Why is a Triangle a Triangle?

Written by Donna Boucher

Donna has been a teacher, math instructional coach, interventionist, and curriculum coordinator. A frequent speaker at state and national conferences, she shares her love for math with a worldwide audience through her website, Math Coach’s Corner. Donna is also the co-author of Guided Math Workshop.

For a long time, young children learned shapes by sight, without regard to attributes (characteristics).  An octagon looked like a stop sign, by golly, and any 8-sided figure that didn’t look like a stop sign must not be an octagon.  Standards today, whether they are common core or our Texas TEKS, emphasize defining shapes based on attributes. ANY 8-sided polygon is an octagon.  An octagon is defined as such because it is a polygon with 8 sides.  Period.

Let’s look at some of the common core standards:

K.G.2–Correctly name shapes regardless of their orientations or overall size.

K.G.4–Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/”corners”) and other attributes (e.g., having sides of equal length).

1.G.1–Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.

2.G.1–Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.  Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

What are some things you notice?  First, I notice orientation and size.  Be sure kiddos see lots of examples of each of the shapes.  The shapes below are all triangles, although the look quite different.  Geoboards are a GREAT tool for exploring different shapes.

I also notice that both 1st and 2nd grade mention drawing shapes.  How much practice do your kiddos get with that?  Think what a rich exercise it would be to have all your students draw “a five sided closed figure“.  Imagine all the different looking shapes you’d get!

Here’s a little assessment I made for my 2nd grade teachers.  Click here to grab it. For more information on helping kiddos identify geometric attributes, check out this blog post.


  1. Amy B

    Why this post can’t be any more PERFECT!!!!!!! You are A.W.E.S.O.M.E.!!!!

    • Donna Boucher

      Just good timing, Amy. 🙂

  2. Christen

    I cannot agree more! My children are fascinated by seeing an eight or nine or even ten sided figure they cannot recognize. Love this!


    • Donna Boucher

      Love the curiosity of kids! Thanks for sharing, Christen. 🙂

  3. Linda

    Thank you, Donna! I always love your explanations and I’ll definitely be using this assessment with my second graders. Thanks so much for sharing it!

    • Donna Boucher

      Thanks, Linda. I really appreciate your comment! 🙂


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