Sunday, February 22, 2015

Algebra Skills in the Geometry Classroom



There was a time when Geometry was seen as the stand alone class in the math family tree.  When I was in high school, you could take Geometry in 10th grade or 11th, before or after Algebra II.  Basically you took it where ever and whenever it best fit in to your schedule.  Geometry at time was all about shapes, angles and proofs.  There was little to no Algebra used and the little that you did need, you could sort of fake it.  Not anymore.  Now Geometry is Algebra based.  With the advent of constantly changing standards and continually changing standardized testing each  math class is now a continuation of the previous one, often relying heavily on mastery of the previous one to be successful in the next.

When I start a new school year in Geometry I spend the first day or two reviewing how to set-up and solve linear equations.  Why you may ask?  Simple.  Every new concept that we do from solving for parts of segments and angles all the way through surface area and volume, can and will, involve finding the value of a missing variable.  This is done more often than not through a linear equation, usually in one variable to the first power.  In regards to solving equations, we even use them as the basis for our proof structure.  When I begin to introduce how to write a proof, I don't start with Geometric proofs, I start with Algebraic.  I ask my students to solve multi-step linear equations and to tell me what they did in each step.  This not only gets them used to the structure, but also reinforces why they do what they do when solving a linear equation.

As we move further on into the school year even more concepts from Algebra begin to pop up.  One of the most prevalent is the use of the Cartesian Coordinate Plane.  We first encounter it when we are finding the length (distance) of a segment.  We graph the two endpoints and use the Distance and Midpoint formulas to find how long the segment is and where the halfway point is.  Since this is more of a review, then a new concept however, I teach it using Task Cards for the students to practice versus spending a day on it like it is a new lesson.  We continue using the coordinate plane and Algebraic Concepts when we graph triangles and quadrilaterals and use the distance, midpoint and slope formulas to classify our shapes.  The last time that we explicitly use the coordinate plane is in our unit on Transformations when we graph our figures and reflect, translate, rotate and dilate them using coordinates.  

The other major Algebraic concept that use consistently is square roots and radicals.  We first encounter them when we solve the distance formula but at point it is a pretty basic use.  Once, however, we hit our unit on Right Triangles and Trigonometry, squares roots stick with us for the rest of the school year.  We use them to solve our right triangles and to find missing pieces of quadrilaterals.  We also use them when finding the tangent, radii and diameter lines for circles and the surface area and volume of three dimensional figures.  
For these reasons, and so many more, I stress mastery of concepts, not just retention of them for a test in my Algebra class.  I am honest with my students and I tell them that this ideas will not "go away" once Algebra is done.  They will use them again in Algebra II and then will take Algebra I and II skills with them as they move into Geometry.  Additionally, we talk extensively about which of these skills will be useful in the workforce and why.  I try to be as transparent as possible with my students and normally it works in my favor.  What Algebra skills have you seen move beyond Algebra?

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