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Mathematics: Measurement

red, white, blue, yellow nesting cups

Measurement is a basic math concept for time, quantity, size, weight, and volume. Children learn these properties naturally through play. Think about the concepts learned while filling and spilling, nesting and stacking. Fill the pail. The pail is full. Spill the contents of the pail. The pail is empty. Full or empty, the pail has weight and dimensions. The pail is its lightest when empty, heaviest when full. Between empty and full, t volume and  weight vary.

Variety of Materials

Children learn sizes, order, and spatial relations as they explore, stack, and nest boxes and cups in a variety of materials, each with its own properties. Consider graduated boxes. These may be constructed of cardboard, wood, or molded plastic. Both plastic and cardboard will be lighter than wooden. Experience with a variety of nesting and stacking toys broadens children’s understanding of the properties of different materials and the ways those materials predict how the toys can be used.

Size, Order, and Spatial Relations

 Nesting Cylinders and Nesting Boxes give children an opportunity to experience nesting and stacking different shapes. Exploring both invites an experiential understanding of similarities and differences. Similarities include three sizes of each shape. Measuring confirms the dimensions of each and shows their corresponding heights. Weighing each shows their corresponding weights. During play children discover differences as well. The small cylinder will fit inside the medium box while the small box stays on top of the medium cylinder.

Learning Words

Such play enhances emerging cognitive, language, and mathematics skills. Learning words to describe the relative positions of the boxes and cylinders develops spatial awareness. And sets the stage for geometry. Think of the concepts being explored: small, medium, and large. Smaller and larger, shorter and taller. Lighter and heavier. Inside and outside. On top of, in the middle, on the bottom.

Wooden toys are classic and durable, apt to withstand rigorous play and be handed down to the next generation. That said, sturdy plastic nesting and stacking toys invite sand and water play that would be ill advised with their wooden counterparts.


Children explore volume as they fill and spill the 10 round, graduated, plastic ambi Building Beakers. Pouring sand or water from a smaller into a larger beaker demonstrates differences in volume. The child readily discovers that what fills one beaker is too little or too much for another. Experimentation may lead to discovering how many of the smallest beakers are needed to fill the largest.

Developmental Age Matters

How far a child goes with such experimentation varies with developmental age and personal interest. The play and learning development of a one-year-old obviously differs from that of a three-year-old. Dropping the smallest beaker into a larger one, then dumping the smaller one out, over and over again, is appropriate beginning play. Learning simple concepts-empty and full, in and out, small and large-lays the foundation for more complex learning. Nesting and stacking require differentiating sizes and ordering the beakers to fit one inside the other or one atop the other. Repetition further solidifies concept acquisition and readies the child for taking the next step in learning mathematics.

PlayopolisToys – for the diverse needs of the citizens of play

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Learning Colors, Shapes, and Sizes Experientially

Learning to identify colors, shapes, and sizes begins at birth as adults introduce these concepts in casual, albeit one-way, conversation. Initially we comment on the color of objects in the environment, perhaps saying, as we dress our child to go outdoors, “Let’s put on your blue jacket.” Later when allowing the child a choice, we’re likely to use color in describing the choices available – blue jacket or red hoodie. Through spontaneous comments, we’re continually imparting information that our child takes in and processes.

Play also provides opportunities for us to give words to objects. If a toddler is engaged in a fill and spill activity with nesting and stacking cups, dropping the smallest into the largest, then dumping it out, we might comment on color or size as we observe the child at play. If the child is stacking one atop another, we can supply words to describe spatial relationships as well. “I see the little red one is on top of the bigger blue one.” Or conversely, the big yellow one is under the smaller white one.” This is an experiential approach to learning concepts and acquiring language. Learning from experience, through open-ended play and thoughtful commentary, is the most natural way of learning.

PlayopolisToys offers an array of engaging toddler toys that invite open-ended play that fosters learning and builds skills. We offer similar but different ways for toddlers to experience the benefits of playing with nesting and stacking toys. Each choice offers unique features that enhance the play experience.

Consider Stack & Fit, a set of five graduated, open-topfive graduated square stacking cups, square boxes with rounded-corners and raised rims on the bottoms. Stack & Fit is ideal for beginners. The limited number of cups makes play more accessible and manageable. Toddlers fill and spill, nest, stack, and knock down, over and over again, learning cause and effect and developing motor, cognitive, and language skills. Nested the cups resemble flower petals. Stacked a skyscraper. Raised rims facilitate successful stacking and keep cups from sliding. Graduated cups measure 3 1/2″, 3″,2 1/2″, 2″, and 1 1/2″ square. Adding sand and water enhances play as the child observes differences in volume and weight.


10 textured bottom, graduated stacking cups


Another choice, Ambi Building Beakers, expands play with 10 graduated, round cups, ranging in diameter from 1 1/2” to 4 1/4” and in height from 1 1/8” to 2 3/8”. With its primary + white beakers, the colors are familiar to toddlers. What makes Ambi Building Beakers most distinctive are the unique-to-each-beaker raised designs on the bottoms. Press the beakers in sand or into modeling dough or clay to create imprints. These patterns develop tactile discrimination and enhance the play of tactile learners and the blind and visually impaired. Two pinholes in the bottom of each beaker invite water play.

 PlayopolisToys – for the diverse needs of the citizens of play