Math puzzles and brain teasers are the academic version of sneaking veggies into a slice of cake. Kids have so much fun solving problems and playing games that they won’t even realize they’re applying mathematical concepts, practicing computation skills, and using logical reasoning. They’re great items to use as bell work or enrichment to excite and entice students about math.
Teachers who incorporate free math puzzles in their classrooms report higher levels of motivation and positive attitudes about math. That should come as no surprise because they’re so much fun to solve, students won’t realize they're “doing math.” Puzzles also help students develop creativity, problem-solving skills, and reflective learning.1
Try it for yourself. Put your creative problem-solving skills to use and see if you can solve these math puzzles. Then, share them with your students.
10 of the Best Math Puzzles For Students of All Ages
We asked four of our Sphero Heroes to share their best examples of math puzzles they use in their own classrooms. Let’s jump in and see what Garrett Gross, Beth Doiron, Celine Gallien, and Brandon Hazzard recommend!
1. Area Maze Puzzles
An Area Maze is a logic puzzle that you solve by applying problem solving and logical reading strategies to find the missing value.2 Instead of just calculating the area of a 2-D or 3-D shape, students apply geometric rules, computation, and logical reasoning. The only rule is that the solution cannot be a fraction or decimal. According to Sphero Hero Celine Gallien, “Area Maze puzzles are accessible to those who have a basic understanding of finding the area of a rectangle.” You can easily customize these puzzles for students in grades 5 through 12, and Gallien also suggests letting students create their own.
2. Dots in a Square
Dots in a Square is a simple and free math puzzle, and its simplicity is what makes it so effective for developing creative problem-solving skills.3 For this puzzle, students start with 9 equidistant circles that form the shape of a square. They must connect all of the dots in the square using four straight lines, and they have to do this without lifting their pencils. Dots in a Square works for upper elementary through secondary students.
This is a fun way to get kids in grades 5 through 12 practicing computation skills. In this cool math puzzle, they’re given a series of fireworks labeled with colored stars.4 The challenge is to figure out which of the fireworks still needs to be launched. To do this, they have to count the total number of stars for each color and the total number of stars in each color floating in the air above the firework. They subtract the number of launched stars from the total number of stars to determine which firework is still waiting to be used.
4. Multiplication Squares
Sphero Hero Garrett Gross recommends Multiplication Squares, created by Tracy Graves. This is a fun game that students in the 4th and 5th grades can play with partners or small groups.5 They take turns rolling dice and multiplying the numbers they get. For example, a student who rolls a 2 and an 8 has a 16. Then they find the product on the playing card and draw one line to connect the dots on one side of the square. The goal is to capture the most squares. Consider laminating the playing board and giving students dry-erase markers so you can erase and reuse the cards.
5. Order of Operations Brain Teasers
Order of Operations teasers is a fun way to practice rules for solving different parts of math problems. Instead of numbers, students see images. Part of the fun is figuring out which numbers the images represent. You can easily customize these brain teasers for special occasions and themes. Sphero Hero Brandon Hazzard adds, “I always like these order of operations brain teasers. They make you have to use order of operations, but also observe as, generally, the last line is an accumulation of subtle objects.” They’re ideal for students in grades 5 through 12.
6. Number Cube
A number cube puzzle appears deceptively simple.4 This puzzle features a row of cubes with numbers printed on the visible sides. Students then use the cubes to determine which number belongs in a given series. This requires identifying how to calculate the numbers on the cube to equal the numbers in the series. It’s a great tool for practicing computation and problem-solving. Try it with upper elementary through secondary students.
7. Red Card Blue Card
Students who need additional practice working with factoring can benefit from Red Card Blue Card. This puzzle is recommended by Sphero Hero Beth Doiron, from New Brunswick, Canada. For this puzzle, you’ll need five red cards and four blue cards to write on. Explain the scenario to students: Sally has five cards (numbers 1 through 5) and four blue cards (numbers 3 through 6). Students then figure out how to line up the cards in alternative colors while also matching factors. This puzzle is suitable for students in grades 4 through 6.
Stardoku is an adaptation of the popular Sudoku puzzles, and it’s a fantastic option for the little ones — kindergarten and first grade.6 In this puzzle, kids place colored stars in the grid so that each row and column have one of each color. Start with a 4x4 grid for beginners and work your way up to a more challenging 6x6 grid.
9. Symbol Sums
A symbol sum puzzle allows students to practice their computation skills.4 Even better, they’re easy to make and customize for endless practice. Give students an equation that’s missing computation symbols. The challenge is to fill in the missing computation symbols to make the equation correct. Feel free to suspend the order of operations if you need more options. Try symbol sums with upper elementary and secondary students.
10. Turn the Fish
For this fun logic puzzle, students start with a set of eight matchsticks (or pencils) arranged in the shape of a fish.3 The task is to move three of the matchsticks or pencils to make the fish appear to be swimming in the opposite direction. This is a great puzzle for partner or small group work so students can practice communication and team-building skills as they work together to solve a problem. Try this brain teaser with upper elementary through secondary students.
Get Started Solving All These Math Puzzles with Your Students
Math puzzles are a powerful way to encourage students' interest in math and help them practice their skills. As you start to incorporate puzzles into your classroom, remember to choose ones that are at the right level for your students and use them intentionally. They're a great practice tool, but not a complete replacement for instruction. Most of all, have fun with them! Let students see their own enthusiasm for math and problem-solving.
- Kulkarni, D. (2013). Recreational and educational value of math puzzles. Edutopia. https://www.edutopia.org/blog/recreational-educational-value-math-puzzles-deepak-kulkarni
- Bellos, A. (August 3, 2015). Can you solve it? Are you smarter than a Japanese schoolchild? The Guardian. https://www.theguardian.com/science/2015/aug/03/alex-belllos-monday-puzzle-question-area-maze-smarter-than-japanese-schoolchild
- Homeschoolmath.net (n.d.). Favorite math puzzles for kids. https://www.homeschoolmath.net/online/favorite_puzzles.php
- Jones, M. (September 20, 2021). 30 Math puzzles (with answers) to test your smarts. Reader’s Digest. https://www.rd.com/article/math-puzzles/
- Brittney Field. (n.d.). Multiplication squares revised. Games 4 Gains. https://wes.pasco.k12.fl.us/wp-content/uploads/wes/2017/05/MultiplicationSquaresGame_R.pdf
- Starduko. (n.d.). Turtle Diary. https://www.turtlediary.com/game/picture-sudoku.html