can make a list of the information we were given and the information we need to find:

Information We Were Given
The distance to the beach is 263 km.
The car can travel 640,000 m on 60 L of gas.
It costs $1.60 per litre of gas from Station A.
It costs $1.70 per litre of gas from Station B.
Is any of this extra information that we do not need? No, we need all of this information.

What We Need to Find
The number of litres of gas he will need to get to the beach.
The cost of his gas for the trip if he fills up at Station A.
The cost of his gas for the trip if he fills up at Station B.
Which option (Station A or Station B) is more economical. (We already know this is Station A because gas costs less per litre at Station A than it does at Station B.)

The Third Step - Make a Plan to Solve the Word Problem

We can convert the number of metres he can travel on 60 L of gas into the number of kilometres he can travel on 60 L of gas, then we can divide the number of litres by the number of kilometres to get the number of litres per kilometre. Then, we can multiply the number of litres of gas required per kilometre by 263 kilometres (the distance to the beach). Following that, we can multiply the number of litres of gas needed to travel to the beach by the cost per litre of gas at Station A, by the cost per litre of gas at Station B, and compare the results to determine which station is the more economical choice (however, since the cost of gas is less per litre at Station A than it is at Station B, we already know that Station A will be more economical).

The Fourth Step - Solve the Word Problem

We follow the steps in our plan to solve the word problem, so we start by converting the number of metres he can travel on 60 L of gas into the number of kilometres he can travel on 60 L of gas: 640,000 m/1,000 m/km = 640 km

Then we divide the number of litres by the number of kilometres to get the number of litres per kilometre:

60 L/640 km = 0.09375 L/km

We multiply the number of litres per kilometre by the number of kilometres he must drive to get to the beach to get the total volume of gas required to travel to the beach:

(0.09375 L/km)(263 km) = 24.65625 L

We multiply that number of litres by the cost per litre of gas at Station A:

(24.65625 L)($1.60/L) = $39.45

We multiply that number of litres by the cost per litre of gas at Station B:

(24.65625 L)($1.70/L) = $41.92 (rounded to the nearest cent)

We can see that the cost of the gas is less at Station A than it is at Station B. Next, we will go one step further than the problem asked us to, and we will determine how much he will save by purchasing the gas at Station A instead of at Station B:

$41.92 - $39.45 = $2.47

The Fifth Step - Check the Answer

We can check that we converted the distance from metres into kilometres correctly by converting the number of kilometres into metres and determining whether we get the number with which we started:

(640 km)(1,000 m/km) = 640,000 m

Yes! We get the number with which we started!

We can check that we found the number of litres per kilometre correctly by multiplying the number of litres per kilometre by the number of kilometres and determining whether we get the number of litres with which we started:

(0.09375 L/km)(640 km) = 60 L

Yes! We get the number of litres with which we started!

To verify that we got the correct number of litres of gas that will be required to travel to the beach, we can divide the number of litres required by the number of litres per kilometre and determine whether we get the number of kilometres he must drive to get to the beach:

24.65625 L/0.09375 L/km = 263 km

Yes! We got the number of kilometres that he must drive to get to the beach!

To check that we got the correct cost for buying the necessary number of litres of gas from Station A, we can divide the total cost of the gas by the cost per litre of gas at Station A and determine whether we get the number of litres that are required:

$39.45/$1.60/L = 24.65625 L

Yes! That is the number of litres that are required!

To check that we got the correct cost for buying the necessary number of litres of gas from Station B, we can divide the total cost of the gas by the cost per litre of gas at Station B and determine whether we get the number of litres that are required (approximately, since the total cost of the gas from Station B was rounded to the nearest cent):

$41.92/$1.70/L = 24.6588 L

While this result is not the exact number of litres that are required, we know that we had rounded the total cost of the gas from station B to the nearest cent, and 24.6588 L is very close to 24.65625 L, so we are confident that our answer is correct.

We knew, based on the price per litre, that Station A would be more economical than Station B. We can also check our answer by finding the difference in the cost per litre of gas at Station A and the cost per litre of gas at Station B and then multiplying that difference in cost by the number of litres required to determine whether the amount that we calculated he would save by buying the gas at Station A instead of at Station B is correct:

$1.70/L - $1.60/L = $0.10/L

($0.10/L)(24.65625 L) = $2.47 (rounded to the nearest cent).

Yes! Our answer is the amount of money he would save by buying the gas at Station A instead of at Station B!

Finally, we write a sentence that answers the questions we were asked:

The cost of buying the gas necessary from Station A to drive to the beach is $39.45 and the cost of buying the gas necessary from Station B to drive to the beach is $41.92. Therefore, buying the gas from Station A is more economical, and he would save $2.47 by buying the gas from Station A.

Have fun at the beach, Mr. Sand!

Want resources to help with reviewing middle years math number skills? Check out Some of Our Favourite Resources for Middle Years Math Number Skills!