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Problem Solving Activities: 7 Strategies
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Problem solving can be a daunting aspect of effective mathematics teaching, but it does not have to be! In this post, I share seven strategic ways to integrate problem solving into your everyday math program.
In the middle of our problem solving lesson, my district math coordinator stopped by for a surprise walkthrough.
I was so excited!
We were in the middle of what I thought was the most brilliant math lesson– teaching my students how to solve problem solving tasks using specific problem solving strategies.
It was a proud moment for me!
Each week, I presented a new problem solving strategy and the students completed problems that emphasized the strategy.
Genius right?
After observing my class, my district coordinator pulled me aside to chat. I was excited to talk to her about my brilliant plan, but she told me I should provide the tasks and let my students come up with ways to solve the problems. Then, as students shared their work, I could revoice the student’s strategies and give them an official name.
What a crushing blow! Just when I thought I did something special, I find out I did it all wrong.
I took some time to consider her advice. Once I acknowledged she was right, I was able to make BIG changes to the way I taught problem solving in the classroom.
When I Finally Saw the Light
To give my students an opportunity to engage in more authentic problem solving which would lead them to use a larger variety of problem solving strategies, I decided to vary the activities and the way I approached problem solving with my students.
Problem Solving Activities
Here are seven ways to strategically reinforce problem solving skills in your classroom.
Seasonal Problem Solving
Many teachers use word problems as problem solving tasks. Instead, try engaging your students with non-routine tasks that look like word problems but require more than the use of addition, subtraction, multiplication, and division to complete. Seasonal problem solving tasks and daily challenges are a perfect way to celebrate the season and have a little fun too!
Cooperative Problem Solving Tasks
Go cooperative! If you’ve got a few extra minutes, have students work on problem solving tasks in small groups. After working through the task, students create a poster to help explain their solution process and then post their poster around the classroom. Students then complete a gallery walk of the posters in the classroom and provide feedback via sticky notes or during a math talk session.
Notice and Wonder
Before beginning a problem solving task, such as a seasonal problem solving task, conduct a Notice and Wonder session. To do this, ask students what they notice about the problem. Then, ask them what they wonder about the problem. This will give students an opportunity to highlight the unique characteristics and conditions of the problem as they try to make sense of it.
Want a better experience? Remove the stimulus, or question, and allow students to wonder about the problem. Try it! You’ll gain some great insight into how your students think about a problem.
Math Starters
Start your math block with a math starter, critical thinking activities designed to get your students thinking about math and provide opportunities to “sneak” in grade-level content and skills in a fun and engaging way. These tasks are quick, designed to take no more than five minutes, and provide a great way to turn-on your students’ brains. Read more about math starters here !
Create your own puzzle box! The puzzle box is a set of puzzles and math challenges I use as fast finisher tasks for my students when they finish an assignment or need an extra challenge. The box can be a file box, file crate, or even a wall chart. It includes a variety of activities so all students can find a challenge that suits their interests and ability level.
Calculators
Use calculators! For some reason, this tool is not one many students get to use frequently; however, it’s important students have a chance to practice using it in the classroom. After all, almost everyone has access to a calculator on their cell phones. There are also some standardized tests that allow students to use them, so it’s important for us to practice using calculators in the classroom. Plus, calculators can be fun learning tools all by themselves!
Three-Act Math Tasks
Use a three-act math task to engage students with a content-focused, real-world problem! These math tasks were created with math modeling in mind– students are presented with a scenario and then given clues and hints to help them solve the problem. There are several sites where you can find these awesome math tasks, including Dan Meyer’s Three-Act Math Tasks and Graham Fletcher’s 3-Acts Lessons .
Getting the Most from Each of the Problem Solving Activities
When students participate in problem solving activities, it is important to ask guiding, not leading, questions. This provides students with the support necessary to move forward in their thinking and it provides teachers with a more in-depth understanding of student thinking. Selecting an initial question and then analyzing a student’s response tells teachers where to go next.
Ready to jump in? Grab a free set of problem solving challenges like the ones pictured using the form below.
Which of the problem solving activities will you try first? Respond in the comments below.
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This is a very cool site. I hope it takes off and is well received by teachers. I work in mathematical problem solving and help prepare pre-service teachers in mathematics.
Thank you, Scott! Best wishes to you and your pre-service teachers this year!
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A Guide to Problem Solving
When confronted with a problem, in which the solution is not clear, you need to be a skilled problem-solver to know how to proceed. When you look at STEP problems for the first time, it may seem like this problem-solving skill is out of your reach, but like any skill, you can improve your problem-solving with practice. How do I become a better problem-solver? First and foremost, the best way to become better at problem-solving is to try solving lots of problems! If you are preparing for STEP, it makes sense that some of these problems should be STEP questions, but to start off with it's worth spending time looking at problems from other sources. This collection of NRICH problems is designed for younger students, but it's very worthwhile having a go at a few to practise the problem-solving technique in a context where the mathematics should be straightforward to you. Then as you become a more confident problem-solver you can try more past STEP questions. One student who worked with NRICH said: "From personal experience, I was disastrous at STEP to start with. Yet as I persisted with it for a long time it eventually started to click - 'it' referring to being able to solve problems much more easily. This happens because your brain starts to recognise that problems fall into various categories and you subconsciously remember successes and pitfalls of previous 'similar' problems." A Problem-solving Heuristic for STEP Below you will find some questions you can ask yourself while you are solving a problem. The questions are divided into four phases, based loosely on those found in George Pólya's 1945 book "How to Solve It". Understanding the problem
- What area of mathematics is this?
- What exactly am I being asked to do?
- What do I know?
- What do I need to find out?
- What am I uncertain about?
- Can I put the problem into my own words?
Devising a plan
- Work out the first few steps before leaping in!
- Have I seen something like it before?
- Is there a diagram I could draw to help?
- Is there another way of representing?
- Would it be useful to try some suitable numbers first?
- Is there some notation that will help?
Carrying out the plan STUCK!
- Try special cases or a simpler problem
- Work backwards
- Guess and check
- Be systematic
- Work towards subgoals
- Imagine your way through the problem
- Has the plan failed? Know when it's time to abandon the plan and move on.
Looking back
- Have I answered the question?
- Sanity check for sense and consistency
- Check the problem has been fully solved
- Read through the solution and check the flow of the logic.
Throughout the problem solving process it's important to keep an eye on how you're feeling and making sure you're in control:
- Am I getting stressed?
- Is my plan working?
- Am I spending too long on this?
- Could I move on to something else and come back to this later?
- Am I focussing on the problem?
- Is my work becoming chaotic, do I need to slow down, go back and tidy up?
- Do I need to STOP, PEN DOWN, THINK?
Finally, don't forget that STEP questions are designed to take at least 30-45 minutes to solve, and to start with they will take you longer than that. As a last resort, read the solution, but not until you have spent a long time just thinking about the problem, making notes, trying things out and looking at resources that can help you. If you do end up reading the solution, then come back to the same problem a few days or weeks later to have another go at it.
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20 Effective Math Strategies To Approach Problem-Solving
Katie Keeton
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.
This article explores mathematical problem solving strategies, logical reasoning and critical thinking skills to help learners with solving math word problems independently in real-life situations.
What are problem-solving strategies?
Problem-solving strategies in math are methods students can use to figure out solutions to math problems. Some problem-solving strategies:
- Draw a model
- Use different approaches
- Check the inverse to make sure the answer is correct
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.
Strategies can help guide students to the solution when it is difficult ot know when to start.
The ultimate guide to problem solving techniques
Download these ready-to-go problem solving techniques that every student should know. Includes printable tasks for students including challenges, short explanations for teachers with questioning prompts.
20 Math Strategies For Problem-Solving
Different problem-solving math strategies are required for different parts of the problem. It is unlikely that students will use the same strategy to understand and solve the problem.
Here are 20 strategies to help students develop their problem-solving skills.
Strategies to understand the problem
Strategies that help students understand the problem before solving it helps ensure they understand:
- The context
- What the key information is
- How to form a plan to solve it
Following these steps leads students to the correct solution and makes the math word problem easier .
Here are five strategies to help students understand the content of the problem and identify key information.
1. Read the problem aloud
Read a word problem aloud to help understand it. Hearing the words engages auditory processing. This can make it easier to process and comprehend the context of the situation.
2. Highlight keywords
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.
3. Summarize the information
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.
4. Determine the unknown
A common problem that students have when solving a word problem is misunderstanding what they are solving. Determine what the unknown information is before finding the answer. Often, a word problem contains a question where you can find the unknown information you need to solve. For example, in the question ‘How many apples are left?’ students need to find the number of apples left over.
5. Make a plan
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.
Strategies for solving the problem
1. draw a model or diagram.
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.
Similarly, you could draw a model to represent the objects in the problem:
2. Act it out
This particular strategy is applicable at any grade level but is especially helpful in math investigation in elementary school . It involves a physical demonstration or students acting out the problem using movements, concrete resources and math manipulatives . When students act out a problem, they can visualize and contectualize the word problem in another way and secure an understanding of the math concepts. The examples below show how 1st-grade students could “act out” an addition and subtraction problem:
The problem | How to act out the problem |
Gia has 6 apples. Jordan has 3 apples. How many apples do they have altogether? | Two students use counters to represent the apples. One student has 6 counters and the other student takes 3. Then, they can combine their “apples” and count the total. |
Michael has 7 pencils. He gives 2 pencils to Sarah. How many pencils does Michael have now? | One student (“Michael”) holds 7 pencils, the other (“Sarah”) holds 2 pencils. The student playing Michael gives 2 pencils to the student playing Sarah. Then the students count how many pencils Michael is left holding. |
3. Work backwards
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.
For example,
To solve this problem working backwards, start with the final condition, which is Sam’s grandmother’s age (71) and work backwards to find Sam’s age. Subtract 20 from the grandmother’s age, which is 71. Then, divide the result by 3 to get Sam’s age. 71 – 20 = 51 51 ÷ 3 = 17 Sam is 17 years old.
4. Write a number sentence
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.
5. Use a formula
Specific formulas help solve many math problems. For example, if a problem asks students to find the area of a rug, they would use the area formula (area = length × width) to solve. Make sure students know the important mathematical formulas they will need in tests and real-life. It can help to display these around the classroom or, for those who need more support, on students’ desks.
Strategies for checking the solution
Once the problem is solved using an appropriate strategy, it is equally important to check the solution to ensure it is correct and makes sense.
There are many strategies to check the solution. The strategy for a specific problem is dependent on the problem type and math content involved.
Here are five strategies to help students check their solutions.
1. Use the Inverse Operation
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.
2. Estimate to check for reasonableness
Once students reach an answer, they can use estimation or rounding to see if the answer is reasonable. Round each number in the equation to a number that’s close and easy to work with, usually a multiple of ten. For example, if the question was 216 ÷ 18 and the quotient was 12, students might round 216 to 200 and round 18 to 20. Then use mental math to solve 200 ÷ 20, which is 10. When the estimate is clear the two numbers are close. This means your answer is reasonable.
3. Plug-In Method
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.
If students use the equation 20m+80=300 to solve this problem and find that m = 11, they can plug that value back into the equation to see if it is correct. 20m + 80 = 300 20 (11) + 80 = 300 220 + 80 = 300 300 = 300 ✓
4. Peer Review
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.
5. Use a Calculator
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.
Step-by-step problem-solving processes for your classroom
In his book, How to Solve It , published in 1945, mathematician George Polya introduced a 4-step process to solve problems.
Polya’s 4 steps include:
- Understand the problem
- Devise a plan
- Carry out the plan
Today, in the style of George Polya, many problem-solving strategies use various acronyms and steps to help students recall.
Many teachers create posters and anchor charts of their chosen process to display in their classrooms. They can be implemented in any elementary, middle school or high school classroom.
Here are 5 problem-solving strategies to introduce to students and use in the classroom.
How Third Space Learning improves problem-solving
Resources .
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.
Explore the range of problem solving resources for 2nd to 8th grade students.
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Third Space Learning offers one-on-one math tutoring to help students improve their math skills. Highly qualified tutors deliver high-quality lessons aligned to state standards.
Former teachers and math experts write all of Third Space Learning’s tutoring lessons. Expertly designed lessons follow a “my turn, follow me, your turn” pedagogy to help students move from guided instruction and problem-solving to independent practice.
Throughout each lesson, tutors ask higher-level thinking questions to promote critical thinking and ensure students are developing a deep understanding of the content and problem-solving skills.
Problem-solving
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.
Teaching students how to choose and implement problem-solving strategies helps them develop mathematical reasoning skills and critical thinking they can apply to real-life problem-solving.
READ MORE :
- 8 Common Core math examples
- Tier 3 Interventions: A School Leaders Guide
- Tier 2 Interventions: A School Leaders Guide
- Tier 1 Interventions: A School Leaders Guide
There are many different strategies for problem-solving; Here are 5 problem-solving strategies: • draw a model • act it out • work backwards • write a number sentence • use a formula
Here are 10 strategies for problem-solving: • Read the problem aloud • Highlight keywords • Summarize the information • Determine the unknown • Make a plan • Draw a model • Act it out • Work backwards • Write a number sentence • Use a formula
1. Understand the problem 2. Devise a plan 3. Carry out the plan 4. Look back
Some strategies you can use to solve challenging math problems are: breaking the problem into smaller parts, using diagrams or models, applying logical reasoning, and trying different approaches.
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Ultimate Guide to Metacognition [FREE]
Looking for a summary on metacognition in relation to math teaching and learning?
Check out this guide featuring practical examples, tips and strategies to successfully embed metacognition across your school to accelerate math growth.
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Using NRICH Tasks to Develop Key Problem-solving Skills. This article, written for primary teachers, discusses what we mean by 'problem-solving skills' and draws attention to NRICH tasks which can help develop specific skills.
Rich Tasks. Every student deserves to have the opportunity to problem-solve and engage in genuine mathematical thinking. Rich tasks are designed to make these rich learning experiences possible. We’ve written these tasks to launch quickly, engage students, and promote the habits of mind mathematicians need: perseverance & pattern-seeking ...
Use a three-act math task to engage students with a content-focused, real-world problem! These math tasks were created with math modeling in mind– students are presented with a scenario and then given clues and hints to help them solve the problem.
Below you will find some questions you can ask yourself while you are solving a problem. The questions are divided into four phases, based loosely on those found in George Pólya's 1945 book "How to Solve It".
Looking for free math worksheets? You’ve found something even better! That’s because Khan Academy has over 100,000 free practice questions. And they’re even better than traditional math worksheets – more instantaneous, more interactive, and more fun! Just choose your grade level or topic to get access to 100% free practice questions ...
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.