As a fourth- and fifth-grade teacher, I’ve found that using puzzles in the classroom has benefits for students of all learning levels and abilities. Solving puzzles adds variety to daily lessons, helps children practice math concepts, and develops mathematical thinking—not to mention that puzzles are a fun and engaging way to bring math “to life”!
Puzzles serve as a great motivator for all types of math learners because they promote creativity, perseverance, and strategic thinking. Students who are struggling in math may find a new route through puzzling. At the same time, students who are comfortable with (or even proficient in) mathematical concepts can be challenged to think about learning in a different way. Puzzles can help solidify concepts and encourage deeper understanding, and they also provide the opportunity to manipulate, problem solve, and promote creativity.
Types of Math Puzzles
I have used a variety of puzzles in my classroom that have helped my students learn a number of different math skills:
These puzzles offer students practice with their visual and spatial skills. Mazes also help develop this skill set.
Pentominoes are a fun way to practice geometry skills as well as visual and spatial skills. Here’s how I use them: First, my students learn about what makes a shape a pentomino and how a set of pentominoes can be manipulated into larger or more complex shapes. After becoming more comfortable, students learn how to put several pentominoes together to create their own puzzles. Once their pieces are arranged, they trace the outside of the new shape, remove the pentominoes, and challenge their peers to solve their puzzle. It’s a great example of bringing math to life for students, and giving them the opportunity to develop their own ideas and spatial understandings.
These popular puzzles are ones that give children an opportunity to practice using their deductive reasoning skills and problem-solving skills.
There are all kinds of logic puzzles, but I use grid logic puzzles most often. Each puzzle has a series of categories and a number of options within each category. Each option is used once, and the goal is to figure out which options are linked together based on a series of clues. Each puzzle has one solution and is solved using simple logical processes.
Just like their previous work with pentominoes, after giving my students several logic puzzles, they are now creating their own! Many of the students choose to create puzzles with a classmate, which provides opportunities for collaboration and discussion about the puzzle. This helps to build classroom community. In addition to learning how to problem solve, students are learning about the importance of being specific, composing clear clues and directions (algorithms), and reviewing their work.
Math riddles are another type of puzzle that challenges students to think critically, logically, and creatively. Examples are polygon riddles and other brainteasers.
Math riddles are an excellent tool to help students think critically and to practice their problem-solving skills. One example of how I use math riddles is during our geometry unit, when the students are learning about polygons. I give the students one clue at a time, and they remove possibilities from their shape cards. An example of a polygon riddle: Clue 1: This polygon is not a parallelogram. Clue 2: This polygon does not have any right angles. Clue 3: This polygon does not have any obtuse angles. Clue 4: This polygon has exactly 2 congruent sides. What is the name of the polygon? Answer: Isosceles triangle. These riddles reinforce the students’ understanding of shapes and geometry vocabulary like parallel sides, perpendicular sides, types of angles, and lines of symmetry. After solving several riddles, the students create their own puzzles to share with each other. Another type of puzzle that challenges kids to think creatively is brainteasers, such as: What occurs twice in a week, once in a year but never in a day? Answer: The letter e.
Puzzles are a wonderful way to draw kids into math learning. After all, solving math problems is, in a way, just like solving puzzles. When kids see mathematics as puzzles, they are more engaged and have a more flexible approach to learning math.
Jackie Metcalf is a fourth- and fifth-grade teacher at the University of Pittsburgh’s Falk Laboratory School in Pittsburgh, Pennsylvania. She has been teaching for 19 years. She is married and has two children who enjoy puzzles.
There is something universally appealing about puzzles, no matter what our age or particular passion: jigsaw puzzles, word searches, mazes, Sudoku, or any of the puzzle-type games we have stored on our phones. The best puzzles are challenging but not to the point of frustration. They draw on our intelligence and our cleverness, and require both persistence and little bit of luck. As a result, you feel like you’ve truly earned your success – which is satisfying indeed.
The same holds true for puzzles for children, with the added requirement that they be developmentally appropriate. Logic, vocabulary, skills, and even humor vary by age, and they all play a big part in helping the puzzler feel successful. Kids love the thrill of the challenge, and they love feeling smart, all the more so if they’ve had to work at it. At Highlights for Children, we’re best-known for our Hidden Pictures puzzles (which, our spies in the dentist offices tell us, adults love as much as children). In addition to being fun and tricky (Where IS that pencil?), they offer some very concrete cognitive benefits:
Figure ground perception is the formal term for distinguishing items from their backgrounds (made famous by the image of two profile faces forming a vase between them). When kids scan an illustration and look for objects in the negative spaces between images, they are sharpening this skill, which is an important pre-requisite for learning to identify letters and numbers.
Object Constancy refers to the ability to recognize the properties of an object, and to understand that even when it changes in form or appearance it is still the same object. Have you noticed how each of our artists draws a banana in a unique way? Yet savvy puzzlers are always able to recognize them.
Visual Discrimination is the ability to see and appreciate both the similarities and differences between objects. Again, this is an important skill in the development of proficiency in both reading and math.
But perhaps the most important benefit of puzzling is persistence: the ability – the willingness – to work through a problem, to try and try again, to stay motivated and engaged, even when things are difficult. That’s a skill that will help kids throughout their lives, no matter how many different types of bananas they encounter.
Over the past 15 years I have studied the effects of media on children, and I continue to work to help create good content for children, both on and off screen. But as a mother of three children, I understand at a deeper level that digital screen media are growing in prominence in the lives of children – at all ages. And with the plethora of screen media options occupying more and more available downtime for kids, I have begun to appreciate even more those activities that are not tied to a screen. Puzzles are one such activity.
So what is it about puzzling that is educational, and what skills can be learned from such activities? Well, puzzling can build skills at every developmental stage. As children attempt to solve a puzzle, they learn to feel a sense of mastery. It also teaches them to persist in order to accomplish a goal. Each type of puzzle brings with it some specific skills that can be learned. Here are just a few:
Distinguish Differences in Visual Images. Hidden Pictures® puzzles develop the ability to distinguish differences in visual images. This skill helps children pay attention to details and understand subtle differences between similar-looking objects. This is especially important as children learn to read and distinguish letters such as b, d, p, and q. Children also learn how objects correspond in shape, size, color or design. As they work on these pictures, children begin to understand and identify the properties of objects, and they learn that objects that change in form and/or appearance are still the same object.
Develop Coordination and Visual Discrimination. Completing mazes takes coordination of small muscle movement and hand-eye coordination. Children also learn visual discrimination through determining how to reach an end-goal by using their sight to follow a path to reach the finish. These skills can help children both with handwriting skills as well as visual tracking skills needed to learn to read. In addition, it can help with more obvious hand-eye coordination skills such as catching a ball or hitting a ball with a bat.
Developing Matching Ability. Matching games allow children to practice important skills such as matching shapes and patterns (a pre-math skill), and then letters and words (a pre-reading skill). This, in turn, will give them one-to-one correspondence skills where they will be able to match one set with a member of another set (for example one sock with one shoe), which is important for learning properties of objects and how things can go together in different categories.
When possible, sit down with your child and puzzle together. Not only will it be a bonding experience, but your puzzling skills can model effective solving strategies for your child.
January 29 is National Puzzle Day!