Spatial Sense and Visualization in Mathematics in the Junior Grades

Division(s): Junior
Level(s): Grade 4, Grade 5, Grade 6
Keyword(s): spatial ,, visual

Exploring spatial visual sense in the junior grades. When children are able to visually represent their understanding, comprehension and problem-solving skills improve.

Teachers met to co-plan, co-teachand co-debrief spatial visual activities across the junior grades. We  gathered data (observational, conversational, product-based) to inform the development of spatial sense in students’ mathematical understanding. We also reflected upon and observed how visual and spatial sense can inform our daily assessment, and how students use visual models to build understanding.

Team Members

  • Sharon Ethier

    District School Board of Niagara

  • Teresa Jessome

    District School Board of Niagara

  • Val Vanderhoeven

    District School Board of Niagara

  • Rae Catella

    District School Board of Niagara

Professional Learning Goals

We learned that if a student had a difficult time visualizing or drawing the math, they also had a difficult time answering the question and explaining their understanding. Using math tools and visual representations (number lines, grids, T-charts, base 10) on a regular basis made them a little more comfortable taking risks to try and draw their thinking. It also helped us to know what they were thinking, what their misconceptions were, and what our next steps could be. We also learned that this is an ongoing learning/teaching process, and something that will definitely be built upon next year.

We were impressed by certain activities students could do that would help to develop their ability to visualize and verbalize spatially. For example, using hole punch activities, games like Swish and Shapeometry gave each student language that they could use to describe the math that they saw and experienced.

Activities and Resources

Each meeting we had arranged to discuss student data and progress toward our goal. We mapped curriculum expectations to specific models and manipulatives and activities which would facilitate a specific learning outcome for student thinking.

  • Use of manipulatives on a regular basis in problem-solving, such as Base Ten Blocks, Pattern Blocks, Cube-A-Links, Geoboards, Polydrons, Nets/3D shapes, Pentominoes, 100s Grids and Relational Rods
  • Intentional practise and instruction with models, such as number lines, area models, T-charts, set models, grid models, etc.
  • Spatial tools, such as graduated cylinders for measurement, balance scales, etc.
  • Spatial sense activities, such as Swish, Blokus, Block by Block, Brick by Brick, Shapeometry, Dominoes, etc.
  • Resources, such as SuperSource (as applicable for grade level activities) and Instructional Coach
  • Use of technology to track, monitor and learn from student thinking

Unexpected Challenges

We found that some students experienced frustration if they had limited spatial experience before our classes. Students often wanted to simply find the answer or were uncomfortable representing their thinking visually unless they could check it with the calculator. We had to do a lot of building up of student work and examining samples to help build student confidence before jumping right in to spatial and visual activities.

Enhancing Student Learning and Development

This project helped us to learn about student learning and development. Students, through exposure and guided practice, became comfortable and confident with trying to visually represent their thinking. They were able to have an entry point to understanding the math in a variety of problems to solve. Teachers were able to identify areas of misconception and teach to fill the gap or correct misconceptions and facilitate new learning. Students could explain their thinking so they also became peer supports for others when they shared their strategies with others.


We were offered opportunities to share and update our staff members with our project outcomes. We used this information to contribute to the school-wide improvement plan, regarding Sense Making in Mathematics. Staff were interested and have implemented the strategies as part of their math programming.

Project Evaluation

We felt that the project was a success because the goal was for students to use visual representations independently in mathematics. We determined the success of that because when given an activity or assignment/question, they automatically went to drawing a picture or using math tools without being told. Students have commented that visual representations makes it easier to answer the question and were sometimes able to draw out something that they could not verbally communicate. This helped kids who cannot write or participate in math talk (verbal) as every child could find an entry point to these activities.

Resources Used

Supersource Math Resources

“The Super Source is a series of books, each of which contains a collection of activities to use with a specific manipulative.”

Open Questions for the Three-Part Lesson (Junior Edition) by Marian Small

“These teacher resource books use a highly visual format to present easy-to-use questions and sample responses that cover all the expectations in the Number Sense and Numeration strand of the Ontario curriculum.”

Teaching Student-Centered Mathematics by John A. Van de Walle et al.

“… presents a large collection of high-quality tasks and activities that can engage students in the mathematics that is important for them to learn.”