Mathematics Through Play

We find that play lends itself perfectly to mathematics instruction. When students are fully engaged in play, their interest is high and their stress levels are low. They are highly receptive to learning, making it easy to build on what they already know and engage them in mathematical thinking through thoughtful questioning and problem-solving.

The Play Interest or Inquiry as a Starting Point

When planning for mathematics instruction, we typically begin by identifying one big mathematical idea or one strand that naturally connects to the overall play interest or inquiry taking place in our classroom.

For example, during an inquiry into plants, Measurement became a natural focus as we observed and documented growth. In addition to measuring plants, we measured objects and people throughout the classroom. We also integrated literature into our mathematics learning by reading Jack and the Beanstalk. Inspired by the story, we traced and measured our school’s tallest teacher in a variety of ways.

From there, we extended our learning from linear measurement to area. We investigated how many beans could fit into our own hands, compared our results with classmates, and even compared them to the hands of our “Jack and the Beanstalk” teacher.

Mathematics Strands

Once we have identified our primary mathematics strand (or strands), we intentionally plan centre experiences that provide meaningful opportunities for children to explore and extend their learning in these areas.

At the same time, mathematics is such an integral part of everyday life that opportunities to explore every strand naturally emerge through play. Just imagine trying not to address Number Sense—it is part of who we are as humans.

The mathematics strands outlined in the Ontario curriculum are:

• Number Sense and Numeration
• Measurement
• Geometry and Spatial Sense
• Patterning
• Data Management and Probability

Opportunities to explore shapes, measure objects, sort materials, create patterns, gather and record data, and investigate number concepts are present wherever children are engaged in meaningful play.

We choose one primary strand to intentionally target through play and planned instruction so that we can ensure all children receive instruction and assessment across every strand. While children are engaged in play, we intentionally observe and extend learning related to our primary strand while also capitalizing on the many mathematical opportunities that naturally arise.

Mathematical Processes

While focusing on the mathematics strands, we are also intentionally developing children’s mathematical processes.

The Ontario curriculum identifies the following mathematical processes:

• Problem Solving
• Reasoning and Proving
• Reflecting
• Selecting Tools and Strategies
• Connecting
• Representing
• Communicating

Although we may choose one process to highlight during a particular inquiry or learning cycle, these processes are deeply interconnected and rarely occur in isolation.

For more information about the mathematical processes and mathematics strands in Ontario, consult the mathematics section of the Full-Day Early Learning–Kindergarten Program Draft Document or refer to kindergarten_english_june3.pdf.

Indigenous Lead

When a strong Indigenous and multicultural interest emerged in our classroom, we selected Patterning as our primary mathematical focus. Having recently explored Measurement, we continued to reinforce that learning while also incorporating Number Sense.

Our targeted mathematical processes were Reasoning and Proving and Reflecting, while remaining responsive to the many other processes that naturally emerged throughout children’s play.

Fine Motor Centre

At the Fine Motor Centre, we provided lacing beads, snap-on beads, linking chains, and books to inspire children to create necklaces, belts, bracelets, and other imaginative designs. As children explored patterning, number sense, and measurement, they also strengthened their fine motor skills.

Later, we introduced three-dimensional lacing shapes to extend learning about 3-D geometric solids.

Interest Table

The Interest Table featured drums and bells of various sizes for exploration, encouraging children to investigate musical patterns while comparing size, sound, and quantity.

Creative Area

The Creative Area always offers a variety of open-ended materials for exploration. During this inquiry, we added materials for creations such as feathers, beads and items from nature for the cildren to explore and create with.

Dramatic Play Centre

The Dramatic Play Centre was transformed into a home environment, complete with a tent and a collection of natural and found materials.

This environment created countless opportunities for counting, one-to-one correspondence, problem-solving, and rich mathematical language.

Mathematical Conversations

Across all learning centres, we used purposeful questioning to deepen children’s understanding of patterning while drawing out mathematical language related to patterning, number sense, and measurement.

Some of our questions included:

• Which one is longer or shorter?
• How can we find out?
• How many beads did you use?
• How many more beads do you have than…?
• Are these the same size?
• What might come next in this pattern?
• Could you use these beads to create a different pattern?
• How did you know what came next?
• Is there another way you could…?

Not every learning centre during a particular week will naturally lend itself to a direct mathematical focus. However, there are always opportunities to encourage mathematical language and problem-solving throughout children’s play.

The Block Centre

The Block Centre is always an ideal place to foster mathematical thinking. It naturally encourages vocabulary such as:

• more
• less
• same
• taller
• shorter
• wider
• narrower
• bigger
• smaller
• how many?

while also providing countless opportunities for problem-solving.

During this inquiry, we added Big Blocks, stones, feathers, sticks, and a large collection of plastic animals.

We have found that when natural materials are combined with Big Blocks, children frequently attempt to balance the blocks on the natural objects. These experiences create authentic opportunities to explore balance, stability, measurement, comparison, and problem-solving.

Math Trajectories Activities

After working with students in small instructional groups, we often make available several of the activities from Learning and Teaching Early Math: The Learning Trajectories Approach by Douglas H. Clements and Julie Sarama.

For additional information, please see our Math – Planned Instruction section.

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