Mathematics Problem Solving Strategies

[Gwenda Arguin]

Byusing these sentence starters, students ended up with several paragraphs (some short, some long) to explain how they approached and solved the math problem, AND how they knew they were correct.

I was teaching 5th grade in elementary school at this time, and we had a full hour for math every day. So, fitting in problem solving practice a few times a week was pretty easy, after students understood the process.

I really liked spending the time on these types of math problems, because they often led to discussion of other math concepts, and they reinforced concepts already learned.

I used math problems from a publication that focused on various strategies, like:

Math strategies for problem-solving help students use a range of approaches to solve many different types of problems. It involves identifying the problem and carrying out a plan of action to find the answer to mathematical problems.

Problem-solving skills are essential to math in the general classroom and real-life. They require logical reasoning and critical thinking skills. Students must be equipped with strategies to help them find solutions to problems.

Students need to have a toolkit of math problem-solving strategies at their disposal to provide different ways to approach math problems. This makes it easier to find solutions and understand math better.

When keywords are highlighted in a word problem, it helps the student focus on the essential information needed to solve it. Some important keywords help determine which operation is needed.

For example, if the word problem asks how many are left, the problem likely requires subtraction.

Ensure students highlight the keywords carefully and do not highlight every number or keyword. There is likely irrelevant information in the word problem.

Read the problem aloud, highlight the key information and then summarize the information. Students can do this in their heads or write down a quick summary.

Summaries should include only the important information and be in simple terms that help contextualize the problem.

Once students understand the context of the word problem, have dentified the important information and determined the unknown, they can make a plan to solve it.

The plan will depend on the type of problem. Some problems involve more than one step to solve them as some require more than one answer.

Encourage students to make a list of each step they need to take to solve the problem before getting started.

Students may find it useful to draw a model, picture, diagram, or other visual aid to help with the problem solving process.

It can help to visualize the problem to understand the relationships between the numbers in the problem. In turn, this helps students see the solution.

Working backwards is a popular problem-solving strategy. It involves starting with a possible solution and deciding what steps to take to arrive at that solution.

This strategy can be particularly helpful when students solve math word problems involving multiple steps. They can start at the end and think carefully about each step taken as opposed to jumping to the end of the problem and missing steps in between.

When faced with a word problem, encourage students to write a number sentence based on the information. This helps translate the information in the word problem into a math equation or expression, which is more easily solved.

It is important to fully understand the context of the word problem and what students need to solve before writing an equation to represent it.

For simpler problems, a quick and easy problem solving strategy is to use the inverse operation.

For example, if the operation to solve a word problem is 56 8 = 7 students can check the answer is correct by multiplying 8 7.

As good practice, encourage students to use the inverse operation routinely to check their work.

This method is particularly useful for algebraic equations. Specifically when working with variables.

To use the plug-in method, students solve the problem as asked and arrive at an answer. They can then plug the answer into the original equation to see if it works. If it does, the answer is correct.

Peer review is a great tool to use at any grade level as it promotes critical thinking and collaboration between students.

The reviewers can look at the problem from a different view as they check to see if the problem was solved correctly.

Problem solvers receive immediate feedback and the opportunity to discuss their thinking with their peers.

This strategy is effective with mixed-ability partners or similar-ability partners. In mixed-ability groups, the partner with stronger skills provides guidance and support to the partner with weaker skills, while reinforcing their own understanding of the content and communication skills.

If partners have comparable ability levels and problem-solving skills, they may find that they approach problems differently or have unique insights to offer each other about the problem-solving process.

A calculator can be introduced at any grade level but may be best for older students who already have a foundational understanding of basic math operations.

Provide students with a calculator to allow them to check their solutions independently, accurately, and quickly.

Since calculators are so readily available on smartphones and tablets, they allow students to develop practical skills that apply to real-world situations.

Third Space Learning offers a free resource library is filled with hundreds of high-quality resources. A team of experienced math experts carefully created each resource to develop students mental arithmetic, problem solving and critical thinking.

Educators can use many different strategies to teach problem-solving and help students develop and carry out a plan when solving math problems. Incorporate these math strategies into any math program and use them with a variety of math concepts, from whole numbers and fractions to algebra.

This is the underlying procedure or schema students are being asked to use. Once they have a list of schema for different mathematical operations (addition, multiplication and so on), they can take turns to apply them to an unfamiliar word problem and see which one fits.

Model the process of writing down every step you take to complete a math problem and provide working out paper when students are solving a problem. This will allow students to keep track of their thoughts and pick up errors before they reach a final solution.

But checking is important too. It allows them to pinpoint areas of difficulty as they come up, and it enables them to tackle more complex problems that require multiple checks before arriving at a final answer.

Problem-solving is a critical life skill that everyone needs. Whether you're dealing with everyday issues or complex challenges, being able to solve problems effectively can make a big difference to your quality of life.

While there is no one 'right' way to solve a problem, having a toolkit of different techniques that you can draw upon will give you the best chance of success. In this article, we'll explore 17 different math problem-solving strategies you can start using immediately to deepen your learning and improve your skills.

The beauty of these techniques is they go beyond strictly mathematical application. It's more about understanding a given problem, thinking critically about it and using a variety of methods to find a solution.

We're going to use Polya's 4-step model as the framework for our discussion of problem-solving activities. This was developed by Hungarian mathematician George Polya and outlined in his 1945 book How to Solve It. The steps are as follows:

This may seem like an obvious one, but it's crucial that you take the time to understand what the problem is asking before trying to solve it. Especially with a math word problem, in which the question is often disguised in language, it's easy for children to misinterpret what's being asked.

This is a great strategy for younger students who are still learning to read. By reading the problem aloud, they can help to clarify any confusion and better understand what's being asked. Teaching older students to read aloud slowly is also beneficial as it encourages them to internalise each word carefully.

Using dot points or a short sentence, list out all the information given in the problem. You can even underline the keywords to focus on the important information. This will help to organise your thoughts and make it easier to see what's given, what's missing, what's relevant and what isn't.

This is a no-brainer for visual learners. By drawing a picture, let's say with division problems, you can better understand what's being asked and identify any information that's missing. It could be a simple sketch or a more detailed picture, depending on the problem.

Visualising a scenario can also be helpful. It can enable students to see the problem in a different way and develop a more intuitive understanding of it. This is especially useful for math word problems that are set in a particular context. For example, if a problem is about two friends sharing candy, kids can act out the problem with real candy to help them understand what's happening.

What does this word tell me? Which operations do I need to use? Keyword analysis involves asking questions about the words in a problem in order to work out what needs to be done. There are certain key words that can hint at what operation you need to use.

Once you understand the problem, it's time to start thinking about how you're going to solve it. This is where having a plan is vital. By taking the time to think about your approach, you can save yourself a lot of time and frustration later on.

There are many methods that can be used to figure out a pathway forward, but the key is choosing an appropriate one that will work for the specific problem you're trying to solve. Not all students understand what it means to plan a problem so we've outlined some popular problem-solving techniques during this stage.

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