Inviting Children to Create their own Math Games

Children learn best from experiences and when given the opportunity to create their own math games children can become meaning-makers and construct their own knowledge and understanding. They become a partner in learning where their ideas are valued and tested.

We value setting out math provocations that have an intentional focus: A place where children can refine specific skills in a prescribed way. However, when viewing the child as competent and capable we also value opportunities for children to create their own math games with open-ended materials. Often children use math learning they’ve acquired from explicit instruction in small groups and apply and develop these skills in math games they’ve created. Adding intentional loose parts and math materials provide opportunities for rich mathematical learning where children can take their learning in multiple directions.

The Ontario Early Years Policy Framework presents a view of the child as competent, curious, and capable of complex thinking. If we embrace this view, and see children as able communicators, collaborators and meaning-makers who are forming relationships every day with people and materials, who are capable of empathy, whimsy, sensitivity and joy, how would the classroom reflect this?  (Ontario Ministry of Education, 2013, p. 12).

The following photos show some invitations to create math learning with open-ended materials. We often use placemats, mirrors, cork boards, cutting boards, and dry-erase boards to define a play space. We set out intentional materials and combine them in different ways to provoke mathematical thinking. Below each photo is a description of ways we’ve observed children use the materials to construct their knowledge.

create-math-games-4Children have used this provocations to tell math stories, order numbers, and count using 1-1 correspondence.

create-math-games-5Children have used this provocation with Tap the Magic Tree to tell counting stories, subitize, order numbers, and count forwards.

create-math-games-6We’ve observed children representing numbers, ordering numbers, identify more than/less than with these natural materials.

create-math-games-2Children have used this movable number line to order numbers forwards and backwards, think about 1 more/1 less, 2 more/2 less, represent numbers with 10 frames/rekenrek/subtilizing dots, count by 2’s, and use the subitizing tiles to add.

create-math-post-7With cuisenaire rods we’ve observed children think about numbers to five, create designs, create colour patterns, create number patterns, and 1 more.

create-math-games-3This child created a game where she thought about 2 more. She used a counter to move up and down the number path. This 10 frame was made with tongue depressors to make an extra large 10 frame.


Open-Ended Questions

The following are some open-ended questions that can provoke thinking while at math play:

  • How do you know?
  • What other math does this make you think of?
  • When/where do you use this math at home? school? other?
  • Have you seen this before (shapes, pattern, etc)?
  • How is this like something you’ve done before?
  • What strategy did you use?
  • What was the hardest part about…?
  • What math words did you use or learn?
  • What were the steps involved?
  • How did you solve the problem?
  • How would you explain to a small child that doesn’t know this?
  • Draw a picture to show how you solved the problem.
  • How did you show your thinking?
  • How else could you have?
  • How else might you solve the problem?
  • How are these____ the same?
  • How are they different?
  • About how long?(many tall, wide, heavy, big, more, less, etc)
  • What would you do if?
  • What else could you have done?
  • If I do this… what will happen?
  • Is there any way you could….?
  • Why did you?
  • How did you?
  • What math words help you understand/explain what you did?


Documenting Observations & Next Steps: Assessment

The following link is to math assessments our teams uses to document math goals and learning. Scroll down near the end of the post to view.


How have children used open-ended materials to create math games in your learning environment?


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