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Tuesday, October 11, 2011

DA with Quadratics

Before, I have assessed Quadratic functions in the traditional sense with worksheets, homework checks and quizzes.  This year I wanted to assess my students' knowledge through an open-ended project and allow for differientated assessment.

Here is the task:

Quadratic Graph Project
1.      Take a digital copy of a picture which has a parabolic shape in it.
2.      Log on to www.prezi.com using the following log on:
***I just created a class log on and password***
3.      Select blank template.
4.      Select insert picture, and import your picture onto the prezi.
5.      Using insert à shapes àlines, draw in two axes.  Neither axis may go through the vertex of the parabola.
6.      Using either the pen tool or the circle tool, create a point on the vertex of the parabola
7.      Label the vertex using points which are appropriate.
a.       Vertex:____________
8.      Label another co-ordinate on the graph.
a.       Point:_____________
9.      Using your vertex and co-ordinate you created, determine the value of a, either as a fraction or a whole number, if your parabola was written in standard form .  Show your work on Prezi.
a.      
10.    Label another 4 points on your graph.  Try to space out the co-ordinates evenly across the parabola.
a.       Point 1:_______
b.      Point 2:_______
c.       Point 3:_______
d.      Point 4:_______
e.       Vertex:_______
11.  We will now have the calculator create the function.
a.       On your calculator, push STAT, then EDIT…
b.      In the first column (L1) input all the x-values, and in the second column (L2) input all the y-values of the points.
c.       Click STAT, then the right arrow  (à) to the CALC menu, then scroll down to QUADREG.
d.      Write down the values your calculator gives you, to the nearest hundredth if necessary.
                                 a:__________
                                 b:__________
                                 c:__________
12.  Inputting your values into general formyour function will be_____________________
13.  Change your general form into standard form, by completing the square.  Show your work in prezi.
a.       Your standard form now is ________________
b.      State the vertex, domain, range, direction of opening, and axis of symmetry from the function above.
14.  Write a couple of sentences explaining any differences from the vertex you stated in part 7, and the vertex in part 13.
15.  Using the equation from Part 9, determine the functions x and y intercepts, if the picture was extended such that it intercepts both axes.  Solve this part by graphing.
a.       x-intercept________
b.      y-intercept________
16.  Using the equation from Part 12, determine the functions x and y intercepts, if the picture was extended such that it intercepts both axes.  Solve this part by the quadratic formula.
a.       x-intercept________
b.      y-intercept________
Here is an example of my student working up to Section 14.



3 comments:

  1. Terry KaminskiOctober 11, 2011 at 6:24 PM

    Great form of differentiated assessment. I have a couple of questions. Why did you have the students use Prezi instead of say Geogebra or Sketchpad? Could have shown their work in Geogebra using text boxes and could have gotten very exact coordinates of points on parabolic shape.

    Are you going to use a rubric to assess the student work? If so, can you please share the rubric.

    Only thing that makes me cringe a little is that each step in this assessment depends on the students getting the previous step correct. But, good assessment is meant to be messy not nice!!

    Thanks for sharing this idea. Makes the rest of us think how we can change our assessment practices.

    ReplyDelete
  2. DaveOctober 12, 2011 at 7:43 PM

    I like to use Microsoft Paint to do this kind of curve-fitting. It's easy to get the exact coordinates of a pixel if you zoom to 800%.

    ReplyDelete
  3. Michaela GrocholskiMay 2, 2012 at 4:16 PM

    This is so interesting - I wish I had seen this when I was student teaching in the fall, I could have done this with the class. Thank you for sharing this!

    ReplyDelete