Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
We first meet geometry through shapes and their properties. The activities in this category touch upon many aspects of shape.
Geometry and spatial sense are vast; developing deep understanding takes years and encompasses many subfields. The mathematics here spans a range as well, but by no means "covers" geometry in grades K8.
Symmetry, coordinates, and proportion are the core ideas of the following three activities, which approach shape and properties of shape from different directions. Take a look at the background to each activity for additional ideas and connections.
Our first school activities about shape may have been about identifying different figures. We were asked to color the triangles red and the circles blue. Later, especially using concrete manipulatives, we explored how shapes relate to one another: Can you make a square out of triangles? Can you cover the floor with hexagons? Soon we learned about measurement and began to work with area, perimeter, and volume.
We used symmetry to help make figures and describe them elegantly. By the end of elementary school, our developing proportional reasoning let us make scale drawingsand that led to our understanding about similarity.
Around the same time, we began to identify locations with coordinateswhich leads us to analytic geometry, where we use coordinates to help study shape. (In the Taxicab Treasure Hunt activity, you use the coordinates of city blocks.)
Such activities across the grades traditionally come together when we are asked to reason soundly about the properties of shapesusually in the geometry class that follows algebra.
The new NCTM Standards discuss geometry in Chapter 3: Geometry.
Mathematics instructional programs should include attention to geometry and spatial sense so that all students analyze characteristics and properties of two- and three-dimensional geometric objects;