A few months ago, I got into an eye-opening disagreement with my 4-year-old son, Knox, about shapes.
He and I were messing around with some magnetic shapes, sticking them to a metal door that leads to our garage. We used the shapes to create houses, ice cream cones, and all sorts of designs. When one of the square shapes fell off the door, I picked it up and stuck it back up"sideways." Now it looked different from its original orientation with the base no longer horizontal but balancing on a vertex (corner). Knox, immediately chastised me and "fixed" the square. When I asked why he did that, he told me it was because shapes couldn't be "sideways."
Knox sits "squarely" in Stage 0 of the Van Hiele Levels of Geometric Thought. This stage--Visualization--is right where 4-year-old Knox ought to be. It's the stage where kids say things like, "I know it's a square because it looks like a square." They rely on a shape's appearance rather than its attributes (like the number or length of its sides) to recognize, name and classify shapes.
But it's time for this almost-kindergartener to begin to moving along the trajectory of geometric understanding to Stage 1--Analysis. At this stage, he can start to discuss properties of shapes (like the number or length of sides, the angles, and congruence) rather than just the way a shape looks.
Here is an activity called Straw Triangles found on page 197 of my new book Math-Positive Mindsets: Growing a Child's Mind without Losing Yours from Math Solutions that helps kids move forward in their thinking about shapes.
Straw Triangles is important because it helps students gain understanding about the attributes of shapes and how triangles can look very different but still all be triangles because they have 3 sides and 3 vertices.
Materials: For this preschool and kindergarten activity, you’ll need plastic or paper drinking straws, play dough, and scissors. If you don’t have these at home, some substitution ideas are: coffee stirrers and mini marshmallows.
Mathematical learning objectives and connections:
Use concrete materials to build geometric shapes and explore a shape's defining attributes.
Instructions: Have children cut straws to different lengths. Connect 3 straws using balls of play dough as vertices. Make as many different triangles as possible. Discuss how the triangles are all alike (they all have 3 sides and 3 vertices) and different (they have different side lengths). **That's why you need the scissors. Who wants a bunch of boring equilateral triangles?
What connections should the teacher or parent be looking for?
At this stage, children recognize, name, and classify shapes based on their appearance. They might say things like, “I know it’s a triangle because it looks like a triangle.” Recognizing how a shape looks, while an important stage, is just the beginning of geometric understanding. Your children might instantly recognize an equilateral triangle (3 sides the same length) but resist identifying an isosceles triangle (2 sides the same length) as another type of triangle.
To help them build vocabulary and understanding about the defining attributes of triangles, introduce a simple definition—a triangle is a shape with 3 sides and 3 vertices. Help your children count the sides and vertices of each Straw Triangle to help them see the shapes each meet the definition.
Outcomes:
Straw Triangles encourages math conversations and expands math vocabulary. It also promotes counting and length comparisons.
Watch the video to see how the activity went with Knox. Try it out with your kids and let me know how it goes. You can tweet me at @DrCarrieCutler or send me a message via this website. I'd love to hear how Straw Triangles goes with your kids!