- 1st Grade Math
- 2nd Grade Math
- 3rd Grade Math
- 4th Grade Math
- 5th Grade Math
- 6th Grade Math
- 7th Grade Math
- 8th Grade Math

## 10 Strategies for Problem Solving in Math

## What Are Problem Solving Strategies in Math?

## Strategies for Problem Solving in Math

## Understand the Problem

## Guess and Check

## Work It Out

## Work Backwards

## Find a Pattern

## Draw a Picture or Diagram

## Trial and error method

## Review answers with peers

Check out the Printable Math Worksheets for Your Kids!

- Specify your child’s math level
- Get practice worksheets for self-paced learning
- Your teacher sets up a personalized math learning plan for your child

## Related posts

## What Is Standardized Testing?

## 13 Successful Teaching Strategies

## Some of the Most Exciting Math Projects Ideas for Students

You are using an outdated browser. Please upgrade your browser to improve your experience.

## Math Problem Solving Strategies That Make Students Say “I Get It!”

Even students who are quick with math facts can get stuck when it comes to problem solving.

But you can teach these strategies for problem solving. You just need to know what they are.

We’ve compiled them here divided into four categories:

## Strategies for understanding a problem

## Read and reread the question

Teach students to interpret a question by using self-monitoring strategies such as:

- Rereading a question more slowly if it doesn’t make sense the first time
- Asking for help
- Highlighting or underlining important pieces of information.

## Identify important and extraneous information

## Schema approach

[Number/Quantity A] with [Number/Quantity B] removed becomes [end result].

Here are four common strategies students can use for problem solving.

## Visualizing

## Guess and check

## Find a pattern

## Work backward

- Starting with 12
- Taking the 8 from the 12
- Being left with 4
- Checking that 4 works when used instead of x

## Documenting working out

## Check along the way

- Does that last step look right?
- Does this follow on from the step I took before?
- Have I done any ‘smaller’ sums within the bigger problem that need checking?

Here are some checking strategies you can promote:

## Check with a partner

## Reread the problem with your solution

## Fixing mistakes

## Need more help developing problem solving skills?

## Get access to 900+ unique problem solving activities

## Privacy Overview

A website that teaches math lessons and more.

Sign Up For the Monthly Math Centers

## Strategies for Math Problem Solving

How do you teach strategies for solving math word problems?

Is there a step by step problem solving method that my students can use?

## 1. Drawing a Picture or Diagram.

## 2. Find a Pattern.

## 3. Guess and Check.

## 4. Make a List.

## 5. Use Reasoning.

- Does the information make sense?
- What do these numbers have in common?
- Is there a pattern or relationship between the numbers?
- What can you conclude about the information?
- Does this word problem ask you to find something?

Try one or all the strategies and download the problem solving guide today!

## Hi I’m Kelly!

- school Campus Bookshelves
- menu_book Bookshelves
- perm_media Learning Objects
- login Login
- how_to_reg Request Instructor Account
- hub Instructor Commons
- Download Page (PDF)
- Download Full Book (PDF)
- Periodic Table
- Physics Constants
- Scientific Calculator
- Reference & Cite
- Tools expand_more
- Readability

selected template will load here

## Module 1: Problem Solving Strategies

1. Image of Pólya by Thane Plambeck from Palo Alto, California (Flickr) [CC BY

First, you have to understand the problem.

After understanding, then make a plan.

Look back on your work. How could it be better?

Problem Solving Strategy 1 (Guess and Test)

Step 1: Understanding the problem

We are given in the problem that there are 25 chickens and cows.

All together there are 76 feet.

Chickens have 2 feet and cows have 4 feet.

We are trying to determine how many cows and how many chickens Mr. Jones has on his farm.

Going to use Guess and test along with making a tab

Many times the strategy below is used with guess and test.

Make a table and look for a pattern:

Notice we are going in the wrong direction! The total number of feet is decreasing!

Better! The total number of feet are increasing!

1. Click on this link to see an example of “Guess and Test”

http://www.mathstories.com/strategies.htm

2. Click on this link to see another example of Guess and Test.

http://www.mathinaction.org/problem-solving-strategies.html

Videos to watch demonstrating how to use "Draw a Picture".

1. Click on this link to see an example of “Draw a Picture”

2. Click on this link to see another example of Draw a Picture.

Problem Solving Strategy 3 ( Using a variable to find the sum of a sequence.)

Gauss's strategy for sequences.

last term = fixed number ( n -1) + first term

Ex: 2, 5, 8, ... Find the 200th term.

To find the sum of a sequence: sum = [(first term + last term) (number of terms)]/ 2

Sum = (2 + 599) (200) then divide by 2

Check in question 3: (10 points)

Find the 320 th term of 7, 10, 13, 16 …

Then find the sum of the first 320 terms.

Problem Solving Strategy 4 (Working Backwards)

Videos to watch demonstrating of “Working Backwards”

https://www.youtube.com/watch?v=5FFWTsMEeJw

1. We start with 11 and work backwards.

2. The opposite of subtraction is addition. We will add 7 to 11. We are now at 18.

3. The opposite of doubling something is dividing by 2. 18/2 = 9

4. This should be our answer. Looking back:

Christina is thinking of a number.

Problem Solving Strategy 5 (Looking for a Pattern)

Definition: A sequence is a pattern involving an ordered arrangement of numbers.

We first need to find a pattern.

Example 3: 10, 7, 4, 1, -2… find the next 2 numbers.

In this sequence, the numbers are decreasing by 3. So the next 2 numbers would be -2 -3 = -5

Example 4: 1, 2, 4, 8 … find the next two numbers.

So each number is being multiplied by 2.

1. Click on this link to see an example of “Looking for a Pattern”

2. Click on this link to see another example of Looking for a Pattern.

Problem Solving Strategy 6 (Make a List)

Example 1 : Can perfect squares end in a 2 or a 3?

List all the squares of the numbers 1 to 20.

1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400.

Videos demonstrating "Make a List"

How many ways can you make change for 23 cents using only pennies, nickels, and dimes? (10 points)

Problem Solving Strategy 7 (Solve a Simpler Problem)

How would we find the nth term?

1. To get from 1 to 3 what did we do?

2. To get from 3 to 9 what did we do?

Looking back: How would you find the nth term?

Find the 10 th term of the above sequence.

Problem Solving Strategy 8 (Process of Elimination)

This strategy can be used when there is only one possible solution.

It is more than 1 but less than 100.

a. We know it is an odd number between 1 and 100.

b. It is greater than 20 but less than 35

21, 23, 25, 27, 29, 31, 33, 35. These are the possibilities.

Check in question 6: (8 points)

The sum of the digits is divisible by 2.

The number is a multiple of 11.

Click on this link for a quick review of the problem solving strategies.

https://garyhall.org.uk/maths-problem-solving-strategies.html

## 3 Reads Strategy for Successful Problem Solving in Math

We have to read the problem closely to truly understand what is being asked of us as mathematicians.

## 3 Reads Strategy for Word Problems

## 2nd Read: Read for the Unknown

## 3rd Read: Read for Quantities

## Make a Plan

The posters will be sent to you when you fill out the form below.

You have successfully joined our subscriber list.

## Newsletter Sign Up

## Please Read!

I hope it helps you and your kiddos!

## Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

This site uses Akismet to reduce spam. Learn how your comment data is processed .

## ▹ FAVORITES ◃

## ▹ NEWSLETTER ◃

## Hi! I’m Tessa!

© 2023 Tales from Outside the Classroom ● All Rights Reserved

## Let's keep in touch! Sign up for my newsletter!

You will receive a confirmation email shortly. After confirming, you will be officially subscribed.

## Math Problem-Solving: Combining Cognitive & Metacognitive Strategies

- Reading the problem. The student reads the problem carefully, noting and attempting to clear up any areas of uncertainly or confusion (e.g., unknown vocabulary terms).
- Paraphrasing the problem. The student restates the problem in his or her own words.
- ‘Drawing’ the problem. The student creates a drawing of the problem, creating a visual representation of the word problem.
- Creating a plan to solve the problem. The student decides on the best way to solve the problem and develops a plan to do so.
- Predicting/Estimating the answer. The student estimates or predicts what the answer to the problem will be. The student may compute a quick approximation of the answer, using rounding or other shortcuts.
- C omputing the answer. The student follows the plan developed earlier to compute the answer to the problem.
- Checking the answer. The student methodically checks the calculations for each step of the problem. The student also compares the actual answer to the estimated answer calculated in a previous step to ensure that there is general agreement between the two values.
- The student first self-instructs by stating, or ‘saying’, the purpose of the step (‘ Say ’).
- The student next self-questions by ‘asking’ what he or she intends to do to complete the step (‘ Ask ’).
- The student concludes the step by self-monitoring, or ‘checking’, the successful completion of the step (‘ Check ’).
- Verifying that the student has the necessary foundation skills to solve math word problems
- Using explicit instruction techniques to teach the cognitive and metacognitive strategies
- Ensuring that all instructional tasks allow the student to experience an adequate rate of success
- Providing regular opportunities for the student to be engaged in active accurate academic responding
- Offering frequent performance feedback to motivate the student and shape his or her learning.

## Attachments

- Say-Ask-Check Student Self-Coaching (Metacognitive) Prompts
- Burns, M. K., VanDerHeyden, A. M., & Boice, C. H. (2008). Best practices in intensive academic interventions. In A. Thomas & J. Grimes (Eds.), Best practices in school psychology V (pp.1151-1162). Bethesda, MD: National Association of School Psychologists.
- Montague, M. (1992). The effects of cognitive and metacognitive strategy instruction on the mathematical problem solving of middle school students with learning disabilities. Journal of Learning Disabilities, 25, 230-248.
- Montague, M., & Dietz, S. (2009). Evaluating the evidence base for cognitive strategy instruction and mathematical problem solving. Exceptional Children, 75, 285-302.

## Crocodile Maths – A Problem-Solving Strategy

by Romero Esposito | Mar 7, 2023 | Crocodiles

## What Is The Crocodile Symbol Called In Math?

## What Does ≥ Mean?

The symbol * indicates that there is more than or equal to something.

## The Power Of Symbols In Text Messaging

## What Is This Maths Symbol Called?

## The Use Of ∈ In Math And Linguistics

## Recently Posted

EVERYTHING YOU NEED FOR THE YEAR >>> ALL ACCESS

## Math Problem Solving Strategies

Grab your Problem Solving Strategy Freebie Here !

## 1. C.U.B.E.S.

- Why I like it: Gives students a very specific ‘what to do.’
- Why I don’t like it: With all of the annotating of the problem, I’m not sure that students are actually reading the problem. None of the steps emphasize reading the problem but maybe that is a given.

## 2. R.U.N.S.

- Why I like it: Students are forced to think about what type of problem it is (factoring, division, etc) and then come up with a plan to solve it using a strategy sentence. This is a great strategy to teach when you are tackling various types of problems.
- Why I don’t like it: Though I love the opportunity for students to write in math, writing a strategy statement for every problem can eat up a lot of time.

## 3. U.P.S. CHECK

U.P.S. Check stands for understand, plan, solve, and check.

- Why I like it: I love that there is a check step in this problem solving strategy. Students having to defend the reasonableness of their answer is essential for students’ number sense.
- Why I don’t like it: It can be a little vague and doesn’t give concrete ‘what to dos.’ Checking that students completed the ‘understand’ step can be hard to see.

## 4. Maneuvering the Middle Strategy AKA K.N.O.W.S.

UPDATE: IT DOES HAVE A NAME! Thanks to our lovely readers, Wendi and Natalie!

- Know: This will help students find the important information.
- Need to Know: This will force students to reread the question and write down what they are trying to solve for.
- Organize: I think this would be a great place for teachers to emphasize drawing a model or picture.
- Work: Students show their calculations here.
- Solution: This is where students will ask themselves if the answer is reasonable and whether it answered the question.

## 5. Digital Learning Struggle

## Printable and Digital Math Performance Tasks

Check out these related products from my shop.

## Reader Interactions

Great idea! Thanks so much for sharing with our readers!

LOVE this idea! Will definitely use it this year! Thank you!

I would love an anchor chart for RUBY

That’s brilliant! Thank you for sharing!

Going off of your idea, Natalie, how about the following?

I’m doing this one. Love it. Thank you!!

## Math problem solving strategies with examples

## Problem Solving Strategies

- Data Protection
- Average satisfaction rating 4.8/5
- Explain mathematic problem
- Homework Help Solutions
- 24/7 Customer Help

## 17 Maths Problem Solving Strategies Boost your Learning

Improve your academic performance

Get support from expert teachers

## Module 1: Problem Solving Strategies

## Math Problem Solving Strategies That Make Students Say I

## 5 Strategies to Learn to Solve Math Word Problems

Mathematics understanding that gets you

The best way to protect your data is to keep it secure.

Keep up with the latest news and information by subscribing to our email list.

- Bipolar Disorder
- Race and Identity
- Stress Management
- Brain Health
- Relationships
- Online Therapy
- History and Biographies
- Student Resources
- Sleep and Dreaming
- Self-Improvement
- Mental Strength
- Family & Relationships
- Anxiety & Depression
- Coronavirus
- Mental Health
- Verywell Mind Insights
- The Winter Issue
- Editorial Process
- Meet Our Review Board
- Crisis Support

## Problem-Solving Strategies and Obstacles

JGI / Jamie Grill / Getty Images

## What Is Problem-Solving?

The problem-solving process involves:

- Discovery of the problem
- Deciding to tackle the issue
- Seeking to understand the problem more fully
- Researching available options or solutions
- Taking action to resolve the issue

## Problem-Solving Mental Processes

Several mental processes are at work during problem-solving. Among them are:

- Perceptually recognizing the problem
- Representing the problem in memory
- Considering relevant information that applies to the problem
- Identifying different aspects of the problem
- Labeling and describing the problem

## Problem-Solving Strategies

## Trial and Error

## How to Apply Problem-Solving Strategies in Real Life

- Create a flow chart . If you have time, you can take advantage of the algorithm approach to problem-solving by sitting down and making a flow chart of each potential solution, its consequences, and what happens next.
- Recall your past experiences . When a problem needs to be solved fairly quickly, heuristics may be a better approach. Think back to when you faced a similar issue, then use your knowledge and experience to choose the best option possible.
- Start trying potential solutions . If your options are limited, start trying them one by one to see which solution is best for achieving your desired goal. If a particular solution doesn't work, move on to the next.
- Take some time alone . Since insight is often achieved when you're alone, carve out time to be by yourself for a while. The answer to your problem may come to you, seemingly out of the blue, if you spend some time away from others.

## Obstacles to Problem-Solving

- Assumptions: When dealing with a problem, people can make assumptions about the constraints and obstacles that prevent certain solutions. Thus, they may not even try some potential options.
- Functional fixedness : This term refers to the tendency to view problems only in their customary manner. Functional fixedness prevents people from fully seeing all of the different options that might be available to find a solution.
- Irrelevant or misleading information: When trying to solve a problem, it's important to distinguish between information that is relevant to the issue and irrelevant data that can lead to faulty solutions. The more complex the problem, the easier it is to focus on misleading or irrelevant information.
- Mental set: A mental set is a tendency to only use solutions that have worked in the past rather than looking for alternative ideas. A mental set can work as a heuristic, making it a useful problem-solving tool. However, mental sets can also lead to inflexibility, making it more difficult to find effective solutions.

## Get Advice From The Verywell Mind Podcast

Follow Now : Apple Podcasts / Spotify / Google Podcasts

## How to Improve Your Problem-Solving Skills

- Recognize that a problem exists . If you are facing a problem, there are generally signs. For instance, if you have a mental illness , you may experience excessive fear or sadness, mood changes, and changes in sleeping or eating habits. Recognizing these signs can help you realize that an issue exists.
- Decide to solve the problem . Make a conscious decision to solve the issue at hand. Commit to yourself that you will go through the steps necessary to find a solution.
- Seek to fully understand the issue . Analyze the problem you face, looking at it from all sides. If your problem is relationship-related, for instance, ask yourself how the other person may be interpreting the issue. You might also consider how your actions might be contributing to the situation.
- Research potential options . Using the problem-solving strategies mentioned, research potential solutions. Make a list of options, then consider each one individually. What are some pros and cons of taking the available routes? What would you need to do to make them happen?
- Take action . Select the best solution possible and take action. Action is one of the steps required for change . So, go through the motions needed to resolve the issue.
- Try another option, if needed . If the solution you chose didn't work, don't give up. Either go through the problem-solving process again or simply try another option.

Dunbar K. Problem solving . A Companion to Cognitive Science . 2017. doi:10.1002/9781405164535.ch20

National Alliance on Mental Illness. Warning signs and symptoms .

Mayer RE. Thinking, problem solving, cognition, 2nd ed .

## 5 Teaching Mathematics Through Problem Solving

Consider the following worthwhile-problem criteria developed by Lappan and Phillips (1998):

- The problem has important, useful mathematics embedded in it.
- The problem requires high-level thinking and problem solving.
- The problem contributes to the conceptual development of students.
- The problem creates an opportunity for the teacher to assess what his or her students are learning and where they are experiencing difficulty.
- The problem can be approached by students in multiple ways using different solution strategies.
- The problem has various solutions or allows different decisions or positions to be taken and defended.
- The problem encourages student engagement and discourse.
- The problem connects to other important mathematical ideas.
- The problem promotes the skillful use of mathematics.
- The problem provides an opportunity to practice important skills.

Key features of a good mathematics problem includes:

- It must begin where the students are mathematically.
- The feature of the problem must be the mathematics that students are to learn.
- It must require justifications and explanations for both answers and methods of solving.

## Mathematics Tasks and Activities that Promote Teaching through Problem Solving

## Choosing the Right Task

- Teachers must do the activity first. What is problematic about the activity? What will you need to do BEFORE the activity and AFTER the activity? Additionally, think how your students would do the activity.
- What mathematical ideas will the activity develop? Are there connections to other related mathematics topics, or other content areas?
- Can the activity accomplish your learning objective/goals?

## Low Floor High Ceiling Tasks

The strengths of using Low Floor High Ceiling Tasks:

- Allows students to show what they can do, not what they can’t.
- Provides differentiation to all students.
- Promotes a positive classroom environment.
- Advances a growth mindset in students
- Aligns with the Standards for Mathematical Practice

Examples of some Low Floor High Ceiling Tasks can be found at the following sites:

- YouCubed – under grades choose Low Floor High Ceiling
- NRICH Creating a Low Threshold High Ceiling Classroom
- Inside Mathematics Problems of the Month

## Math in 3-Acts

Act Three is the “reveal.” Students share their thinking as well as their solutions.

- Dan Meyer’s Three-Act Math Tasks
- Graham Fletcher3-Act Tasks ]
- Math in 3-Acts: Real World Math Problems to Make Math Contextual, Visual and Concrete

## Number Talks

- The teacher presents a problem for students to solve mentally.
- Provide adequate “ wait time .”
- The teacher calls on a students and asks, “What were you thinking?” and “Explain your thinking.”
- For each student who volunteers to share their strategy, write their thinking on the board. Make sure to accurately record their thinking; do not correct their responses.
- Invite students to question each other about their strategies, compare and contrast the strategies, and ask for clarification about strategies that are confusing.

## Saying “This is Easy”

When the teacher says, “this is easy,” students may think,

- “Everyone else understands and I don’t. I can’t do this!”
- Students may just give up and surrender the mathematics to their classmates.
- Students may shut down.

Instead, you and your students could say the following:

## Using “Worksheets”

- Provide your students a bridge between the concrete and abstract
- Serve as models that support students’ thinking
- Provide another representation
- Support student engagement
- Give students ownership of their own learning.

Adapted from “ The Top 5 Reasons for Using Manipulatives in the Classroom ”.

involves teaching a skill so that a student can later solve a story problem

when we teach students how to problem solve

teaching mathematics content through real contexts, problems, situations, and models

20 seconds to 2 minutes for students to make sense of questions

## Share This Book

## 4 Math Problem Solving Strategies

These useful Math problem-solving strategies will help you pass the GED Math test.

## Fast & Easy Online GED Classes

Get Your Diploma in 2 Months. It doesn’t matter when you left school.

The four problem-solving strategies discussed here come with examples as well and include:

## Problem-Solving Strategy 1: Work Backward

## Online GED classes- Simple, Fast & Easy. Pass your GED next month.

## Problem-Solving Strategy 2: Make A List Or A Table

quarters dimes nickels 1 1 0 1 0 2 0 3 1 0 2 3 0 1 5 0 0 7

## Problem-Solving Strategy 3: Solve A Simpler Problem

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55

Notice the following: 1 + 10 = 11 2 + 9 = 11 3 + 8 = 11 4 + 7 = 11 5 + 6 = 11

1 + 2 + 3 … 499 + 500 = 250 x 501 = 125,250

We can apply a similar problem-solving strategy by using subgoals. Let’s consider the following:

## Problem-Solving Strategy 4: Guess & Check

## Problem Solving in Mathematics

## Use Established Procedures

## Look for Clue Words

Common clue words for addition problems:

Common clue words for subtraction problems:

Common clue words for multiplication problems:

Common clue words for division problems:

## Read the Problem Carefully

- Ask yourself if you've seen a problem similar to this one. If so, what is similar about it?
- What did you need to do in that instance?
- What facts are you given about this problem?
- What facts do you still need to find out about this problem?

## Develop a Plan and Review Your Work

- Define your problem-solving strategy or strategies. This might mean identifying patterns, using known formulas, using sketches, and even guessing and checking.
- If your strategy doesn't work, it may lead you to an ah-ha moment and to a strategy that does work.

If it seems like you’ve solved the problem, ask yourself the following:

- Does your solution seem probable?
- Does it answer the initial question?
- Did you answer using the language in the question?
- Did you answer using the same units?

If you feel confident that the answer is “yes” to all questions, consider your problem solved.

## Tips and Hints

Some key questions to consider as you approach the problem may be:

- What are the keywords in the problem?
- Do I need a data visual, such as a diagram, list, table, chart, or graph?
- Is there a formula or equation that I'll need? If so, which one?
- Will I need to use a calculator? Is there a pattern I can use or follow?

## Problem Solving Strategies

## Pólya’s How to Solve It

- First, you have to understand the problem.
- After understanding, then make a plan.
- Carry out the plan.
- Look back on your work. How could it be better?

- What if the picture was different?
- What if the numbers were simpler?
- What if I just made up some numbers?

This brings us to the most important problem solving strategy of all:

## Problem 2 (Payback)

## Think/Pair/Share

Watch the solution only after you tried this strategy for yourself.

## Problem 3 (Squares on a Chess Board)

## Think / Pair / Share

- Describe all of the patterns you see in the table.
- Can you explain and justify any of the patterns you see? How can you be sure they will continue?
- What calculation would you do to find the total number of squares on a 100 × 100 chess board?

## Problem 4 (Broken Clock)

- What is the sum of all the numbers on the clock’s face?
- Can I find two consecutive numbers that give the correct sum? Or four consecutive numbers? Or some other amount?
- How do I know when I am done? When should I stop looking?

The home of mathematics education in New Zealand.

## Problem Solving Strategies

What are problem solving strategies.

Common Problem Solving Strategies

- Guess (includes guess and check, guess and improve)
- Act It Out (act it out and use equipment)
- Draw (this includes drawing pictures and diagrams)
- Make a List (includes making a table)
- Think (includes using skills you know already)

## An In-Depth Look At Strategies

- Guess and check is one of the simplest strategies. Anyone can guess an answer. If they can also check that the guess fits the conditions of the problem, then they have mastered guess and check. This is a strategy that would certainly work on the Farmyard problem described below but it could take a lot of time and a lot of computation. Because it is so simple, you may have difficulty weaning some students away from guess and check. As problems get more difficult, other strategies become more important and more effective. However, sometimes when students are completely stuck, guessing and checking will provide a useful way to start to explore a problem. Hopefully that exploration will lead to a more efficient strategy and then to a solution.
- Guess and improve is slightly more sophisticated than guess and check. The idea is that you use your first incorrect guess to make an improved next guess. You can see it in action in the Farmyard problem. In relatively straightforward problems like that, it is often fairly easy to see how to improve the last guess. In some problems though, where there are more variables, it may not be clear at first which way to change the guessing.
- Young students especially, enjoy using Act it Out . Students themselves take the role of things in the problem. In the Farmyard problem, the students might take the role of the animals though it is unlikely that you would have 87 students in your class! But if there are not enough students you might be able to include a teddy or two. This is an effective strategy for demonstration purposes in front of the whole class. On the other hand, it can also be cumbersome when used by groups, especially if a largish number of students is involved. Sometimes the students acting out the problem may get less out of the exercise than the students watching. This is because the participants are so engrossed in the mechanics of what they are doing that they don’t see the underlying mathematics.
- Use Equipment is a strategy related to Act it Out. Generally speaking, any object that can be used in some way to represent the situation the students are trying to solve, is equipment. One of the difficulties with using equipment is keeping track of the solution. The students need to be encouraged to keep track of their working as they manipulate the equipment. Some students need to be encouraged and helped to use equipment. Many students seem to prefer to draw. This may be because it gives them a better representation of the problem in hand. Since there are problems where using equipment is a better strategy than drawing, you should encourage students' use of equipment by modelling its use yourself from time to time.
- It is fairly clear that a picture has to be used in the strategy Draw a Picture . But the picture need not be too elaborate. It should only contain enough detail to help solve the problem. Hence a rough circle with two marks is quite sufficient for chickens and a blob plus four marks will do a pig. All students should be encouraged to use this strategy at some point because it helps them ‘see’ the problem and it can develop into quite a sophisticated strategy later.
- It’s hard to know where Drawing a Picture ends and Drawing a Diagram begins. You might think of a diagram as anything that you can draw which isn’t a picture. But where do you draw the line between a picture and a diagram? As you can see with the chickens and pigs, discussed above, regular picture drawing develops into drawing a diagram. Venn diagrams and tree diagrams are particular types of diagrams that we use so often they have been given names in their own right.
- There are a number of ways of using Make a Table . These range from tables of numbers to help solve problems like the Farmyard, to the sort of tables with ticks and crosses that are often used in logic problems. Tables can also be an efficient way of finding number patterns.
- When an Organised List is being used, it should be arranged in such a way that there is some natural order implicit in its construction. For example, shopping lists are generally not organised. They usually grow haphazardly as you think of each item. A little thought might make them organised. Putting all the meat together, all the vegetables together, and all the drinks together, could do this for you. Even more organisation could be forced by putting all the meat items in alphabetical order, and so on. Someone we know lists the items on her list in the order that they appear on her route through the supermarket.
- Being systematic may mean making a table or an organised list but it can also mean keeping your working in some order so that it is easy to follow when you have to go back over it. It means that you should work logically as you go along and make sure you don’t miss any steps in an argument. And it also means following an idea for a while to see where it leads, rather than jumping about all over the place chasing lots of possible ideas.
- It is very important to keep track of your work. We have seen several groups of students acting out a problem and having trouble at the end simply because they had not kept track of what they were doing. So keeping track is particularly important with Act it Out and Using Equipment. But it is important in many other situations too. Students have to know where they have been and where they are going or they will get hopelessly muddled. This begins to be more significant as the problems get more difficult and involve more and more steps.
- In many ways looking for patterns is what mathematics is all about. We want to know how things are connected and how things work and this is made easier if we can find patterns. Patterns make things easier because they tell us how a group of objects acts in the same way. Once we see a pattern we have much more control over what we are doing.
- Using symmetry helps us to reduce the difficulty level of a problem. Playing Noughts and crosses, for instance, you will have realised that there are three and not nine ways to put the first symbol down. This immediately reduces the number of possibilities for the game and makes it easier to analyse. This sort of argument comes up all the time and should be grabbed with glee when you see it.
- Finally working backwards is a standard strategy that only seems to have restricted use. However, it’s a powerful tool when it can be used. In the kind of problems we will be using in this web-site, it will be most often of value when we are looking at games. It frequently turns out to be worth looking at what happens at the end of a game and then work backward to the beginning, in order to see what moves are best.
- Then we come to use known skills . This isn't usually listed in most lists of problem solving strategies but as we have gone through the problems in this web site, we have found it to be quite common. The trick here is to see which skills that you know can be applied to the problem in hand. One example of this type is Fertiliser (Measurement, level 4). In this problem, the problem solver has to know the formula for the area of a rectangle to be able to use the data of the problem. This strategy is related to the first step of problem solving when the problem solver thinks 'have I seen a problem like this before?' Being able to relate a word problem to some previously acquired skill is not easy but it is extremely important.

## Uses of Strategies

Different strategies have different uses. We’ll illustrate this by means of a problem.

What Strategies Can Be Used At What Levels

So you see that a very simple strategy like guess and check can develop to a very deep level.

## What are the strategies for problem solving

## 5 Strategies for Problem Solving

I appreciate your loyalty and support.

## 14 Effective Problem

## Problem Solving Strategies for the Workplace [2023] Asana

Mathematical equations are used to express relationships between numbers and symbols.

Improve your theoretical performance

The best way to improve your theoretical performance is to practice as often as possible.

Improve your academic performance

You can improve your academic performance by studying regularly and attending class.

## Problem Solving Strategies

I enjoy spending my free time with my family and friends.

The best method for you will depend on your individual needs and goals.

Completing a task step-by-step can help ensure that it is done correctly and efficiently.

Our team is available 24/7 to help you with whatever you need.

## Problem solving strategies with examples

## Problem Solving Strategies for the Workplace [2023] Asana

You can build a bright future by taking advantage of opportunities and planning for success.

Knowing is the first step to understanding.

Free time to spend with your friends

I love spending time with my friends when I have free time.

- Arts & Music
- English Language Arts
- World Language
- Social Studies - History
- Holidays / Seasonal
- Independent Work Packet
- Easel by TPT
- Google Apps

## Interactive resources you can assign in your digital classroom from TPT.

## Easel Activities

## Easel Assessments

Unlock access to 4 million resources — at no cost to you — with a school-funded subscription..

word problem solving with table making strategy for free

## Resource Types

All resource types, results for word problem solving with table making strategy for free.

## Math Problem Solving Strategies Posters

## Interactive Math 2nd Grade 12 Activities CCSS Aligned with "I Can" Statements

## Problem Solving Unit 1: Make a List or Table

## Math Interactive Notebook Part One

## Social Emotional Flashcards | Toddler Curriculum Materials

## Book 2 Chapter 1 Material

## Ratios and Proportions Mini-Unit | Proportional Reasoning | Distance Learning

Also included in: 6th Grade Math MEGA BUNDLE - Review, Interventions, Escape Rooms - Entire Year

## Problem Solving Make a Table FREE Practice Problem

## Guided Math Dry-Erase Mat- Addition and Subtraction for Kindergarten/First Grade

TPT empowers educators to teach at their best.

## Keep in Touch!

## Get FIVE days of free math lessons!

## Teaching Math Problem Solving Strategies

Teaching math problem solving strategies in middle school.

- “In this problem, I need to….”
- “From the problem, I know….”
- “I already know…”
- “To solve the problem, I will…”
- “I know my answer is correct because…”

## Benefits of Sentence Starters

Sometimes this process took quite a long time, but it was helpful, because:

- It made many students slow down and think a bit more about what they were doing mathematically.
- Students took a little more time to analyze the problem (rather than picking out the numbers and guessing at an operation!).

- Guess and Check
- Work Backwards
- Draw a Picture
- Use Logical Reasoning
- Create a Table
- Look for a Pattern
- Make an Organized List.

## Teaching Math Problem Solving in Middle School

- I tried to use the problem solving as warm-ups some days, but it would often take 30 minutes or more, especially if we got into a good discussion, leaving little time for a lesson.
- I found that spending too many class periods using the problem solving ended up putting me too far behind in the curriculum (although I’d argue that my students became better thinkers:-), so I had to make some alterations.
- highlight/underline the question in the problem
- shorten up the writing to bullet points
- highlight/underline the important information in the problem

## Math Problem Solving Steps

Find Out When they Find Out, students identify what they need to know to solve the problem.

- They underline the question the problem is asking them to answer and highlight the important information in the problem.
- They shouldn’t attempt to highlight anything until they’ve identified what question they are answering – only then can they decide what is important to that question.
- In this step, they also identify their own background knowledge about the concepts in that particular math problem.

- Make an Organized List: when there are many possible answers/combinations; or when making a list may help identify a pattern.
- Guess and Check: when you can make an educated guess and then use an incorrect guess to help you decide if the next guess should be higher or lower. This is often used when you’re looking for 2 unknown numbers that meet certain requirements.
- Work Backwards: when you have the answer to a problem or situation, but the “starting” number is missing
- when data needs to be organized
- with ratios (ratio tables)
- when using the coordinate plane
- with directional questions
- with shape-related questions (area, perimeter, surface area, volume)
- or when it’s just hard to picture in your mind
- Find a Pattern: when numbers in a problem continue to increase, decrease or both
- when the missing number(s) can be expressed in terms of the same variable
- when the information can be used in a known formula (like area, perimeter, surface area, volume, percent)
- when a “yes” for one answer means “no” for another
- the process of elimination can be used

Solve Students use their chosen strategy to find the solution.

- Reread the question; make sure your solution answers the question.
- Redo the math problem and see if you get the same answer.
- Check with a different method, if possible.
- If you used an equation, substitute your answer into the equation.
- Ask – does your answer make sense/is it reasonable?

## Teaching the Math Problem Solving Strategies

- Students keep reference sheets in their binders, so they can quickly refer to the steps and strategies. A few newer reference math wheels can be found in this blog post .
- For example, I often find that a ‘Guess and Check’ problem can be solved algebraically, so we’ll do the guessing and checking together first, and then we’ll talk about an algebraic equation – some students can follow the line of thinking well, and will try it on their own the next time; for others, the examples are exposure, and they’ll need to see several more examples before they give it a try.

## Using Doodle Notes to Teach Problem Solving Strategies

This year, I’m trying something new – I created a set of Doodle Notes to use during our unit.

- The first page is a summary of the steps and possible strategies.
- There’s a separate page for each strategy, with a problem to work through AND an independent practice page for each

## read next...

## Five Math Lessons to Help You Ace Your Teacher Observation

## 9 Quick and Easy Valentine’s Day Math Activities

## Five Reasons to Use Mixed Math Practice

## New Year Activities for Middle School Math

## FIND IT FAST

Select the image above to learn more!

## Buy new: $9.95

- Free returns are available for the shipping address you chose. You can return the item for any reason in new and unused condition: no shipping charges
- Learn more about free returns.
- Go to your orders and start the return
- Select the return method

## Sorry, there was a problem.

Read instantly on your browser with Kindle for Web .

Using your mobile phone camera - scan the code below and download the Kindle app.

## Problem Solving Strategies for Elementary-School Math Paperback – June 24, 2020

## Enhance your purchase

- Reading age 7 - 12 years
- Print length 124 pages
- Language English
- Grade level 2 - 6
- Dimensions 5.98 x 0.26 x 9.02 inches
- Publisher Now Publishers Inc
- Publication date June 24, 2020
- ISBN-10 1680839845
- ISBN-13 978-1680839845
- See all details

## Customers who viewed this item also viewed

## Product details

- Publisher : Now Publishers Inc; Illustrated edition (June 24, 2020)
- Language : English
- Paperback : 124 pages
- ISBN-10 : 1680839845
- ISBN-13 : 978-1680839845
- Reading age : 7 - 12 years
- Grade level : 2 - 6
- Item Weight : 6.2 ounces
- Dimensions : 5.98 x 0.26 x 9.02 inches
- #3,720 in Children's Math Books (Books)

## Customer reviews

## Top reviews from the United States

There was a problem filtering reviews right now. please try again later..

- Amazon Newsletter
- About Amazon
- Accessibility
- Sustainability
- Press Center
- Investor Relations
- Amazon Devices
- Amazon Science
- Sell products on Amazon
- Sell apps on Amazon
- Supply to Amazon
- Protect & Build Your Brand
- Become an Affiliate
- Become a Delivery Driver
- Start a package delivery business
- Advertise Your Products
- Self-Publish with Us
- Host an Amazon Hub
- › See More Ways to Make Money
- Amazon Rewards Visa Signature Cards
- Amazon Store Card
- Amazon Secured Card
- Amazon Business Card
- Shop with Points
- Credit Card Marketplace
- Reload Your Balance
- Amazon Currency Converter
- Amazon and COVID-19
- Your Account
- Your Orders
- Shipping Rates & Policies
- Amazon Prime
- Returns & Replacements
- Manage Your Content and Devices
- Your Recalls and Product Safety Alerts
- Amazon Assistant
- Conditions of Use
- Privacy Notice
- Your Ads Privacy Choices

- Daily Deals
- Brand Outlet
- Help & Contact
- Watchlist Expand Watch List Loading... Sign in to see your user information
- Recently Viewed
- Bids/Offers
- Purchase History
- Saved Searches
- Saved Sellers
- Collection beta
- The eBay vault
- Notification
- Expand Cart Loading... Something went wrong. View cart for details.
- Back to home page
- Share | Add to Watchlist

## People who viewed this item also viewed

Be the first to write a review .

## Item Information

## Oops! Looks like we're having trouble connecting to our server.

Refresh your browser window to try again.

An error occurred, please try again.

## Bottom panel for Description

## More to explore :

- Math Education Textbooks ,
- Math Textbooks 1900-1949 ,
- Nonfiction Success Paperbacks Books ,
- Nonfiction Success Fiction & Nonfiction Books ,
- Math Paperback Educational Textbooks in Russian ,
- Spanish Math Workbook, Study Guide Textbooks & Educational Books ,
- English Math Workbook, Study Guide Textbooks & Educational Books ,
- Ages 2-3 Children's Books ,
- Abeka 4th Grade School Textbooks & Study Guides ,
- Age 2-3 Picture Books for Children

## IMAGES

## VIDEO

## COMMENTS

This strategy is a self-monitoring method for math students since it demands that they first understand the problem. If they immediately start solving the problem, they risk making mistakes. Using this strategy, students will keep track of their ideas and correct mistakes before arriving at a final answer.

Problem Solving Strategy 9 (Find the Math, Remove the Context). Sometimes the problem has a lot of details in it that are unimportant, or at least unimportant for getting started. The goal is to find the underlying math problem, then come back to the original question and see if you can solve it using the math.

This is a math intervention strategy that can make problem solving easier for all students, regardless of ability. Compare different word problems of the same type and construct a formula, or mathematical sentence stem, that applies to them all. For example, a simple subtraction problems could be expressed as:

There are five strategies for math problem solving to word problems that you can teach your students in thirty minutes class. Before introducing these skills make sure you have reviewed how to read word problems first . The second step in the problem solving process is to teach strategies that will help your students become better problem solvers.

Problem Solving Strategy 1 (Guess and Test) Make a guess and test to see if it satisfies the demands of the problem. If it doesn't, alter the guess appropriately and check again. Keep doing this until you find a solution. Example: Mr. Jones has a total of 25 chickens and cows on his farm.

3 Reads Strategy for Successful Problem Solving in Math Word Problems are often the hardest part of our math instruction. They can visually overwhelm students. They often contain extraneous information or multiple steps for completion. Students often struggle to persevere through complex problems.

First, the student is taught a 7-step process for attacking a math word problem (cognitive strategy). Second, the instructor trains the student to use a three-part self-coaching routine for each of the seven problem-solving steps (metacognitive strategy). In the cognitive part of this multi-strategy intervention, the student learns an explicit ...

Elementary Math Problem Solving -Acting it OutIn this video, we explore one of eight problem-solving strategies for the primary math student. Students are in...

The crocodile maths strategy can be used to solve addition, subtraction, multiplication, and division problems. Can you solve the crocodile math problem that stumped Scottish students? There was an uproar on social media because of the difficulty, and Scottish students cried. Check out my video for a quick explanation of the problem and how it ...

This strategy for selecting and teaching word problems guides students to develop their understanding of math concepts. By Tara Koehler, John Sammon. March 1, 2023. Johner Images / Alamy. Word problems in mathematics are a powerful tool for helping students make sense of and reason with mathematical concepts.

Math Problem Solving Strategies 1. C.U.B.E.S. C.U.B.E.S stands for circle the important numbers, underline the question, box the words that are keywords, eliminate extra information, and solve by showing work. Why I like it: Gives students a very specific 'what to do.'

Math Problem Solving Strategies That Make Students Say I In these lessons, we will learn some math problem solving strategies for example, Verbal Model (or Logical Reasoning), Algebraic Model, Block Model (or

Problem-solving helps you figure out how to achieve these desires. The problem-solving process involves: Discovery of the problem. Deciding to tackle the issue. Seeking to understand the problem more fully. Researching available options or solutions. Taking action to resolve the issue.

Problem solving in mathematics is one of the most important topics to teach; learning to problem solve helps students develop a sense of solving real-life problems and apply mathematics to real world situations. It is also used for a deeper understanding of mathematical concepts.

There are 7 strategies that are normally covered in our math challenge program: DRAW A PICTURE/DIAGRAM/MODEL LOOK FOR PATTERNS WORK BACKWARD ACT IT OUT GUESS AND CHECK MAKE AN ORGANIZED LIST OR TABLE USE LOGICAL REASONING

The book illustrates various strategies for solving math problems; each chapter illustrates a specific strategy by providing completely worked out solutions for several problems (around 10 to 15 per chapter). The only thing I found missing was end-of-chapter exercises or even a set of miscellaneous problems at the end of the book for the ...

A very useful strategy to solve Math problems is to first solve a far simpler problem. When we use this strategy, we first solve a more familiar or simpler case of a similar problem. Then, we can use the same relationships and concepts to solve the original Math problem. Example 1: The Math problem is: What is the sum of the integers 1 through 500?

Define your problem-solving strategy or strategies. This might mean identifying patterns, using known formulas, using sketches, and even guessing and checking. If your strategy doesn't work, it may lead you to an ah-ha moment and to a strategy that does work. If it seems like you've solved the problem, ask yourself the following:

Problem Solving Strategy 9 (Find the Math, Remove the Context). Sometimes the problem has a lot of details in it that are unimportant, or at least unimportant for getting started. The goal is to find the underlying math problem, then come back to the original question and see if you can solve it using the math.

Common Problem Solving Strategies Guess (includes guess and check, guess and improve) Act It Out (act it out and use equipment) Draw (this includes drawing pictures and diagrams) Make a List (includes making a table) Think (includes using skills you know already)

What are the strategies for problem solving - Discovery of the problem Deciding to tackle the issue Seeking to understand the problem more fully Researching ... Mathematicians work to clear up the misunderstandings and false beliefs that people have about mathematics. Determine math question Math is the study of numbers, space, and structure ...

Here are some strategies to solve a math problem. These strategies begin with Math Practice Standard 1: Make sense of problems and persevere in solving them. They all start with read the problem carefully to figure out what it asks. Read each sentence carefully to make sure you comprehend it. Decide what the problem includes that you need to ...

Using the guess and check problem solving strategy to help solve math word problems. Example: Jamie spent $40 for an outfit. She paid for the items using $10. Solving word questions. Word questions can be tricky, but there are some helpful tips you can follow to solve them.

Full set of problems available here. Great for differentiation, at math centers, or whole class. Practice with other problem solving techniques. You may also like: Problem Solving Strategies: Printables for the classroom and notebook Ratio: 3 ways to explore ratio (common core aligned) Rational vs. Irrational Numbers: 3 kinesthetic activities ...

Math Problem Solving Steps. Now, when I teach these problem solving strategies, our steps are: Find Out, Choose a Strategy, Solve, and Check Your Answer. Find Out. When they Find Out, students identify what they need to know to solve the problem. They underline the question the problem is asking them to answer and highlight the important ...

The book contains more than 100 challenging problems that are suitable for elementary-school students, along with their step-by-step solution to help the reader master these strategies. This book will help you: - Learn seven useful problem solving strategies that can be used in many challenging math problems.

Strategize it! The No. 1 issue math students struggle with is solving word problems. Math Problem Solving provides a solution. Each lesson teaches a key problem-solving strategy by breaking it down into manageable steps and then providing guided and independent practice to reinforce the learning. Plus-it aligns with your core math program and ...