Introduction to Quadratics (Algebra One)

Our last unit of the year is Quadratic Functions. We've just finished our "mini unit" of algebra skills necessary for working with Quadratics. There are all sorts of concepts that the common core curriculum expects us to cover in Quadratics without being overly clear as to what goes in Algebra One and Algebra Two. I think the push is to cover it all in Algebra One now, but we ran out of time and didn't get to everything. And this was with an advanced level class that meets every day for 82 minutes in a block schedule for 180 school days. Phew!  But over time I think we will get to more of what we are supposed to as students come from classes in previous years that cover more of the common core, it's a slow evolution. So we do our best.

My approach to Quadratics is to treat them as just another type of function that we are trying to figure out, analyze and use when appropriate.

My lesson plan for this first day is as follows:

Objectives

Students will be able to

·         See that there are problem situations that are neither linear or exponential – in this case quadratic. They will initially see these in the context of area problems. They will examine two scenarios and analyze their results with the aid of a quadratic function equation.

What will students do to learn this?

Initiating activity

·         Go over HW sheet from after the test. Discuss how the equations and graphs are different from what we graphed so far this year (squared variable, U shape).

exploring parabolas

• ·         Explore – given fencing measuring 48 m, find all possible sized rectangular enclosures that can be formed (small group, blue graph paper – 2 each person). Create table of data IV = width and DV = area. Graph on one large first quadrant graph (blue graph paper) then do on calculator (scatter plot).  Is this graph continuous or discrete?
• ·         Discuss resulting shape (parabola) and brainstorm characteristics you see (U shape, opens downward, crosses x-axis (where),  has a highest point (where), symmetrical… discuss how this is the new function type we will be exploring.  It does have important characteristics which we will learn to identify and interpret in real world situations.
• ·         What really is a parabola? Paper folding (math=love) with patty pan paper. Full discussion. ISN page – what is a parabola. Define parts (vertex, axis of symmetry). Parabolas usually open up or down – but can also open sideways.
• ·         Go back to area problem - run quadratic regression on data. See equation and its perfect fit. y = -x² + 24x identify specific characteristics on this graph paper (vertex, x-intercepts, y-intercept, axis of symmetry)
• ·         Add to ISN – graph of data (on graph paper) with parts labeled. Characteristics of a Parabolas graphic organizer, Quadratic function frayer diagram, paper folded parabola with parts identified.
• ·         If time do “what is a parabola” foldable.
• ·         Do two class examples graphing with tables (one opening up or down, one opening right or left). Are they both functions?

·         HW – worksheet of graphing

Here are my ISN pages:

For the detailed instructions on how to do this paper folding parabola check out Sarah Hagan's blog math=love post Wax Paper Parabolas.

And this folder has all my ISN templates for this unit (8 blog posts worth! I'll post this link on each blog). It's way easier to upload them all together.

Here are supporting materials I used for this topic.