Learning Geometry Concepts Through Exploration

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 Introducing... Polygons!

My third graders are knee-deep in geometry. For any of you that teach geometry, you know that it is full of new vocabulary.  I really find that my students learn best when they have the opportunity to figure out the meaning of words and concepts through discovery. So instead of simply telling them what a polygon is, I created a chart out of butcher paper where one half was labeled, "examples of polygons" and the other side was labeled, "non-examples of polygons." I held up pictures that were examples of polygons and I showed the class pictures of figures that were not polygons. While I was holding up the pictures, however, I did not tell them whether the figure was a polygon or not. In the beginning, students were simply making guesses as to whether or not the figure was a polygon. As we continued through the activity, they began to see patterns and notice that the pictures on the "examples of polygons" side were closed and had straight lines. They observed that the "not polygons" side had curved lines and some were not completely closed. By the end of the activity the students had defined the word "polygon" on their own. I love to see my students think for themselves! Below is the activity I used for this polygon lesson. The next day I had my students sort the polygon examples and non examples in their math notebooks. You could also laminate the polygon cards and use them as a sorting activity for a math center. Enjoy!

There are three types of triangles?!?

When introducing isosceles (how many years of third grade do I need to teach before I can spell this word correctly?!), scalene, and equilateral triangles, I also stick to the "learning through discovery" method.  I had the students figure out the meaning of the different types of triangles through an engaging, hands-on activity. Here is what I did: I placed about twelve different pictures of equilateral, scalene, and isosceles (there goes that red squiggly line again)  triangles around the room. Each picture was labeled with the triangle's name, however it did not show the measurements. The students found a ruler, a partner, got out of their seats, and traveled around the classroom measuring each side of the triangles. 

 The students also had a paper that they used to record the triangle name and its measurements. By the end of the activity, they had written down the several different measurements for all three triangles. After the time was complete, we gathered together as a class to discuss their findings. While the students shared, I recorded their responses on chart paper. While we were discussing the triangles, the students immediately noticed that all of the equilateral triangles had the same measurement on all three sides and the scalene triangles had all different measurements. This activity allowed the students to develop their own definition of the triangles through exploration.