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20 Best Math Puzzles to Engage and Challenge Your Students

Written by Maria Kampen

Reviewed by Joshua Prieur, Ed.D.

Solve the hardest puzzle

Use Prodigy Math to boost engagement, offer differentiated instruction and help students enjoy math.

• Teacher Resources

1. Math crossword puzzles

2. math problem search, 3. math riddles.

It’s time for math class, and your students are bored.

It might sound harsh, but it’s true -- less than half of 8th grade students report being engaged at school according to this Gallup survey , and engagement levels only drop as students get older.

Math puzzles are one of the best -- and oldest -- ways to encourage student engagement. Brain teasers, logic puzzles and math riddles give students challenges that encourage problem-solving and logical thinking. They can be used in classroom gamification , and to inspire students to tackle problems they might have previously seen as too difficult.

Math puzzles for kids

Puzzles to Print

Take a crossword, and make it math: that’s the basic concept behind this highly adaptable math challenge. Instead of words, students use numbers to complete the vertical and horizontal strips. Math crossword puzzles can be adapted to teach concepts like money, addition, or rounding numbers. Solutions can be the products of equations or numbers given by clues.

Have students practice their addition, subtraction, multiplication and division skills by searching for hidden math equations in a word search-style puzzle . It can be adapted to any skill you want students to practice, and promotes a solid understanding of basic math facts.

My PreCalc students love riddles... can you figure out where the other dollar went?? #MathRiddles pic.twitter.com/BclqW9nq98 — Rachel Frasier (@MsFrasierMHS) January 8, 2019

Do your students love word problems ? Try giving them some math riddles that combine critical thinking with basic math skills. Put one up on the board for students to think about before class begins, or hand them out as extra practice after they’ve finished their work.

Prodigy is an engaging, game-based platform that turns math into an adventure! While it’s not a math puzzle in the traditional sense, Prodigy uses many of the same principles to develop critical thinking skills and mathematical fluency.

Students complete standards-aligned math questions to earn coins, collect pets and go on quests. Teachers can deliver differentiated math content to each student, prep for standardized tests and easily analyze student achievement data with a free account.

See how it works below!

KenKenKenKen

is a “grid-based numerical puzzle” that looks like a combined number cross and sudoku grid. Invented in 2004 by a famous Japanese math instructor named Tetsuya Miyamoto, it is featured daily in The New York Times and other newspapers. It challenges students to practice their basic math skills while they apply logic and critical thinking skills to the problem.

6. Pre-algebraic puzzles

Pre-algebraic puzzles use fun substitutions to get students ready to perform basic functions and encourage them to build problem-solving skills. They promote abstract reasoning and challenge students to think critically about the problems in front of them. As an added bonus, students who suffer from math anxiety might find the lack of complicated equations reassuring, and be more willing to attempt a solution.

7. Domino puzzle board

Games 4 Gains

There are hundreds of ways to use dominoes in your math classroom, but this puzzle gives students a chance to practice addition and multiplication in a fun, hands-on way. You can have students work alone or in pairs to complete the puzzle.

This online game and app challenges players to slide numbered tiles around a grid until they reach 2048. It’s super fun and not as easy as it sounds, so consider sending it home with students or assigning it after the rest of the lesson is over. It encourages students to think strategically about their next move, and it’s a great tool for learning about exponents.

Math in English

Kakuro , also called “Cross Sums,” is another mathematical crossword puzzle. Players must use the numbers one through nine to reach “clues” on the outside of the row. Decrease the size of the grid to make it easier for younger players, or keep it as is for students who need a challenge. Students can combine addition and critical thinking and develop multiple skills with one fun challenge.

10. Magic square

Magic squares have been around for thousands of years, and were introduced to Western civilization by translated Arabic texts during the Renaissance. While magic squares can be a variety of sizes, the three by three grid is the smallest possible version and is the most accessible for young students.

This is also a great math puzzle to try if your students are tactile learners. Using recycled bottle caps, label each with a number from one to nine. Have your students arrange them in a three by three square so that the sum of any three caps in a line (horizontally, vertically and diagonally) equals 15.

11. Perimeter magic triangle

This activity uses the same materials and concept as the magic square, but asks students to arrange the numbers one to six in a triangle where all three sides equal the same number. There are a few different solutions to this puzzle, so encourage students to see how many they can find.

Sudoku is an excellent after-lesson activity that encourages logical thinking and problem solving. You’ve probably already played this classic puzzle, and it’s a great choice for your students. Sudoku puzzles appear in newspapers around the world every day, and there are hundreds of online resources that generate puzzles based on difficulty.

13. Flexagon

There’s a pretty good chance that by now, fidget spinners have infiltrated your classroom. If you want to counter that invasion, consider challenging your students to create flexagons. Flexagons are paper-folded objects that can be transformed into different shapes through pinching and folding, and will keep wandering fingers busy and focused on the wonders of geometry.

14. Turn the fish

This puzzle seems simple, but it just might stump your students. After setting up sticks in the required order, challenge them to make the fish swim in the other direction -- by moving just three matchsticks.

15. Join the dots

Cool Math 4 Kids

This puzzle challenges students to connect all the dots in a three by three grid using only four straight lines. While it may sound easy, chances are that it will take your class a while to come up with the solution. (Hint: it requires some “out of the box” thinking.)

16. Brain teasers

While they don’t always deal directly with math skills, brain teasers can be important tools in the development of a child’s critical thinking skills. Incorporate brain teasers into a classroom discussion, or use them as math journal prompts and challenge students to explain their thinking.

Bonus: For a discussion on probability introduce an older class to the Monty Hall Problem, one of the most controversial math logic problems of all time.

17. Tower of Hanoi

This interactive logic puzzle was invented by a French mathematician named Edouard Lucas in 1883. It even comes with an origin story: According to legend, there is a temple with three posts and 64 golden disks.

Priests move these disks in accordance with the rules of the game, in order to fulfill a prophecy that claims the world will end with the last move of the puzzle. But not to worry -- it’s going to take the priests about 585 billion years to finish, so you’ll be able to fit in the rest of your math class.

Starting with three disks stacked on top of each other, students must move all of the disks from the first to the third pole without stacking a larger disk on top of a smaller one. Older students can even learn about the functions behind the solution: the minimum number of moves can be expressed by the equation 2n-1, where n is the number of disks.

18. Tangram

Tangram puzzles -- which originated in China and were brought to Europe during the early 19th century through trade routes -- use seven flat, geometric shapes to make silhouettes. While Tangrams are usually made out of wood, you can make sets for your class out of colored construction paper or felt.

Tangrams are an excellent tool for learners who enjoy being able to manipulate their work, and there are thousands of published problems to keep your students busy.

Similar to Sudoku, Str8ts challenges players to use their logic skills to place numbers in blank squares. The numbers might be consecutive, but can appear in any order. For example, a row could be filled with 5, 7, 4, 6 and 8 . This puzzle is better suited to older students, and can be used as a before-class or after-lesson activity to reinforce essential logic skills.

20. Mobius band

Is it magic? Is it geometry? Your students will be so amazed they might have a hard time figuring it out. Have them model the problem with strips of paper and see for themselves how it works in real life. With older students, use mobius bands to talk about geometry and surface area.

Why use math puzzles to teach?

Math puzzles encourage critical thinking.

Critical thinking and logic skills are important for all careers, not just STEM-related ones. Puzzles challenge students to understand structure and apply logical thinking skills to new problems.

A study from the Eurasia Journal of Mathematics, Science and Technology Education found that puzzles “develop logical thinking, combinatorial abilities, strengthen the capacity of abstract thinking and operating with spatial images, instill critical thinking and develop mathematical memory.”

All these skills allow young students to build a foundation of skills they’ll draw on for the rest of their lives, no matter what kind of post-secondary route they pursue.

They help build math fluency

Math games can help students build a basic understanding of essential math concepts, and as another study shows, can also help them retain concepts longer .

In the study, early elementary students gradually moved from using the “counting” part of their brains to complete math problems to the “remembering” part that adults use, suggesting math puzzles and repeated problems can help build the essential skill of math fluency .

Many of the math puzzles above allow students to practice essential addition, subtraction, multiplication and division skills, while advanced or modified problems can be used to introduce pre-algebraic concepts and advanced logic skills.

Math puzzles connect to existing curricula

No matter what curriculum you’re using, there’s a good chance it emphasizes problem-solving, critique and abstract thinking. This is especially true of Common Core math and similar curricula.

How Math Skills Impact Student Development

Math puzzles allow students to develop foundational skills in a number of key areas, and can influence how students approach math practically and abstractly. You can also tie them into strategies like active learning and differentiated instruction.

Instead of just teaching facts and formulas, math puzzles allow you to connect directly with core standards in the curriculum. You can also use them to provide a valuable starting point for measuring how well students are developing their critical thinking and abstract reasoning skills.

Tips for using math puzzles in the classroom

View this post on Instagram A post shared by Sarah Werstuik (@teach.plan.love)

Now that you’ve got some great math puzzles, it might be tricky to figure out how to best incorporate them into your classroom. Here are some suggestions for making the most of your lesson time:

Make sure the puzzles are the right level for your class

If the problems are too easy, students will get bored and disengage from the lesson. However, if the problems are too difficult to solve, there’s a good chance they’ll get frustrated and give up early.

There’s a time and a place

While fun math puzzles are a great way to engage your students in developing critical thinking skills, they’re not a tool for teaching important math concepts. Instead, use them to reinforce the concepts they’ve already learned.

Kitty Rutherford , a Mathematics Consultant in North Carolina, emphasizes that math puzzles and games shouldn’t be based solely on mental math skills , but on “conceptual understanding” that builds fluency over time. Math puzzles help build the essential balance between thinking and remembering.

Give them space to figure it out

Rachel Keen , from the Department of Psychology at the University of Virginia, conducted a study about problem-solving skills in preschoolers. She found that “playful, exploratory learning leads to more creative and flexible use of materials than does explicit training from an adult.”

Give your students space to struggle with a problem and apply their own solutions before jumping in to help them. If the problem is grade-appropriate and solvable, students will learn more from applying their own reasoning to it than just watching you solve it for them.

Model puzzles for your students

Use problems like the mobius strip to awe and amaze your students before drawing them into a larger discussion about the mathematical concept that it represents. If possible, make math puzzles physical using recycled craft supplies or modular tools.

Afterward, have a class discussion or put up math journal prompts. What methods did your students try? What tools did they use? What worked and what didn’t? Having students explicitly state how they got to their solution (or even where they got stuck) challenges them to examine their process and draw conclusions from their experience.

Final thoughts on math puzzles

Be aware that it might take a while to get all your students on board -- they could be hesitant about approaching unfamiliar problems or stuck in the unenthusiasm that math class often brings. Consider creating a weekly leaderboard in your classroom for the students that complete the most puzzles, or work through a few as a class before sending students off on their own.

Instead of yawns and bored stares , get ready to see eager participants and thoughtful concentration. Whether you choose to use them as an after-class bonus, a first day of school activity or as part of a targeted lesson plan, math puzzles will delight your students while also allowing them to develop critical skills that they’ll use for the rest of their lives.

What are you waiting for? Get puzzling!

Math and Logic Puzzles

If you REALLY like exercising your brain, figuring things 'round and 'round till you explode, then this is the page for you !

Whosoever shall solve these puzzles shall Rule The Universe!

... or at least they should ...

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3 Fun Activities for Strengthening Numeracy Skills

These activities give middle and high school students a chance to play with numbers—and learn at the same time.

One of the main reasons so many middle and high school students struggle to master grade-level math concepts is because they lack a strong foundation in numeracy skills. The incremental nature of mathematics requires students to develop their numeracy skills as they progress through the grade levels, but students can seem to be doing OK in the early grades even if they don’t fully understand some of the concepts .

Middle and high school teachers don’t always have time within the instructional block to do a formal review lesson on basic numeracy skills with students. However, there are enrichment activities that we can incorporate into our instructional blocks to help students strengthen their skills. Here are a few that I’ve had success with.

The Hundred Challenge

The Hundred Challenge is a math activity that asks students to apply their basic math skills to create equations that equal each of the digits between 1 and 100—but they can only use the four digits the teacher supplies, like 1,4,7, and 9. The rules are as follows:

• All four digits must be used in each equation.
• Each digit can only be used once in each equation.
• Any operation—addition, subtraction, division, multiplication—or symbol—parentheses, radicals, exponents, etc.—can be used to create equations.
• Digits can be combined to form new digits (e.g., 1 and 4 can be combined to form 14 or 41), fractions (e.g., 1 and 7 can be combined to form 1/7 or 7/1), and decimals (e.g., 4 and 9 can be combined to form 4.9 or .49).

Some numbers will have only one possible equation, given the four digits allowed, while others will have several, so this challenge reveals the differentiated math strategies and learning experiences of the students.

For instance, my high-intervention students tend to create equations for the digits between 1 and 50. They create basic equations by simply inserting operation signs between the required digits, like 49 – 17 = 32, or 1 + 4 + 7 – 9 = 3.

My advanced students usually take more computational risks when creating their equations, and they attempt to create equations for the digits on the higher end of the chart (typically between 75 and 100). The types of equations that these students create typically involve the use of exponents and parentheses to demonstrate their knowledge of order of operations.

I usually use the Hundred Challenge as a collaborative learning activity, but it can function as a living learning center in the classroom for students who finish their independent work early and need more challenge problems to compute. Each student has a sheet with the numbers from 1 to 100 listed, and they fill it up with equations over time.

Do Now: Equation or Expression of the Day

Each and every day, I write a mathematical expression or equation in place of the day of that specific date. When students enter the classroom, they solve the mathematical expression or equation—they know the date, usually, so they’re able to check their work right away. For instance, instead of writing “October 28, 2020,” I may write, “October 3(x – 23) = 15, 2020.” For this particular equation, students would have to solve the equation 3(x – 23) = 15 in order to uncover the day number.

Once students figure out the solution, they then have to create at least two mathematical expressions or equations that also equal the solution. For example, a student may create the expression 4! + (2 x 2) = 28. I give students no more than five minutes to solve the equation and then review the problem with them. This is a great opportunity to have some students come to the board to share the expressions they created.

In my experience, students get really excited about the equations or expressions they create and love to compare them with those of their peers. I’ve even had some students volunteer to create the equations or expressions for future dates.

To make the exercise more challenging, you can set specific conditions for the equations or expressions your students create, which ensures that students don’t give you pedestrian expressions or equations like 28 + 0 or 28 + x = 28.

The ultimate goal of these Do Now exercises is to provide students with opportunities to apply and synthesize their mathematical background knowledge skills. They help students strengthen their abilities to solve and create multistep algebraic equations and expressions. And these exercises are differentiated: Students can access them at their developmentally appropriate level and take academic risks with the knowledge that they’ll receive instructional support from me and their peers.

Cryptarithmetic Puzzles

In a cryptarithmetic puzzle, the digits are replaced by letters of the alphabet. The goal is for students to uncover the puzzle by determining the digit for each letter. The rules for uncovering the puzzle are as follows:

• Each letter represents a digit between 0 and 9. A letter cannot represent multiple digits, and a digit cannot be represented by multiple letters.
• Numbers must not begin with a zero.
• There is only one solution to the puzzle.

For example, the puzzle SEVEN + SEVEN + SEVEN + NINE = THIRTY translates to 49,793 + 49,793 + 49,793 + 3,239 = 152,618 (S = 4, E = 9, V = 7, N = 3, I = 2, T = 1, H = 5, R = 6, and Y = 8). Cryptarithmetic puzzles can also be expressed as multidigit subtraction, multiplication, and division problems. (You can find more cryptarithmetic puzzles here .)

As an extension activity, teachers can challenge students to create their own cryptarithmetic puzzles and have their classmates try to solve them. I typically use these puzzles as a learning center or enrichment activity that students can complete if they finish their independent work early.

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!

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Small Group Math Activities

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• Math Stations

Discover small group math activities that promote student engagement and foster a love for math. This blog post explores 10 activities, including math games, hands-on manipulatives, real-world investigations, technology tools, problem solving activities, and more to help you transform your math stations into a dynamic learning environment.

I have a secret confession to make. 

Teaching reading has never been my cup of tea. 

Don’t get me wrong, I adore immersing my students in captivating books and opening their minds to new worlds. 

But when it comes to reading workshop, let’s just say it didn’t exactly light a fire in my soul. 

The never-ending cycle of reading from the textbook series and completing author’s purpose, inference, and comprehension worksheets felt mundane and, dare I say it, a bit dull. #yawn 🥱 

Despite my best efforts, I struggled to make it truly exciting. 

So, when the opportunity to introduce math workshop came knocking, I must admit, I wasn’t exactly jumping for joy.

It’s All About Engagement

Math stations are a powerful tool for promoting student engagement and deepening our students’ mathematical understanding. 

By incorporating engaging activities into your math station rotations, you can create a dynamic learning environment that sparks excitement and curiosity in your students. 

In this blog post, we will explore 10 engaging small group math activities that will captivate your students and inspire them to develop a love for math.

10 Small Group Math Activities for Any Math Station Rotation

Activity 1: Math Games Galore

Math games are a fantastic way to make learning fun and interactive. These small group math activities provide opportunities for students to practice math skills while communicating mathematically with their peers. Here are a few examples of card and dice games that can be incorporated into your math station rotations:

• War Games: This classic math game requires only a deck of cards. Partners each turn over a card and use their math skills to compare the numbers, such as whole numbers, fractions, decimals, or even simple expressions. The player with the higher value wins the round. Players continue playing until no cards are remaining. 
• Cover-Up Games: This simple board game requires two dice. In turn, each student rolls the dice and completes the problem associated with the dice sum. Then, they cover the solution with a marker in a grid trying to get four in a row, column, or diagonal. 
• Traditional Board Games: Pair a set of task cards with a traditional board game to create this math station activity. After correctly answering a question, students can roll a die or toss a coin to move along the path.

Activity 2: Hands-On Manipulatives

Hands-on manipulatives bring abstract math concepts to life, making them more concrete and tangible. These activities provide students with a visual and kinesthetic experience, enhancing their understanding of mathematical concepts. Consider incorporating the following manipulative-based activities into your math stations:

• Pattern Block Puzzles: Provide students with pattern blocks and challenge them to create different shapes and designs, exploring concepts like symmetry, fractions, and geometry.
• Base Ten Blocks: Use base ten blocks to reinforce place value concepts. Students can build and represent numbers and explore operations with whole numbers and decimals.
• Data Analysis with Spinners: Use spinners with different sections labeled with numbers or categories. Students spin the spinner multiple times, record the results, and represent the data they collected by creating a frequency table, bar graph, or dot plot.

Want to use math manipulatives but need more resources? Try virtual manipulatives !

Activity 3: Puzzle Power

Puzzles are not only engaging but also promote critical thinking and problem solving skills. They challenge students to think creatively and persevere through complex tasks. Here are a few puzzle-based activities to include in your math stations:

• Number Crossword: Create a crossword puzzle where students respond to math-related clues and fill in the corresponding numbers in the grid.
• Logic Grids: Challenge students with logic puzzles that require them to use deductive reasoning and critical thinking skills to solve.
• Sudoku: Provide students with Sudoku puzzles focusing on numbers, shapes, or mathematical operations, encouraging them to apply logical reasoning to complete the puzzles.

Activity 4: Real-World Math Investigations

Real-world math investigations allow students to apply their mathematical knowledge and skills to authentic situations. These activities promote problem-solving, critical thinking, and the ability to connect math and the real world. Consider the following examples for your math station rotations:

• Recipe Conversions: Provide students with recipes that need to be converted to serve a different number of people. Students must adjust ingredient quantities using proportional reasoning and fractions.
• Budgeting and Shopping: Give students a budget and a list of items with prices, such as a local grocery ad or restaurant menu. They must plan a shopping trip, choose items based on their budget, and calculate the total cost.
• Measurement Scavenger Hunt: Create a list of objects in the classroom or nearby hallway students need to measure using various units of measurement. Students will use rulers, measuring tapes, or scales to gather the data and record their measurements.

Activity 5: Technology Tools

Incorporating technology into math stations can engage students and provide interactive learning experiences. Consider utilizing the following online resources and educational apps:

• Online Math Games and Activities: Websites such as IXL Learning, Prodigy, and Math Playground provide opportunities to gamify the learning experience. Students can earn points and virtual rewards while building math skills. 
• Digital Activities: Activities designed for Google Classroom and Seesaw provide engaging opportunities for students to use digital tools to review math concepts and skills .
• Digital Task Cards: Take task cards to the next level with digital task cards . Task cards created for use at Boom Learning or even with Google Forms can increase student engagement while students practice essential math skills.

Activity 6: Ready-Made Math Activities

In addition to creating your small group math activities, incorporating ready-made resources can provide a valuable and time-saving option for engaging your students. These pre-made activities offer an interactive and hands-on way to reinforce math skills and concepts. 

• Electronic Flashcard Games: Electronic flashcard games provide an exciting and interactive way for students to practice and reinforce math facts. These games often offer various difficulty levels and customizable options to cater to students’ needs. Math Whiz and Math Shark are two of my favorites!
• VersaTiles: VersaTiles is a hands-on, puzzle-inspired activity with an interactive workbook system designed to reinforce math skills. Students use a unique answer case and answer tiles to complete activities and self-check their answers. It’s a favorite of my elementary and middle school students alike!
• Marcy Cook Tiling Tasks: Marcy Cook Tiling Tasks are critical thinking activities that require students to use a set of tiles labeled 0-9 to complete math puzzles. These tasks promote problem-solving skills, logical reasoning, and mathematical thinking. Students arrange the tiles to fill in the blanks and create equations and solutions that satisfy the given conditions. 

Activity 7: Math Task Cards

Math task cards offer various practice opportunities and allow students to work independently. They are also easy to make and readily available on teacher marketplaces across the web. Here are some examples of task card activities: 

• Showdown: Partners select one card and complete it individually. Then, students “showdown” and share their responses using math talk and supporting each other as necessary. 
• Math Game: Pair a set of task cards with a game board to gamify the learning experience! Students place their game markers at the start line. To move down the path, students must correctly respond to a task card, toss a die (or flip a coin), and move the number of spaces indicated on the die or based on the side of the coin visible after the coin toss (heads = 2 spaces, tails = one space).
• Cover Up: To create a Cover Up game, program a 4 x 4 grid with the solutions to a set of task cards. Then, when students respond correctly, they can cover the answer with a board marker, such as centimeter cubes, color tiles, Bingo chips, or beans. The goal is to get four markers in a row, column, or diagonal. Note: This activity works best with multiple-choice questions, true or false questions, or questions with numerical answers.  

Activity 8: Math Picture Books

Integrating math and literature activities enhances students’ mathematical understanding and develops their reading comprehension, critical thinking, and analytical skills. Consider incorporating the following math and literacy activities into your math stations:

• Math Investigations: Use the storyline in a book to practice a skill. For example, use the Pigs Will Be Pigs book by Amy Axelrod to practice adding and subtracting decimals as the pigs find money hidden around their home and then spend it at a restaurant. 
• Story-based Problems: Use the book as a springboard to reinforce a specific skill. Either re-create scenarios from the book or create new problems based on the problems the characters faced in the story such as comparing the amounts in two different groups after reading Amanda Bean’s Amazing Dream by Cindy Neuschwander.
• Famous Mathematicians Book Study: Create a set of questions to help students learn more about famous mathematicians, such as Katherine Johnson , and provide students with access to a physical or digital biography to read and use to respond to the questions.

Activity 9: Calculator Challenges

Incorporating calculator challenges into your math stations can allow upper elementary students to deepen their understanding of math concepts while developing their computational skills. Calculator activities engage students in hands-on exploration, problem-solving, and critical thinking while building their technology proficiency skillset. 

These activities encourage students to use calculators to investigate, solve problems, and make connections. Consider incorporating the following calculator challenges into your math stations:

• The Broken Calculator Challenge: In this challenge, students are shown an image of a calculator with only three or four working buttons. Students then determine how to use the remaining keys on the broken calculator to create specific values, such as using +, x, 2, and 3 to achieve a value of 8.
• Calculator Corrections: This task requires students to determine how to correct a calculator mistake without clearing the calculator. Using the calculator, students determine how to fix a mistake, check the answer, and make adjustments as necessary. After completing the task, students can justify the changes they made. For example, Brandi wanted to enter the number 4265 into her calculator. By mistake, she typed 4165. Without clearing her calculator, how can she fix her mistake? 
• Target Number: For this task, students represent place value in numbers, determine what number to add or subtract to reach the target number, and use the calculator to check their process. For example, students are given the following directions: Start with 7,254. Find a number to subtract that will result in a 0 in the hundreds column.

Activity 10: Problem Solving and Critical Thinking

Problem-solving and critical thinking are essential life skills for students to develop. Engage your students in meaningful and challenging math experiences by incorporating problem solving and critical thinking activities into your small group math activities. Click here for a list of problem solving activities ; that encourage students to think critically, analyze situations, and apply their mathematical knowledge to real-world scenarios.

A Shift in Thinking

While I never found a way to make reading workshop exciting, math workshop was my students’ favorite part of the day. 

Integrating various small group math activities into the rotation was the key to keeping students engaged in learning and wanting more. 

If you’re new to math stations, the best way to get started is to choose 1-2 new activities to implement. Consider adding another activity after students are comfortable with the previous activities and staying engaged with minimal support.

Adding new small group math activities gradually will help maintain order during the rotation and save your sanity! If you’d like more tips and tools for managing math stations, download the Math Station Management Toolbox using the form at the bottom of this post. 

Math station rotation boards are an excellent organizational tool for implementing the small group math activities above. This visual display helps students understand the structure of the math station rotation and enhances their independence and accountability. 

The small group math activities shared above can be assigned to specific stations on the rotation board. Then, teachers can use the math station rotation board to effectively monitor student progress as they rotate through various math stations. 

Experiment with these small group math activities and adapt them to meet the needs and interests of your students, ensuring math station time is an exciting and transformative experience for all.

What are your favorite small group math activities? Respond in the comments below. 

Shametria Routt Banks

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3 Problem-Solving Math Activities

Scottie Altland · September 5, 2018 · 1 Comment

A problem is simply a “problem” because there is no immediate, known solution. Problem solving activities in mathematics extend well beyond traditional word problems .

You can provide your student with activities that promote application of math skills while “busting boredom” at the same time! Puzzles and riddles, patterns, and logic problems can all be valuable exercises for students at all levels of mathematics. By engaging in short, fun activities like these, you can help your student become a more skillful, resilient, and successful problem-solver.

When practicing problem-solving skills, be certain to give your student time to explore a problem on her own to see how they might get started. Then discuss their approach together. It is important to provide support during the problem-solving process by showing that you value their ideas and helping them to see that mistakes can be useful. You can do this by asking open-ended questions to help your student gain a starting point, focus on a particular strategy, or help see a pattern or relationship. Questions such as, “What have you done before like this?”, “What can be made from …?” or “What might happen if you change…?” may serve as prompts when they needs inspiration.

Try the activities below to boost your student’s problem-solving skills.

Download the activities here .

1) Toothpick Puzzles

Toothpick puzzles (also referred to as matchstick puzzles) provide students a visualization challenge by applying their knowledge of basic geometric shapes and orientations. The only supplies you need are a box of toothpicks, a workspace, and a puzzle to solve. The goal is for students to transform given geometric figures into others by adding, moving, or removing toothpicks. These puzzles range in complexity and can be found online or in math puzzle books. As an extension, challenge your student to create their own puzzle for someone else to solve.

Sample toothpick puzzles of varying difficulty:

Download solutions to this activity here.

2) Fencing Numbers

The goal of this activity is to create a border or “fence” around each numeral by connecting dots horizontally and vertically so that each digit is bordered by the correct number of line segments.

Print a sheet of dot paper .

Use pencils and scissors to cut the size grid you want to use.

This game can be modified for abilities by adjusting the size of the grid and amount of numerals written. For example, a beginning student might begin with a grid that is 5 x 5 dots with a total of four numerals, while a more advanced student might increase the grid to 7 x 7 dots with six to eight numerals.

Begin by writing the digits 0, 1, 2, and 3 spread repeatedly in between “squares” on the dot paper. Each digit represents the number of line segments that will surround that square. For instance, a square that contains a 3 would have line segments on three sides, and a square that contains a 2 would have line segments on two sides, and so on. See the example boards and solutions for a 5 x 5 grid below.

Beware; there may be multiple solutions for the same problem! Thus, encourage your student to replicate the same problem grid multiple times and look for different solutions. A more advanced student can be challenged to create their own problem. Can they make a grid with only one solution? Is it possible to make a problem with four or more possible solutions?

3) It’s Knot a Problem!

Exercise lateral thinking skills– solving a problem through an indirect and creative approach that is not immediately obvious. You need two people, two pieces of string (or yarn) about one meter long each (or long enough so the person who will wear it can easily step over it), and some empty space to move around. If possible, use two different colored pieces of string. Each person needs a piece of string with a loop tied in both ends so it can be worn like “handcuffs”. Before tying off the loop on the second wrist, the participants loop the string around each other so they are hooked together. The figure below illustrates how the strings should appear when completed.

The goal is to unhook the strings while following these guidelines:

1) The string must remain tied and may not be removed from either participant’s wrists. 2) The string cannot be broken, cut, or damaged in any way.

Caution! This activity not only tests problem-solving skills, but it also promotes positive communication, teamwork, and persistence.

Problem-solving skills are not always taught directly but often learned indirectly through experience and practice. When incorporating problem solving activities aim to make them open-ended and playful to keep your student engaged. Incorporating fun activities like these from time to time foster creative and flexible thinking and can help your student transfer problem solving skills to other subject areas. By providing guidance and helping your student to see a problem from different perspectives, you will help foster a positive disposition towards problem-solving. As your student continues to learn how to effectively solve problems, they increase their understanding of the world around them and develop the tools they need to make decisions about the way they approach a problem.

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February 25, 2020 at 11:13 am

The ideas are very brilliant it encourages critical thinking and also help student think for a solution. Awesome!😍

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K-5 Math Centers

K-5 math ideas, 3rd grade math, need help organizing your k-5 math block, 5 ways to include math problem solving activities in your classroom.

Are you looking for math problem solving activities that are not too easy and not too hard, but juuust right? I’ve got something just for you and your students.

Solve and Explain Problem Solving Tasks are open-ended math tasks that provide just the right amount of challenge for your kids. Here’s a little more about them.

Open-ended math problem solving tasks:

• promote multiple solution paths and/or multiple solutions
• boost critical thinking and math reasoning skills
• increase opportunities for developing perseverance
• provide opportunities to justify answer choices
• strengthen kids written and oral communication skills

What Makes These So Great?

• All Common Core Standards are covered for your grade level
• 180+ Quality questions that are rigorous yet engaging
• They are SUPER easy to assemble
• Provide opportunities for meaningful math discussions
• Perfect for developing a growth mindset
• Easily identify student misconceptions so you can provide assistance
• Very versatile (check out the different ways to use them below)

You can find out more details for your grade level by clicking on the buttons below.

I’m sure you really want to know how can you use these with your kids. Check out the top 5 ideas on how to use Solve and Explain Problem Solving Tasks in your classroom.

How and When Can I Use Them?

Solve and Explain Tasks Cards are very versatile. You can use them for:

• Math Centers  – This is my favorite way to use these! Depending on your grade level, there are at least two (Kinder – 2nd) or three (3rd-5th) tasks types per Common Core standard. And each task type has 6 different questions. Print out each of the different tasks types on different color paper. Then, let students choose which one question from each task type they want to solve.

• Problem of the Day  – Use them as a daily math journal prompt. Print out the recording sheet and project one of the problems on your white board or wall.  Students solve the problem and then glue it in their spiral or composition notebooks.

• Early Finisher Activities  -No more wondering what to do next!Create an early finishers notebook where students can grab a task and a recording sheet. Place the cards in sheet protectors and make copies of the Early Finisher Activity Check-Off card for your kids to fill out BEFORE they pull a card out to work on. We want to make sure kids are not rushing through there first assignment before moving on to an early finisher activity.

• Weekly Math Challenges  – Kids LOVE challenges! Give students copies of one of the problems for homework. Then give them a week to complete it. Since many of the questions have multiple solutions and students have to explain how they got their answers, you can have a rich whole group discussion at the end of the week (even with your kindergarten and 1st grade students).

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• Formative Assessments  – Give your students a problem to solve. Then use the Teacher Scoring Rubric to see how your kids are doing with each standard. Since they have to explain their thinking, this is a great way to catch any misconceptions and give feedback to individual students.

So this wraps up the top 5 ways that you can use problem solving tasks in your classroom.  Click your grade level below to get Solve and Explain problem solving tasks for your classroom.

• Read more about: K-5 Math Ideas

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• National Numeracy Day - 22nd May 2024/

Numeracy Through Problem Solving

Numeracy Through Problem Solving is a sequence of five modules which develop students' ability to use mathematics together with other skills. In tackling problems of concern or situations of interest in everyday life - the original definition of numeracy, which was reinforced by the Cockcroft Report. The five modules have all been designed for pupils of all abilities to complement the GCSE Mathematics curriculum for 16 year olds in England and Wales. Each module is designed to take between 10 and 20 hours to complete. Each provides a theme within which the students take responsibility for planning, organising or designing. They are based around the everyday interests of most students. Students work both individually and in groups and are able to choose which areas of mathematics to deploy. They also implement the results of their own decisions - a vital educational experience! It has been developed with students of all abilities in the age range 13-16, and their teachers. Each module package provides comprehensive materials for both teaching and assessment, related to a practical context which has proved interesting and enjoyable to the students who have taken part in its development. It is accessible to those who normally find mathematics difficult, while at the same time it provides a challenge for the most able.

• Mathematics
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• Include Physical Resources

Design a Board Game

In this Shell Centre module, groups carefully design and produce their own board games. These games are then played and evaluated by other class members.

This involves developing ideas from 2-dimensional shape-and-...

Be a Shrewd Chooser

In this Shell Centre activity, students research and provide expert consumer advice for clients in their class.

Students listen to a radio show on audiotape which contains a number of interviews with people who have...

Plan a Trip

In this Shell Centre module students plan and undertake a class trip using costings, scheduling, surveys and everyday arithmetic.

In a card game simulation, groups undertake and record imaginary trips, encounter problems and errors of judgement, then seek to correct them by better planning. Groups share...

Be a Paper Engineer

In this Shell Centre activity students design make and evaluate 3D paper products including gift boxes and pop-up greetings cards. They explore 3D shape-and-space, making generalisations using words and algebra.

In groups, students make a wide variety of pop-up cards, gift boxes and envelopes in order to...

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Description:

Numeracy focuses on the core skills of applying numerical concepts. It is the ability of understanding fundamental mathematical operations such as multiplication, division, addition and subtraction. These activities are created for all ages and all cognitive levels.

Activities should be adapted based on the learner's cognitive ability.

Numeracy activities are important for learners to develop logical thinking and strategies in everyday life. Learners also need numeracy to make sense of numbers, solve problems, play sports, cook and understand instructions.

Ask the learner to write a math story or word problem and have someone else draw it out and solve it!

This activity ensures that learners understand the real world applications of mathematics and encourages them to use math to solve these problems

Ask the learner to think about a very short story for their word problem. Think of questions such as:

- Who is the character in the story?

- Where is the story happening?

- What is his or her problem?

- What question are you looking to answer?

Once the learner has the story, think about the math involved:

- How many steps will be needed to solve the problem?

- Which operation/s will be needed? (addition, subtraction, multiplication, and division)

- How large will the numbers be?

Finally, tell the learner to write the problem and ask someone else to solve it by drawing a picture and writing a number sentence to go with it!

Emily made 10 cookies at home for her family and herself. Her brother ate 4 cookies, how many are left for the rest of the family?

Choose a number and then show different ways to split a number into two whole numbers.

This activity ensures that learners understand how to create connections between numbers using addition.

Ask the learner to create a list with numbers and pick one number from the list, or ask the learner to think of a number in their head and say it out loud. Alternatively the learner can roll one or two dice to decide the number.

Next, ask the learner how many ways they can split the number into whole numbers. For example, if their number is 10, they can come up with:

- 10 can be added using the numbers 5, 5

- 10 can be added using the numbers 8, 2

- 10 can be added using the numbers 7, 3

- 10 can be added using the numbers 6, 4

Finally, tell the learner to see how many ways they can think of to reach their chosen number.

Ask the learner to play this with a partner or in a group, and whoever has the most ways of reaching the number, wins.

Ask the learner to try to split the number with different mathematical operations such as subtraction, division and multiplication.

Ask the learner to set a goal for themselves: “I will think of 5 different ways to make this number.”

Roll two or more dice and create math equations to solve for.

This activity ensures that learners know their math facts automatically.

Ask the learner to decide what operation they wish to do (addition, subtraction, multiplication or division)

Next, get two dice and roll them.

Finally, solve the problem.

For example: if they chose addition and rolled 2 on one dice and 3 on another dice, do 2 + 3 and solve this equation.

Assist the learner in creating their own dice like the picture!

If the learner wants to work with bigger numbers, then change the numbers on the dice.

The learner can play this with a partner or in a group, and whoever has the most correct answers, wins.

Set a timer for the learner and keep rolling the dice and solving the equations. Start the timer again and then tell the learner to try to beat their previous score.

For a longer project where the learner can create their own math games, please refer to Math Cards here: Link

Two or more people pick a card each. The person with the higher number will move their car one step ahead. Whoever reaches the finish line first, wins.

To ensure the learners are able to compare number values.

Help the learner create about 20-30 number cards. (cut an A4 piece of paper in 8 or 12 cards)

Next, ask the learner to get two toy cars and create a race track on some chart paper like the one in the picture.

Then, place the cars on the starting position and each person pick up a number card. The person with the higher number moves one step forward.

Finally, the person who reaches the finish line first, wins.

Use numbers in the tens, hundreds or thousands or even larger to make it more challenging. The number cards can also be decimals, fractions or integers if the learner knows them.

Two or more people take turns putting a playing card one on top of another. The person who calculates the decided number first says snap and collects the cards. Keep going until one person loses all their cards.

This activity ensures the learners are able to compute their basic math facts automatically.

Deal all the number cards equally among the players.

Next, ask the learner to decide which operation they wish to work with and what the total must be. For example: They decide they want to work with addition and the total number must be 10.

Then, hand out the cards to each player, facing down. Each player takes a turn picking up a card from their own pile and placing it face up in the center, one on top of each other.

Keep calculating the top 2 cards (e.g., 3+4, 2+8), and when the numbers equal the predetermined total (e.g., 10), a player calls “Snap” while slapping their hand onto the top of the pile of cards. The first player to do this wins the pile and adds these cards to the bottom of their pile.

The player that runs out of cards is out of the game and the player with the most cards wins.

If the learner wants to include the other cards (e.g., WILD, Jacks etc.), then assign each of them a number value.

Ask the learner to make their own number cards. About 30-40, with any number they wish to have.

Two or more people take turns picking up two cards at a time and adding them. The person who gets the higher total collects the cards. Keep going till one person loses all their cards.

Deal all the number cards from a playing cards deck equally among all players. If the learner wants to include the other cards (e.g., WILD, Jacks etc.), then assign each of them a number value.

Then, hand out the cards to each player, facing down. Each player takes turn placing two cards, facing up, in front of them.

Next, add the numbers on the cards (e.g.: if they get 3 and 2, then their answer is 5). Tell everyone the answer. The player with the highest answer adds everyone’s cards to the bottom of their pile.

If the player gets the same number in both cards, they can DOUBLE their answer! (e.g.: if they get 3 and 3, add them and get 6 and then double this to get 12 as the final answer!)

Play this game with subtraction or multiplication too!

Two or more people take turns subtracting. The person who gets the lower total collects the cards. Keep going until one person loses all their cards.

This activity ensures the learners are able to do basic operations mentally.

Deal the number cards (1-9) from a playing cards deck to all the players.

Next, the players look at their cards and make a 2 digit number using two cards (e.g.: if I have 3, 6, 7 and 9, I can make numbers such as 36 and 97, etc.)

Then, each player subtracts the smallest number from their largest number and tells the answer (e.g.: 97-36= 51). This should be done mentally, if possible.

The player with the highest number for the answer keeps their cards, but the other players return their cards to the bottom of the middle pile.

Keep going until the cards are all done. The person with the most cards wins.

This game can be played with addition, multiplication or division too!

Use only 1 digit numbers, using 1 card, and subtracting the smallest number from the largest number.

Using a deck of cards, shuffle the cards and then lay 5 cards out on the table and all other cards face down in a pile on the side.

Next, the first player picks one card from the deck of the cards and lays it face up beside the pile.

Then, the players attempt to create an equation using any of the 5 cards to make the number they have turned over.

For example: if they have placed 5 cards - 3, 6, 2, 5 and 10 on the table, and 7 is the number they chose, then they can make the equations 5 + 2, or 10 – 3, or 5x2 - 3 and so on that all equal 7.

The first player to think of an equation says “Made My Number” and says the equation. If they are correct, they keep those number cards and the number card chosen, all of which are then replaced in the next round.

If the players are unable to make the number, just place the chosen card at the bottom of the pile and pick a new one. Keep going until the cards are all done. The person with the most cards wins.

This game can be played by using a timer and challenging players to come up with as many equations within the time limit as possible!

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Learning and Development

Maths problem-solving – Activities for Early Years settings

• Written By: Judith Dancer
• Subject: Maths

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Critical thinking doesn’t have to be a daunting prospect. There are simple, effective and exciting ways to encourage children’s maths problem-solving skills, says Judith Dancer…

Maths is a subject many adults lack confidence in. Having struggled with it at school they often avoid it, wherever possible, when grown up.

But if maths seems scary for some people, then maths problem-solving can cause even more anxiety. There is no ‘safety net’ of knowing the ‘correct answer’ beforehand. This is because maths problem-solving lends itself to investigation and exploration with lots of possible tangents.

Understandably this is often the area of maths where many practitioners feel least confident. However, young children, who are not restrained by right answers, feel the most enthused and animated.

The non-statutory  Development Matters Guidance , as part of ‘creating and thinking critically’ in the Characteristics of Effective Learning, identifies that practitioners need to observe how a child is learning, noting how a child is:

• thinking of ideas;
• finding ways to solve problems;
• finding new ways to do things;
• making links and noticing patterns in their experience;
• making predictions;
• testing their ideas;
• developing ideas of grouping, sequences, cause and effect;
• planning, making decisions about how to approach a task, solve a problem and reach a goal;
• checking how well their activities are going;
• changing strategy as needed;
• reviewing how well the approach worked.

All of these elements are, at one time or another, part of the problem-identifying and solving process – although not at the same time and in the same problem.

Role of the adult

Maths problem-solving for young children involves them understanding and using two kinds of maths:

• Maths knowledge – learning and applying an aspect of maths such as counting, calculating or measuring.
• Maths thinking skills – reasoning, predicting, talking the problem through, making connections, generalising, identifying patterns and finding solutions.

The best maths problems for children are the ones that they identify themselves. They will be enthused, fascinated and more engaged in these ‘real’, meaningful problems.

Children need opportunities to problem-solve together. As they play, they will often find their own mathematical problems.

One of the key roles of practitioners is to provide time, space and support for children. We need to develop situations and provide opportunities in which children can refine their maths problem-solving skills and apply their mathematical knowledge.

Supporting maths problem-solving

You can effectively support children’s developing maths problem-solving strategies through:

• Modelling maths talk and discussion – language is part of maths learning because talking problems through is vital. Children need to hear specific mathematical vocabulary in context. You can promote discussion through the use of comments, enabling statements and open-ended questions.
• Providing hands-on maths problem-solving activities across all areas of the setting. Children learn maths through all their experiences and need frequent opportunities to take part in creative and engaging experiences. Maths doesn’t just happen in the maths learning zone!
• Identifying potential maths learning indoors and outdoors. Provide rich and diverse open-ended resources that children can use in a number of different ways to support their own learning. It is important to include natural and everyday objects and items that have captured children’s imaginations, including popular culture.

Maths problem-solving possibilities

Spell it out.

This experience gives children lots of opportunities to explore calculating, mark making, categorising and decisions about how to approach a task.

What you need to provide:

• Assorted containers filled with natural materials. This includes leaves, pebbles, gravel, conkers, twigs, shells, fir cones, mud and sand. Include some ‘treasure’ – sequins, gold nuggets, jewels and glitter.
• Bottles and jugs of water, large mixing bowls, cups, a ‘cauldron’, small bottles, spoons and ladles.
• Cloaks and wizard hats.
• Laminated ‘spells’ – e.g. “To make a disappearing spell, mix 2 smooth pebbles, 2 gold nuggets, 4 fir cones, a pinch of sparkle dust, 3 cups of water”.
• Writing frameworks for children’s own spell recipes and a shiny ‘Spell Book’ to stick these in.
• Temporary mark-making opportunities such as chalk on slate.

The important thing with open-ended maths problem-solving experiences like this is to observe, wait and listen. Then, if appropriate, join in as a co-player with children, following their play themes.

So if children are mixing potions, note how children sort or categorise the objects. What strategies do they use to solve problems? What happens if they want eight pebbles and they run out? Observe what they do next.

When supporting children’s maths problem-solving, you need to develop a wide range of strategies and ‘dip into’ these appropriately. Rather than asking questions, it is often more effective to make comments about what you can see. For example, say, “Wow, it looks as though there is too much potion for that bottle”.

Acting as a co-player offers lots of opportunities to model mathematical behaviours. This might include reading recipes for potions and spells out loud, focusing on the numbers – one feather, three shells…

Going, going, gone

We all know that children will engage more fully when involved in experiences that fascinate them. If a particular group has a real passion for cars and trucks , consider introducing maths problem-solving opportunities that extend this interest.

This activity offers opportunities for classifying, sorting, counting, adding and subtracting, among many other things.

• Some unfamiliar trucks and cars and some old favourites. Ensure these include metal, plastic and wooden vehicles that can be sorted in different ways.
• Masking tape and scissors.
• Sticky labels and markers.

Mark out some parking lots on a smooth floor, or huge piece of paper using masking tape. Lining paper is great for this. Line the vehicles up around the edge of the floor area.

Encourage one child to select two vehicles that have something the same about them. Ask the child, “What is the same about them?”.

When the children have agreed on what is the same – e.g. size, materials, colour, lorries or racing cars – the child selects a ‘parking lot’ to put the vehicles in. So this first parking lot could be for ‘red vehicles’.

Another child chooses two more vehicles that have something the same. Do they belong in the same ‘parking lot’, or a different parking lot? E.g. these vehicles could both be racing cars.

What happens when a specific vehicle could belong in both lots? E.g. it could belong in the set of red vehicles and also belongs in the set of racing cars.

Support the children as they discuss the vehicle. Make new ‘parking lots’ with masking tape and create labels for the groups, if you choose.

Observe children’s strategies

It’s really important to observe the strategies the children use. Where appropriate, ask the children to explain what they are doing and why.

If necessary, introduce and model the use of the vocabulary ‘the same as’ and ‘different from’. Follow children’s discussions and interests. If they start talking about registration plates, consider making car number plates for all the wheeled toys outdoors.

Do the children know the format of registration plates? Can you take photos of cars you can see in the local environment?

Camping out

Constructing camps and dens outdoors is a good way to give children the opportunity to be involved in lots of maths problem-solving experiences and construction skills learning. This experience offers opportunities for using the language of position, shape and space, and finding solutions to practical problems.

• Materials to construct a tent or den such as sheets, curtains, poles, clips and string.
• Rucksacks, water bottles, compasses and maps.
• Oven shelf and bricks to build a campfire or barbecue.
• Buckets and bowls and water for washing up.

Encourage the children to explore the resources and decide which materials they need to build the camp. Suggest they source extra resources as they are needed.

Talk with the children about the best place to make a den or erect a tent and barbecue. During the discussion, model the use of positional words and phrases.

Follow children’s play themes. This could include going on a scavenger hunt collecting stones, twigs and leaves and going back to the campsite to sort them out.

Encourage children to try different solutions to the practical problems they identify. Use a running commentary on what is happening without providing the solution to the problem.

Look for opportunities to develop children’s mathematical reasoning skills by making comments such as, “I wonder why Rafit chose that box to go on the top of his den.”

If the children are familiar with traditional tales, you could extend this activity by laying a crumb trail round the outdoor area for children to follow. Make sure that there is something exciting at the end of the trail. It could be a large dinosaur sitting in a puddle, or a bear in a ‘cave’.

Children rarely have opportunities to investigate objects that are really heavy. Sometimes they have two objects and are asked the question, “Which one is heavy?” when both objects are actually light.

This experience gives children the chance to explore really heavy things and measures (weight). They also need to cooperate and find new ways to do things.

• A ‘building site’ in the outdoor area. Include hard hats, builders’ buckets, small buckets, shovels, spades, water, sand, pebbles, gravel, guttering, building blocks, huge cardboard boxes and fabric (this could be on a tarpaulin).
• Some distance away, builders’ buckets filled with damp sand and large gravel.
• Bucket balances and bathroom scales.

With an open-ended activity such as this, it is even more important to observe, wait and listen as the children explore the building site and the buckets full of sand and gravel.

Listen to the discussions the children have about moving the sand and the gravel to the building site. What language do they use?

Note the strategies they use when they can’t lift the large buckets. Who empties some of the sand into smaller buckets? Who works together collaboratively to move the full bucket? Does anyone introduce another strategy, for example, finding a wheelbarrow or pull-along truck?

Where and when appropriate, join in the children’s play as a co-player. You could act in role as a customer or new builder. Ask, “How can I get all this sand into my car?”. “How much sand and gravel do we need to make the cement for the foundations?”.

Extend children’s learning by modelling the language of weight:

• heavy/heavier than/heaviest
• light/lighter than/lightest
• about the same weight as/as heavy as
• balance/weigh

Judith Dancer is an author, consultant and trainer specialising in communication and language and mathematics. She is co-author, with Carole Skinner, of  Foundations of Mathematics – An active approach to number, shape and measures in the Early Years .

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NRICH Starter Problem Selection

Are you a student who likes to think about mathematical problems? Why not test and develop your skills with this special selection of NRICH problems? They have been chosen because they only make use of simple mathematical concepts (the sort encountered as some point early in Stage 3): the emphasis is on the thinking rather than the knowledge. Why not print out the table and tick off the problems you have solved? Will you be able to crack them all? Don't forget, if you get stuck you can look at the Hint or Solution at the top of each problem. Happy solving!