maths problem solving ideas

Problem Solving Activities: 7 Strategies

• Critical Thinking

Problem solving can be a daunting aspect of effective mathematics teaching, but it does not have to be! In this post, I share seven strategic ways to integrate problem solving into your everyday math program.

In the middle of our problem solving lesson, my district math coordinator stopped by for a surprise walkthrough. 

I was so excited!

We were in the middle of what I thought was the most brilliant math lesson– teaching my students how to solve problem solving tasks using specific problem solving strategies. 

It was a proud moment for me!

Each week, I presented a new problem solving strategy and the students completed problems that emphasized the strategy. 

Genius right? 

After observing my class, my district coordinator pulled me aside to chat. I was excited to talk to her about my brilliant plan, but she told me I should provide the tasks and let my students come up with ways to solve the problems. Then, as students shared their work, I could revoice the student’s strategies and give them an official name. 

What a crushing blow! Just when I thought I did something special, I find out I did it all wrong. 

I took some time to consider her advice. Once I acknowledged she was right, I was able to make BIG changes to the way I taught problem solving in the classroom. 

When I Finally Saw the Light

To give my students an opportunity to engage in more authentic problem solving which would lead them to use a larger variety of problem solving strategies, I decided to vary the activities and the way I approached problem solving with my students. 

Problem Solving Activities

Here are seven ways to strategically reinforce problem solving skills in your classroom. 

Seasonal Problem Solving

Many teachers use word problems as problem solving tasks. Instead, try engaging your students with non-routine tasks that look like word problems but require more than the use of addition, subtraction, multiplication, and division to complete. Seasonal problem solving tasks and daily challenges are a perfect way to celebrate the season and have a little fun too!

Cooperative Problem Solving Tasks

Go cooperative! If you’ve got a few extra minutes, have students work on problem solving tasks in small groups. After working through the task, students create a poster to help explain their solution process and then post their poster around the classroom. Students then complete a gallery walk of the posters in the classroom and provide feedback via sticky notes or during a math talk session.

Notice and Wonder

Before beginning a problem solving task, such as a seasonal problem solving task, conduct a Notice and Wonder session. To do this, ask students what they notice about the problem. Then, ask them what they wonder about the problem. This will give students an opportunity to highlight the unique characteristics and conditions of the problem as they try to make sense of it. 

Want a better experience? Remove the stimulus, or question, and allow students to wonder about the problem. Try it! You’ll gain some great insight into how your students think about a problem.

Math Starters

Start your math block with a math starter, critical thinking activities designed to get your students thinking about math and provide opportunities to “sneak” in grade-level content and skills in a fun and engaging way. These tasks are quick, designed to take no more than five minutes, and provide a great way to turn-on your students’ brains. Read more about math starters here ! 

Create your own puzzle box! The puzzle box is a set of puzzles and math challenges I use as fast finisher tasks for my students when they finish an assignment or need an extra challenge. The box can be a file box, file crate, or even a wall chart. It includes a variety of activities so all students can find a challenge that suits their interests and ability level.

Calculators

Use calculators! For some reason, this tool is not one many students get to use frequently; however, it’s important students have a chance to practice using it in the classroom. After all, almost everyone has access to a calculator on their cell phones. There are also some standardized tests that allow students to use them, so it’s important for us to practice using calculators in the classroom. Plus, calculators can be fun learning tools all by themselves!

Three-Act Math Tasks

Use a three-act math task to engage students with a content-focused, real-world problem! These math tasks were created with math modeling in mind– students are presented with a scenario and then given clues and hints to help them solve the problem. There are several sites where you can find these awesome math tasks, including Dan Meyer’s Three-Act Math Tasks and Graham Fletcher’s 3-Acts Lessons . 

Getting the Most from Each of the Problem Solving Activities

When students participate in problem solving activities, it is important to ask guiding, not leading, questions. This provides students with the support necessary to move forward in their thinking and it provides teachers with a more in-depth understanding of student thinking. Selecting an initial question and then analyzing a student’s response tells teachers where to go next. 

Ready to jump in? Grab a free set of problem solving challenges like the ones pictured using the form below. 

Which of the problem solving activities will you try first? Respond in the comments below.

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...

2 Responses

This is a very cool site. I hope it takes off and is well received by teachers. I work in mathematical problem solving and help prepare pre-service teachers in mathematics.

Thank you, Scott! Best wishes to you and your pre-service teachers this year!

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.

10 Fun Math Problem Solving Activities

I love using fun games and activities to get my kids excited about math. That’s why I was so excited to discover Beast Academy Playground! The site includes a wide variety of math problem solving activities, games, puzzles, and ideas that can be used with your current homeschool curriculum. If you’re looking for some fun ways to get your child interested in math again or some new ideas for teaching math at home, this is a great place to start.

I received compensation in exchange for my honest review, but all the opinions in this post are my own.

What is Beast Academy Playground?

As a homeschool parent, I know that fun math problem solving activities are hard to come by. Practicing math can be frustrating and boring for kids. And, it’s not enough to just teach math facts – children need to learn how to solve complex problems too!

Beast Academy Playground is the perfect solution. This site was created by Beast Academy, a homeschool curriculum for kids ages 8-13 that’s written as a comic book. Beast Academy Playground is a website that includes a growing library of fun activity ideas for kids ages 4-11.

The site includes both tabletop games that can be played with paper and pencil and more active games that can be played outside. Parents can sort the activities by concept, age, number of players, and more to find the perfect activity to complement any math lesson. New activities, games, and crafts are added to the site weekly.

Key Features of Beast Academy Playground

I love that every game on the site includes variations. These are different ways to adapt the game to fit the number of kids in your family or the age and grade level of your child.

In addition, most of the games can be played alone or in small groups. This makes Beast Academy Playground so easy for the whole family to use together!

Beast Academy Playground was developed by the experts at Art of Problem Solving, who are global leaders in K-12 math education. Each activity is intentionally designed to help kids learn new math concepts.

I was excited to see that each game also includes learning notes. This section helps parents understand what their kids will be learning when they play the game. I felt like I was prepared to be a better math teacher after I read the tips in this section!

Check out Beast Academy Playground and learn more now!

How to use Math Problem Solving Activities in Your Homeschool

Introduce a new concept.

One way to use problem-solving activities in your math lessons is to help introduce a new concept. For example, when we were learning about even and odd numbers, we started our math lesson by playing the Odds vs. Evens game from Beast Academy Playground. This simple math problem solving activity is a variation on the game Rock Paper Scissors. This was a fun way to help us review addition facts while introducing the concept of odd and even numbers.

Practice Problem-Solving Skills

Another great way to use Beast Academy Playground is to help kids practice their problem-solving skills. One fun problem solving game that my kids love is the Fox and Hare game. In this outdoor game, the fox needs to use strategy to try to catch the hare on a grid, while the hare tries to avoid capture. You can change the size of the grid to create a variety of problems for kids to solve.

Practice Math Facts

If your kids need extra practice with their math facts, games and math puzzles can be a fun way to practice these important skills. Beast Academy Playground has games for addition and subtraction, as well as concepts like skip counting that will help kids learn their multiplication facts.

One favorite that we enjoyed was Troll Hole . In this game, we took turns writing numbers on a special game board. In the end, we had to add up all the numbers to see who was the winner. My kids had so much fun with the theme of this game and loved getting to draw the troll in the hole!

Independent learning

As homeschool parents, we always need ideas for independent learning activities. Beast Academy Playground includes some great math problem solving games that are perfect for self-directed math learning. The many different activities on the site include several fun activities for one player that kids can work through independently to reinforce their math skills.

For extra review

Hands-on activities are also helpful when kids need a little extra review on a topic. For example, we played Kanga Ruler to help review skip counting. The kids loved this game because it was active and fun!

Top 10 Math Problem Solving Activities from Beast Academy Playground

Here are 10 of our favorite games that help kids develop a deeper understanding of mathematical concepts, all while having fun at the same time.

Trashketball

In this game, kids aim and try to score a basket into a trash can. Then, they add up the points they score. You can modify this game to add extra intellectual challenges for older kids or adapt the math so that younger kids can play too!

Trashketball was my kids’ favorite Beast Academy game, hands down. They loved trying to score as many baskets as they could. They had so much fun that they decided to keep playing even after our math lesson was finished!

Learn how to play Trashketball here.

In this math game for young children, kids race to stack towers of number cards. This is a great way to review numbers and counting. My kids really enjoyed trying to build the tallest tower that they could!

Learn how to play Towers here.

Bumper Cars

Although it took us a few tries to understand the strategy behind this game, my kids loved the concept of trying to figure out new ways to move the cars on the road. This was another great mathematical practice for strategy and solving difficult math problems.

Learn how to play Bumper Cars here.

Hungry Monster

This was a great way to practice inequalities and comparing numbers, and my kids loved feeding the correct answer in each inequality to the hungry monster!

Learn how to play Hungry Monster here.

Fruit Flies

In this math game for older problem solvers, kids try to claim as many grapes as they can for themselves, while blocking their opponent from getting any. This game is like an interactive logic puzzle, and it’s a good way for kids to learn critical thinking skills.

Learn how to play Fruit Flies here.

Blind Heist

In this game, Battleship meets addition as kids try to build the highest towers on their own secret side of the board. There are many different solutions and strategies to be successful, and my kids loved trying different solutions to this open-ended problem.

Learn how to play Blind Heist here.

Möbius Madness

This is a classic brain teaser for a reason- my kids were fascinated by the magic of a piece of paper with only one side. My kids were able to follow the directions easily and afterwards, they were excited to show their magical piece of paper to everyone who would watch.

Learn how to play Möbius Madness here.

This fast-paced card game was the perfect way to help my kids practice their addition facts.

Learn how to play Fifteen here.

Cookie Cutter

This game helps kids practice both spatial reasoning skills and fine motor skills at the same time. And, the result is a fun picture that they can color!

Learn how to play Cookie Cutter here.

Odd Knights

This was a fun way to practice even and odd (and it even led to a history lesson about the Knights of the Round Table!)

Learn how to play Odd Knights here.

What math problem solving activities will you use?

Whether it’s for extra practice or math review , Beast Academy Playground has something for every math learner. This site is a great resource to find exciting games that help kids develop number sense, problem solving, and logical thinking skills. If you want fun and engaging math activities that don’t require a textbook, this is the place to go. For more math problem solving activities and fun math games, check out Beast Academy Playground !

Find hands on activities to teach spelling and reading here!

Similar Posts

Forbrain Headset Review for Homeschool Learning

As a homeschool parent and a former teacher, I’m always on the lookout for tools and tricks that can help motivate my kids to want to learn at home. That’s why I’m so glad I discovered the Forbrain Headset from Forbrain by Sound for Life. This unique device uses technology to help kids focus on…

41 Best Educational Board Games for Kids

Playing a board game is a great way for kids to have fun while learning at the same time. Here are the best educational board games, as recommended by teachers and homeschool parents. I only recommend products that I use and that we love. This post contains affiliate links and I may earn a small…

Using a Literature Based History Curriculum for Your Homeschool

My kids love to read. Our favorite part of our homeschool day is always when we get to read together. I love reading out loud to them, and they love to read independently as well. That’s why I was so excited to discover the Sonlight History/Bible/Literature D: Intro to American History, Year 1 of 2…

STEMWerkz Online Elementary STEM Curriculum

My son loves science. He is always asking questions trying to figure out why things work the way they do. But, it can be a challenge to teach science in a way that is fun and engaging as a homeschool parent. Experiments take a lot of time and energy to set up, and it can…

Dr. Robin’s School Human Body Homeschool Science Curriculum Review

Lately, my son has been interested in learning about the human body. He has SO many questions, and as a parent who does not have a medical background, it has been hard for me to answer all of them. That’s why I was so excited to discover Dr. Robin’s School of Pre-Medicine! This human body…

Teach by Dennis DiNoia Review

As a homeschool mom and a former public school teacher, I know how important it is to help my kids become adults who want to learn on their own, and who know how to do so. However, it can be easy as a homeschool parent to get so focused on finishing the day’s plans in…

Leave a Reply Cancel reply

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

Learn by doing

Guided interactive problem solving that’s effective and fun. master concepts in 15 minutes a day., data analysis, computer science, programming & ai, science & engineering, join over 10 million people learning on brilliant, over 50,000 5-star reviews on ios app store and google play.

Master concepts in 15 minutes a day

Whether you’re a complete beginner or ready to dive into machine learning and beyond, Brilliant makes it easy to level up fast with fun, bite-sized lessons.

Effective, hands-on learning

Visual, interactive lessons make concepts feel intuitive — so even complex ideas just click. Our real-time feedback and simple explanations make learning efficient.

Learn at your level

Students and professionals alike can hone dormant skills or learn new ones. Progress through lessons and challenges tailored to your level. Designed for ages 13 to 113.

Guided bite-sized lessons

We make it easy to stay on track, see your progress, and build your problem solving skills one concept at a time.

Stay motivated

Form a real learning habit with fun content that’s always well-paced, game-like progress tracking, and friendly reminders.

Guided courses for every journey

All of our courses are crafted by award-winning teachers, researchers, and professionals from MIT, Caltech, Duke, Microsoft, Google, and more.

• Foundational Math
• Software Development
• Foundational Logic
• Data Science
• High School Math
• Engineering
• Statistics and Finance

Courses in Foundational Math

• Solving Equations
• Measuring with Geometry
• Mathematical Fundamentals
• Reasoning with Algebra
• Functions and Quadratics

10k+ Ratings

60k+ Ratings

We use cookies to improve your experience on Brilliant. Learn more about our cookie policy and settings .

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

32 Mathematical Ideas: Problem-Solving Techniques

Jenna Lehmann

Solving Problems by Inductive Reasoning

Before we can talk about how to use inductive reasoning, we need to define it and distinguish it from deductive reasoning.

Inductive reasoning is when one makes generalizations based on repeated observations of specific examples. For instance, if I have only ever had mean math teachers, I might draw the conclusion that all math teachers are mean. Because I witnessed multiple instances of mean math teachers and only mean math teachers, I’ve drawn this conclusion. That being said, one of the downfalls of inductive reasoning is that it only takes meeting one nice math teacher for my original conclusion to be proven false. This is called a counterexample . Since inductive reasoning can so easily be proven false with one counterexample, we don’t say that a conclusion drawn from inductive reasoning is the absolute truth unless we can also prove it using deductive reasoning. With inductive reasoning, we can never be sure that what is true in a specific case will be true in general, but it is a way of making an educated guess.

Deductive reasoning depends on a hypothesis that is considered to be true. In other words, if X = Y and Y = Z, then we can deduce that X = Z. An example of this might be that if we know for a fact that all dogs are good, and Lucky is a dog, then we can deduce that Lucky is good.

Strategies for Problem Solving

No matter what tool you use to solve a problem, there is a method for going about solving the problem.

• Understand the Problem: You may need to read a problem several times before you can conceptualize it. Don’t become frustrated, and take a walk if you need to. It might take some time to click.
• Devise a Plan: There may be more than one way to solve the problem. Find the way which is most comfortable for you or the most practical.
• Carry Out the Plan: Try it out. You may need to adjust your plan if you run into roadblocks or dead ends.
• Look Back and Check: Make sure your answer gives sense given the context.

There are several different ways one might go about solving a problem. Here are a few:

• Tables and Charts: Sometimes you’ll be working with a lot of data or computing a problem with a lot of different steps. It may be best to keep it organized in a table or chart so you can refer back to previous work later.
• Working Backward: Sometimes you’ll be given a word problem where they describe a series of algebraic functions that took place and then what the end result is. Sometimes you’ll have to work backward chronologically.
• Using Trial and Error: Sometimes you’ll know what mathematical function you need to use but not what number to start with. You may need to use trial and error to get the exact right number.
• Guessing and Checking: Sometimes it will appear that a math problem will have more than one correct answer. Be sure to go back and check your work to determine if some of the answers don’t actually work out.
• Considering a Similar, Simpler Problem: Sometimes you can use the strategy you think you would like to use on a simpler, hypothetical problem first to see if you can find a pattern and apply it to the harder problem.
• Drawing a Sketch: Sometimes—especially with geometrical problems—it’s more helpful to draw a sketch of what is being asked of you.
• Using Common Sense: Be sure to read questions very carefully. Sometimes it will seem like the answer to a question is either too obvious or impossible. There is usually a phrasing of the problem which would lead you to believe that the rules are one way when really it’s describing something else. Pay attention to literal language.

This chapter was originally posted to the Math Support Center blog at the University of Baltimore on November 6, 2019.

Math and Statistics Guides from UB's Math & Statistics Center Copyright © by Jenna Lehmann is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

Share This Book

Mastery-Aligned Maths Tutoring

“The best thing has been the increase in confidence and tutors being there to deal with any misunderstandings straight away."

FREE daily maths challenges

A new KS2 maths challenge every day. Perfect as lesson starters - no prep required!

25 Fun Maths Problems For KS2 And KS3 (From Easy To Very Hard!)

Fun maths problems are one of the things mathematicians love about the subject; they provide an opportunity to apply mathematical knowledge, logic and problem solving skills all at once.  In this article, we’ve compiled 25 fun maths problems, each covering various topics and question types. They’re aimed at students in KS2 & KS3. We’ve categorised them as:

Maths word problems

Maths puzzles, fraction problems, multiplication and division problems, geometry problems, problem solving questions, maths puzzles are everywhere, how should teachers use these maths problems.

Teachers could make use of these maths problem solving questions in a number of ways, such as:

• embed into a relevant maths topic’s teaching.
• settling tasks at the beginning of lessons.
• break up or extend a maths worksheet.
• keep students thinking mathematically after the main lesson has finished.

Some are based on real life or historical maths problems, and some include ‘bonus’ maths questions to help to extend the problem solving fun! As you read through these problems, think about how you could adjust them to be relevant to your students or to practise different skills. 

These maths problems can also be used as introductory puzzles for maths games such as those introduced at the following links:

• KS2 maths games
• KS3 maths games

Need more support teaching reasoning, problem solving and planning for depth ? Read here for free CPD for you and your team of teachers.

1. Home on time – easy

Type: Time, Number, Addition

A cinema screening starts at 14:35. The movie lasts for 2 hours, 32 minutes after 23 minutes of adverts. It took 20 minutes to get to the cinema. What time should you tell your family that you’ll be home?

Answer: 17:50

2. A nugget of truth – mixed

Type: Times Tables, Multiplication, Multiples, Factors, Problem Solving 

Chicken nuggets come in boxes of 6, 9 or 20, so you can’t order 7 chicken nuggets. How many other impossible quantities can you find (not including fractions or decimals)?

Answer: 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 22, 23, 25, 28, 31, 34, 37, or 43

There is actually a theorem which can be used to prove that every integer quantity greater than 43 can be ordered.

3. A pet problem – mixed

Type: Number, Problem Solving, Forming and Solving Equations, Simultaneous Equations, Algebra

Eight of my pets aren’t dogs, five aren’t rabbits, and seven aren’t cats. How many pets do I have?

Answer: 10 pets (5 rabbits, 3 cats, 2 dogs)

4. The price of things – mixed

Type: lateral thinking problem

A mouse costs £10, a bee costs £15, and a spider costs £20. How much does a duck cost? Answer: £5 (£2.50 per leg)

Looking for more word problems, solutions and explanations? Read our article on word problems for primary school.

25 Fun Maths Problems - Printable

Download a printable version of these fun maths problems together with answers and mark scheme.

5. A dicey maths challenge – easy

Type: Place value, number, addition, problem solving

Roll three dice to generate three place value digits. What’s the biggest number you can make out of these digits? What’s the smallest number you can make?

Add these two numbers together. What do you get?

Answer: In most cases, 1,089.

Bonus: Who got a different result? Why?

6. PIN problem solving – mixed

Type: Logic, problem solving, reasoning

I’ve forgotten my PIN. Six incorrect attempts locks my account: I’ve used five! Two digits are displayed after each unsuccessful attempt: “2, 0” means 2 digits from that guess are in the PIN, but 0 are in the right place.

What should my sixth attempt be?

Answer: 6347

7. So many birds – mixed

Type: Triangular Numbers, Sequences, Number, Problem Solving

On the first day of Christmas my true love gave me one gift. On the second day they gave me another pair of gifts plus a copy of what they gave me on day one. On day 3, they gave me three new gifts, plus another copy of everything they’d already given me. If they keep this up, how many gifts will I have after twelve days?

Answer: 364

Bonus: This could be calculated as 1 + (1 + 2) + (1 + 2 + 3) + … but is there an easier way? What percentage of my gifts do I receive on each day?

8. I 8 sum maths questions – mixed

Type: Number, Place Value, Addition, Problem Solving, Reasoning

Using only addition and the digit 8, can you make 1,000? You can put 8s together to make 88, for example.

Answer: 888 + 88 + 8 + 8 + 8 = 1,000 Bonus: Which other digits allow you to get 1,000 in this way?

9. Quizzical – easy

Type: Fractions, Adding Fractions, Equivalent Fractions, Fractions to Percentages

4 friends entered a maths quiz. One answered \frac{1}{5} of the maths questions, one answered \frac{1}{10} , one answered \frac{1}{4} , and the other answered \frac{4}{25} . What percentage of the questions did they answer altogether?

Answer: 71%

10. Ancient problem solving – mixed

Type: Fractions, Reasoning, Problem Solving

Ancient Egyptians only used unit fractions (like \frac{1}{2} , \frac{1}{3} or \frac{1}{4} ). For \frac{2}{3} , they’d write \frac{1}{3} + \frac{1}{3} . How might they write \frac{5}{8} ?

Answer: \frac{1}{8} + \frac{1}{8} + \frac{1}{8} + \frac{1}{8} + \frac{1}{8} is correct. So is \frac{1}{2} + \frac{1}{8} .

Bonus: Which solution is better? Why? Can you find any more? What if subtractions are allowed?

Learn more about unit fractions here

11. everybody wants a pizza the action – hard.

An infinite number of mathematicians buy pizza. The first wants \frac{1}{2} pizza. The second wants \frac{1}{4} pizza. The third & fourth want \frac{1}{8} and \frac{1}{16} each, and so on. How many pizzas should they order?

Answer: 1 Each successive mathematician wants a slice that is exactly half of what is left:

12. Shade it black – hard

Type: Fractions, Reasoning, Problem Solving What fraction of this image is shaded black?

Answer: \frac{1}{3}

Look at the L-shaped part made up of two white and one black squares: \frac{1}{3} of this part is shaded. Zoom in on the top-right quarter of the image, which looks exactly the same as the whole image, and use the same reasoning to find what fraction of its L-shaped portion is shaded. Imagine zooming in to do the same thing again and again…

13. Giving is receiving – easy

Type: Number, Reasoning, Problem Solving

5 people give each other a present. How many presents are given altogether?

14. Sharing is caring – mixed

I have 20 sweets. If I share them equally with my friends, there are 2 left over. If one more person joins us, there are 6 sweets left. How many friends am I with?

Answer: 6 people altogether (so 5 friends!)

15. Times tables secrets – mixed

Type: Area, 2D Shape, Rectangles

Here are 77 letters:

BYHRCGNGNEOEAAHGHGCURPUTSTSASHHSBOBOREOPEEMEMEELATPEPEFADPHLTLTUT IEEOHOHLENRYTITIIAGBMTNTNFCGEIIGIG

How many different rectangular grids could you arrange all 77 letters into?

Answer: Four: 1⨉77, 77⨉1, 11⨉7 & 7⨉11. If the letters are arranged into one of these, a message appears, reading down each column starting from the top left.

Bonus: Can you find any more integers with the same number of factors as 77? What do you notice about these factors (think about prime numbers)? Can you use this system to hide your own messages?

16. Laugh it up – hard

Type: Multiples, Lowest Common Multiple, Times Tables, Division, Time

One friend jumps every \frac{1}{3} of a minute. Another jumps every 31 seconds. When will they jump together? Answer: After 620 seconds

17. Pictures of matchstick triangles – easy

Type: 2D Shapes, Equilateral Triangles, Problem Solving, Reasoning

Look at the matchsticks arranged below. How many equilateral triangles are there?

Answer: 13 (9 small, 3 medium, 1 large)

Bonus: What if the biggest triangle only had two matchsticks on each side? What if it had four?

18. Dissecting squares – mixed

Type: Reasoning, Problem Solving

What’s the smallest number of straight lines you could draw on this grid such that each square has a line going through it?

19. Make it right – mixed

Type: Pythagoras’ theorem

This triangle does not agree with Pythagoras’ theorem. 

Adding, subtracting, multiplying or dividing each of the side lengths by the same integer can fix it. What is the integer?

Answer: 3 

8 – 3 = 5

The new side lengths are 3, 4 and 5 and  32 + 42 = 52.

20. A most regular maths question – hard

Type: Polygons, 2D Shapes, tessellation, reasoning, problem-solving, patterns

What is the regular polygon with the largest number of sides that will self-tessellate?

Answer: Hexagon.

Regular polygons tessellate if one interior angle is a factor of 360°. The interior angle of a hexagon is 120°. This is the largest factor less than 180°.

21. Pleased to meet you – easy

Type: Number Problem, Reasoning, Problem-Solving

5 people meet; each shakes everyone else’s hand once. How many handshakes take place?

Person A shakes 4 people’s hands. Person B has already shaken Person A’s hand, so only needs to shake 3 more, and so on.

Bonus: How many handshakes would there be if you did this with your class?

22. All relative – easy

Type: Number, Reasoning, Problem-Solving

When I was twelve my brother was half my age. I’m 40 now, so how old is he?

23. It’s about time – mixed

Type: Time, Reasoning, Problem-Solving

When is “8 + 10 = 6” true?

Answer: When you’re telling the time (8am + 10 hours = 6pm)

24. More than a match – mixed

Type: Reasoning, Problem-Solving, Roman Numerals, Numerical Notation

Here are three matches:

How can you add two more matches, but get eight? Answer: Put the extra two matches in a V shape to make 8 in Roman Numerals:

25. Leonhard’s graph – hard

Type: Reasoning, Problem-Solving, Logic

Leonhard’s town has seven bridges as shown below. Can you find a route around the town that crosses every bridge exactly once?

Answer: No!

This is a classic real life historical maths problem solved by mathematician Leonhard Euler (rhymes with “boiler”). The city was Konigsberg in Prussia (now Kaliningrad, Russia). Not being able to find a solution is different to proving that there aren’t any! Euler managed to do this in 1736, practically inventing graph theory in the process.

Many of these 25 maths problems are rooted in real life, from everyday occurrences to historical events. Others are just questions that might arise if you say “what if…?”. The point is that although there are many lists of such problem solving maths questions that you can make use of, with a little bit of experience and inspiration you could create your own on almost any topic – and so could your students. 

For a kick-starter on creating your own maths problems, read our article on KS3 maths problem solving .

Looking for additional support and resources at KS3? You are welcome to download any of the secondary maths resources from Third Space Learning’s resource library for free. There is a section devoted to GCSE maths revision with plenty of maths worksheets and GCSE maths questions . There are also maths tests for KS3, including a Year 7 maths test , a Year 8 maths test and a Year 9 maths test Other valuable maths practice and ideas particularly around reasoning and problem solving at secondary can be found in our KS3 and KS4 maths blog articles. Try these fun maths problems for KS2 and KS3, SSDD problems , KS3 maths games and 30 problem solving maths questions . For children who need more support, our maths intervention programmes for KS3 achieve outstanding results through a personalised one to one tuition approach.

DO YOU HAVE STUDENTS WHO NEED MORE SUPPORT IN MATHS?

Every week Third Space Learning’s specialist online maths tutors support thousands of students across hundreds of schools with weekly online 1 to 1 maths lessons designed to plug gaps and boost progress.

Since 2013 these personalised one to 1 lessons have helped over 150,000 primary and secondary students become more confident, able mathematicians.

Learn how the programmes are aligned to maths mastery teaching or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

Related articles

Maths Problem Solving: Engaging Your Students And Strengthening Their Mathematical Skills

Free Year 7 Maths Test With Answers And Mark Scheme: Mixed Topic Questions

What Is A Number Square? Explained For Primary School Teachers, Parents & Pupils

What Is Numicon? Explained For Primary School Teachers, Parents And Pupils

FREE Guide to Maths Mastery

All you need to know to successfully implement a mastery approach to mathematics in your primary school, at whatever stage of your journey.

Ideal for running staff meetings on mastery or sense checking your own approach to mastery.

Privacy Overview

20 Math Center Ideas

• Math , Planning

Every year about this time, I start to notice my students getting bored with the same usual math centers . That means I need to go online and start hunting down new math center ideas to find something that will hold their interest, but also teach them a thing or two about math. That’s when I decided it was time to create a list! In fact, I have a list of 20 math center ideas to share with you – and they aren’t just specific games of mine to purchase (as you sometimes see on the internet). They are activities you can implement without any purchase of my products – for any concept! Bonus!

20 Math Center Ideas for your Elementary Classroom

1.)  Card Games.   Most classrooms have at least one set of cards, but if not, you can find them at the dollar store. There are a variety of games you can have your students play and still practice their math concepts. For instance, remove the face cards and the aces and then have students play any variation of top-it. Divide the set of cards up evenly among the pair of students; 2 students each flip a card at once and perform whichever operation you prefer (add, subtract, multiply). The first student to say the correct answer first gets both cards. Students keep going until there are no cards left. The student with the most cards wins!

You can also take a set of 3″x5″ index cards and cut them in half creating mini-cards. Then program them to be any set of numbers you wish. Then students can perform any operation, play a game of go fish, play rummy (place them in order), or any other fun game!

2.) Dice Games.   I really can’t mention card games without mentioning dice games as one of the math center ideas. Just like with card games, you can find dice at the dollar store, but you can also create your own using wooden blocks. I like to do this to program them with fractions or decimals. Then I have students play games such as adding the numbers and seeing how close they can get to one without going over.

3.)  Bowling Math Centers.  This math center idea is sure to delight your students! Using paper towel rolls, toilet paper rolls, or even plastic water bottles you can create bowling pins with numbers on them. If you cover them with packaging tape, you can wipe the numbers off for reuse again and again. Students can then bowl to add the pins knocked down. This makes a great center for fractions, large numbers, decimals, and you could use it for elapsed time. In the past, I have even placed task cards on them and students had to complete the pins they knocked down. It’s definitely engaging! You can read more about it here .

4.)  Journaling.   What student couldn’t use a little extra practice writing in math? I believe they all could. Provide students with a writing prompt related to whatever you are working on in math. It doesn’t need to be fancy; You could write it on an index card, or have it in strips for students to glue into their math journal. They then respond in their journal. Students could respond to a question such as, “What is a fraction?”   It doesn’t need to be complicated. You’re basically having students explain math in their own words. You could even include a portion where they can illustrate it.

5.) Craftivities.  Every once in a while, why not consider creating a craftivity for your center activity? This could be anything from the simple construction of a mobile or model of a product. Students enjoy hands-on activities and it’s a great way to learn.

6.)  Manipulatives. Manipulatives are a great way to make math more concrete, especially with difficult concepts. Place manipulatives in a center with some directions and students can practice over and over until they really have the concept down.

7.) Technology.   There are a lot of great apps and websites out there that really help students practice both math skills and math test prep. I’ve mentioned many websites in my blog post, 5 Great Math Apps for Grades 3-5 . There are also great websites like the Math Playground , IXL , MobyMax , and Reflex . There are even free sites that students can access from home such as AAA Math , Cool Math , and Fun Brain .

9.)  Math Sorts.   These can be created easily with a computer or index cards. You can also just purchase them. Students can easily sort math based on similarities or attributes, such as in my Polygon Sort below.

10.)  Practice Sheets.  Of course, you can use regular worksheets to help students practice the math concepts you are teaching, but you can also use these sheets to remediate, reteach, review, or even enrich. There is nothing wrong with a “Stay at Your Seat” kind of center.

11.)  Problem Solving.   Why not create a center that is solely based on problem-solving? My students struuuuuuugggggglllle with problem-solving. So they could definitely use some extra practice. This center provides the perfect opportunity for that. Do you know that appendix section in the common core standards? They provide you with examples of different types of problems you could create. Go from there. Or, start the first few weeks off with the students creating the problems first and trading papers to check each other’s work. Then create some yourself. You can also mimic the ones in your textbook. Step it up a notch by throwing in some error analysis once in a while.

12.) Interactive Bulletin Boards.   I love creating them, but I will admit, it sometimes requires a little time and thought on your part – but you can definitely do them! Back around Halloween, I created this one made of a haunted house. On the outside of the windows, ghosts, and other objects were the math problems, on the inside were the self-checking answers. It was a great center (and is also perfect for early finishers ). (Note:  The image below was set up on a tri-board.)

Another interactive bulletin board I have created in the past was Math-no-poly. It was something I created for an end of the year review. My students really enjoyed it and it helped us focus on what we still needed to learn.

These math center ideas were definitely a blast!

13.) Math Stretchers.   I talked a little about Math Stretchers in my Math Workshop Series . This is a form of a math warm-up that can be used for any of the math categories. It’s a great way to prepare the student’s brain for the math they are about to encounter and to start thinking about math more in their everyday life. This can be something as simple as collecting data each day regarding lunch or focusing on the number of the day.

14.)  Calendar.   I have always loved using the calendar portion in math workshop, even in the upper grades. Yes, even in fifth grade. Yes, even if I didn’t have the official kit or book. I got creative. I just focused on what my students needed to know and found a way to integrate it in each day. You create small square pieces with patterns that change daily around a common theme, such as angles, polygons, fractions, etc. You can create nearly anything! The point is to gather students around and get them talking about math based on the math they are surrounded within their daily lives.

15.)  Interactive Notebook Pieces.   Interactive notebook pieces are not just a waste of time if you do them correctly. Students can actually use them to help remember important information and to practice solving problems. They can also be very engaging. For instance, Have students list all the multiples out on individual “French Fries” for each number and put them inside a French Fry box (envelope glued in their notebook).

16.) Regular Math Center Games . There are lots of games you can purchase in Teacher Stores, on Teachers Pay Teachers, or even make that can help reinforce a concept. I really help understand the importance of Game-Based Learning and provide 5 tips to using them in the classroom here .

17.) Vocabulary.   Consider creating a math center that provides your students with the opportunity to practice the important vocabulary of the concepts you are working on. This can include a personal word wall, a class word wall, or just a list of words you have been learning. Students can complete any vocabulary activity. There are many blog posts here on this blog that provides you with engaging activities to do. Just search vocabulary over in the search bar on the right.

18.) Task Cards.   Task cards do not have to be a whole group activity. You can provide students with a set of task cards to work on in stations or have them move around within their group. I have even placed task cards around the room that they quietly had to move to while the others worked. You don’t necessarily have to do the entire set either. If you don’t want to purchase any, don’t. Take a worksheet, cut each individual question out and glue them to index cards. Viola! Task cards!

19.) Real World Math.   Students really need to see math in the context of the real world. Why not make one of your math center ideas a real-world math center? This can be a range of math centers, from current events to STEM. For current events, have students find examples in the current events that use whatever concept you are working on. This is not limited to social studies. You could have students complete a “mini-stem” project, a project-based learning activity, or even just an activity related to real-life, such as planning for a family Bar-B-Que.

20.) Fact Fluency.   Students really need to practice their basic facts in nearly every grade. They need to memorize them. The best way to memorize them is with constant practice. That is where this center comes in! Provide students with lots of opportunities to learn and practice their basic facts. This can be done in the form of activities (such as with my Math Workshop Shortcuts Unit ), games, flashcards, math fact practice , or other engaging activity.

With these 20 math center ideas, you are sure to find something to keep your students from getting bored and to keep them hooked on math!

Are you looking for engaging math centers for your students that you can purchase to save yourself some planning time? Check out my centers and games here .

FIND IT NOW!

Check me out on tpt.

CHECK THESE OUT

Three Types of Rocks and Minerals with Rock Cycle Circle Book

Partitioning Shapes Equal Share Fractions Halves, Thirds, Fourths Math Puzzles

Want to save time?

COPYRIGHT © 2016-2024. The Owl Teacher | Privacy page | Disclosure Page | Shipping | Returns/Refunds

BOGO on EVERYTHING!