problem solving strategies for math 5th grade

• 1st Grade Math
• 2nd Grade Math
• 3rd Grade Math
• 4th Grade Math
• 5th Grade Math
• 6th Grade Math
• 7th Grade Math
• 8th Grade Math
• Knowledge Base
• Math for kids

10 Strategies for Problem Solving in Math

May 19, 2022

8 minutes read

When faced with problem-solving, children often get stuck. Word puzzles and math questions with an unknown variable, like x, usually confuse them. Therefore, this article discusses math strategies and how your students may use them since instructors often have to lead students through this problem-solving maze.

What Are Problem Solving Strategies in Math?

If you want to fix a problem, you need a solid plan. Math strategies for problem solving are ways of tackling math in a way that guarantees better outcomes. These strategies simplify math for kids so that less time is spent figuring out the problem. Both those new to mathematics and those more knowledgeable about the subject may benefit from these methods.

There are several methods to apply problem-solving procedures in math, and each strategy is different. While none of these methods failsafe, they may help your student become a better problem solver, particularly when paired with practice and examples. The more math problems kids tackle, the more math problem solving skills they acquire, and practice is the key.

Strategies for Problem-solving in Math

Even if a student is not a math wiz, a suitable solution to mathematical problems in math may help them discover answers. There is no one best method for helping students solve arithmetic problems, but the following ten approaches have shown to be very effective.

Understand the Problem

Understanding the nature of math problems is a prerequisite to solving them. They need to specify what kind of issue it is ( fraction problem , word problem, quadratic equation, etc.). Searching for keywords in the math problem, revisiting similar questions, or consulting the internet are all great ways to strengthen their grasp of the material. This step keeps the pupil on track.

1:1 Math Lessons

Want to raise a genius? Start learning Math with Brighterly

Guess and check.

One of the time-intensive strategies for resolving mathematical problems is the guess and check method. In this approach, students keep guessing until they get the answer right.

After assuming how to solve a math issue, students should reintroduce that assumption to check for correctness. While the approach may appear cumbersome, it is typically successful in revealing patterns in a child’s thought process.

Work It Out

Encourage pupils to record their thinking process as they go through a math problem. Since this technique requires an initial comprehension of the topic, it serves as a self-monitoring method for mathematics students. If they immediately start solving the problem, they risk making mistakes.

Students may keep track of their ideas and fix their math problems as they go along using this method. A youngster may still need you to explain their methods of solving the arithmetic questions on the extra page. This confirmation stage etches the steps they took to solve the problem in their minds.

Work Backwards

In mathematics, a fresh perspective is sometimes the key to a successful solution. Young people need to know that the ability to recreate math problems is valuable in many professional fields, including project management and engineering.

Students may better prepare for difficulties in real-world circumstances by using the “Work Backwards” technique. The end product may be used as a start-off point to identify the underlying issue.

In most cases, a visual representation of a math problem may help youngsters understand it better. Some of the most helpful math tactics for kids include having them play out the issue and picture how to solve it.

One way to visualize a workout is to use a blank piece of paper to draw a picture or make tally marks. Students might also use a marker and a whiteboard to draw as they demonstrate the technique before writing it down.

Find a Pattern

Kids who use pattern recognition techniques can better grasp math concepts and retain formulae. The most remarkable technique for problem solving in mathematics is to help students see patterns in math problems by instructing them how to extract and list relevant details. This method may be used by students when learning shapes and other topics that need repetition.

Students may use this strategy to spot patterns and fill in the blanks. Over time, this strategy will help kids answer math problems quickly.

When faced with a math word problem, it might be helpful to ask, “What are some possible solutions to this issue?” It encourages you to give the problem more thought, develop creative solutions, and prevent you from being stuck in a rut. So, tell the pupils to think about the math problems and not just go with the first solution that comes to mind.

Draw a Picture or Diagram

Drawing a picture of a math problem can help kids understand how to solve it, just like picturing it can help them see it. Shapes or numbers could be used to show the forms to keep things easy. Kids might learn how to use dots or letters to show the parts of a pattern or graph if you teach them.

Charts and graphs can be useful even when math isn’t involved. Kids can draw pictures of the ideas they read about to help them remember them after they’ve learned them. The plan for how to solve the mathematical problem will help kids understand what the problem is and how to solve it.

Trial and Error Method

The trial and error method may be one of the most common problem solving strategies for kids to figure out how to solve problems. But how well this strategy is used will determine how well it works. Students have a hard time figuring out math questions if they don’t have clear formulas or instructions.

They have a better chance of getting the correct answer, though, if they first make a list of possible answers based on rules they already know and then try each one. Don’t be too quick to tell kids they shouldn’t learn by making mistakes.

Review Answers with Peers

It’s fun to work on your math skills with friends by reviewing the answers to math questions together. If different students have different ideas about how to solve the same problem, get them to share their thoughts with the class.

During class time, kids’ ways of working might be compared. Then, students can make their points stronger by fixing these problems.

Check out the Printable Math Worksheets for Your Kids!

There are different ways to solve problems that can affect how fast and well students do on math tests. That’s why they need to learn the best ways to do things. If students follow the steps in this piece, they will have better experiences with solving math questions.

Jessica is a a seasoned math tutor with over a decade of experience in the field. With a BSc and Master’s degree in Mathematics, she enjoys nurturing math geniuses, regardless of their age, grade, and skills. Apart from tutoring, Jessica blogs at Brighterly. She also has experience in child psychology, homeschooling and curriculum consultation for schools and EdTech websites.

As adults, we take numbers for granted, but preschoolers and kindergartners have no idea what these symbols mean. Yet, we often demand instant understanding and flawless performance when we start teaching numbers to our children. If you don’t have a clue about how to teach numbers for kids, browse no more. You will get four […]

Teaching children is a complex process because they require more attention than an adult person. You may need to employ different teaching strategies when teaching kids. But what are teaching strategies? Teaching strategies are the methods to ensure your kids or students learn efficiently. But not all strategies yield similarly, and if the one you […]

Book 1 to 1 Math Lesson

Kid’s grade

After-School Math Program Boost Your Child's Math Abilities! Ideal for 1st-12th Graders, Perfectly Synced with School Curriculum!

After-School Math Program

Related posts.

What Is Standardized Testing?

As students progress through grades and levels in school, their teachers need to monitor the progress. The best way for teachers and schools to assess students is to apply standardized testing. The following sections will analyze standardized testing and help you make the right call when deciding whether your child or students should go through […]

Jun 30, 2022

How to Teach Counting: All You Need to Know

Counting is a fundamental skill alongside reading, and kids should start learning to count much earlier than in pre-K. While counting seems simple, it’s a more complicated process under close consideration, especially when you explain it to kids. As we go on, you will learn how to teach a child to count using the stages, […]

Mar 14, 2022

ADHD And Math: How to Help Kids

Does your child with ADHD dread math? This subject can be hard to understand, even for adults. So, it is no wonder that a student with a different style of thinking has a tough time, and it is natural to ask yourself, «Are kids with ADHD good at math?»  This article will provide useful tips […]

Apr 19, 2024

We use cookies to help give you the best service possible. If you continue to use the website we will understand that you consent to the Terms and Conditions. These cookies are safe and secure. We will not share your history logs with third parties. Learn More

• PRINT TO PLAY
• DIGITAL GAMES

Problem-Solving Strategies

October 16, 2019

There are many different ways to solve a math problem, and equipping students with problem-solving strategies is just as important as teaching computation and algorithms. Problem-solving strategies help students visualize the problem or present the given information in a way that can lead them to the solution. Solving word problems using strategies works great as a number talks activity and helps to revise many skills.

Problem-solving strategies

1. create a diagram/picture, 2. guess and check., 3. make a table or a list., 4. logical reasoning., 5. find a pattern, 6. work backward, 1. create a diagram/draw a picture.

Creating a diagram helps students visualize the problem and reach the solution. A diagram can be a picture with labels, or a representation of the problem with objects that can be manipulated. Role-playing and acting out the problem like a story can help get to the solution.

Alice spent 3/4 of her babysitting money on comic books. She is left with $6. How much money did she make from babysitting?

2. Guess and check

Teach students the same strategy research mathematicians use.

With this strategy, students solve problems by making a reasonable guess depending on the information given. Then they check to see if the answer is correct and they improve it accordingly.  By repeating this process, a student can arrive at a correct answer that has been checked. It is recommended that the students keep a record of their guesses by making a chart, a table or a list. This is a flexible strategy that works for many types of problems. When students are stuck, guessing and checking helps them start and explore the problem. However, there is a trap. Exactly because it is such a simple strategy to use, some students find it difficult to consider other strategies. As problems get more complicated, other strategies become more important and more effective.

Find two numbers that have sum 11 and product 24.

Try/guess  5 and 6  the product is 30 too high

  adjust  to 4 and 7 with product 28 still high

  adjust  again 3 and 8 product 24

3. Make a table or a list

Carefully organize the information on a table or list according to the problem information. It might be a table of numbers, a table with ticks and crosses to solve a logic problem or a list of possible answers. Seeing the given information sorted out on a table or a list will help find patterns and lead to the correct solution.

To make sure you are listing all the information correctly read the problem carefully.

Find the common factors of 24, 30 and 18

Logical reasoning is the process of using logical, systemic steps to arrive at a conclusion based on given facts and mathematic principles. Read and understand the problem. Then find the information that helps you start solving the problem. Continue with each piece of information and write possible answers.

Thomas, Helen, Bill, and Mary have cats that are black, brown, white, or gray. The cats’ names are Buddy, Lucky, Fifi, and Moo. Buddy is brown. Thoma’s cat, Lucky, is not gray. Helen’s cat is white but is not named Moo. The gray cat belongs to Bill. Which cat belongs to each student, and what is its color?

A table or list is useful in solving logic problems.

Since Lucky is not gray it can be black or brown. However, Buddy is brown so Lucky has to be black.

Buddy is brown so it cannot be Helen’s cat. Helen’s cat cannot be Moo, Buddy or Lucky, so it is Fifi.

Therefore, Moo is Bill’s cat and Buddy is Mary’s cat.

5. Find a pattern.

Finding a pattern is a strategy in which students look for patterns in the given information in order to solve the problem. When the problem consists of data like numbers or events that are repeated then it can be solved using the “find a pattern” problem-solving strategy. Data can be organized in a table or a list to reveal the pattern and help discover the “rule” of the pattern.

 The “rule” can then be used to find the answer to the question and complete the table/list.

Shannon’s Pizzeria made 5 pizzas on Sunday, 10 pizzas on Monday, 20 pizzas on Tuesday, and 40 pizzas on Wednesday. If this pattern continues, how many pizzas will the pizzeria make on Saturday?

6. Working backward

Problems that can be solved with this strategy are the ones that  list a series of events or a sequence of steps .

In this strategy, the students must start with the solution and work back to the beginning. Each operation must be reversed to get back to the beginning. So if working forwards requires addition, when students work backward they will need to subtract. And if they multiply working forwards, they must divide when working backward.

Mom bought a box of candy. Mary took 5 of them, Nick took 4 of them and 31 were given out on Halloween night. The next morning they found 8 pieces of candy in the box. How many candy pieces were in the box when mom bought it.

For this problem, we know that the final number of candy was 8, so if we work backward to “put back” the candy that was taken from the box we can reach the number of candy pieces that were in the box, to begin with.

The candy was taken away so we will normally subtract them. However, to get back to the original number of candy we need to work backward and do the opposite, which is to add them.

8 candy pieces were left + the 31 given out + plus the ones Mary took + the ones Nick took

8+31+5+4= 48   Answer: The box came with 48 pieces of candy.

Selecting the best strategy for a problem comes with practice and often problems will require the use of more than one strategies.

Print and digital activities

I have created a collection of print and digital activity cards and worksheets with word problems (print and google slides) to solve using the strategies above. The collection includes 70 problems (5 challenge ones) and their solution s and explanations.

sample below

How to use the activity cards

Allow the students to use manipulatives to solve the problems. (counters, shapes, lego blocks, Cuisenaire blocks, base 10 blocks, clocks) They can use manipulatives to create a picture and visualize the problem. They can use counters for the guess and check strategy. Discuss which strategy/strategies are better for solving each problem. Discuss the different ways. Use the activities as warm-ups, number talks, initiate discussions, group work, challenge, escape rooms, and more.

Ask your students to write their own problems using the problems in this resource, and more, as examples. Start with a simple type. Students learn a lot when trying to compose a problem. They can share the problem with their partner or the whole class. Make a collection of problems to share with another class.

For the google slides the students can use text boxes to explain their thinking with words, add shapes and lines to create diagrams, and add (insert) tables and diagrams.

Many of the problems can be solved faster by using algebraic expressions. However, since I created this resource for grades 4 and up I chose to show simple conceptual ways of solving the problems using the strategies above. You can suggest different ways of solving the problems based on the grade level.

Find the free and premium versions of the resource below. The premium version includes 70 problems (challenge problems included) and their solutions

There are 2 versions of the resource

70 google slides with explanations + 70 printable task cards

70 google slides with explanations + 11 worksheets

You might also like

Multiplying fractions/mixed numbers/simplifying

Adding and subtracting fractions

AM/PM, 24-hour clock, Elapsed Time – ideas, games, and activities

Teaching area, ideas, games, print, and digital activities

Multi-Digit Multiplication, Area model, Partial Products algorithm, Puzzles, Word problems

Place Value – Representing and adding 2/3 digit numbers with manipulatives

Multiplication Mission – arrays, properties, multiples, factors, division

Fractions Games and activities – Equivalence, make 1, compare, add, subtract, like, unlike

Diving into Division -Teaching division conceptually

Expressions with arrays

Decimals, Decimal fractions, Percentages – print and digital

Solving Word Problems- Math talks-Strategies, Ideas and Activities-print and digital

Check out our best selling card games now available at amazon.com and amazon.ca.

Chicken Escape

A multiplayer card game that makes mental math practice fun! Chicken Escape is a fast-paced multiplayer card game. While playing…

Dragon Times – A math Adventure card game

Dragon Times is an educational fantasy card game that aims to motivate children to practice multiplication and division facts while…

• Home   |  
• About   |  
• Contact Us   |  
• Privacy   |  
• Newsletter   |  
• Shop   |  
• 🔍 Search Site
• Easter Color By Number Sheets
• Printable Easter Dot to Dot
• Easter Worksheets for kids
• Kindergarten
• All Generated Sheets
• Place Value Generated Sheets
• Addition Generated Sheets
• Subtraction Generated Sheets
• Multiplication Generated Sheets
• Division Generated Sheets
• Money Generated Sheets
• Negative Numbers Generated Sheets
• Fraction Generated Sheets
• Place Value Zones
• Number Bonds
• Addition & Subtraction
• Times Tables
• Fraction & Percent Zones
• All Calculators
• Fraction Calculators
• Percent calculators
• Area & Volume Calculators
• Age Calculator
• Height Calculator
• Roman Numeral Calculator
• Coloring Pages
• Fun Math Sheets
• Math Puzzles
• Mental Math Sheets
• Online Times Tables
• Online Addition & Subtraction
• Math Grab Packs
• All Math Quizzes
• 1st Grade Quizzes
• 2nd Grade Quizzes
• 3rd Grade Quizzes
• 4th Grade Quizzes
• 5th Grade Quizzes
• 6th Grade Math Quizzes
• Place Value
• Rounding Numbers
• Comparing Numbers
• Number Lines
• Prime Numbers
• Negative Numbers
• Roman Numerals
• Subtraction
• Add & Subtract
• Multiplication
• Fraction Worksheets
• Learning Fractions
• Fraction Printables
• Percent Worksheets & Help
• All Geometry
• 2d Shapes Worksheets
• 3d Shapes Worksheets
• Shape Properties
• Geometry Cheat Sheets
• Printable Shapes
• Coordinates
• Measurement
• Math Conversion
• Statistics Worksheets
• Bar Graph Worksheets
• Venn Diagrams
• All Word Problems
• Finding all possibilities
• Logic Problems
• Ratio Word Problems
• All UK Maths Sheets
• Year 1 Maths Worksheets
• Year 2 Maths Worksheets
• Year 3 Maths Worksheets
• Year 4 Maths Worksheets
• Year 5 Maths Worksheets
• Year 6 Maths Worksheets
• All AU Maths Sheets
• Kindergarten Maths Australia
• Year 1 Maths Australia
• Year 2 Maths Australia
• Year 3 Maths Australia
• Year 4 Maths Australia
• Year 5 Maths Australia
• Meet the Sallies
• Certificates

CHALLENGE ZONE 5th Grade Math Problems

Welcome to our 5th Grade Math Problems. Here you will find our range of challenging math problem worksheets which are designed to give children the opportunity to apply their skills and knowledge to solve a range of longer problems.

These problems are also a great way of developing perseverance and getting children to try different approaches in their math.

For full functionality of this site it is necessary to enable JavaScript.

Here are the instructions how to enable JavaScript in your web browser .

5th Grade Math Problems

Here you will find a range of problem solving worksheets.

The 5th grade math problems on the sheets are longer math problems designed to encourage children to use a range of math skills to solve them.

The skills the problems will help to develop include:

• systematic working
• logical thinking
• number fact knowledge
• fraction problems
• trial and improvement strategies
• working backwards
• working systematically
• searching for all possible answers.

At fifth grade, the problems are more advanced with children needing to become more systematic in their approach and experimenting using trial and improvement strategies.

Many of the problems have addition 'What if ...' questions with them to extend learning and get children looking for alternative solutions.

These sheets are great for extending learning for more able mathematicians, or using in a whole class problem solving lesson.

• 5th Grade Math Word Problems
• Bertie's Big Win

Bertie's Big Win is a problem involving both money and fractions which can be worked backwards. The aim of the problem is to work out how much money Bertie started with from the clue that are given.

• PDF version
• Fox vs Rabbit #2

Fox vs Rabbit is an activity involving mathematical modelling of a fox chasing a rabbit. The rabbit has a head-start, but the fox is faster. The aim is to find out when the fox will catch the rabbit, and whether or not the rabbit has time to reach his burrow.

• 1..2..3..4.. Challenge

The 1..2..3..4.. Challengs is a number problem involving using the numbers 1, 2, 3 and 4 along with arithmetic operators to make the numbers from 1 to 20. It is great for practicing PEMDAS and getting children to persevere and develop their mental arithmetic skills.

There are 2 versions of the problem sheet, one with a pre-prepared template for filling in, and a second blank version for children to show their own recording system.

• Blank version
• Frazer's Wall #2

Frazer's Wall #2 is a fraction problem solving activity which involves trying to work out the number of bricks that were laid in each day to find out how long it would take to make a wall. This problem is best solved by using a table or working it out one day at a time.

• Millenary Math

Millenary Math is a time problem involving what the time will be in a thousand years/weeks/hours/minutes, etc. It is a good activity for converting units of time and knowing facts like how many days are in each month. There is no answer sheet, as the activity involves using the current time.

• Sally's Fruit Punch #3

Sally's Fruit Punch is a money and scaling activity. The aim is to use the information to work out how much ingredients are needed. The ingredients then need to be priced to work out a total cost.

• Sally's Fruit Punch #3 UK Version
• Share the Treasure #5

Share the Treasure is a fraction sharing activity where the aim is to work backwards to find out how many bars of treasure the pirates had before they shared them all out. It is a good activity for developing fraction problem solving and working backwards.

• Something Fishy #2

Something Fishy is a money problem which involves working out exactly how many of each fish were bought in order to have spent a fixed amount of money on the fish. It is a good activity for using lists and tables to find all possibilities. It is also great for perseverance!

• Something Fishy #2 UK Version
• The Five Primes

The Five Primes is a number activity involving finding five primes with different totals. It is a good activity for learning prime numbers up to 30, and also for working systematically.

• The Rock Race #3

The Rock Race is a 5th grade math problem which needs some perseverance to complete. The aim of the activity is to try different routes around the 6 rocks to determine which route is the shortest.

• Who Chose Which?

Who Chose Which is a logical number activity where you need to use the clues to work out which numbers each of the salamanders chose.

• Birthday Bonanza

Birthday Bonanza is a logic problem which requires logical thinking to work out who got which present and how old each of them was.

• Number Totals Investigation

Number Totals Investigation is a PEMDAS number task which involves using 3 digits and operations to make the largest or smallest possible total.

Looking for some easier math problems?

We have a range of easier word problems on our 4th grade math problems page.

The problems on this page are at a simpler level than those here.

Many of the problems, e.g. Share the Treasure, The Rock Race, Something Fishy have easier versions on this page.

• 4th Grade Math Problems

Looking for some more fifth grade math word problems?

Here you will find our selection of free 5th grade math word problems.

Each sheet is availabel in both standard and metric units (where applicable).

Each sheet comes complete with a separate answer sheet.

All the problems are based around 'real life' such as the planets, heights of mountains, or length of rivers.

Using these sheet will help your child to:

• apply their addition, subtraction, multiplication and division skills;
• apply their knowledge of rounding and place value;
• solve a range of problems including "real life" problems and ratio problems.

All the worksheets help to support Elementary math benchmarks.

• 5th Grade Math Puzzles

Here you will find a range of printable 5th grade math puzzles for your child to enjoy.

The puzzles will help your child practice and apply their addition, subtraction, multiplication and division facts as well as developing their thinking and reasoning skills in a fun and engaging way.

Using these puzzles will help your child to:

• learn and practice their addition facts, including decimals;
• practice their subtraction facts, including decimals;
• practice and apply multiplication and division facts;
• develop problem solving skills and reasoning.

All the puzzles support elementary math benchmarks for 5th grade.

Fifth Grade Math Games

Here you will find a range of free printable 5th Grade Math games.

All children like to play Math games, and you will find a good range of Grade 5 Math Games here for your child to play and enjoy.

The following games involve different 5th Grade Math activities which you and your child can enjoy together.

All the free 5th Grade Math Worksheets in this section follow the Elementary Math Benchmarks for Grade 5.

• Math Games 5th Grade

How to Print or Save these sheets 🖶

Need help with printing or saving? Follow these 3 steps to get your worksheets printed perfectly!

• How to Print support

Subscribe to Math Salamanders News

Sign up for our newsletter to get free math support delivered to your inbox each month. Plus, get a seasonal math grab pack included for free!

• Newsletter Signup

Return to 5th Grade Math Worksheets Hub

Return to Math Problem Worksheets Hub

Return from 5th Grade Math Problems to Math Salamanders Homepage

Math-Salamanders.com

The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.

New! Comments

TOP OF PAGE

© 2010-2024 Math Salamanders Limited. All Rights Reserved.

• Privacy Policy
• Copyright Policy

10 tips to boost 5th grade math skills

by: The GreatSchools Editorial Team | Updated: May 5, 2024

Print article

Headaches over math homework? Here’s how you can help.

Fraction action

Line ’em up working with decimal numbers, mental math workout, volume is not just a button on the remote, what’s your estimate, the scoop on fractions, factors made simple, gathering and graphing data, graphing made concrete, ideas for summer math practice, homes nearby.

Homes for rent and sale near schools

3 things to say when your child says, "I'm bad at math."

Math tips for every grade

Who's afraid of Algebra II?

Yes! Sign me up for updates relevant to my child's grade.

Please enter a valid email address

Thank you for signing up!

Server Issue: Please try again later. Sorry for the inconvenience

5 Essential Problem Solving Techniques

• Critical Thinking

In the first post in this series, I talked about the difference between solving problems and problem solving. This week, I will continue my series on problem solving and share five essential problem solving techniques for your problem solving routines.

A strong problem-solving routine is essential for helping students develop their problem-solving strategy toolboxes. Over the years, I have used a variety of routines that have helped my students develop problem-solving strategies and critical thinking skills. (Read more about my favorite routine here !) Through a lot of trial and error, I found several routines that worked well for my students. (I will share more about them next week!) Today, I want to share some trade secrets with you to help you get the most from your problem-solving routines with five essential problem-solving techniques.

Five Essential Problem Solving Techniques

1. share student thinking and strategies..

This is essential! I can’t tell you how many times I have seen teachers give a great problem solving or critical thinking task and then never allow students to share their responses. Sometimes, our students are the best teachers and they can get a message across when we struggle to do so. Also, providing an opportunity for students to talk to other students about their thinking increases math vocabulary and builds communication skills.

After students have had an opportunity to share their thinking with a group member or partner, I encourage you to discuss the task as a class. This gives the teacher an opportunity to reiterate correct thinking, modify incorrect thinking, ask questions, build math vocabulary, and increase students’ communication skills.

Read more about getting started with math talk in the classroom here .

2. Solve non-routine problems.

In an earlier blog post, I emphasized the importance of using non-routine problems with students. Not only are students typically more engaged, but students have the opportunity to use strategies beyond writing an equation/number sentence or drawing a picture. If you’re interested in some fun, non-routine tasks, please check out my Solve It! Friday page.

One of the things many people say they love about math is the fact that there is a right and wrong answer. While there certainly are wrong answers, sometimes, there can be more than one right answer. These types of tasks really stretch some kids’ thinking. They also provide a natural venue for discussion. Students can debate the answers only to discover that more than one works!

3. Discuss efficiency.

During problem-solving experiences, students will often use beautiful and complicated solution strategies to solve problems. While we want to encourage outside-of-the-box thinking, we also want students to attend to efficiency. One way to do this is to have several students share their solutions. They can then discuss what strategies are best for specific types of problems. When discussing difficulty becomes a regular part of your routine, students will begin to utilize their problem-solving strategies in a way that not only gets them to the correct answer but also using an efficient method.

4. Make connections.

Recently, I wrote about making connections as part of my Summer PD series. Read it here ! When students make connects, it deepens their understanding of other content and skills. One way to do this is to connect the problem-solving task to grade-level content and skills. Another way is to have students represent problems in a variety of ways, i.e. pictures, numbers, words, or equations. Each representation is crafted in a specific way, so being able to translate words into an equation or numbers into a picture is a big skill that has many benefits.

5. Use “high ceiling, low floor tasks.”

The term “high ceiling, low floor” refers to a task having multiple entry points to allow all students a way to access the task; however, it also includes ways to extend the tasks for those students who are ready for more of a challenge. These types of tasks increase participation because students can participate at a level that is comfortable for them. Students are also able to showcase what they can do instead of what they are unable to do. Even better, these tasks provide instant opportunities for differentiation because all students can participate in a way that allows them to be most successful.

Using a regular problem-solving routine can help students develop the tools necessary to be powerful thinkers of mathematics; however, in order to get the most from the routines, certain problem-solving techniques must be included. While you may not want to add all of the above techniques to your routine, I encourage you to commit to adding one or two of them this year. I highly recommended starting with “sharing student thinking and strategies.” It’s probably the most important technique of all of the problem-solving routines. It will get you the most bang for your buck!

Sound Off! How do get the most from your problem-solving routine? Which problem-solving techniques do you think are most important?

Shametria Routt Banks

• Assessment Tools
• Content and Standards
• Differentiation
• Math & Literature
• Math & Technology
• Math Routines
• Math Stations
• Virtual Learning
• Writing in Math

You may also like...

3 Responses

Hi, can you provide an example of a high ceiling, low floor task? Thank you!

Hi Jen! Great question! The high ceiling, low floor tasks give all students a chance to engage in the task but have places to go to extend the learning for students. One problem that comes to mind is a task where students are asked to find combinations of numbers to achieve a goal, like the following problem: Farmer Brown’s niece Angie is in charge of her uncle’s farm while he is on vacation. He gave her strict instructions to make sure none of the animals ran away. When Angie counted the pigs and chickens, she counted 32 legs. How many pigs and chickens did she count? All students should be able to determine a combination of pigs and chickens; however, what if I added a new condition to say: Angie counted a total of 12 animals. This changes the level of rigor because students are now looking for a specific combination. Some students will struggle with this but others may be ready to tackle it; so, using tasks that have a high-ceiling allow for this flexibility. Check out more high ceiling, low floor tasks here: https://www.youcubed.org/task-grades/low-floor-high-ceiling/ .

Leave a Reply Cancel reply

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

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

©2024 The Routty Math Teacher.   All Rights Reserved.  Designed by Ashley Hughes.

Privacy overview.

High Impact Tutoring Built By Math Experts

Personalized standards-aligned one-on-one math tutoring for schools and districts

Free ready-to-use math resources

Hundreds of free math resources created by experienced math teachers to save time, build engagement and accelerate growth

35 Math Questions For 5th Graders: Answers With Worked Examples

Anantha Anilkumar

In 5th grade math, the toughest questions are often the reasoning questions. In this article, we’ve put together a collection of math questions for 5th graders, organized by the different kinds of reasoning questions that students may encounter on standardized tests and beyond.

Why Focus On Math Reasoning Questions?

Most fifth graders find reasoning questions to be the most difficult. Unsurprisingly, we teach thousands of students in the weeks leading up to standardized tests. Teaching them math reasoning skills at the elementary level is a big part of what we do here at Third Space Learning.

We even recently made the decision to restructure our elementary lessons to introduce math reasoning questions earlier in their learning journey as the difficulty level was just too high at the end of the lesson. We  definitely feel fifth grade teachers’ pain!

Whatever level your students are currently achieving in math, math reasoning questions will appear from elementary to high school, so it is an essential skill for the future.

If you find you have children in your class with a lot more catching up to do than others, then we may be able to support them with some personalized one-on-one tutoring if you get in touch.

Reasoning Questions for 5th Grade

Help your 5th grade students to feel confident with different types of reasoning questions.

35 Math Questions For 5th Graders

There are 7 types of math reasoning questions that fifth graders are likely to encounter:

For each of these types we’ll examine an example problem, looking at the question, the correct answer, and how to go about answering this problem.

We’ll also look at further examples of each type of math reasoning question and answer, again with worked examples and an explanation of how to answer each.

Our aim is to provide you with a sample of the types of math reasoning questions and how to teach the reasoning and problem solving skills they’ll need to solve them.

For more word problems like this, check out our collection of 2-step and multi-step word problems . For advice on how to teach children to solve problems like this, check out these math problem solving strategies.

Math Question Type 1: Single step word problems

The simplest type of reasoning question students are likely to encounter, single step problems are exactly that: students are asked to interpret a written question and carry out a single mathematical step to solve it.

Take a look at the question below:

Reasoning Question 1

Answer: $0.65

A relatively easy question to interpret–the first step will be to rewrite the amounts given so that they can properly line up the place values in order to solve. From here the simple mathematical step is subtraction i.e. $2.00 – $1.35 = 0.65.

The most crucial skill for grade schoolers in this question is a solid understanding of money as relating to place value. If this understanding is present, the mathematical step itself is quite easy.

Below are several more examples:

Reasoning Question 2

Answer : 7 hours 24 minutes

Students need to understand that one hour is equal to 60 minutes. From here the single mathematical step is division: 444/60, to find a whole number answer with a remainder.

Reasoning Question 3

Answer : 48 cm 3

Students must multiply length by width by height, using the amounts provided by the question.

Reasoning Question 4

Answer : 1,488 cubic cm

A simple enough calculation (multiplying) if students are aware that the volume of a rectangular prism can be found by multiplying the area of the base by the height.

Reasoning Question 5

Answer : 7,590

A single, relatively simple rounding problem – students should recognize that ’94’ is the place they should focus on for this problem.

Math Question Type 2: Multiple step worded problems

A more complex version of the single step word problem, multi-step problems require students to interpret a written problem, but solving it then requires the use of two or three math skills.

For example, consider this question below:

Answer: $1.85

This question encompasses three different math skills: multiplying (and dividing) decimals, addition and subtraction. Students can choose to work out the multiplication or division first, but must complete both before moving on.

Once these values have been worked out the next steps are relatively simple – adding the two values together, and subtracting the total from $5.

Multi-step problems are particularly valuable to include in practice tests because they require children to apply their knowledge of math language and their reasoning skills several times across the course of a single question, usually in slightly different contexts.

More examples:

Answer : $5,520

There are two steps to this problem, but both are multiplication. The first is to work out how much money is made per day – 92 x $15. This product is then multiplied by 4 – the number of days – to get to the answer.

Answer : 1360 miles

Another two step problem. The first step is to work out 4 of 3,400 miles. Then divide this by 10 to solve for 4/10 of 3,400.

Answer : $153

There are four steps involved in solving this problem: multiplication (doubling $51), division (dividing $51 in half), multiplication again (doubling half of $51–which some students may recognize those last two steps were unnecessary as that brings us back to $51), and addition (putting the two costs together).

Given the number of steps involved it can be easy for students to make arithmetic mistakes.

Answer : 11.45 lbs

A two-step problem again: multiplying 3.45 lbs by 4, then subtracting 2.35 lbs from the total. 

Math Question Type 3: Problems involving measurements

As their name suggests, these questions ask students to solve a problem that includes one or more units of measurement.

Answer: 40 washes

This is a two step problem; students must first be able to read and convert kilograms to grams (and therefore know the relationship and conversions between the two units- 1,000 grams to 1 kilogram), multiply 2.6 by 1,000 which equals 2,600, then divide 2,600 by 65. The quotient is the number of washes possible.

Further examples:

Answer : 50g

A relatively simple division problem, relying on students having knowledge that 200g is one fifth of a kilogram.

Answer : 5.12 miles

Another three step problem, and this requires students to subtract and divide decimals – subtracting 12.63 miles from the total amount, taking the difference, 13.91, and subtracting 3.67 miles, and then dividing that difference, 10.24, in half to obtain the distance the other two friends ran.

Answer : 84 inches/7 foot

To find 8 feet in inches, students must multiply 8 by 12. This gives the answer 96 inches. Students must then divide 96 by 40 to find the height of one box: 2.4 inches. Multiply 2.4 by 5 and minus this from the original 96 inch tower. 

Interesting to note that the units for the answer may or may not be specified – an answer given in inches or feet will be accepted, however sometimes the unit will be specified in the answer box. This is why we encourage students to keep an eye on whether units are provided in the answer box.

Answer : 0.05 lbs

As with the running question there are three steps involved to solve this problem: subtracting the heaviest car from the total amount (3.85 – 1), figuring out the weight of the remaining three cars (2.85/3) and subtracting 0.95 from 1 to get the remaining amount of 0.05 lbs.

Question Type 4: Problems involving drawing

Problems involving drawing require students to construct an accurate drawing by following a set of instructions, or through reflection, translation, or scaling.  

Answer: Any pair of lines that make a square of 4 units, a rectangle of 6 units, and a square of 25 units.

This question is considerably more complex than it appears, and incorporates aspects of multiplication as well as spatial awareness. One potential solution is to work out the area of the card (35), then work out the possible square numbers that will fit in (understanding that square numbers produce a square when drawn out as on a grid), and which then leave a single rectangle behind.

A lot of work for a single point!

Some further examples:

Answer : Any quadrilateral made by joining the dots that has 3 acute angles e.g. an arrowhead shape.

Answer : An accurately drawn angle.

This question demands students to have an understanding of and ability to accurately use a protractor. Often, a mark scheme allows some room for error – “between 34 and 36 degrees” is acceptable.

As with the question above, a small amount of room for error is given as it acceptable to be between 139 and 141 degrees.

Answer : Points drawn at (2,1), (5,1) and (2,4).

Math Question Type 5: Explanation questions

These problems ask children to explain a mathematical statement or error.

As an example:

Answer: If the distance from P to R is 800 yards and the distance from P to Q is (Q -> R x 4), it must be 4/5 of 800 = 640 yards. Therefore Olivia is wrong.

More than most problems, this type requires students to actively demonstrate their reasoning skills as well as their mathematical ones. Here students must articulate either in words or (where possible) numerically that they understand that Q to R is 1/5 of the total, that therefore P to Q is 4/5 of the total distance, and then calculate what this is via division and multiplication.

Further examples below:

Answer : No, 2/100 is the same as 2 divided by 100, which equals 0.02.

Answer : No; multiplication and division have the same priority in the order of operations, so in a problem like 40 x 6 ÷2, you would carry out the multiplication first as it occurs first.

Answer : No

Any explanation that provides a counter-example is acceptable e.g. “Not if the number is 1”, “Not for 0,” “Not if the number is less than 1” etc.

Answer : Any answer that refers to the fact that there is a 5 in the hundredths place, AND a 9 in the thousandths place, so that the number has to be rounded up as far as the ten-thousands place.

Math Question Type 6: Sequence questions

Another relatively simple kind of reasoning question, sequence problems involve students completing mathematical sequences.

Consider this example:

Answer: 35 , 42, 49, 56 , 63, 70

The question’s instructions point clearly to the solution: figure out what the increase between numbers is, then apply this via addition or subtraction to find the missing numbers.

Higher achieving students might quickly pick up that this is in fact the 7 times table and rely on their knowledge of multiplication facts to obtain the answer – this should be encouraged so long as they then check their answer in the normal method to ensure they haven’t made a mistake.

Answer(s) : 8/8 or 1 and 2 1/8 (OR 17/8)

Both answers must be correct to receive the point. Students must recognize that 3/4 is the same as 6/8, so the sequence is increasing in 3/8 each time. The first number is 3/8 less than 1 3/8 and the final number is 3/8 greater than 1 3/4. They then must be able to add and subtract fractions to obtain the answers.

Answer(s) : 4.2 and 7

Answer(s) : 128, 135 and 156.

Answer(s) : 0 and 24

This number line question can be a little tricky; students need to figure out that the marks on the line represent increments of 3, and count backwards and forwards in 3’s to obtain the missing numbers.

Math Question Type 7: Ordering questions

A slightly more complex variation of the sequence question, ordering problems require students to put a set of numbers, fractions or measures in the correct order.

A good example is this fifth grade math question below:

Answer: 3/5, 3/4, 6/5

This question throws a wrench in things by including an improper fraction, but this is hardly unusual. These sorts of questions are just the place to find other ‘curveballs’ such as equivalent fractions, mixed numbers, decimal numbers, and fractions all mixed into one problem.

A good knowledge of the fundamentals of fractions is essential here: students must understand what a larger denominator means, and the significance of a fraction with a numerator greater than its denominator.

Answer : D,C,A,B

Encourage students to convert all the fractions to one denominator value to make ordering easier.

Answer : (descending down the ‘Place’ column) 3rd, 5th, 2nd, 4th

Students could use many strategies to solve this problem. The most time consuming would be to rewrite all the fractions with a common denominator. More efficient strategies would include reasoning about the size of the fractions in comparison to ½ or 1. For instance, a student may notice that ⅜ is the only fraction less than ½, putting Ben in 5th place. 4/8 is exactly ½ whereas the others are greater than ½, putting Michael in 4th place. Then the student may recognize that 10/12 is closer to 1 than ¾, completing the rest of the table.

Answer : C, B, D, A

Answer : D, A, C, B

7 Top Tips For Answering 5th Grade Math Reasoning Questions

Now that we’ve covered how to answer some specific types of reasoning questions, here are some more generic tips for success in standardized tests. They may not all be applicable to every single question, but will apply to at least two, usually more.

• Get students in the habit of identifying what information they’re given in a question, and what they need to know to solve the problem. This helps them start to form the steps needed to find the solution.
• Ask students to ‘spot the math’ in a question – which operations or skills do they actually need to use to solve the problem? This is useful even for arithmetic questions – it’s no surprise how often children can misread a question.
• Check the units! Especially in questions involving multiple measures, it can be easy to give the answer in the wrong one. The answer box might give a specific unit of measurement, so students should work to give their answer in that unit.
• In a similar vein, remind students to convert different units of measurement in a question into the same unit to make calculations easier e.g. lbs to oz.
• Encourage numerical answers where possible. Even in explanation questions demonstrating the mathematical equation is a better explanation than trying to write it out.
• The bar model can be a useful way of visualizing many different types of questions, and might make it easier to spot the ‘steps’ needed for the solution.
• Check your work! Even if the work is ultimately irrelevant to the question, you can lose points if it is wrong.

Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade tutoring – 3rd grade tutoring – 4th grade tutoring – 5th grade tutoring – 6th grade tutoring – 7th grade tutoring – 8th grade tutoring Why not learn more about how it works ?

The content in this article was originally written by Anantha Anilkumar at Third Space Learning and has since been revised and adapted for US schools by elementary math teacher Katie Keeton.

Related articles

Free 5th Grade Math Quiz And Many More Downloadable 5th Grade Math Resources

18 Math Word Problems For 4th Grade: Develop Their Problem Solving Skills Across Single and Mixed Upper Elementary Topics

Five Ways Math Helps Children In Life

Screen Time For Kids: Making It Positive

Multiplication Word Problems Worksheets [FREE]

Multiplication worksheets to develop reasoning and problem solving skills for grades 3, 4 and 5!

This handy resource includes ready-to-use worksheets with questions and answers.

Privacy Overview

• Grade 5 Lessons and Practice
• Grade 6 Lessons and Practice
• Grade 7 Lessons and Practice
• Grade 8 Lessons and Practice
• Grade 9 Lessons and Practice
• Grade 10 Lessons and Practice
• Grade 11 Lessons and Practice
• Grade 12 Lessons and Practice
• Financial Literacy
• Whiteboard Templates
• Grade 5 Math Quizzes
• Grade 6 Math Quizzes
• Grade 7 Math Quizzes
• Grade 8 Math Quizzes
• Grade 9 Math Quizzes
• Grade 10 Math Quizzes
• Grade 11 Math Quizzes
• Grade 12 Math Quizzes

Search block

Math learning strategies grade 5.

Math is a great subject. When you understand math, you can apply its principles to many situations in life and find solutions to problems.

Below are 3 simple math learning strategies (grade 5) to help you succeed in math.

Check Out IntoMath Grade 5 Interactive Quizzes

Strategy 1: Learn the basics

When we start building a house – we start with the foundation. Then we keep adding the walls, the roof and all the fancy elements.

Learning math is like building a house – you need to have a solid foundation to start building the walls and the roof, adding mosaics or creating arches.

That foundation in math are things like operations with integers, fractions and decimals, divisibility rules, times tables, squares and square roots, exponent rules, angle theorems and so on.

Without a solid foundation it is impossible to build a solid and beautiful house.

Strategy 2: In math things don’t just happen – there is logic in everything

Once you are good with basics, you will start seeing and recognizing patterns. As you progress to a more complex math – you will better understand why things in math are the way they are. Math is like a house of cards, where one concept supports another or one idea is derived from another. Once you understand one, you will understand the ones based on it. You miss one – and your house of cards will fall.

Therefore, try to not just follow the steps, but understand why you are following those steps, starting from the very basics.

Strategy 3: Practice

When you learn to play a musical instrument or play sports, you are not immediately a pro at what you do. Achieving good results requires lots of practice and dedication.

Math works the same way. The more you practice, the better you are at it. The better you get, the more confident you feel about it and all of a sudden math comes so easy!

Consistency, dedication and perseverance are key to being good at math.

Mathematics is a global language, one of the most logical things in this world. Do not be afraid of it – follow the three math learning strategies above and enjoy your success!

Grade 5 IntoMath Learning Plan

SUCCESSburger Poster

Grit Labels

Math Homework Strategies Infographic

Solving Word Problems Strategies Infographic

Ways to Engage Kids in Math Infographic

Why Do Math Inforgraphic

• Skip to main content
• Skip to primary sidebar

CLICK HERE TO LEARN ABOUT MTM ALL ACCESS MEMBERSHIP FOR GRADES 6-ALGEBRA 1

Maneuvering the Middle

Student-Centered Math Lessons

Math Problem Solving Strategies

How many times have you been teaching a concept that students are feeling confident in, only for them to completely shut down when faced with a word problem?  For me, the answer is too many to count.  Word problems require problem solving strategies. And more than anything, word problems require decoding, eliminating extra information, and opportunities for students to solve for something that the question is not asking for .  There are so many places for students to make errors! Let’s talk about some problem solving strategies that can help guide and encourage students!

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.’
• 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.

R.U.N.S. stands for read the problem, underline the question, name the problem type, and write a strategy sentence. 

• 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.

Here is the strategy that I adopted a few years ago.  It doesn’t have a name yet nor an acronym, (so can it even be considered a strategy…?)

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.

Ideas for Promoting Showing Your Work

• White boards are a helpful resource that make (extra) writing engaging!
• Celebrating when students show their work. Create a bulletin board that says ***I showed my work*** with student exemplars.
• Take a picture that shows your expectation for how work should look and post it on the board like Marissa did here.

Show Work Digitally

Many teachers are facing how to have students show their work or their problem solving strategy when tasked with submitting work online. Platforms like Kami make this possible. Go Formative has a feature where students can use their mouse to “draw” their work. 

If you want to spend your energy teaching student problem solving instead of writing and finding math problems, look no further than our All Access membership . Click the button to learn more. 

Students who plan succeed at a higher rate than students who do not plan.   Do you have a go to problem solving strategy that you teach your students? 

Editor’s Note: Maneuvering the Middle has been publishing blog posts for nearly 8 years! This post was originally published in September of 2017. It has been revamped for relevancy and accuracy.

Problem Solving Posters (Represent It! Bulletin Board)

Check out these related products from my shop.

Reader Interactions

18 comments.

October 4, 2017 at 7:55 pm

As a reading specialist, I love your strategy. It’s flexible, “portable” for any problem, and DOES get kids to read and understand the problem by 1) summarizing what they know and 2) asking a question for what they don’t yet know — two key comprehension strategies! How about: “Make a Plan for the Problem”? That’s the core of your rationale for using it, and I bet you’re already saying this all the time in class. Kids will get it even more because it’s a statement, not an acronym to remember. This is coming to my reading class tomorrow with word problems — thank you!

October 4, 2017 at 8:59 pm

Hi Nora! I have never thought about this as a reading strategy, genius! Please let me know how it goes. I would love to hear more!

December 15, 2017 at 7:57 am

Hi! I am a middle school teacher in New York state and my district is “gung ho” on CUBES. I completely agree with you that kids are not really reading the problem when using CUBES and only circling and boxing stuff then “doing something” with it without regard for whether or not they are doing the right thing (just a shot in the dark!). I have adopted what I call a “no fear word problems” procedure because several of my students told me they are scared of word problems and I thought, “let’s take the scary out of it then by figuring out how to dissect it and attack it! Our class strategy is nearly identical to your strategy:

1. Pre-Read the problem (do so at your normal reading speed just so you basically know what it says) 2. Active Read: Make a short list of: DK (what I Definitely Know), TK (what I Think I Know and should do), and WK (what I Want to Know– what is the question?) 3. Draw and Solve 4. State the answer in a complete sentence.

This procedure keep kids for “surfacely” reading and just trying something that doesn’t make sense with the context and implications of the word problem. I adapted some of it from Harvey Silver strategies (from Strategic Teacher) and incorporated the “Read-Draw-Write” component of the Eureka Math program. One thing that Harvey Silver says is, “Unlike other problems in math, word problems combine quantitative problem solving with inferential reading, and this combination can bring out the impulsive side in students.” (The Strategic Teacher, page 90, Silver, et al.; 2007). I found that CUBES perpetuates the impulsive side of middle school students, especially when the math seems particularly difficult. Math word problems are packed full of words and every word means something to about the intent and the mathematics in the problem, especially in middle school and high school. Reading has to be done both at the literal and inferential levels to actually correctly determine what needs to be done and execute the proper mathematics. So far this method is going really well with my students and they are experiencing higher levels of confidence and greater success in solving.

October 5, 2017 at 6:27 am

Hi! Another teacher and I came up with a strategy we call RUBY a few years ago. We modeled this very closely after close reading strategies that are language arts department was using, but tailored it to math. R-Read the problem (I tell kids to do this without a pencil in hand otherwise they are tempted to start underlining and circling before they read) U-Underline key words and circle important numbers B-Box the questions (I always have student’s box their answer so we figured this was a way for them to relate the question and answer) Y-You ask yourself: Did you answer the question? Does your answer make sense (mathematically)

I have anchor charts that we have made for classrooms and interactive notebooks if you would like them let me me know….

October 5, 2017 at 9:46 am

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

October 8, 2017 at 6:51 pm

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

December 18, 2019 at 7:48 am

I would love an anchor chart for RUBY

October 15, 2017 at 11:05 am

I will definitely use this concept in my Pre-Algebra classes this year; I especially like the graphic organizer to help students organize their thought process in solving the problems too.

April 20, 2018 at 7:36 am

I love the process you’ve come up with, and think it definitely balances the benefits of simplicity and thoroughness. At the risk of sounding nitpicky, I want to point out that the examples you provide are all ‘processes’ rather than strategies. For the most part, they are all based on the Polya’s, the Hungarian mathematician, 4-step approach to problem solving (Understand/Plan/Solve/Reflect). It’s a process because it defines the steps we take to approach any word problem without getting into the specific mathematical ‘strategy’ we will use to solve it. Step 2 of the process is where they choose the best strategy (guess and check, draw a picture, make a table, etc) for the given problem. We should start by teaching the strategies one at a time by choosing problems that fit that strategy. Eventually, once they have added multiple strategies to their toolkit, we can present them with problems and let them choose the right strategy.

June 22, 2018 at 12:19 pm

That’s brilliant! Thank you for sharing!

May 31, 2018 at 12:15 pm

Mrs. Brack is setting up her second Christmas tree. Her tree consists of 30% red and 70% gold ornaments. If there are 40 red ornaments, then how many ornaments are on the tree? What is the answer to this question?

June 22, 2018 at 10:46 am

Whoops! I guess the answer would not result in a whole number (133.333…) Thanks for catching that error.

July 28, 2018 at 6:53 pm

I used to teach elementary math and now I run my own learning center, and we teach a lot of middle school math. The strategy you outlined sounds a little like the strategy I use, called KFCS (like the fast-food restaurant). K stands for “What do I know,” F stands for “What do I need to Find,” C stands for “Come up with a plan” [which includes 2 parts: the operation (+, -, x, and /) and the problem-solving strategy], and lastly, the S stands for “solve the problem” (which includes all the work that is involved in solving the problem and the answer statement). I find the same struggles with being consistent with modeling clearly all of the parts of the strategy as well, but I’ve found that the more the student practices the strategy, the more intrinsic it becomes for them; of course, it takes a lot more for those students who struggle with understanding word problems. I did create a worksheet to make it easier for the students to follow the steps as well. If you’d like a copy, please let me know, and I will be glad to send it.

February 3, 2019 at 3:56 pm

This is a supportive and encouraging site. Several of the comments and post are spot on! Especially, the “What I like/don’t like” comparisons.

March 7, 2019 at 6:59 am

Have you named your unnamed strategy yet? I’ve been using this strategy for years. I think you should call it K.N.O.W.S. K – Know N – Need OW – (Organise) Plan and Work S – Solution

September 2, 2019 at 11:18 am

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

K now N eed to find out O rganize (a plan – may involve a picture, a graphic organizer…) W ork S ee if you’re right (does it make sense, is the math done correctly…)

I love the K & N steps…so much more tangible than just “Read” or even “Understand,” as I’ve been seeing is most common in the processes I’ve been researching. I like separating the “Work” and “See” steps. I feel like just “Solve” May lead to forgetting the checking step.

March 16, 2020 at 4:44 pm

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

September 17, 2019 at 7:14 am

Hi, I wanted to tell you how amazing and kind you are to share with all of us. I especially like your word problem graphic organizer that you created yourself! I am adopting it this week. We have a meeting with all administrators to discuss algebra. I am going to share with all the people at the meeting.

I had filled out the paperwork for the number line. Is it supposed to go to my email address? Thank you again. I am going to read everything you ahve given to us. Have a wonderful Tuesday!

• 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

This action is not available.

Module 1: Problem Solving Strategies

• Last updated
• Save as PDF
• Page ID 10352

Unlike exercises, there is never a simple recipe for solving a problem. You can get better and better at solving problems, both by building up your background knowledge and by simply practicing. As you solve more problems (and learn how other people solved them), you learn strategies and techniques that can be useful. But no single strategy works every time.

Pólya’s How to Solve It

George Pólya was a great champion in the field of teaching effective problem solving skills. He was born in Hungary in 1887, received his Ph.D. at the University of Budapest, and was a professor at Stanford University (among other universities). He wrote many mathematical papers along with three books, most famously, “How to Solve it.” Pólya died at the age 98 in 1985.1

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

In 1945, Pólya published the short book How to Solve It , which gave a four-step method for solving mathematical problems:

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?

This is all well and good, but how do you actually do these steps?!?! Steps 1. and 2. are particularly mysterious! How do you “make a plan?” That is where you need some tools in your toolbox, and some experience to draw upon.

Much has been written since 1945 to explain these steps in more detail, but the truth is that they are more art than science. This is where math becomes a creative endeavor (and where it becomes so much fun). We will articulate some useful problem solving strategies, but no such list will ever be complete. This is really just a start to help you on your way. The best way to become a skilled problem solver is to learn the background material well, and then to solve a lot of problems!

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.

Mr. Jones has a total of 25 chickens and cows on his farm. How many of each does he have if all together there are 76 feet?

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.

Step 2: Devise a plan

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:

Procedure: Make a table reflecting the data in the problem. If done in an orderly way, such a table will often reveal patterns and relationships that suggest how the problem can be solved.

Step 3: Carry out the plan:

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

Better! The total number of feet are increasing!

Step 4: Looking back:

Check: 12 + 13 = 25 heads

24 + 52 = 76 feet.

We have found the solution to this problem. I could use this strategy when there are a limited number of possible answers and when two items are the same but they have one characteristic that is different.

Videos to watch:

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

Check in question 1:

Place the digits 8, 10, 11, 12, and 13 in the circles to make the sums across and vertically equal 31. (5 points)

Check in question 2:

Old McDonald has 250 chickens and goats in the barnyard. Altogether there are 760 feet . How many of each animal does he have? Make sure you use Polya’s 4 problem solving steps. (12 points)

Problem Solving Strategy 2 (Draw a Picture). Some problems are obviously about a geometric situation, and it is clear you want to draw a picture and mark down all of the given information before you try to solve it. But even for a problem that is not geometric thinking visually can help!

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

The fix number is the the amount each term is increasing or decreasing by. "n" is the number of terms you have. You can use this formula to find the last term in the sequence or the number of terms you have in a sequence.

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

Last term = 3(200-1) +2

Last term is 599.

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

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

Sum = 60,100

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)

This is considered a strategy in many schools. If you are given an answer, and the steps that were taken to arrive at that answer, you should be able to determine the starting point.

Videos to watch demonstrating of “Working Backwards”

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

Karen is thinking of a number. If you double it, and subtract 7, you obtain 11. What is Karen’s number?

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:

9 x 2 = 18 -7 = 11

5. We have the right answer.

Check in question 4:

Christina is thinking of a number.

If you multiply her number by 93, add 6, and divide by 3, you obtain 436. What is her number? Solve this problem by working backwards. (5 points)

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.

Ask yourself as you search for a pattern – are the numbers growing steadily larger? Steadily smaller? How is each number related?

Example 1: 1, 4, 7, 10, 13…

Find the next 2 numbers. The pattern is each number is increasing by 3. The next two numbers would be 16 and 19.

Example 2: 1, 4, 9, 16 … find the next 2 numbers. It looks like each successive number is increase by the next odd number. 1 + 3 = 4.

So the next number would be

25 + 11 = 36

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

-5 – 3 = -8

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

This example is a little bit harder. The numbers are increasing but not by a constant. Maybe a factor?

So each number is being multiplied by 2.

16 x 2 = 32

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.

Now look at the number in the ones digits. Notice they are 0, 1, 4, 5, 6, or 9. Notice none of the perfect squares end in 2, 3, 7, or 8. This list suggests that perfect squares cannot end in a 2, 3, 7 or 8.

How many different amounts of money can you have in your pocket if you have only three coins including only dimes and quarters?

Quarter’s dimes

0 3 30 cents

1 2 45 cents

2 1 60 cents

3 0 75 cents

Videos demonstrating "Make a List"

Check in question 5:

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)

Geometric Sequences:

How would we find the nth term?

Solve a simpler problem:

1, 3, 9, 27.

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

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

Let’s set up a table:

Term Number what did we do

Looking back: How would you find the nth term?

Find the 10 th term of the above sequence.

Let L = the tenth term

Problem Solving Strategy 8 (Process of Elimination)

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

I’m thinking of a number.

The number is odd.

It is more than 1 but less than 100.

It is greater than 20.

It is less than 5 times 7.

The sum of the digits is 7.

It is evenly divisible by 5.

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.

c. The sum of the digits is 7

21 (2+1=3) No 23 (2+3 = 5) No 25 (2 + 5= 7) Yes Using the same process we see there are no other numbers that meet this criteria. Also we notice 25 is divisible by 5. By using the strategy elimination, we have found our answer.

Check in question 6: (8 points)

Jose is thinking of a number.

The number is not odd.

The sum of the digits is divisible by 2.

The number is a multiple of 11.

It is greater than 5 times 4.

It is a multiple of 6

It is less than 7 times 8 +23

What is the number?

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

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

• Our Mission

7 Real-World Math Strategies

We asked our audience how they’re using the real world to teach math and compiled their most intriguing responses.

Math used to be all rote memorization and pencil-to-paper equations disconnected from the real world, but more and more teachers are realizing the importance of making practical, relevant connections in math.

We asked our audience of educators: How do you use the real world to teach math? We’ve collected some of the most interesting answers, ways teachers are connecting math to the everyday lives of their students.

The Real-World Math Wall

To get her fifth-grade students thinking about the math in their lives—and to head off the inevitable “we’ll never use this in the real world” complaint—Samantha Baumgardner, a teacher at Woodrow Petty Elementary School in Taft, Texas, has them bring in a common item and write three ways it relates to math on a notecard. These objects form the class’s real-world math wall.

An interesting rule: Once something is placed on the wall, the same item can’t be brought in again—pushing students to think outside the box to make real-world math connections. Students bring in objects like playing cards, cake pans, softball score sheets, and cookie recipes. One student brought in a medicine dropper and by way of explanation wrote, “The medicine dropper helps you measure water, and it also helps you with cooking steak.”

A School Water Audit

At North Agincourt Jr. Public School in Scarborough, Canada, Krista Dunlop-Sheppard, a bilingual resource and home school teacher for grades 1–6, has her students conduct a water audit at home and at their school. Her students have a wide range of math ability: In a single class, she has students with learning disabilities, students who are gifted, and students who have no diagnoses but need extra support. Modifying a pilot project created by the Toronto Zoo Education Department , students add, subtract, find averages, and measure liquids—like the flow rate of all the water fountains, toilets, and urinals—to measure the amount of water their school uses in a day.

They also interview custodians to discover their daily water usage while mopping floors, and do online research to find out how much water the cafeteria dishwasher uses. When finished, students suggest ways for the school to conserve—like collecting rainwater in a barrel to water plants, and cleaning paint brushes in a bucket instead of using running water. In June, students repeat the water audit and see if the changes they implemented made a difference.

Acting Out Restaurant Scenarios

There’s nothing wrong with using money to teach negative and positive numbers, or pizza to introduce fractions, but Justin Ouellette—a third- to fifth-grade International Baccalaureate educator at Suzhou Singapore International School in China—takes these exercises a memorable step further, bringing in menus so students can act out true-to-life restaurant scenarios. Going dutch on dinner and tipping reinforces addition, subtraction, decimals, and percents, Ouellette says.

If you need a good resource: Ouellette has used this free lesson plan about a fictional eatery called the Safari Restaurant.

Integrating Math Into English and History

Making real-world math connections can happen outside of math class, too.

While reading Elie Wiesel’s Night , 12th-grade students at Kittatinny Regional High School in Hampton Township, New Jersey, calculate the volume of 11 million pennies to help them imagine the impact of the lives lost during the Holocaust. Ashley Swords, a resource center English teacher for grades nine to 12, uses pennies because they are small and plentiful and allow her to recontextualize a familiar, everyday object.

Students perform other calculations to amplify the impact of the lessons—at the school’s football field, for example, they determine the volume of Swords herself and then calculate how many football fields would be needed to bury the 11 million Holocaust victims if they were each Swords’s size and were buried in graves 10 feet deep. Guesses ranged from two to 20 football fields, with students finally concluding that it would take about 343 football fields.

Swords knew this lesson was a success when a group of six seniors got emotional after completing it and realizing the magnitude of the deaths in World War II.

Math Recipes

Recipes were perhaps the most popular idea among the elementary teachers who responded to our request for real-world math examples. Fifth-grade teacher Gabi Sanfilippo of Meadow Ridge in Orland Park, Illinois, for example, asked her students to write down one to two ways they used math outside of the classroom during spring break—and more than half of her students wrote that they practiced using measurements and fractions while baking and cooking with their families.

In class, students practice halving, tripling, or quadrupling recipes based on how many people they’d cook or bake for. Most teachers don’t actually cook in class, but often students cook at home to practice their new skills.

Another educator, Elizabeth Eagan of Bastrop Independent School District in Texas, brings in a toaster oven to bake in class. She teaches the visually impaired, from newborns to 22-year-olds, using recipes in large print, braille, or audio to show the real-world application of adding and subtracting fractions.

Eagan prints out recipes at 129 percent for her low-vision students or converts the text to braille using  braille transcription software , and then prints them using a braille printer . She purchased Stir It Up , a cookbook in both braille and print that makes it easier for families and teachers to help their students if they haven’t mastered the tactile language. Students may use electronic magnifying glasses like Pebble and Ruby. For audio, Eagan records herself reading the recipes, has a peer or parent help, or uses the app Seeing AI , which can scan and read recipes aloud.

Grocery Store Field Trip

Many teachers make real-world math connections to grocery shopping. Leanna Agcaoili’s second-grade students at Joseph J. Fern Elementary School in Honolulu, Hawaii, are tasked with creating a healthy meal for their family on a $20 budget. On a grocery store field trip, students practice adding and subtracting one- and two-digit whole numbers—and learn about money and budgeting in the process.

Agcaoili says she’ll do a practice run in class next year, noting that the first time through some students had difficulty finding their ingredients.

Graphing Favorite Halloween Candy Wrappers

After Halloween, Dottie Wright Berzins, a retired public school teacher, had her students bring in wrappers from their favorite Halloween candy. Depending on the age, the students then created graphs showing their favorite candies.

Younger ages built life-size candy bar graphs, marking the x- and y-axis with masking tape on the floor and using the wrappers to represent the bars. Older students constructed tally charts and paper graphs, and followed ads, tracked which brands advertised more, interviewed peers about their favorite candy, made predictions, and created what-if scenarios—like what if the price of chocolate increased—how would that variable impact the graph?

• Create account

Math and Special Education Blog

8 problem solving strategies for the math classroom.

Posted by Colleen Uscianowski · February 25, 2014

Would you draw a picture, make a list  possible number pairs that have the ratio 5:3, or guess and check? 

Explicit strategy instruction should be an integral part of your math classroom, whether you're teaching kindergarten or 12th grade.

Teach students that they can choose from a list of strategies to solve a problem, and often there isn't one correct way of finding a solution.

Demonstrate how you solve a word problem by thinking aloud as you choose and execute a strategy.

Ask students if they would solve the problem differently and praise students for coming up with unique ways of arriving at an answer.

Here are some problem-solving strategies I've taught my students:

Below is a helpful chart to remind students of the many problem-solving strategies they can use when solving word problems. This useful handout is a great addition to students' strategy binders, math notebooks, or math journals.  

How do you teach problem-solving in your classroom? Feel free to share advice and tips below!    

Sign up to receive a FREE copy of our problem-solving poster.

• Homework Help
• Article Directory

Learning 5th Grade Math: Outcomes and Teaching Strategies

•  / 

Most states have adopted the Common Core State Standards for math and English. The 5th grade math standards are the outcomes presented here. However, as common as the standards may be, teachers are generally free to determine their own teaching strategies. Some of the possibilities are shown here.

5th Grade Math Instruction

Outcomes for 5th grade math are divided into six logical areas in the Common Core State Standards, with two or more outcomes listed for each area. An outcome may be defined as a student's measurable knowledge or skill in a given subject. Here are the areas, along with some desired outcomes:

Algebra - Logic and Procedures

1. Use parentheses and brackets in algebraic sentences and know how to solve problems that have these marks. 2. When given two rules, write an algebraic sentence, noticing patterns and comparisons and explaining them.

Base Ten Procedures

1. Use and explain the system of place values. 2. Multiply whole numbers with multiple digits, divide 4-digit dividends by 2-digit divisors and work with decimals in addition, subtraction, multiplication and division.

1. Add and subtract fractions with different denominators by using equivalent fractions. 2. Multiply and divide fractions and relate that to multiplication and division of whole numbers.

Measurements and Interpretation of Data

1. Convert measurements within a single system to measurement, such as inches to yards. 2. Use given fractional measurements to make a line plot. Conversely, solve problems using a line plot and its information. 3. Understand what volume is and how to figure the volume of cubes and right rectangular prisms using addition and multiplication.

1. Solve problems by graphing points on a coordinate plane. 2. Categorize 2-dimensional figures based on their number of sides and types of angles.

Math Skills and Problem-Solving Practices

1. Develop capacity for logical, critical, abstract and quantitative thinking. 2. Learn perseverance and precision in solving problems. 3. Know how to model what is learned, strategically using suitable tools. 4. Watch for structure in problems, and be able to use it, along with regular procedures, in problem solving and mathematical reasoning.

Teaching Strategies

When teaching math in any grade, it can be beneficial to provide frequent review to give students a chance to internalize the material. In addition, consider balancing individual work with cooperative group work to build a learning environment in the classroom. Lecture, discussions, flash cards and worksheets may be enhanced by the additional use of the following:

• Manipulative objects (such as pattern blocks or tiles)
• Pictures and videos
• Stories and poems
• Songs and chants

When it comes to games, as the teacher you can use games that are played either by individual students, groups of students or the whole class. These games can include paper and pencil games such as puzzles, board games, interactive computer games or physically active math games that involve students using math skills along with gross motor skills such as kicking, running and throwing.

Other Articles You May Be Interested In

Imagine a math teaching tool so effective that it need only be employed twice per week for less than an hour to result in huge proficiency gains. Impossible, you say? Not so...and MIND Research Institute has the virtual penguin to prove it.

Should kindergartners put away the building blocks and open the math books? According to recent research, earlier is better when it comes to learning mathematical concepts. But that could put undue pressure on kids, parents and even teachers.

We Found 7 Tutors You Might Be Interested In

Huntington learning.

• What Huntington Learning offers:
• Online and in-center tutoring
• One on one tutoring
• Every Huntington tutor is certified and trained extensively on the most effective teaching methods
• What K12 offers:
• Online tutoring
• Has a strong and effective partnership with public and private schools
• AdvancED-accredited corporation meeting the highest standards of educational management

Kaplan Kids

• What Kaplan Kids offers:
• Customized learning plans
• Real-Time Progress Reports track your child's progress
• What Kumon offers:
• In-center tutoring
• Individualized programs for your child
• Helps your child develop the skills and study habits needed to improve their academic performance

Sylvan Learning

• What Sylvan Learning offers:
• Sylvan tutors are certified teachers who provide personalized instruction
• Regular assessment and progress reports

Tutor Doctor

• What Tutor Doctor offers:
• In-Home tutoring
• One on one attention by the tutor
• Develops personlized programs by working with your child's existing homework
• What TutorVista offers:
• Student works one-on-one with a professional tutor
• Using the virtual whiteboard workspace to share problems, solutions and explanations

Find the Perfect Tutor

Our commitment to you, free help from teachers, free learning materials, helping disadvantaged youth, learning tools.

• Make learning fun with these online games!
• Looking for ways to bring learning home? Check out our blog.

Want to Help Your Child Learn?

More articles.

• Not Your Father's Algebra As 45 States Look to Math Reform
• Too Much Emphasis on Reading and Math?
• Reading and Math Targeted by Miami's 'Teach for America'
• New York Down, Other Cities Up in Math Scores
• Old-Fashioned Building Blocks Can Help With Math and Other Academic Basics
• Native American Students Struggling, Lagging in Math and Reading
• Robot-Building Enhances Math and Science Skills
• Charter Schools Tops in Math and Reading
• Reading Options for Teenagers
• The Shortest Day: Learning About the Winter Solstice
• Elementary Concepts: Fifth Grade Reading
• Teaching Reading to Older Kids Who Have Learning Disabilities
• GED Pennsylvania: What Is the Pennsylvania GED Test?
• G.E.D. Test Online: Can I Take the G.E.D. Online?
• Logic Games and Your Child
• My Teacher's at the Door: Home Visits on the Rise
• Math Assessments for Students Entering High School
• Your Move: Does Chess Have a Place in School Curriculum?
• Math Games for Grade Six
• Sexual Harassment Plagues Teen Girls
• Quizs for Kids
• Reading Fun for 7th Graders
• Online 6th Grade Grammar Help
• Tips to Helping your Seventh Grader with Factoring and Multiples in Their Math Homework
• School Worksheets for Kids
• Where Can I Find Free Math Answers for 5th Grade Math Problems
• 5th Grade Math Help Probability and Statistics
• 5th Grade Math Assessment
• 5th Grade Math Rounding Decimals to the Nearest Thousandth
• 5th Grade Math Drill
• 5th Grade Math Facts
• 5th Grade Math Bee'
• 5th Grade Math Graphs
• 5th Grade Math Activities
• 5th Grade Math Help for Decimals
• Privacy Policy
• Resource Directory

© 2003 - 2024 All other trademarks and copyrights are the property of their respective owners. All rights reserved.

Steals & Deals: Up to 77% off wireless earbuds, packing cubes, more travel essentials

• TODAY Plaza
• Share this —

• Watch Full Episodes
• Read With Jenna
• Inspirational
• Relationships
• TODAY Table
• Newsletters
• Start TODAY
• Shop TODAY Awards
• Citi Concert Series
• Listen All Day

Follow today

More Brands

• On The Show

5th grade math tips: Here's how to help your student

Hoping to help your fifth-grader with math skills ? Here are some basic tips that experts suggest for fifth-graders .

Highlight real-world uses of math

As the math they’re learning becomes more complicated and less obviously connected with their everyday experience, some children start to develop math anxiety. It’s important to keep your child engaged with math and to help her understand the real-life applications of the concepts she’s learning in school. Coming up with a budget for back-to-school supplies or for a monthly allowance is one way for them to practice addition and subtraction. Asking them to help you with cooking or baking shows them how fractions work. Helping you calculate prices when you’re grocery shopping is also good practice.

Parenting Guides 5th grade math skills: Find out what you need to know for your student

Help prepare for math class.

Help your child reduce stress over math by familiarizing their with the concepts they will be covering in class. Ask their teacher for a syllabus and refer to this to preview each evening the material that will be covered in the following day’s math class. Skim over these pages with them. No need to spend time working out the meaning of concepts or trying sample problems, although you can consult the glossary for definitions of unfamiliar words. Even this slight increase in familiarity with the terms that will come up the next day will help your child approach math with more confidence.

Read problems out loud

If your child is struggling with math problems, have them read each problem out loud slowly and carefully so your child can hear the problem and think about what is being asked. This helps them break down the problem and come up with problem-solving strategies.

Keep math positive

Speak positively about math and reward effort rather than grades or ability. Think about how important reading is and how we are told to model this behavior for our children. We need to place math in the same category. Don’t discount the importance of math by saying, “I’m not a math person, I was never good at math.” Help your child read books that incorporate math, such as "Millions of Cats" by Wanda Gag, or"OnBeyond a Million: An Amazing Math Journey," by David Schwartz.

Consult online resources

Familiarize yourself with the range of online resources that can help your 5th grader practice and review the math concepts they are learning.

Practice calculations using decimals

Connect the work with decimals that your child is doing in class to the real world by encouraging their to shop for bargains. Have them divide the cost of bulk-packaged items by the number of single items to find the cost per item. So how much are you paying per roll of paper towel or per can of soda when you buy in bulk? Or ask them to calculate how much of a savings you’ll make per item with sale prices offering volume discounts.

parenting-guides 5th Grade Parenting Guides

Practice using fractions.

Help your fifth grader familiarize themselves with fractions by asking their to scale recipes for your family. Have them start by halving or doubling a recipe. When they feel comfortable doing this, ask them to convert it by 11⁄2, allowing a recipe that is supposed to feed a family of four to work for a family of six.

Set up a bank account

Set up a bank account for your child. Before you do this, discuss with their the basic concepts of banking – interest, checking and saving accounts, credit and debit cards, etc. The experience will help get them excited about saving and increasing their money.

Highlight math in sports

Sports provide a fun and engaging way of exploring a host of mathematical concepts, starting with basic addition. Any hard-core baseball fan knows that the game can’t truly be appreciated without an understanding of some essential statistics, like a player’s batting average and runs batted in. If your child is passionate about a sport, encourage them to explore it through math.

Play games that use math

Play family games that help foster math skills. These include card games like Go Fish, which requires counting and sorting cards into sets, or board games like Monopoly.

To find out what your fifth-grader will be learning in math class, check out our fifth grade math skills page .

TODAY's Parenting Guides resources were developed by NBC News Learn with the help of subject-matter experts, including Joyce Epstein, Director, Center on School, Family and Community Partnerships, Johns Hopkins University; Pamela Mason, Program Director/Lecturer on Education, Harvard Graduate School of Education; Denise Walston, Director of Mathematics, Council of the Great City Schools; Nell Duke, Professor, University of Michigan; Leanna Baker, Retired Math Teacher; Bon Crowder, Math Teacher and Blogger, MathFour.com; and Robin Schwartz, VP, Association of Teachers of Math of NYC, and align with the Common Core State Standards.

Resources and

Guiding Curiosity, Igniting Imagination!

4 Math Word Problem Solving Strategies

5 Strategies to Learn to Solve Math Word Problems

A critical step in math fluency is the ability to solve math word problems. The funny thing about solving math word problems is that it isn’t just about math. Students need to have strong reading skills as well as the growth mindset needed for problem-solving. Strong problem solving skills need to be taught as well. In this article, let’s go over some strategies to help students improve their math problem solving skills when it comes to math word problems. These skills are great for students of all levels but especially important for students that struggle with math anxiety or students with animosity toward math.

Signs of Students Struggling with Math Word Problems

It is important to look at the root cause of what is causing the student to struggle with math problems. If you are in a tutoring situation, you can check your students reading level to see if that is contributing to the issue. You can also support the student in understanding math keywords and key phrases that they might need unpacked. Next, students might need to slow their thinking down and be taught to tackle the word problem bit by bit.

How to Help Students Solve Math Word Problems

Focus on math keywords and mathematical key phrases.

The first step in helping students with math word problems is focusing on keywords and phrases. For example, the words combined or increased by can mean addition. If you teach keywords and phrases they should watch out for students will gain the cues needed to go about solving a word problem. It might be a good idea to have them underline or highlight these words.

Cross out Extra Information

Along with highlighting important keywords students should also try to decipher the important from unimportant information. To help emphasize what is important in the problem, ask your students to cross out the unimportant distracting information.  This way, it will allow them to focus on what they can use to solve the problem.

Encourage Asking Questions

As you give them time to read, allow them to have time to ask questions on what they just read. Asking questions will help them understand what to focus on and what to ignore. Once they get through that, they can figure out the right math questions and add another item under their problem-solving strategies.

Draw the Problem

A fun way to help your students understand the problem is through letting them draw it on graph paper. For example, if a math problem asks a student to count the number of fruits that Farmer John has, ask them to draw each fruit while counting them. This is a great strategy for visual learners.

Check Back Once They Answer

Once they figured out the answer to the math problem, ask them to recheck their answer. Checking their answer is a good habit for learning and one that should be encouraged but students need to be taught how to check their answer. So the first step would be to review the word problem to make sure that they are solving the correct problem. Then to make sure that they set it up right. This is important because sometimes students will check their equation but will not reread the word problem and make sure that the equation is set up right. So always have them do this first! Once students believe that they have read and set up the correct equation, they should be taught to check their work and redo the problem, I also like to teach them to use the opposite to double check, for example if their equation is 2+3=5, I will show them how to take 5 which is the whole and check their work backwards 5-3 and that should equal 2. This is an important step and solidifies mathematical thinking in children.

Mnemonic Devices

Mnemonic devices are a great way to remember all of the types of math strategy in this post. The following are ones that I have heard of and wanted to share:

CUBES Word Problem Strategy

Cubes is a mnemonic to remember the following steps in solving math word problems:

C: Circle the numbers

U: Underline the question

B: Box in the key words

E: Eliminate the information

S: Solve the problem & show your work

RISE Word Problem Strategy

Rise is another way to explain the steps needed to solve problems:

R: Read and reread

I: Illustrate what is being asked

S: Solve by writing your equation or number sentences

E: Explain your thinking

COINS Word Problem Strategy

C: Comprehend the questions

O: Observe the data

I: Illustrate the problem

N: Write the number sentence (equation)

Understand -Plan – Solve – Check Word Problem Strategy

This is a simple step solution to show students the big picture. I think this along with one of the mnemonic devices helps students with better understanding of the approach.

Understand: What is the question asking? Do you understand all the words?

Plan: What would be a reasonable answer? In this stage students are formulating their approach to the word problem. 

Solve: What strategies will I use to solve this problem? Am I showing my thinking? Here students use the strategies outlined in this post to attack the problem.

Check: Students will ask themselves if they answered the question and if their answer makes sense. 

If you need word problems to use with your classroom, you can check out my word problems resource below.

Teaching students how to approach and solve math word problems is an important skill. Solving word problems is the closest math skill that resembles math in the real world. Encouraging students to slow their thinking, examine and analyze the word problem and encourage the habit of answer checking will give your students the learning skills that can be applied not only to math but to all learning. I also wrote a blog post on a specific type of math word problem called cognitively guided instruction you can read information on that too. It is just a different way that math problems are written and worth understanding to teach problem solving, click here to read .

Share This Story, Choose Your Platform!

Related posts.

How to play the card game Garbage

Teaching Number Tracing and Formation to Students

fun games with math

Leave a comment cancel reply.

 subscribe to our newsletter

• Math for Kids
• Parenting Resources
• ELA for Kids
• Teaching Resources

How to Teach Number Formation in 5 Easy Steps

13 Best Resources for Math Videos for Kids: Math Made Fun

How to Teach Skip Counting to Kids in 9 Easy Steps

10 Best Math Intervention Strategies for Struggling Students

How to Teach Division to Kids in 11 Easy Steps

How to Cope With Test Anxiety in 12 Easy Ways

Developmental Milestones for 4 Year Olds: The Ultimate Guide

Simple & Stress-Free After School Schedule for Kids of All Ages

When Do Kids Start Preschool: Age & Readiness Skills

Kindergarten Readiness Checklist: A Guide for Parents

How to Teach Letter Formation to Kids in 9 Easy Steps

15 Best Literacy Activities for Preschoolers in 2024

12 Best Poems About Teachers Who Change Lives

6 Effective Ways to Improve Writing Skills

40 Four Letter Words That Start With A

60 Fun Animal Facts for Kids

12 Best Behavior Management Techniques for the Classroom

13 Best Online Teaching Tips for Teachers

How to Teach Kids to Write in 9 Easy Steps

13 Challenges for Teachers and How to Address Them

1. Diagnostic Assessment

2. differentiated instruction, 3. use of manipulatives, 4. visual aids and graphic organizers, 5. math vocabulary building, 6. integrating technology, 7. peer tutoring, 8. scaffolded instruction, 9. real-world application, 10. regular feedback and encouragement.

Have you ever found yourself standing before your class, explaining a math concept for the umpteenth time, only to see a sea of confused faces staring back at you? It’s a moment many educators experience, signaling a disconnect that’s neither the fault of the teacher nor the students. This common scenario underscores the urgent need for effective math intervention strategies to address diverse learning needs.

SplashLearn: Most Comprehensive Learning Program for PreK-5

SplashLearn inspires lifelong curiosity with its game-based PreK-5 learning program loved by over 40 million children. With over 4,000 fun games and activities, it’s the perfect balance of learning and play for your little one.

In this blog, we’ll dive deep into math intervention strategies, outlining what they are and how you can implement them to make a real difference in your student’s learning journey. 

What is Math Intervention?

At its core, math intervention is a targeted approach designed to help students overcome the hurdles they face with mathematical concepts. Unlike the broad strokes of regular math instruction, math intervention zooms in on specific challenges, offering a lifeline to those who find themselves adrift in a sea of numbers and equations.

The primary goal of math intervention is straightforward: to ensure every student achieves proficiency in math by addressing their individual learning gaps . This is done through various intervention strategies for math, which are tailored to meet the unique needs of each student. The strategies deployed are as diverse as the learners, from one-on-one tutoring sessions to small group work.

​​10 Math Intervention Strategies for Struggling Students

Diagnostic assessment acts as a compass, guiding educators to identify specific areas where students struggle with math. It’s about gathering insights into each student’s unique challenges.

How it can be done:

• Use pre-tests to evaluate students’ knowledge before starting a new unit.
• Employ quizzes and surveys to understand students’ comfort levels with various math topics.
• Analyze errors in homework and tests to pinpoint misconceptions.

With Splashlearn , you can track your student’s progress and identify areas that they need help with. Here is how the SplashLearn teacher dashboard looks:

Recognizing that every student’s learning journey is unique, differentiated instruction tailors teaching methods to suit individual needs. It ensures that all students find pathways to understanding and success in math.

• Group students based on their skill levels for targeted teaching.
• Offer varied types of content delivery—visual, auditory , and kinesthetic —to cater to different learning styles .
• Adjust the pace of instruction to meet the needs of each learner.

The use of physical tools, or manipulatives , transforms abstract math concepts into tangible learning experiences. This strategy helps students visualize mathematical ideas, fostering a deeper understanding.

• Integrate blocks, beads, or counting sticks during lessons to illustrate concepts.
• Encourage students to use manipulatives to solve problems and demonstrate their thought processes.
• Create interactive activities that incorporate these tools to enhance engagement and comprehension.

This strategy involves using diagrams, charts, and other visual tools to make complex math concepts easier to understand. Presenting information visually allows students to see the connections and relationships between ideas, enhancing their comprehension and retention.

• Create flowcharts or diagrams to outline steps in a math process.
• Use graphic organizers to break down problem-solving strategies.
• Incorporate visual aids in lessons to illustrate concepts like fractions , geometry , and algebra .

A strong grasp of math vocabulary is crucial for students to follow instructions, understand questions, and express their mathematical thinking. This approach focuses on developing a comprehensive math language, aiding in clearer communication and deeper understanding.

• Introduce and practice key vocabulary terms in context during lessons.
• Use word walls in the classroom to display and reinforce important terms.
• Encourage students to use specific math language in their explanations and reasoning.

Leveraging technology in math education offers dynamic and interactive ways for students to engage with mathematical concepts. Educational software and apps can provide personalized learning experiences, immediate feedback , and various resources to support diverse learning needs.

• Implement math learning apps and online platforms for practice and exploration.
• Use interactive whiteboards or projectors to demonstrate problems and solutions.
• Incorporate simulations and virtual manipulatives to offer hands-on learning in a digital format.

Peer tutoring is a collaborative learning strategy where students help each other understand math concepts and solve problems. This method fosters a supportive learning environment, encouraging students to communicate, collaborate, and learn from one another.

• Pair up students with differing skill levels to facilitate learning and mentorship.
• Organize group study sessions focused on specific math topics or challenges.
• Encourage older students or those proficient in math to lead tutoring sessions for their peers.

Scaffolded Instruction is a teaching method where the teacher gradually reduces their support, allowing students to become more independent in their learning process. It’s like teaching someone to ride a bike with training wheels and gradually removing them as they gain confidence and skill. This approach is crucial in math interventions for elementary students, offering them the stepping stones to mastery and independence.

• Start with highly structured activities where the teacher leads the process.
• Gradually shift to tasks that require more independence from students.
• Provide tools and resources, like cheat sheets or reference materials, that students can use on their own.

This strategy involves linking math concepts to everyday situations and problems. It shows students the practical side of math, making learning more engaging and meaningful. When students see how math works in the real world, it enhances their understanding and appreciation of the subject. Mathematics intervention programs incorporating real-world applications can significantly increase students’ motivation and interest in math.

• Use examples from cooking, shopping, or sports to teach math concepts.
• Encourage students to identify and solve real-life math problems.
• Integrate projects that require students to apply math skills in real-world scenarios.

Providing students with ongoing feedback and positive reinforcement is key to effective math intervention programs. This strategy helps build students’ confidence, keep them motivated, and guide their progress by letting them know where they stand and how to improve.

• Offer timely, specific feedback on students’ work and progress.
• Celebrate successes, no matter how small, to encourage persistence.
• Use constructive criticism to guide students towards better understanding and strategies.

Who Needs Math Intervention?

Identifying which students need a helping hand in math isn’t always straightforward. Here’s how teachers can pinpoint those who might benefit most from math intervention:

1. The Identification Process

• Teachers are often the first to notice when a student struggles. You might see a student repeatedly making the same mistakes, showing frustration, or avoiding math tasks altogether. These are clear signals that additional support could be necessary.
• It’s important to consider not just one bad test score but a pattern of difficulties. Consistent struggles with homework, quizzes, or classwork can indicate that a student might need intervention.

2. The Role of Standardized Tests

• Standardized tests provide a snapshot of a student’s math skills compared to grade-level expectations. Scores significantly below average are a red flag that a student may need targeted help.
• While these tests are useful, they’re just one piece of the puzzle. Remembering that they don’t capture everything about a student’s abilities or potential is crucial.

3. Teacher Observations

• Teachers see students in action every day. You know who participates eagerly and who hangs back. Your detailed observations in the classroom are invaluable for identifying students who might not fully grasp math concepts.
• Sometimes, it’s not just about who can’t do the math but also about who lacks confidence or shows little interest. These students might also benefit from intervention strategies that boost their engagement and self-assurance.

4. Parent Feedback

• Parents can offer perspectives on how their child feels about math at home, including anxiety, frustration, or a lack of interest in homework. This information can be vital in understanding a student’s intervention needs.
• Working together, teachers and parents can share observations and insights, ensuring that students receive support at school and at home.

When to Implement Math Intervention Strategies?

Deciding when to start math intervention strategies and how often to conduct these sessions is key to their success. Let’s break it down into simple, actionable advice:

1. Timing is Everything

• Early Intervention: The sooner, the better. Starting intervention when you notice a student struggling can prevent minor issues from becoming major obstacles. Don’t wait for the problem to grow; tackle it head-on at the first sign of difficulty.
• Before New Units or Concepts: If possible, introduce intervention strategies before moving on to more complex topics. This helps ensure all students have a solid foundation to build new knowledge.

2. Frequency Matters

• Regular, Consistent Sessions: Consistency is crucial for math intervention. Whether it’s daily or a few times a week, setting a regular schedule helps students know what to expect and builds the routine into their learning process.
• Adaptable to Student Needs: The frequency of intervention sessions may need to adjust based on how quickly a student progresses. Some may need more intensive support initially, with the possibility of tapering off as they gain confidence and skill.

3. Best Practices for Intervention Sessions

• Short, Focused Sessions: Keep intervention sessions short and focused. Long sessions can be overwhelming, especially for students already struggling with math. Aim for short bursts of concentrated learning to keep students engaged and not burnt out.
• Small Group or One-on-One: Depending on the available resources, try to keep groups small or work one-on-one with students. This ensures that each student gets the attention they need to address their specific challenges.

Role of Teachers in Math Intervention

Teachers are at the heart of successful math intervention programs. Their role goes beyond just delivering content; it encompasses planning, implementing, assessing, and collaborating to ensure each student receives the support they need. Let’s simplify and outline these responsibilities:

1. How to Plan Intervention Strategies

• Teachers start by identifying the specific math skills or concepts students struggle with, using assessments and observations.
• Based on these needs, teachers select appropriate intervention strategies that will best support student learning.

2. Implementing Intervention Strategies

• Teachers provide targeted instruction tailored to each student’s individual needs. This might involve breaking down concepts into smaller, more manageable steps, using manipulatives, or incorporating technology.
• It’s crucial to create a learning environment where students feel safe to express confusion, ask questions, and make mistakes. This supportive atmosphere encourages growth and learning.

3. Assessing Intervention Effectiveness

• Teachers continually monitor students’ progress through regular assessments and feedback. This helps to adjust intervention strategies as needed to ensure they are effective.
• Based on assessment results, teachers may need to adjust their approach, trying different strategies to find what works best for each student.

4. Collaboration Is Key

• Teachers communicate with parents to provide updates on their child’s progress and to discuss ways to support learning at home.
• Collaboration with special educators, school psychologists, and other professionals is essential. These experts can offer additional insights and strategies to support students’ learning.

How Can SplashLearn be Used as a Math Intervention Strategy

Math & ela | prek to grade 5, kids see fun ., you see real learning outcomes ..

Watch your kids fall in love with math & reading through our scientifically designed curriculum.

SplashLearn stands out as a powerful tool in the math intervention toolkit, offering interactive, engaging, and personalized learning experiences for students. Here’s how educators can leverage SplashLearn to bolster their math intervention efforts:

1. Adaptive Learning Paths: SplashLearn’s platform adapts to each student’s learning level, providing challenges just right for their current understanding. This personalization ensures that students are neither bored with content that’s too easy nor overwhelmed by content that’s too hard. The scaffolding in skill progression is well-researched, so kids learn to apply concepts independently.

2. Resources for Diverse Learning Needs: The platform offers a range of games and worksheets that cater to different learning styles and needs, making it a valuable resource for differentiated instruction. Whether a student needs practice with basic math skills or more advanced problem-solving abilities, SplashLearn has resources to support their growth.

3. Immediate Feedback without Penalties:

• Encouraging Response to Mistakes: Instead of penalizing wrong answers, SplashLearn responds with encouraging messages like “Hey, let’s try that again!” This approach helps build a positive learning environment , reducing math anxiety and encouraging a growth mindset.
• No Timed Challenges: SplashLearn allows students to work at their own pace by removing the pressure of timed challenges. This is particularly important for learners who need extra time to process and solve problems, ensuring they don’t feel rushed or stressed.

4. Progress Tracking for Educators: Teachers can monitor their student’s progress in real time, gaining insights into their strengths and areas for improvement. This feature enables educators to tailor their intervention strategies more effectively based on detailed data about each student’s learning journey.

5. Facilitates Home-School Connection: SplashLearn can be accessed at home, making it easier for parents to get involved in their child’s math learning. Educators can collaborate with parents, providing updates on their child’s progress and suggestions for supporting their learning outside the classroom.

Implementing effective math intervention strategies and exploring innovative math intervention ideas like SplashLearn can significantly enhance the learning experience for students struggling with math. By tailoring our approach to meet each student’s unique needs, providing supportive and adaptive tools, and fostering a positive learning environment, we can make math accessible and enjoyable for everyone. 

Frequently Asked Questions (FAQs)

What are tier 1 and 2 interventions in math.

Tier 1 interventions are general strategies used in the regular classroom to support all students, while Tier 2 interventions provide targeted support to small groups or struggling individuals.

How do you structure a math intervention class?

A math intervention class is structured around identifying specific learning gaps, using targeted instruction and practice, and regularly assessing progress to adjust strategies as needed.

What is a push in math intervention?

A push in math intervention involves the math specialist or interventionist coming into the classroom to work directly with students in their regular learning environment, providing support alongside the classroom teacher.

What makes a good math intervention?

A good math intervention is tailored to individual student needs, uses evidence-based strategies, provides frequent feedback, and actively engages students in their learning process.

Most Popular

15 Best Report Card Comments Samples

117 Best Riddles for Kids (With Answers)

40 best good vibes quotes to brighten your day, recent posts.

10 Best Online Homeschool Programs

12 Best Activities for Kinesthetic Learners

15 Best Speech Therapy Activities for Toddlers

Math & ela | prek to grade 5, kids see fun., you see real learning outcomes..

Watch your kids fall in love with math & reading through our scientifically designed curriculum.

Parents, try for free Teachers, use for free

• Games for Kids
• Worksheets for Kids
• Math Worksheets
• ELA Worksheets
• Math Vocabulary
• Number Games
• Addition Games
• Subtraction Games
• Multiplication Games
• Division Games
• Addition Worksheets
• Subtraction Worksheets
• Multiplication Worksheets
• Division Worksheets
• Times Tables Worksheets
• Reading Games
• Writing Games
• Phonics Games
• Sight Words Games
• Letter Tracing Games
• Reading Worksheets
• Writing Worksheets
• Phonics Worksheets
• Sight Words Worksheets
• Letter Tracing Worksheets
• Prime Number
• Order of Operations
• Long multiplication
• Place value
• Parallelogram
• SplashLearn Success Stories
• SplashLearn Apps
• [email protected]

© Copyright - SplashLearn

Make study-time fun with 14,000+ games & activities, 450+ lesson plans, and more—free forever.

Parents, Try for Free Teachers, Use for Free

Build Confidence with Math Problem Solving

Daily Problem Solving will help your 5th grade students master the skills they need to be successful with challenging word problems...and have fun doing it .

What you'll get with this download:

Your download includes a full week of Daily Problem Solving for Grade 5 to try out in your own classroom. Developed with the brain in mind, these multi-step word problems will challenge your learners without overwhelming them. Best of all, you'll be able to watch their skills and confidence grow as they begin to internalize strategies for conquering this difficult math skill.

FUN & ENGAGING

Themed-problems and a weekly fun fact make it easy to keep learners engaged

MINIMAL PREP

Formatted for quick & easy implementation that won't add stress to your planning

PRINT & DIGITAL

Includes both print and digital student options for added flexibility

Help Students Master Math Word Problems

I've been using this with my extremely anxious learner and it works wonders to build confidence because we see the improvement.

These have given me such an insight into my students' abilities, and I've watched them improve their skills and successfully solve multi-step word problems.

Jilliana D.

STUDENT PRINTABLES

You'll receive a full week of printable Daily Problem Solving practice for your students. This format includes:

• Paper-saving format that fits a full week on one page
• Space for student work, feedback, and self-reflection
• Themed problems & weekly fun fact to engage

DIGITAL SLIDES

Daily digital slides offer your remote or online learners the opportunity to build problem-solving skills in a structured format designed for success.

• Single slide per day prevents overwhelm or distraction
• Organized with clear space to solve & answer
• Engaging graphics, themed problems, & fun facts

Don’t wait, get started helping your learners master word problems today!

© Differentiated Teaching | Back to the Blog

Math Wheels for Note-taking?

Teaching Math Problem Solving Strategies

Teaching math problem solving strategies in middle school.

There are many math problem solving strategies out there and some are very beneficial to upper elementary and middle school math students. Before we jump into them, I’ll share a little bit of my experiences in teaching math problem solving strategies over the past 25+ years.

During my second year of teaching ( in the early 90s) , I was teaching 5th grade, and our state math testing began to include a greater focus on problem solving and writing in math.

Over the next several years, the other math teachers and I used standard sentence starters to help math students practice explaining their problem solving process. These were starters like:

• “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

By using 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 . 

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!).

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:

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

I LOVED these…I really did (do)! And the students I taught during those years became very good at reasoning and solving problems.

Teaching Math Problem Solving in Middle School

When I moved to 6th grade math in middle school, I tried to keep teaching these strategies, but our math periods are only 44 minutes.

• 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

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 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.

Choose a Strategy This step requires students to think about what strategy will work well with the question they’ve been asked. Sometimes this is tough, so I give them some suggestions for when to use these particular strategies:

• 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.

Check Your Answer I’ve found that many students think “check your answer” means to make sure they have an answer (especially when taking a test), so we practice several strategies for checking:

• 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

• There’s also a blank template, so I can create problem solving homework for students throughout the year, using the same format. I’m hoping that using the Doodle Notes format will make the problem solving strategies a little more fun, interesting, and easy to remember. 

This was a long post about teaching math problem solving strategies! Thanks for sticking with me to the end!

read next...

Master 3rd Grade Math Concepts and More With Math Wheels

How To Tell If Executive Function Skills Impact Math Performance

How to Help Easily Distracted Students by Using Math Wheels

Daily Math Activities to Incorporate and Retain More Math Concepts

Welcome to Cognitive Cardio Math! I’m Ellie, a wife, mom, grandma, and dog ‘mom,’ and I’ve spent just about my whole life in school! With nearly 30 years in education, I’ve taught:

• All subject areas in 4 th  and 5 th  grades
• Math, ELA, and science in 6th grade (middle school)

I’ve been creating resources for teachers since 2012 and have worked in the elearning industry for about five years as well!

FIND IT FAST

Let's connect.

Select the image above to learn more!

Get FIVE days of free math lessons!

Terms of Use        Privacy Policy

COPYRIGHT © 2022 COGNITIVE CARDIO MATH • ALL RIGHTS RESERVED. SITE DESIGN BY LAINE SUTHERLAND DESIGNS