1) TLW recognize a hyperbola from its standard form equation.
2) TLW be able to put an equation for a hyperbola into standard form.
3) TLW be able to graph a hyperbola from its standard equation.
III Instructional Objectives:
1) TLW identify all major characteristics of a hyperbolas standard equation, including transverse axis, slope of asymptotes, center, vertices, and what differentiates it from an ellipse. (Does not include foci.)
2) TLW correctly arrange 9 of 10 hyperbola equations into standard form.
3) TLW sketch 9 of 10 hyperbolas from their standard form equations.
IV Student Entry Level:
Background with completing the square, balancing equations, and graphing parabolas, circles, and ellipses from their standard form equations. Also experienced in putting some conic sections’ equations into standard form.
V Desired Mastery Level: 85%
VI Set:
A. Opening Review Problems:
Name the shape:
x2+y2+4x+2y=8-------circle
x2+4x+y=3-------------parabola
3x2+y2+2x=11---------ellipse
B. New Lesson Introduction
"Today we are going to discus the final type of conic section. For this one, we need a little something extra. Thus far we have only looked at a plane intersecting one cone. However, for algebra purposes, a "cone" is really more like two cones on top of one another, nose-to-nose.
"When we look at it this way, a circle cuts across here [demonstrate], an ellipse cuts similarly, but more at an angle [demonstrate]. If we keep turning it, we’ll cut into only one cone, but never out the other side. That would be a parabola.
"Now we get to pretty much straight up and down. This will cut a chunk off the bottom cone and the top cone. It will look pretty much like this [demonstrate]. This is a hyperbola."
VII Instructional Procedures:
Definition of a hyperbola
"set of points whose absolute value of the difference of the distances from two fixed points is constant"
Differentiate between hyperbola and ellipse (- instead of +)
Graph examples from book
find center
find transverse axis
count a or b in both to form box to mark vertices
sketch asymptotes through corners (slope a/b and –a/b)
draw in curves through vertices getting closer to asymptotes
class works examples
Put examples into standard form
group X’s, Y’s and constants
complete the square twice
check for Hitler (constant in front of parentheses)
add to other side
divide by other side (should be 1=…)
reduce fractions
class works examples
VIII Checking for Understanding: During lesson where it says "class work examples".
IX Supervised Practice: Begin assignment in class so questions can be asked and answered. Walk amongst the class observing work.
X Closure:
Review the steps for putting equation into standard form and graphing hyperbola from standard form while working an example. (Students give me directions for how to work it.)
XI Independent Practice:
Practice section of problem set (select such that there are no more than 12 problems for any one objective.) Adapt directions as needed.
XII Lesson Evaluation:
XIII Materials and their Use:
Text book – homework problems
Cone model – demonstrations
Overhead – notes and some demonstration
Hyperbola overlay transparency – demonstrations
