We are continuing our exploration of 2D geometry. On Friday, students used geoboards to create different quadrilaterals. The challenge was coming up with a system to record our discoveries! Thanks to Alexis, Sarah, Richard, and a few others, we learned how to use the grid paper to our advantage! Check out our 'Pyjama Day' math photos below!
Today we discovered that you can use only two triangles to make any quadrilateral! This discovery was sparked by Sydney's thinking yesterday about how shapes can be combined to form new shapes. Many other interesting math discoveries were also made today. Haroon and Dylan helped us see that any shape with 3 sides/3 vertices can be a triangle, even when it is 'stretched out long', or doesn't look like a 'regular triangle'. Tanner also guided us towards realizing that the best way to divide a quadrilateral into triangles, is to look for ways to connect the vertices. When attempts were made to cut quadrilaterals into triangles, and the vertices weren't used, we ended up making smaller four sided shapes. Ryan, Awwab, Richard and Bailey also explored how many triangles it would take to create pentagons, and hexagons and a surprising pattern was noted (i.e., 4 sides= 2 triangles, 5 sides= 3 triangles, 6 sides= 4 triangles)! We are still wondering about why the heptagons (seven sided shapes) didn't fit this pattern. Matt's also curious about whether the first shape ever created was a triangle, since all the other shapes seem to be able to be decomposed (broken down) into different types of triangles. Ryan, our geometry-internet expert, is on the case! See the photos below of our very interesting math class today!
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May 2012
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