The 5 Best Strategies for Solving Math Word Problems

As a math teacher with years of experience teaching word problems and problem-solving skills, I’ve seen how math word problems can spark both negative feelings and moments of triumph in students.

There is something about applying math strategies to the real world in different ways that can shake the confidence of math students. All it takes is a few negative experiences with math word problems for a student to develop a life-long struggle with math.

That’s why I have put together this problem-solving strategy guide! My goal is to share my 5 best strategies for solving math word problems so that you can worry less about finding the correct solution and focus more on feeling confident when solving problems!

My 5 Best Strategies for Solving Math Word Problems

The key to problem solving lies in building a solid problem-solving process and equipping yourself with confidence in your use of math word problem strategies.

In my teaching experience, I’ve mastered breaking down complex problems into manageable steps in order to help students of all grade levels tackle everything from simple subtraction word problems to advanced algebraic equations.

Below are my five best practices that not only help students find the correct answer but also build the confidence to approach different problems with a positive math mindset!

1. Understand the Problem by Focusing on Key Information

The first step in solving any mathematical problem is understanding the given problem. I always encourage students to read the problem carefully and identify key words and important information that provide clues about what the problem is asking.

One common mistake I see is that students often get distracted by extra information that isn’t necessary for solving the problem. The best way to avoid this is to underline key information and rewrite the question as a complete sentence in your own words.

Example Problem

“A group of 15 people are at a concert. They share 240 square feet of space while carrying 6 backpacks and 3 water bottles. If there are 10 people standing in a section of the space, how much space does each person in that section have?”

Highlight the given information: 240 total square feet, 10 people in a section.
Ignore extra information: The number of backpacks and water bottles isn’t necessary for solving the problem.
Rewrite the question: “How many square feet does each person in the section have?”

By focusing on only the key information and rewriting the problem in a simpler way, students can focus on solving the problem without being distracted by irrelevant details.

2. Break Down the Problem into Manageable Parts

Many math problems, especially complex problems, involve multiple steps.

The second strategy for solving math word problems that I always teach my students is to separate the task into different parts of the problem. This helps make a complex process more manageable.

For example, I often encourage my students to use a math model to start setting up the problem. I also encourage them to reflect on how each previous step connects to the next step of the problem-solving process.

Example Problem

“Find three consecutive integers whose sum is 72.”

We can start by defining the unknown number as x. This tells us that our the next number would be x+1, and the third would be x+2. This math model helps us understand how to proceed to the next step of the solution.

We can then write a math equation: \(x + (x + 1) + (x + 2) = 72\) that can be solved. We solve the equation step by step by first combining like terms.

\[3x + 3 = 72\]

We then use algebra to solve this simple two-step equation.

\[\begin{split} 3x + 3 – 3 & = 72 – 3 \\ \\ 3x &= 69 \\ \\ x&=23 \end{split}\]

This model helps students identify that algebra is the most appropriate strategy to determine the solution to the problem.

3. Use Visual and Logical Reasoning

Using visual representations of math concepts like counters, a task card, or fact families can make even the trickiest math word problems feel approachable.

When teaching mathematical word problems, I always encourage my students to use visual representations, regardless of whether they are in 3rd grade or older kids in high school.

Younger elementary school students might prefer using hands on manipulatives to solve multiplication problems or division word problems for example. High school students might prefer just sticking with drawing a diagram to represent all of the key information visually.

Example Problem

“A farmer has a rectangular garden that measures 30 feet in length and 20 feet in width. She wants to divide it into equal sections, each with an area of 100 square feet, for planting vegetables. How many sections can she create?”

Solve: Divide the total area by the size of each section: 600 ÷ 100 = 6 sections.
Draw a diagram: Sketch a rectangle to represent the garden. Label the dimensions (30 feet by 20 feet) and divide the rectangle into smaller sections, each labeled as 100 square feet.
Highlight the key information visually: Use the total area of the garden (30 × 20 = 600 square feet) and the size of each section (100 square feet) to solve the problem.

Visualizing the problem with a diagram helps students understand the relationship between the total area, the size of each section, and the division process to find the number of sections.

This strategy works well for 3rd-grade students learning multiplication and division concepts and for older students tackling area-related problems.

4. Relate to Similar Problems and Real-World Scenarios

Relating different problems to similar problems students have already solved strengthens their understanding. This helps reinforce how an easy problem can provide strategies for tackling a different problem type that might be more difficult.

For example, if students know how to solve a division problem, such as sharing 12 candies among 4 kids, they can apply the same strategy to calculate portions for a group of people at a restaurant.

5. Review and Reflect on the Answer

The final step in my problem-solving process is reviewing the solution to ensure it matches the original problem. I make sure that I teach students to:

Check their solution against the given information for accuracy.
Substitute their final answer back into the equation to verify that it is the correct solution.
Reflect on any mistakes made to avoid them in future problems.

Example Problem

“A rectangle’s perimeter is 36 meters. If the length is 10 meters, what is the width?”

We can solve this problem by using the perimeter formula: \(P=2L+2W\).

Substituting our known values results in: \(36=2(10)+2W\). We can simplify this to:

\[36=20+2W\]

We then use algebra to solve for the value of \(W\):

\[\begin{split} 36&=20+2W \\ 16 &= 2W \\ W&=8 \end{split}\]

We can then substitute to check our answer. We confirm that the width of 8 metres is the actual answer by revisiting the original problem. Substituting 8 in for W will show that we do in fact get a perimeter of 36 metres.

\[\begin{split} P&=2(10)+2(8) \\ &=20+16 \\ &=36 \end{split}\]

Since the calculated perimeter matches the original problem, we can confirm the solution.

This final reflection step helps foster a positive mindset and a deeper understanding of problem-solving strategies.

Applying Strategies for Solving Math Word Problems

Solving math word problems is a new skill that can initially seem overwhelming, but with consistent practice and the right strategies, you can tackle even the most complex problems with confidence and more positive thoughts.

By focusing on key information, breaking down the problem, using visual aids, connecting to real-world examples, and reflecting on your solutions, you can improve your approach to any problem, whether you’re in 1st grade or beyond.

The more you practice these strategies, the more natural problem-solving will become. As you continue to apply these methods, you’ll not only improve your math skills but also build the confidence to handle problems in everyday situations.

Keep practicing, and you’ll see your ability to solve math word problems grow with each challenge!

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