Resources and Tools for Elementary Math Specialists and Teachers

Algebra/Geometry Connections

This discussion is part of a collection: K-2 Algebraic Thinking

The CCSS have put the K-5 Mathematics focus on operations and algebraic thinking. There exist documents at this early date that recommend the dropping of some geometry topics in K-5. One of those topics is transformations. See Vermont’s Transition to the Common Core: http://vtedprep.wordpress.com/2011/09/06/vermonts-transition-to-the-comm...

If transformations go then is there a basis, either formal or informal, for discussing symmetry? The concept of symmetry may have carry-over benefits in the arithmetic area. One of those areas is in the discussion of the properties of the equal sign, e.g., in using 15 = 7 + 8 instead of its symmetric and more standard version. Are there others ways in which symmetry or transformations aid in the development of algebraic thinking?

Replies

Transformations often serve as an important basis for the discussion and application of the Coordinate Plane in late 5th and early 6th grade. Without transformations (usually taught as Slide, Flips, and Turns) in elementary school, there are more skills need to teach the coordinate plane applications of translation, reflection, and rotation, which are necessary for algebraic thinking. Especially as our middle schoolers move into graphing functions and discussing the ways to transform a function.

Even at the primary level there are opportunities to connect number and geometry with transformations that lead to algebraic systems. I think of some ML resources like reading analog clocks, and Turning Man (4 90 degree turns equal no turns).