PS/IS 686 | Brooklyn, NY

Fifth Grade: Geometry Ponderings

Fifth graders have just wrapped up their geometry unit.  We’ve explored polygons and how we name them, and we went in depth into quadrilaterals and triangles.

With quadrilaterals, we developed a hierarchy to classify the shapes.  The hierarchy helped us realize why a square is a rectangle, but a rectangle isn’t always a square.  The same applied to rhombuses. A square is always a rhombus, but not all rhombuses are squares.

We also classified triangles by their sides and angles and realized that triangles are named by both properties.  The most interesting idea that emerged pertained to the angle names. Students wondered why right triangles only require one right angle, obtuse triangles only require one obtuse angle, but for a triangle to be named acute, it must have all acute angles.  Students then realized that it would be impossible to draw a triangle with more than one right or obtuse angle.  Once there are two of either of these angles, you cannot close the shape with one straight segment, and, therefore, you would not have a triangle.  During this discussion, students inferred that all triangles must have at least two acute angles.

Just a reminder that the State Math Test is next week (May 1 and 2).  Please be sure your child is well rested and has a good breakfast.