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Mathematics: Geometry

Shapes and the arrangement of relative parts within a whole are the subject of geometry. Consider the construction of spider webs. The arrangement of petals forming a rose. Study the facade of a cathedral. The angles and the fitting together of its architectural elements. Or all the parts in myriad shapes that combine to make an automobile. Both the natural and the human-made environments are studies in shapes, angles, and intersections.

Best Shape Sorter Toys

Through observation and experience children learn about shapes and parts. First come basic shapes: round, square, triangular. Among early childhood play experiences are sorting and matching of shapes using a shape sorter. Simple ones are best for beginners, and Ambi Toys Lock A Block is best of class. High contrast between the bright white top and the color matched raised rims outlining each opening facilitates “hitting the target.” Equally importantly, its three dimensional shapes drop easily into place.

As shape discrimination, eye-hand coordination, and fine motor skills improve, children are ready for the next shape learning toys. Fitting two-dimensional shapes into corresponding holes. Sound Puzzle Box is a popular choice that rewards proper placement with distinct auditory responses.

Basic Shapes Puzzles 

Puzzles are all about shape. Again starting simple is key. Chunky shapes facilitate placement. Shapes that fit only in their proper places make a truly self-correcting learning experience. Left to right orientation models the direction of reading and writing. Children are ready to identify and match more unusual shapes only after they easily recognize basic shapes.

Interlocking Pieces Puzzles

After learning individual shapes through puzzles, children move on to explore the arrangement of shapes as parts of a whole. Start simple. The more pieces and the smaller the pieces, the more challenging a puzzle is. Wooden puzzles with thick pieces are easier for small hands to manipulate than thin cardboard ones.

A single layer, wooden 8-piece fish shaped puzzle for toddlers, Rainbow Fish, invites exploration of color and shapes and the way parts fit together to make a whole. With only one way to complete the puzzle, the child has to sort out and make sense of the pieces. Then work out how the parts go together to create the whole, a sometimes frustrating experience that benefits from adult encouragement.

Layered Puzzles 

Layered puzzles introduce perspective and offer graduated challenges. As always, start simple and progress gradually. More layers offer more challenge; however, the number of pieces is a more accurate indicator of difficulty.

Mathematical Concepts Puzzles 

Although most puzzles go together in one and only one way, others offer options, and these literally open doors to understanding of mathematics.

The Binomial square wood puzzle introduces mathematical concepts through observation and experience. Children develop proportional reasoning, area concepts, and place value understanding when they discover four small squares cover the same area as the rectangle and four rectangles the same as one large square. And that’s only the beginning of the possibilities.

Power of Two Puzzle from Red Hen Toys encourages experiential learning of important mathematical ideas from fraction equivalents, fraction multiplication with a common factor of 1:2, proportional reasoning, and area. The 10 puzzle is cut into one-half, one-fourth, one-eighth, one-sixteenth up to 1/128th. Clearly challenging, the beauty of Power of Two lies in the multiple ways the pieces can fit together and the arrangement of relative fractions.

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Artistry in Alphabet Blocks

Classic Early Childhood Play

What early childhood toy is more classic than wooden alphabet blocks? Long before they are ready to learn the letters and numbers on the blocks, children engage in block play. They “fill and spill”, dropping blocks into a container, then dumping them out, again and again. They arrange blocks into a row. Progress to stacking and knocking down. Incorporate blocks into their imaginative play.

Progressive Skill Building

Their play builds fine motor skills from grasp and release to eye-hand coordination and controlled placement required for stacking. Some alphabet blocks feature simple pictures that develop vocabulary when an adult or older child supply the name of the objects. Gradually the child will associate the word with the object and begin to identify the objects by name. Only later do children begin recognizing specific letters and numerals and later still that they combine letters to make words.
Wooden alphabet blocks come in many forms, from smooth cubes with printed letters to cubes with embossed letters on the ends and printed ones on the sides. On some the letters are carved. Blocks handmade from natural hardwood stand out. My favorite are made in the United States of sustainably harvested native hardwoods.

Alphabet Blocks in Multiple Languages

Uncle Goose in Grand Rapids, Michigan, hand makes alphabet blocks in 23 languages, from the most common to the esoteric. These 1 3/4 inch basswood cubes are true artisan blocks designed by creative artists and made by master craftspeople. Four smooth sides with vibrant graphic designs reflecting the culture of the language and two with deeply debossed letters make every set an invitation to cultural awareness.

Upper and Lower Case 

English alphabet blocks are available in both upper case and lower case sets. Children may learn lower case letters more quickly than upper case because the ascenders, as in b, d, h, and t, and descenders, as in g, j, p, q, and y, make the letters easier to identify. Capital letters, by contrast, lack such visual distinctiveness. While playing with alphabet blocks in both cases, children gradually develop an interest in identifying the letters, matching upper and lower case, arranging blocks in alphabetical order, and beginning to spell their names and other simple words.

Alphabet Blocks for Inclusion

Committed to inclusive play, Uncle Goose also offers alphabet and number blocks in Braille and Nemeth math code for the blind and alphabet blocks in ASL, American Sign Language. Indispensable to children who will be learning Braille, the blocks also introduce Braille to the sighted, making children more aware and socially competent. The same applies to children learning ASL. For hearing children, learning to sign the alphabet reenforces competency and bridges gaps between the hearing and the deaf.

 Visually Appealing

Uncle Goose alphabet blocks are visually appealing, whether artfully displayed on a table or waiting in a basket for someone to come along and explore the possibilities. Designed for children three years old and up, these exquisite blocks are made for play. Beautiful alphabet blocks encourage children and adults alike to play, arranging blocks, matching letters, spelling words, whatever brings joy. The time spent playing together fosters attachments and makes fond memories.
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Play and Learn Dough

Nesting, stacking, and shape sorting contribute to a child’s understanding of attributes, those characteristics that define objects, from color, size, and shape to auditory, tactile, and visual. These play experiences develop eye-hand coordination, fine motor, cognitive, and language skills. So does play dough. And the play is open-ended and creative.

little boy and play dough

Working with play dough strengthens hand muscles and develops fine motor skills. Consider all the ways a child can manipulate dough using only her hands: forming a ball or a brick, rolling into a rope, smooshing, squeezing, squishing and squooshing, flattening, patting, poking, pounding, and tearing.

Tools introduce more ways to play and further develop fine motor skills. Consider rolling pins, both smooth and patterned, plastic knives, pizza cutters, and scissors, garlic presses, cookie cutters and presses. Each tool works differently, engaging and strengthening different hand muscles. Incorporating new ways to play enhances cognitive and language development.

Adding popsicle sticks, plastic straws, golf tees and pegs, found objects from a nature walk, from acorn tops and small pine cones to leaves and twigs, encourages creative explorations. Seashells, pebbles, both natural and glass ones, and bottle caps press easily into dough and invite arranging into patterns or outlines of familiar objects. Provide the provocation, step back and watch. You’ll be amazed.

One of the joys of play dough is its centering effect. Simply manipulating a ball of dough relieves stress, calming the mind and soothing the body. Play dough is beneficial to all ages. Keeping a supply on hand means being able to quickly respond to meltdowns. Kneading dough aids self regulation and focus.

Making your own play dough is easy and allows for variations in color, scent, and texture. “Variety is the spice of life,” as the saying goes, and children benefit from similar but different experiences.

You’ll find a world of choices, including gluten free, by searching recipes for making play dough, but here’s the one I learned as a parent at Pacific Oaks Children’s School decades ago. The cream of tartar is the secret to its longevity. Enjoy!

Cooked Play Dough

1     cup flour

1/2  cup salt

1     cup water

Add food coloring to water.

For more vivid colors and scent, add Kool Aid.

1     Tablespoon vegetable oil

2     teaspoons cream of tartar

Mix ingredients and heat in saucepan until ball forms.

Stored in an airtight container this dough lasts months.

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Tips for Selecting Shape Sorters

Remember the expression “a square peg in a round hole”? Immediately we understand what’s being said; someone is a misfit, an individual who does not fit within a specific group. The observation creates a visual impression. We see in our mind’s eye the misfit between a square peg and a round hole. Perhaps because as toddlers we played with one or more shape sorters and learned to “post” shapes into their corresponding spaces.

Shape sorters take many forms, and what works well for one child might not be the best choice for another. When considering shape sorters, remember that toddlers are just beginning to distinguish shapes. Limit shapes to basic ones: circle, square, triangle. The goal is to balance challenge with the likelihood of success. Acquiring skills is an ongoing process that moves forward with experience, repetition, and incremental success.

Shape sorters develop eye-hand coordination, fine motor, cognitive, and language skills. Rewarding matching with a distinctive sound also develops auditory awareness and discrimination. Value-added features expand play possibilities.

Children need to feel competent and confident of their skills before moving on to the next level. If a toy is too complex, the child will avoid it, and we will need to “walk backwards in our minds” to identify the missing link between where she is now and the activity we’ve offered.

With discriminating shapes, stepping back means assessing multiple skills. Does she easily grasp and release? Does she relish every opportunity to” fill and spill”? Are her eye-hand coordination and fine motor skills well developed enough for her to fit a peg in a hole? These activities come before posting shapes. The Classic Pop Up Toy is an engaging, traditional wooden toy featuring four peg figures that pop up and down on concealed springs as the child presses one after another. The removable figures can be color matched to stripes on the front of the box but that’s optional. The focus is on developing eye-hand coordination and fine motor skills required for successful posting. Matching colors and shapes are a next step.

Ambi Lock A Block is my favorite shape sorter. Features that make Lock A Block most successful to Raised rims make sorting shapes easierbeginning sorters also make it a must for inclusive play. Unique attributes that support success in identifying and matching primary colors and basic shapes include high contrast between white top and color matched, raised rim openings and three dimensional shapes that drop into place more readily than shaped dowel pieces. Retrieving shapes by unlocking a door on the front of the block adds another dimension to play. The permanently attached key fits smoothly in the lock and turns easily. The lock clicks as the key turns, adding auditory input.


3-shapes sound emitting shape sorterA perennial favorite among the blind and visually impaired is Hooty-Hoo Shape Sound Sorter. Each shape makes a unique sound as it slides down its clear tube. The basic shapes – circle, square, and triangle – require more precise fitting than the three dimensional ones in Lock A Block, but the auditory response rewards the persistent. For children needing tactile re-enforcement, the openings for the shapes can be outlined with a Wikki Stix. When no longer needed, Wikki Stix peels off easily. Retrieve the shapes by turning Hooty-Hoo Shape Sound Sorter upside down.

When choosing a shape sorter, consider the child who will be playing with the toy. Once you’ve figured out the appropriate skill level, you’ll be able to choose confidently.

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Stack and Learn

Toddlers are scientists. They’re constantly researching “what happens if” and observing the outcome of their experiments. Thus the insistence upon repetition. Consistent results confirm their understanding of cause and effect. Through repetition the children develop a basic understanding of the relationship between actions and effects. The more open-ended and varied the play experiences, the better. Similar but different play experiences allow children to apply what they’ve learned and adapt it to new challenges.

Building beakers nest one inside the other or stack one atop another. The design of classic wooden stackers, on the other hand, limits play to stacking alone. The process of stacking also changes when the object becomes piling rings one atop another on a dowel.  A stacker with a uniform dowel allows placing rings in any order without regard to their relative size, as would be required by a cone shaped post. The child is free to focus on attaining competence at one task before tackling another. This reduces frustration and invites experimenting with different arrangements of the rings. As the child becomes aware of differences in size, she’ll likely stack from largest to smallest as well as experiment with turning the column upside down by arranging rings from smallest to largest, a feat more easily accomplished when stacking on a post than when piling larger building beakers atop smaller ones.

Holgate, an American toymaker, introduced Rocky Color Cone, a classic wooden stacker with a twist, in 1938. The trademarked feature, a rounded bottom, invites children to give Rocky a push and watch as it rocks, spins, and topples over, spilling the rings and setting the stage for another round of stacking and toppling. 

Once a single dowel stacker becomes “old hat,” consider double or triple versions with variations in the shapes and colors of the rings. A triple stacker with uniform dowels invites mixing and matching of rings in three distinctive shapes and color combinations. No longer focusing exclusively on developing motor skills, the preschooler is ready to turn her attention to new challenges.

Stacking develops eye-hand coordination, grasp and release, fine motor control, and spatial awareness. Identifying colors and shapes, recognizing relative sizes, and developing patterns that mix and match these attributes represents cognitive and language skills that come from interacting freely with similar but different toys along a developmental continuum. 

Learning is an incremental process. Understanding patterns is a prerequisite for learning to read. Words are letters arranged in specific patterns. P-L-A-Y is essential. We learn because we play.

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Cooperative Games

Now is the time to explore ways for everyone to enjoy spending time together while schools are closed for the holidays. Fewer hours of daylight and dropping temperatures force us indoors where we’re all too likely to retreat into the digital world. Engaging in a shared activity hones our social skills, enhances our sense of connectedness, and builds memories. What can be challenging is finding something that children and adults enjoy doing together.

Cooking and crafts are easily adaptable so that all ages can participate together. Putting together puzzles and playing a board game are other options. Cooperative games level the playing field as everyone works together to achieve a common goal. From preschoolers to centenarians, all players “put their heads together” to solve a problem and come away with positive feelings. Everyone wins. No one leaves the game gloating or sulking, negative feelings that would surely cast a dark cloud over winners, losers, and everyone else in the house.

Megana Hosein, a mother of four, is an enthusiastic proponent of the value of cooperative board games. She writes, “I love how cooperative board games encourage interacting and thinking with children in a way that is rarely explored in our busy lives. It always amazes me to hear what they have to say about solving dilemmas within the game, and how this taps into greater topics of conversation that might otherwise have gone unrealized. Furthermore, new friends can easily be made over the commonality and cooperation in a board game, both with peers and with adults. Truly a gentle way to introduce social rules and simultaneously focus the active child while drawing out the shy one.

Cooperative board games are an ideal alternative to digital devices. Social engagement and sharing a pleasurable, interactive activity benefit everyone, young and old alike. What better time than the holidays to make memories by playing games?

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More on Block Play


Kapla Blocks are all one size which invites a different approach to block play. Stacking layer upon layer requires balance, controlled movements, dexterity, and eye-hand coordination. Such building brings an awareness of mathematics and science, from numeracy to gravity.


Lightweight, uniform wooden planks invite letter formation and spelling and aid children in acquiring basic numeracy. More dyed planks would invite creating patterns and experimenting with color as a design element when building.


Tower building encourages taking measurements and requires focus, balance, and eye-hand coordination. Builders experiment with different building techniques, discovering the advantages and disadvantages of stacking vertically or horizontally. These high rise builders had to ponder the challenges of building above their heads and find a solution that was both safe for the builders and the tower.

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Block Play

Having written about the importance of limiting exposure to branded products because these come with a script that defines play and limits creativity, I want to show what happens when preschoolers engage in block play. This is classic, open-ended, self-directed play.

With a variety of wood blocks at their disposal, these preschoolers are free to choose what fits their vision. Being creative involves assessing a situation, considering what might be done with what’s available, formulating, and carrying out a plan. When working with others, the process becomes collaborative. Everyone needs to articulate ideas, collaborate, and cooperate to insure a successful outcome.

block play

Here the children have arranged hollow blocks and embellished their structure with unit blocks in different shapes and sizes. In the process, the children explored shape, size, and weight, directionality, spatial relationships, and balance. Some blocks are stacked horizontally, others vertically; open-sides are visible on some, solid sides on others. Working as a team, the children have faced challenges, solved problems, delighted in the process, and relished the outcome.


Unit blocks offer the widest variety of shapes and sizes and invite elaborate building and patterning. To create this structure, the children experimented with symmetry and balance as the crossed arches atop the center ones depend upon careful placement to remain in place. Successfully installing the top element required patience, well developed eye-hand coordination, and motor control.

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How Play Develops Autonomy

Ever think about how we acquire the skills we need for independent living? Or ponder how developing these skills begins with play? Manipulating toys develops fine motor skills, visual awareness, focus, tracking and eye-hand coordination. Independent dressing requires all these skills. Fastening and unfastening involve motor control and strength. Consider buttons, snaps, Velcro, and zippers. Shoes need lacing and tying, hook and loop fasteners not withstanding. Belts must be threaded through loops. And don’t forget buckles and bows.

From an infant grasping and scrunching Baby Paper to a pre-schooler building with blocks, manipulating latches on Peekaboo Lock Boxes, moving beads along a wire maze or fitting pieces of a puzzle together, cause and effect, cognition and visual skills, fingers and hands are steadily developing through play.

Drawing, printing, and reading involve visual tracking, controlling eye movements, eye-hand coordination, finger strength and muscle control. Manipulative toys teach cause and effect, introduce basic math and science, and encourage creativity and problem solving skills. Block play is fundamental, teaching order and prediction, encouraging open-ended play that leads to learning about gravity, weight, balance, proportion, symmetry and asymmetry and developing spatial awareness. Children plan, anticipate and solve problems as they translate ideas into structures. Honing these skills through play prepares children for taking on other challenges with confidence.

Manipulative play can be solitary or shared. Shared play can be intergenerational or with peers. Social interaction teaches valuable life lessons too – collaboration and cooperation, flexibility and compromise, boundary setting and mutual respect. Learning to communicate effectively and listen, comprehend and respond respectfully is essential.

Value play and those who play, as the benefits include skill development and autonomy. Engage them in developing and carrying out a plan to maintain their play space. While easier said than done, firmly and consistently insisting that kids maintain their space and take care of their toys teaches lessons in following instructions, taking responsibility and cooperation that ultimately leads to successful independent living.

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What Happens If…?

What happens if ? I do this, that, or something else altogether? That’s a question children answer through play. Building toys provide endless opportunities to learn cause and effect. Inviting both open-ended and structured play, these toys are essential early childhood skill builders. Cognitive, language, and fine motor skills develop through interacting with various materials in multiple ways. Eye-hand coordination and spatial awareness emerge as children take apart and put together, imagine and build. Block play, from stacking a column of cubes to laying out an elaborate city scape, requires devising a plan and solving problem as they arise and fosters creativity and imaginative play.

Squeezable, embossed, soft plastic blocks

Blocks are essential early childhood toys. Block play begins in infancy with soft, lightweight, easy to grasp blocks. One Two Squeeze Blocks, 10 blocks hand-sculpted on every side with raised images, provide maximum tactile exploration and language learning. Children squeeze and squeak, stack and knock down, experiencing “what happens if…,” and learning cause and effect. Each two-inch cube is an ideal size for tiny hands to grip. One Two Squeeze Blocks also float, adding another dimension to water play.



wooden blocks with plug and dowel connectors

Stack & Play, 18 wooden blocks in bright colors and varying shapes, expands play for toddlers. Stacking without unintentionally knocking off the previously stacked block is challenging. Stack & Play blocks, with their uniform dowel and plug connectors that fit together easily, reduce frustration and make block play more rewarding.



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