Our team continues to learn about supporting student’s spatial sense and this post includes 10 new spatial reasoning invitations with printables. Our previous post on spatial reasoning and thinking called, 10 Playful Spatial Reasoning Provocations, can be viewed here.
The Ontario Kindergarten Curriculum affirms the importance of expanding children’s spatial sense as it can in turn develop a broad range of mathematical and literacy skills.
“Spatial thinking skills and geometric reasoning play a critical role in the development of problem-solving skills, mathematical learning, and reading comprehension(Clements & Sarama, 2011; Wheatley, Brown, & Solano, 1994; Casey et al., 2008).
Under the section “Mathematics in an inquiry stance” the question is posed, “How do they reveal their thinking about shapes and spatial relationships?” The following invitations for learning offer opportunities for children to share and grow their spatial thinking. They support development in deepening student understanding of relationships between shapes, spatial language, perspective taking, composing and decomposing shapes, orienting, and symmetry.
Play Dough Pattern Block Shapes: Can you make a play dough picture with pattern blocks? Our early learners have enjoyed making an imprint with the pattern blocks in the play dough and challenging a partner to match the shapes. This is an opportunity to compose and match shapes.
“Taking Shape”, a research-based resource on spatial reasoning, explains spatial reasoning as, “being able to visualize, or picture things in the mind’s eye, and to mentally move, rotate, stretch, bend, or fold objects and shapes in space.”
Spatial Reasoning…
- is critical to mathematical thinking and achievement
- is malleable and can be improved through education and experience
- allows for multiple entry points
- is often revisited in play
Top View Build: Can you build a structure with a top view that looks like this? This invitation builds perspective taking understanding and area. Printable available here.
When children are given opportunities to explain their spatial thinking they can build their mathematical language and develop deeper key understandings. When conferencing with and documenting children’s learning we support their growth of using spatial language like positional language(ie., on top, under, in front, behind, outside, inside), spatial dimensions(i.e., height, depth, length, wide, narrow), spatial features(i.e., tall, short, fat, parallel, edge, corner), names of shapes, and spatial transformations(i.e., rotate, flip, slide, turn). “Taking Shape” speaks to the importance of gestures are as well, as they too can demonstrate conceptual understandings. Some of the math learning experiences offered in this post are ideas from “Taking Shape” set as playful provocations. I highly recommend “Taking Shape” to early years teams who wish to deepen their understanding of spatial thinking and reasoning so that they can help build the spatial minds of their early learners. It gives research-based pedagogy on teaching and learning in spatial reasoning including engaging lessons, invitations, guided questions, and assessment supports to help move student learning forward.
Can you fill an area with different heights? This is another invitation that supports perspective taking as well as area. Children are invited to visualize possibilities for their creations by attending to different view points(i.e., top, side, front, and back views). Children are also invited to draw these different perspectives or view points.
“Visualize, identify locations, and recognize and represent shapes from different perspectives.” Taking Shape”
Mystery Build: Can you tell a friend how to build your structure and they try without seeing? Player 1 creates a design behind the barrier(we used a clipboard with supporting blocks), explains to player 2 how to build it, and player 2 builds it. Lastly, the reveal. Take away the barrier and a symmetrical design should be presented. Printable available here.
This invitation lends itself to the expectation 17.2 in the Ontario Kindergarten Curriculum document.
17.2 communicate an understanding of basic spatial relationships (e.g., use terms such as “above/below”, “in/out”, “forward/backward”; use visualization, perspective, and movements [flips/reflections, slides/translations, and turns/ rotations]) in their conversations and play, in their predictions and visualizations, and during transitions and routines
Find My Mistake: Close your eyes. What did I change? Children love finding mistakes, what’s different, or what doesn’t belong, and this spatial thinking experience supports symmetry, communicating spatial relationships, and composing shapes. Printable available here.
See It, Cover It, Build It: Make a small shape picture for a friend. See it, cover it, and see if they can build it. Printable available here. This spatial invitation is adapted from “Taking Shape” and invites children to remember the orienteering and composition of a shape. Start small and increase difficulty. With our littles we call the first attempt level 1 and increase in difficulty as the children show success.
There are many pattern templates available online like the one from Make Learning Fun. Our team didn’t have tangrams, but not to worry as they are simple to make out of fabric covered foam from the Dollar Store. Doug Clement’s Trajectories share how children can be shape composers. The picture on the right is without outlines around each shape.
Cork cut into various shapes invites children to use different materials to compose different shapes. Children will use spatial thinking to flip, rotate, and/or reflect shapes to ensure the pieces fit inside the shapes.
Free Play spatial thinking experiences are also very important for children. They can be child-led creative or imitative play. “Taking Shape” notes the importance of offering different shapes to be made accessible during free play to further develop their spatial awareness.
Roll & Cover: You have 2 dice. 1 cube with drawn shapes on it. Roll both dice. The dice tells you what shape to collect and the number dice tells you how many. First player to cover their hexagon wins. Printable available here. This math invitation is adapted from Passionately Curious Educators who shared this on their website at Challenging Young Learners: Games in Early Mathematics and in a workshop that I attended and gained so much from. Check out their website where you can sign up for various webinars.
Symmetry provides opportunity for children to flip, slide, and turn shapes so that they can match reflections. “Symmetry is an area of geometry in which children possess informal knowledge long before they encounter the topic in formal schooling; research with infants and young children shows they are able to recognize symmetry.” (S. Eberle, 2014) and will often gravitate towards symmetryin their free play, such as when they build with blocks (Sarama & Clements, 2009)
Key Understandings
- Uses spatial language
- Uses gestures
- Visualizes
- Composes and decomposes shapes
- Orients objects
- Compares and identifies relationships between shapes
- Accounts for Perspective
- Names shapes
Further Reading
“Taking Shape” by Dr. Cathy Bruce, Joan Moss, Ben Caswell, Tara Flynn, and Zachary Hawes
Learning Trajectories for Primary Grades Mathematics
Ontario Kindergarten Curriculum
Paying Attention to Spatial Reasoning
Why Spatial Reasoning is Crucial for Early Math Education
10 Playful Spatial Reasoning Provocations
inspired by play 
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