Exploring Polygons

This arc, the Blue Band took a deep dive into geometry.  Inspired by the polyhedrons we created for our hot air balloon project we set out to become better acquainted with the shapes we were using.  Paul Lockhart, in his defense of the open ended math problem once said, "“Mental acuity of any kind comes from solving problems yourself, not from being told how to solve them.”  In that spirit we didn't start with all of the vocabulary and relationships between shapes, we let the students discover it all for themselves. The band's first challenge was to create a family tree of different shapes.  Some students grouped their shapes by number of sides, some grouped them by angle and others incorporated both of these aspects.The group's next challenge was to see how many different polygons they could create using 4 triangles.They discovered fourteen different polygons that could be constructed from these four triangles.  We had been slowly becoming more familiar with the vocabulary of polygons. The teams came together to sort them based on number of sides into quadrilaterals, pentagons, hexagons and octogons.We did some explorations into different types of quadrilaterals.  The bands had to use peg boards to see how many different types of quadrilaterals they could make.  We then learned different names for these shapes and labeled them.Our study of shapes culminated with a reading of the Hungry Triangle by Marilyn Burns.  The students then wrote their own stories about a shapes.  Gita wrote about a heart that didn't fit in amongst her fellow polygons because she had curved sides.  Ramses wrote about a triangle chicken that spent all day eating different triangles.  Ronan wrote about a circle that could be considered a polygon with infinite sides.  All of their stories revealed some deeper understanding of shapes and polygons.