Sparking Joy through Representing in Math
This month, we’re exploring how math connects to our everyday lives with a focus on representing our thinking and making math visible. When children use drawings, models, numbers, and words to show their thinking, they deepen their understanding and build confidence as mathematicians.
By encouraging children to explain their reasoning, try different strategies, and visualize their ideas, we help them see math as a creative, meaningful, and joyful part of everyday life
Connecting it Back to the Classroom
In Ontario’s math curriculum, one of the key Mathematical Process expectations is “representing”—showing our thinking in different ways to help us understand and communicate mathematical ideas. In classrooms, students might represent their thinking using drawings, diagrams, models, number lines, graphs, equations, or words. These different forms of representation help make their thinking visible, support deeper understanding, and allow others to follow and respond to their ideas.
When students represent their thinking, they learn that there’s more than one way to solve a problem and build confidence in sharing their strategies. It also helps them make meaningful connections between math concepts. At home, you can support this by asking, “Can you show me how you figured that out?” or “Can you draw or model it a different way?” Representing isn’t just about the answer—it’s about thinking clearly and communicating ideas with understanding.
Engaging in Representations at Home
Encouraging different representations at home doesn’t have to involve fancy materials—everyday items and simple strategies can go a long way. Here are some easy and meaningful ways you can support math representation at home:
Encourage Drawing and Sketching: Invite students to draw pictures, number lines, or bar models to explain their thinking when solving a math problem. Keep scrap paper, a notebook, or a whiteboard handy to make it routine.
Use Household Items as Math Tools: Items like buttons, pasta, coins, socks, rocks, or paper can be used for grouping, counting, comparing, building arrays, fair sharing or patterns. Folding paper is a great way to model fractions. These tools help students represent their thinking concretely before moving to abstract strategies.
Talk About More Than the Answer: Ask open-ended questions like, “How do you know?”, “Can you show it a different way?” “Can you explain your thinking using words or pictures?” These prompts invite children to make their thinking visible and consider other strategies.
Try Journaling or Math Chats: Have students write or talk about how they solved a problem—this could be a few sentences, a picture, or a step-by-step list. Representing in words helps reinforce their understanding and gives insight into their process.
By inviting children to show, explain, and reflect, families help build the habit of thinking deeply about math—not just getting to an answer. These small moments at home make a big impact on mathematical confidence and understanding.
A Fantastic Resource for Families : Polypad
Digital tools like Polypad ( https://polypad.amplify.com/p#numbers) offer powerful ways for students to make their math thinking visual at home. With virtual manipulatives like number tiles, fraction bars, algebra tiles, and geometric tools, students can explore math concepts, test out ideas, and represent their thinking in interactive ways. Using digital tools encourages creativity, flexibility, and experimentation—helping students see patterns, connections, and relationships they might not notice with pencil and paper alone. Best of all, tools like Polypad are free and accessible online, making it easy for families to support rich, visual math learning from home.
Take some time this month to encourage students to represent their thinking and make math visual, we can empower them to see math as a creative, meaningful process—and help them build the confidence to share, explore, and grow as mathematicians!