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Designing for Math Play

 Shorter version of this article is published on Creative Gaga Magazine’s blog


From the wooden toys by 18th century German educator Friedrich Fröbel (Frobel, 1837) to the life-size foam shapes by David Rockwell’s The Imagination Playground (Rockwell, 2008), children have been offered many toys and games to help explore the world of Mathematics by sorting, grouping, counting, arranging or aligning objects in different ways. Preschools and Kindergarten where Math is introduced for the first time in a formal learning environment, often rely on these wooden toys, puzzles and shapes to help understand how numbers or shapes are constructed and deconstructed, count on fingers, practice writing numbers and operators (addition, subtraction, multiplication and division) etc. 

This article proposes 4 novel ways to create learning resources using found (paper/wood/cardboard/fabric) or fabricated materials (3d printing, printing). This will hopefully offer ideas to designers/educators to create learning resources tailored to the needs  or skill levels of their students. The first project is a Textile book, with each page showcasing a different mathematical tactile activity using imaginative characters, the second project is a 3d printed puzzle to help learn fractions, the third is a board game that helps learn fractions and shape formations, and the last project is an Object Collection tabletop game to help learn sorting, grouping and counting. 

Theoretical Background

There are two theories that guide all four projects presented in this article: Constructionism (Papert, 1980) which suggests that children learn by creating artefacts based on mental models, which help them understand how things work, and Spiral Curriculum (Bruner, 1960) which suggests that children can revisit complex topics as their understanding increases, or that any learning content can be made more accessible if structured and presented well according to the child’s needs. All activities presented here were designed to be more adaptive to the child, providing opportunities of free play, easy play or complex play - depending on their level of preparedness to explore the content presented. To explain the Spiral aspect, the projects mention activities that are Level 1 (easy or self exploratory) or Level 2 (complex, require scaffolding). 

Project 1. Woodland Explorer, A Textile Play Book

The idea behind this project came from designing educational playbooks for preschool aged children in rural India, who did not have access to formal schools. Cotton textile industry in India is very strong and often huge amounts of scraps of fabric from Textile Mills is disposed off. Many rural women would sew essentials out of these scrap fabrics. The goal of this project was to show how abundant material from the community (in this case, textile) can be used to design playful textile books, that can not only spark imagination but also help learn foundations of Math. Each page is designed to offer not only free play, but opportunities to learn math in an informal way. This may be particularly helpful for young children who cannot read, or to children who are developmentally challenged and could use a more open-ended learning material. The broader concepts covered in the book are counting, fractions, shape formation, silhouette matching, sensory-tactile counting (counting by feeling and moving objects), sorting according to shape/size/color, reading time and visual fractions, and strategy (such as tic tac toe, and puzzles). 

Figure 1. Textile Pages exploring fractions and sorting

Primary learning goal - Fractions and Sorting 

Secondary learning goal - fine motor skills, sensory play, opportunities for storytelling

The first two pages show “inside view” of the Hedgehog’s home. Child can rearrange the cheese slices in the form of a circle (level 1) and can also arrange them according to the number of holes in the slice (arrange from 1 hole to six holes, Level 2). This makes the book more adaptive to the learning level of the child. Tomatoes, mushrooms and peppers slices can be placed on the pizza to learn about patterns, sorting and counting. The bed flap and fridge opening is to practice fine motor skills. There are also opportunities of building stories around the life of the hedgehog. 

Figure 2. Pages exploring counting and sorting

Primary learning goal : Counting and sorting

Secondary learning goal : Adding, subtracting, patterns, fine motor skills, sensory play, knowledge about nature.

These pages allow the child to “pluck” fruits and collect them in the basket. The fruits can be used to count, sort, arrange, build patterns, add or subtract. There is plenty of opportunity to build a story with the fox character. It is also possible to bring over the hedgehog character from previous page to play with the fox. The vegetables shown on this page also help children learn which ones are grown in the ground (carrots, pumpkins) and which ones are on the tree (apples and pears). 

Figure 3. Pages exploring time and counting

Primary learning goal : Telling time, sequencing numbers from 1-12, silhouette matching

Secondary learning goal : fractions, fine motor skills

The goal of these pages is to help the child learn reading time from an analog clock. The numbers are removable with a velcro backing and can be used to teach the child to count from 1 to 12 and arrange in sequence. The fox’s face has a magnet hidden inside, and can be flipped from an “awake” face to a “Sleeping” face, helping the child understand the time difference between morning and night. Again following the theory of ‘Spiral Curriculum’ there is opportunity for the child to start with just fine motor skills and take the numbers out and put them back, or they can choose to arrange them in sequence, move the clock hands to tell time, or learn to tell time in AM and PM (more advanced). The page on the right side allows the child to match leaf silhouettes (level 1) or also learn the names of each tree leaves (ash, beech, maple, aspen, poplar - level 2). This book can be both self exploratory (level 1) or instructive (level 2, requires scaffolding).

Project 2. Cookie Eater, 3d printed Fractions puzzle

Figure 4. Cookie Eater, A fractions puzzle

The project was designed for a Kindergarten classroom in Central PA, specifically as a teaching aid for the module on fractions. The module was scheduled around Christmas, and hence the theme of a very hungry Gingerbread man emerged, who wanted to eat cookies - but he must be fed one piece at a time. The primary learning goal of this puzzle is to help children learn how simpler shapes combine to form more complex shapes, and the concept of visually understanding half, one fourths, three quarters, and whole. A secondary aim is to allow children to freely play with the puzzle pieces, combine shapes like Tangrams, stack or build structures with them, in order to understand geometry in a more exploratory way. The breakdown of learning opportunities of this puzzle are :

  1. Simple Shape formations : Constructing and Deconstructing Shapes
    1. Diamond = 2 triangles
    2. Square = 4 smaller squares
    3. Square = 2 rectangles
    4. Square = 4 triangles
    5. Circle = 4 pies
    6. Circle = 2 semi circles
    7. Rectangle could be = 2 Squares
    8. Rectangle = 4 rectangles
  2. Complex Shape formations : Constructing and Deconstructing Shapes
    1. Heart = 2 semi-circles + 2 triangles
    2. Hexagon = 6 triangles (available separately to fit in the same socket)
    3. Hexagon = 2 squares + 4 triangles
  3. Fractions
    1. ¼ + ¼ = ½
    2. ¼ + ½ = ¾ 
    3. ¼ + ¼ + ¼ = ¾ 
    4. ½ + ½ = 1
    5. ¼ + ¾ = 1
    6. ¼ + ¼ + ¼ + ¼ = 1
  4. Tangrams - Children can choose to combine puzzle pieces to make their own shapes
  5. Structure Building - Children can stack the puzzle pieces to build stuctures
  6. Counting - Children can count the puzzle pieces (up to 45)
  7. Sorting - can sort by shape and size, possible to sort by color if 3d printed in different colors
  8. Comparisons - large vs small, wide vs narrow, tall vs short, sharp vs smooth etc
  9. Free Play - building stories with the Gingerbread man and cookies, stacking, sorting etc

Project 3. Bricksters, Board game to practice addition and subtraction

Figure 5. Bricksters, A Board Game for practicing addition and subtraction

This project was also designed for a Kindergarten classroom in Central PA, specifically for a module on constructing and deconstructing single digit numbers. The module was scheduled around Halloween, so the board game was designed using images of Halloween characters, tricks and treats. Each player gets a stack of 5 lego bricks (the top brick of this stack has a face and each stack is called a “Brickster”). Players place their Brickster at the starting point and roll the dice. Depending on the number on the dice, they move their stack on the board and either add 1 or 0, or subtract 1 or 0 from their stack of bricks. When all players reach the end, the player with the tallest tower wins. This game helps children practice single digit addition and subtraction, and also helps them count and compare values visually (based on how long the lego tower is). Many variations of this LEGO based math board games are available online to download and print, making it accessible to parents and educators who want a playful alternative to practice addition and subtraction.It is also easy to draw larger numbers (2-3 digit) to make the game more challenging for children who are strong at adding single digits. For larger numbers, lego bricks can be replaced with other units such as stickers, leaves, marbles, pebbles etc which can be easily available in large quantities. 

Project 4. Turtle Pom, Tabletop game to practice counting, sorting and grouping

Figure 6. Turtle Pom, A sorting and Grouping game

This project was designed for a Kindergarten-aged child to practice counting, sorting and grouping Pom-Poms in 4 glittery turtle-shaped coasters. For practitioners willing to try out this idea, the turtle can be replaced with any form of container, and the pom-poms can be replaced with any group of small objects. Children can be asked to group pom-poms by color, number or size. It can also help introduce the concept of division by 2, 3 or 4 (since there are 4 turtles). More containers can be added to show division of pom-poms by a larger number.


The 4 projects shared in this article are not only templates to build other DIY projects off of, but more importantly they offer inspiration to customize Math Play for young learners based on their interests and needs, or based on the school curriculum. Some Guidelines for designing original Math Play Materials are :

  1. Spiral Curriculum Design : Design Math Play  toys for the possibility of adapting to different levels of students. Can they revisit the toy with higher knowledge and still be challenged and learn more? Design in Levels - Level 1 for self exploratory play, Level 2 for scaffolded/guided play
  2. Found vs Fabricated Materials : Look for free, abundant, safe materials to design toys in economically challenged learning environments : fabric scraps, cardboard, paper, leaves, twigs etc. Where precision of design is important, look for fabrication tools such as 3d printing, laser cutting, CNC routing etc
  3. Usability of Toys : Think about safety, functionality, storage and maintenance. 
  4. Economics of Toys : Think about cost, quantity and durability
  5. Appeal : Think of the desired ‘appeal’ - who are we designing for? Baby toys may benefit from bright colors, imaginary characters and rounded edges, whereas older children can comprehend more complex/close to real world designs. 
  6. Engagement : Design Math play toys for engagement - interest, relevance, “low floor, high ceiling” (Papert, 1980)


Clements, Douglas H., and Julie Sarama. 2004. Building Blocks for early childhood mathematics. Early Childhood Research Quarterly 19:181–89. 

Clements, Douglas H., and Julie Sarama. 2005. Math play: How young children approach math. Early Childhood Today 19:50–57.