19 Best Math Problem-Solving Strategies for elementary students

Do you know problem-solving strategies that help you to solve every hardest math problem? If you are finding such math problem-solving strategies, this article is for you. Let’s explore different strategies for solving math problems and enjoy teaching and learning mathematics.

What is Polya’s method for solving math problems?

George Polya is a mathematician who provides the basis for how to solve complex math problems. He writes different books on Math Problem-Solving Strategies. His book “How to solve it”  provides the foundation for every efficient problem-solving method in the Modern World.

Polya’s method for solving math problems involves four steps:

  1. Recognizing the issue,
  2. Making a plan,
  3. Executing the plan and
  4. Assessing the solution.

There are different specific math problem-solving strategies and techniques that you can use to solve the problem.

These include drawing diagrams, making a list or table, working backward, and looking for patterns.

Problem-Solving Strategies in Mathematics

Most students face the problem of problem-solving in math. Whether it’s a word problem or a simple math problem of finding the unknown, they all have unique problem-solving methods. So, math problem-solving strategies are the method and techniques to solve a math problem that leads to accurate answers.

There are numerous ways to find the solution, and methods depend upon the nature of the questions. Here we discuss the top 19 math problem-solving strategies that are helpful in every math question.

According to Polya’s method, we also divide our math problem solving strategies into four categories.

PART 1: Understanding the Problem

PART 2:  Devising a plan

PART 3: Carrying Out the Plan 

PART 4: Evaluating the Plan.


PART: 1 Understand the problem

Understanding is the key to the problem.  If you properly understand the problem,  you solve 50% of your problems. Keep the following question in your mind while working on your math problem-solving. 

  1. What are the keywords in the math problem?
  2. Ask students if they understand what is given and what they must find.
  3. Now check whether students can define the problem in their own words.
  4. Can students divide the problem into a mind map or pictorial form?
  5. What are the things that need to understand the problem?
  6. Encourage students to list down the relevant and irrelevant information from the question.
  7. Give time to students to read the problem. Once they read and understand it, they move on to the common math problem-solving strategies.

PART: 2 Devising a plan

Now it’s clear what the problem is and what we must find. Now move on to making a plan to solve the problem.  According to Polya’s method, here we discuss the top 14 strategies to devise a plan or problem-solving. You can choose anyone according to the problem’s nature and interest.


Be ingenious

Be ingenious and use your creativity to splash complex math problems. Encourage students to create new ideas for problem-solving and then choose the accurate one.


Consider special cases

Consider exceptional cases for your problem. Working on special issues simplifies the problem and helps solve it completely.


Eliminate possibilities

Convert your problem into a pictorial form and then solve each step individually. It helps you better understand the method and gives you the confidence to solve the problem.


Draw a picture

Divide your problem into different steps and solve it to find all the possible solutions. When there is a wrong answer, eliminate this possibility and move to other steps.


Guess and check

Guess the solution to the problem and then check it by putting it back into the equations.


Look for a pattern

Most of the tricky math questions have the same pattern. If you find a way to solve questions, you can solve the whole problem quickly.


Make an Orderly list

Making an orderly list of questions saves a lot of time and gives you a way to tackle the difficult task. Break down your job into a simple list and work on the final solution.


Solve a simpler problem.

Need help understanding the hard problem, start with a more straightforward problem. A simpler Problem makes a base in the method and creates interest in students. Moving from more superficial to harder is the best strategy for teaching math at the elementary level.


Solve an equation

Convert the problem into the form of an equation. It is easy to solve equations. When you solve the equation, you get the final solution to your problem.


Use a formula

Find the relative formula for your problem. Then put your given data into the procedure and calculate the answer.


Use a model

When a maths problem is represented visually, it usually becomes simpler for children, even if it initially seems complex. Some of the best math tactics for problem resolution involve having youngsters visualize and act out the arithmetic problem.

An alternative to visualization is to make tally marks or a picture on a working-out paper. You may also have students use a marker to doodle before writing down the answer as you demonstrate the procedure on the whiteboard.

o the procedure and calculate the answer.


Use direct reasoning

Direct reasoning, sometimes referred to as top-down or forward reasoning, starts with what you already know and uses that knowledge to attempt to solve the problem. This is frequently used when a lot of information is provided about the problem.

By segmenting the issue, you can begin to see how the many elements fit together and ultimately come up with a solution.


Use symmetry

Find the symmetry of the problem. Work or one part and another part will be solved automatically without long calculations.


Work backward

Working backward is also a powerful problem-solving strategy. In this, you know what the solution is. Take the key and then move back and create the original problem.

Working backward is helpful if pupils are required to identify an unknown number in a problem or mathematical language. If the equation is, for instance, 8 + x = 12, students can determine x by:

  • beginning with 12
  • subtracting eight from 12
  • having four leftover
  • Verifying that using 4 in place of x works

PART: 3 Carrying out the Plan

Now your plan is ready, move to the next step and use your problem-solving skills to execute the plan. Typically, this stage is more straightforward than creating the strategy.

 You only need care and patience because you have the essential abilities. Stick to the strategy you’ve picked. If it doesn’t stop failing, throw it away and choose another. Don’t be fooled; this is how maths is done, even by experts.

PART: 4 Evaluating the solution

Once you get the solution now, it is time to verify it. Cross-check your solution by answering the following questions.

  • Take a look at the outcome.
  • Please verify the outcome.
  • Could you verify the argument?
  • Can you come up with an alternate solution?
  • Can you quickly recognize it?

If you can answer all the above questions, that shows you have selected the right math problem-solving strategies.


Some Practice problems of math problem-solving strategies.

Here are some examples of math problems that can be solved using these strategies for elementary students:

  1. Understand the Problem: If there are 10 apples and 5 are eaten, how many apples are left?
  2. Guess and Check: If a student has 10 pencils and gives away 3, how many pencils does the student have left?
  3. Work It Out: If a student has 10 apples and gives away 3, how many apples does the student have left?
  4.  Work Backwards: If a student has 10 apples and wants to give away 3, how many apples does the student need to start with
  5. Visualize: If a student has 10 apples and wants to give away 3, what does the picture look like?
  6. Find a Pattern: If a student has 10 apples and wants to give away 3, what is the pattern.
  7. Think: If a student has 10 apples and wants to give away 3, what is the easiest way to solve this problem
  8. Draw a Picture or Diagram: Draw a picture of a problem that involves adding two numbers together.


What are some examples of math problem-solving strategies?

Some examples of math problem-solving strategies include: guessing and checking, drawing a picture or diagram, making a table or chart, working backward, using logical reasoning, breaking the problem down into smaller parts, and looking for patterns or relationships.

How do you get better at solving problems?

There are numerous methods for enhancing problem-solving abilities. The following advice may be useful to you:

1. Clearly state the issue and your aim or purpose.

2. Compile as many facts regarding the issue as you can, then arrange it by rephrasing, compressing, or summarizing it.

3. Examine the data you’ve acquired, looking for significant relationships, trends, and links.

4. Generate a list of potential remedies for the issue.

5. Determine the viability and efficacy of each prospective option.

6. Decide on the best course of action and create a plan of action to carry it out.

7. Keep track of your development and modify your strategy as necessary.

Additionally, you can engage in brainstorming exercises like mind mapping, approach everyday situations with a “what if” mindset, routinely test new strategies, keep an idea journal in which you jot down all of your ideas, even the ones that seem implausible, play logic games and solve puzzles like sudoku or Wordle, and read trade publications that cover the most recent software and solutions to common problems.

Final Verdict:

You need multiple strategies to solve math word problems. Regardless of your methods, you will end up with an accurate answer. But most power math problem-solving strategies are drawing the picture and making models. And at the end, verify your answer by moving backward.

Do you want to explore more problem-solving strategies, go through the book, and find an accurate way to solve your problem?

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