Spatial Reasoning

Guest blogger: Sasha Fajerstein

posted by Sasha Fajerstein

As teachers, we constantly remind students about the importance of mathematics if you want to be an engineer, chemist, architect, archaeologist, astronaut, astrologist, biologist, and many more. What people don’t realize is that spatial skills are key in transforming mathematics into three-dimensional objects with limitless uses. Spatial reasoning is essentially the ability to think about, visualize, and mentally organize objects in 3 dimensions.

Here is an example of a standard spatial reasoning test question:

Which of the following cubes represents the unfolded picture on the left?

geo-shapesQuestion and photo from

The correct answer to the above question is the cube shown in choice C. These visualization exercises involve the same thought processes that allow surgeons to visualize the next steps in surgery, architects to convert floor plans into real life buildings, engineers to use formulas and programs to form electrical circuits, and so on.

Most people think spatial reasoning is specific to geometry class, but spatial reasoning is involved in all mathematics and science classes. I teach high school students, but spatial reasoning skills can be built and expanded from a very early age. We all use our spatial intelligence on a daily basis. When you look at a map to figure out relative location, rearrange your living room, try to figure out if your stroller will fit down the aisle in the grocery store, or decide whether or not that last pan will fit in the dishwasher; you are using your spatial intelligence skill set. Even something as simple as involving your children in these types of questions, decisions, and activities can help strengthen spatial reasoning skills.

Playing with toys and games that allow imaginative building can help improve spatial skills. Some things that probably come to mind immediately are toys like Legos and building blocks, but there are many more options for individual play or group play and board games available. A great list of construction toys is available here:

There are also countless puzzles and games that involve spatial reasoning skills. A list of board games that involve spatial reasoning is here:

(Blokus is one of my all-time favorite games! I think playing this game has made me much better at visualizing when teaching geometry.)

If the test question above was interesting for you to think about, there are a number of spatial reasoning challenges and tests you can find online. I did a quick Google search for online spatial reasoning tests and I found one similar to the question above at

(This is not a test you’d give young children, but I found it to be a fun mental challenge).

One of the best things about working with construction toys or board games that involve spatial reasoning skills is that they truly are games that allow children to come up with their own plans, outlines, or strategies without one correct answer. This is always the goal of inquiry based mathematics, so introducing games and play objects that allow for this type of thinking early on will go a long way in students’ future success in mathematics.



Sasha Fajerstein

Sasha Fajerstein is a math teacher at New Trier High School in Winnetka, Illinois—one of the highest ranked secondary schools in the nation. This pioneering mathematics educator, who is passionate about integrating new teaching methods and technologies into the classroom, recently collaborated with her colleagues at New Trier to develop and pilot an interactive high school geometry textbook for the iPad. She co-presented a talk about the iPad textbook project at the 2015 Illinois Council of Teachers of Mathematics Conference and also shared her insights into math education as a presenter at the Metropolitan Mathematics Club of Chicago. After earning her B.S. in mathematics from the University of Illinois at Urbana-Champaign, Sasha spent a year teaching English in Costa Rica. Upon returning to the U.S., she served as a math teacher at Nichols Middle School in Evanston, Illinois.

Read more posts by Sasha Fajerstein

8 Replies to “Spatial Reasoning”

  1. We have a light table that the children use to build 3d shapes using magnetic tile shapes. They build towers, cubes, garages, etc and it shows how they are able to identify which shapes are needed to create their structure. They learned that using two triangles will make a square.

  2. When having the children build towers with blocks, talk with the children about which blocks to use and how they can place the blocks to see how tall the tower can be.

  3. While in the block area I have the children try to put blocks together to make different shapes, we also have magnetic tiles that the children absolutely love, they play with them at the light table by putting them together and making different shapes.

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