Wednesday, March 6, 2013

Encouraging A Love of Math

Encouraging and nurturing the love of mathematics can be a challenge both at home and in the classroom. Here are some of the things I do to support reluctant math lovers of all ages.

By puzzles I mean not only logic puzzles and Sudoku, but jigsaw and geometric puzzles. Jigsaw puzzles help develop skills in orientation and visual discrimination. Geometric puzzles also help students to think deeply about the orientation of shapes in space and how they can be put together to make new shapes. Here are some of the puzzles I like to provide.
  • Tangrams - Tangrams are an ancient Chinese puzzle made from a large square cut into seven pieces. The seven shapes include a small square, two small triangles, a medium-sized triangle, two large triangles and a parallelogram. The linked site provides a good description of tangrams. When I use these I actually solve the puzzles, trace the outline of the finished shape on cardstock, and then laminate. For younger students, these outline shapes help them fit the pieces into the puzzle. Once students are comfortable with using them, I use the shapes to teach areafractions and angle measure. Try them out online at Cyberchase Math Games. Then fold your own set or print a set and try to build some shapes. You can also print some tangram puzzles as well as shape outlines for young children. Here's another good resource.

    You can pair this puzzle with the books Grandfather Tang's Story: A Tale Told With Tangrams by Ann Tompert and The Warlord's Puzzle by Virginia Pilegard. Both are stories that use tangrams in a way that encourages kids to build along with their own set of tangrams as they read.

  • Pentominoes - A pentomino is a polyomino composed of five congruent squares connected edge to edge. Can't picture them? Look to the right. You can download a set of your own or try out this terrific starter activity online. Since the area of all twelve pieces equals sixty squares, a challenging puzzle is to try and cover a 6×10 rectangle. Pieces can be flipped and rotated, but this isn't as easy as it seems, and that's surprising given that there are actually more than 2000 solutions! Students can then try to fill rectangles of similar areas (5x12, 4x15, and 3x20). I regularly use pentominoes to teach area and perimeter.

    The book Chasing Vermeer by Blue Balliett is filled with pentominoes. When a Vermeer painting is stolen in transit from the National Gallery in Washington D.C. to the Chicago Institute of Art, Petra and Calder become intent on finding the painting and solving the mystery. Calder carries a set of pentominoes in his pocket at all times, so be sure to print your own set to use while reading this one! Learn more about the book, the author, and the other books in the series at the Scholastic site

  • Geometric Puzzles - I own a number of puzzles created by Kate and Dick Jones, owners of Kadon Enterprises. They are all challenging and extremely well made. You can even try some online before you buy. All puzzles come with books explaining the math and offering many variants on play.

You can find more resources for dissection and shape puzzles on my Pinterest board for  Tangram/Pentomino/Shape Puzzles/Mazes.
  • Sudoku - If you like puzzles and numbers and haven't tried sudoku, you're missing out. For kids  just starting out, try a scaled version of the puzzle (4x4, 6x6, etc.) or something more concrete, like a sudoku board. If you want something even more kid-friendly (less abstract) to develop reasoning skills, try a version with pictures. Go ahead and try an online version of Picture Sudoku.

  • Kakuro and KenKen Variations - Whether you try Kakuro or KenKen/Mathdoku, these games all take the basic rules of sudoku and add in the element of calculation. In Kakuro puzzles (also known as Cross Sums) the numbers 1-9 are used in combination with addition. In some vairations multiplication is used. Here's a good basic guide for solving Kakuro puzzles. In KenKen or Mathdoku, the puzzles can focus on a single operation or all 4. To get started, check out these guidelines for helping kids learn to solve KenKen puzzles.

  • Logic Puzzles - You know the ones I'm talking about here. John, Karen, Tim, Ellen and Sam attend a party. The gifts they bring include a car, a giraffe, a watch, walkie-talkies and blocks. The information keeps coming and it is your job to figure out what each person wore, brought and ate. Phew! These can be great fun! Here's an introduction to logic puzzles and how to solve them. You can begin by solving some simple logic puzzles

You can find several boards devoted to number and logic puzzles at my Pinterest site.

Two great sites with a wide range of number puzzles (printable and online) are Krazydad and Conceptis Puzzles.

Using art in math class is one way to develop visual and spatial skills, as well as pattern recognition and basic geometry skills.
  • Origami - Paper folding is a great way to develop spatial reasoning abilities. It's also fun! You can get great paper at Origami Corner. Try making an origami crane or origami frog. If you have trouble reading origami directions in print, try following along with the videos from Origami-Fun or the Origami Instructor's channel on YouTube. For inspiration, visit the site of artist Robert J. Lang and check out his origami compositions. I'm crazy about his arthropods. Better yet, check out his TED Talk.

    While you're folding you may want to check out The Origami Master by Nathaniel Lachenmeyer and Lissy's Friends by Grace Lin (both picture books), as well as Fold Me a Poem by Kristine O'Connell George (poetry). All these books focus on origami. 

  • Spirograph - If you haven't seen a real spirograph, look here. Kids love making art with these kits. Klutz has simple Spiral Draw book/kit that includes 4 plastic drawing wheels and directions to get you started. Or you can try this Hypotrochoid Art Set. Once a few designs are made, consider the ways to color the design so that a pattern emerges.

  • Tessellations - Tessellations are all around us in the natural world. Here are few examples. If you like the art of M.C. Escher, then you already know all about tessellations. Creating them from cut paper or drawn shapes can be challenging and fun. The Can You Believe THIS Is Math? project has a good introductory set of directions on making tessellations. has a terrific gallery of examples, as well as a lengthy section with detailed directions on different ways to make tessellations. Tessellations can be used to study the types of symmetry in a plane.

Playing games is a great way to develop problem-solving skills as well as practice skills in arithmetic. I had a game corner in my classroom where students could play games when their work was finished. We also had game day on Friday for 20-30 minutes if we'd had a good week. While I know most of these can now be played electronically, there is something to be said for actually sitting down on the floor with kids, rolling dice, and moving pieces around a board. Some of the games on my shelf include:


I've already mentioned a number of books that connect to the ideas shared above. Using children's books is a great way to explore math with kids. Here are some titles that include mathematical content or challenging puzzles that will encourage children to stretch their mathematical muscles in a different way.

The Phantom Tollbooth by Norton Juster - Take a journey with Milo, a young boy who drives through a magic tollbooth into the Lands Beyond and embarks on a quest to rescue the maidens Rhyme and Reason from exile and reconcile the estranged kingdoms of Dictionopolis and Digitopolis. This is a great book for kids enamored of words and/or numbers. If you are a fan, check out The Annotated Phantom Tollbooth.

The Mysterious Benedict Society by Trenton Lee Stewart - Eleven year-old Reynie Muldoon is intrigued by an ad in the paper that asks “Are You a Gifted Child looking for Special Opportunities?” Reynie and dozens of other children show up to answer the ad and take a mind-boggling series of tests, but only Reynie and three others are left at the end. Puzzles and mysteries abound in this adventurous tale. Sequels include The Mysterious Benedict Society and the Perilous Journey and The Mysterious Benedict Society and the Prisoner's Dilemma. After reading the books, try your hand at solving the puzzles in The Mysterious Benedict Society: Mr. Benedict's Book of Perplexing Puzzles, Elusive Enigmas, and Curious Conundrums. You can also play games for the gifted at the Mysterious Benedict Society site.

Books by Greg Tang - Greg Tang has written a series of books that encourage children to look for patterns in math and find more "economical" ways of solving problems. Titles include:
The Best of Times: Math Strategies That Multiply
Grapes of Math: Mind Stretching Math Riddles
Math Appeal
Math Fables: Lessons That Count
Math Fables Too: Making Science Count
Math for All Seasons: Mind-Stretching Math Riddles
Math Potatoes: More Mind-Stretching Brain Food

The Man Who Counted: A Collection of Mathematical Adventures by Malba Tahan - Orginally published in 1949 as O Homem que Calculava, this book of mathematical puzzles was written by Júlio César de Mello e Souza and published under the pen name Malba Tahan.  The book is an enjoyable  series  of "Arabian nights"-style tales, with each story built around a classic mathematical puzzle. In each tale, Beremiz Samir uses his mathematical powers to "settle disputes, give wise advice, overcome dangerous enemies, and win for himself fame and fortune."

The Puzzling World of Winston Breen by Eric Berlin - Winston sees puzzles everywhere. Imagine his dismay when he gives his sister a box for her birthday, only to learn that it has a secret compartment containing four wood sticks with puzzle clues. Readers will solve puzzles right along with Winston and his sister Katie as they try to solve the mystery. You can download puzzles from the Winston Breen books to try them out. There are two sequels to this book, The Potato Chip Puzzles and The Puzzler's Mansion that are also highly entertaining.

The Number Devil: A Mathematical Adventure by Hans Magnus Enzensberger - With full color illustrations, this book tells the story of a twelve year old boy and math hater named Robert, who meets the Number Devil in his dreams. Over  the course of twelve nights, the Number Devil illustrates different mathematical ideas using things like coconuts and furry calculators. Along the way he also takes Robert to Number Paradise where he meets different mathematicians.

Alright, that's it for now. I hope you'll find these ideas helpful in your classroom or at home. If you have a great idea of your own for encouraging a love of math, please share!


  1. What a lovely collection! There's a great game that uses pentominoes, called Katamino. (I posted about it here: