Human Conics by 7RRk8T

VIEWS: 4 PAGES: 7

									                                      Human Conics
CA Standards:
Algebra 1 - Needs to be identified. (The standards do not address a parabola in terms of a focus
and directrix, nor vertex form.) I would add the Geometry standard for circles.
Algebra 2

Learning Objectives
Students will:
    Define conic sections as a locus of points
    Apply locus definitions to draw conic sections
    Collaborate with partners to solve a problem.

Materials
   Sidewalk chalk
   Lightweight rope (about 10-12 feet per group)
   Right angle measures (e.g., 8.5 x 11 sheets of cardstock or right angle rulers)
   Compasses
   Markers or colored pencils or pens
   White boards for games

Lesson Guide

   A. Opening: Vocabulary guessing game
        a. Using the CST released test questions, students will solve the problem and write
           their answers on the white board provided. The first group to provide the write
           (right) and complete solution has the chance to guess the scrambled word.
        b. After all the words are decoded the students will initially fill in the first and second
           column of the vocabulary worksheet. This activity will scaffold and build students’
           understanding of these terms. (See attached worksheet for this activity. Words
           included on the worksheet are locus, parabola, ellipse, directrix, focal
           point/focus/foci, circle, radius, center, perpendicular, vertex, conics, and midpoint)

   B. Work time: Conic construction (In Door).
        a. Give each student a compass and the Human Conics Sheet, have the students
            illustrate the following (questions 1 & 2):
                  i. Circle
                 ii. Ellipse
                iii. Parabola
        b. Have them define the above-mentioned terms based from their illustration, and
            prior knowledge. Have them identify the other terminology that relates to it.
                  i. Circle – radius, center
                 ii. Ellipse – foci or focal points
                iii. Parabola – vertex, directrix

Source: NCTM-Illuminations, Human Conics
          c. Provide time for students to discuss how they construct the locus of points. What
             are some of the limitations and conditions that should be followed to get the
             accurate path of points?

   C. Work time: Conic Construction (Out Door)
      Note: Before going outside, separate students into groups of three. Three students are
      needed for ellipse and parabola, two to represent foci or directrix and one to draw. For
      circle, only two students are required. Students will answer remaining questions on the
      worksheet.

      Task: They will be working in groups to draw a circle, an ellipse, and a parabola.
      Each group will have one piece of chalk and one piece of rope.

      Circle
           Students draw a perfect circle using the chalk and the rope. If students need a hint,
              suggest that they consider themselves to be a human compass.
           If they need further instruction: Fold the rope in half. One student puts the ends
              together, and holds them on the ground to be the center of the circle. The second
              student stretches the rope and puts the chalk in the bend at the midpoint. The
              second student then drags the chalk along the ground, while pulling the role taut.
              Note that students figuring out the activity independently may not fold the rope.
              This is not a problem.
      Questions:
           How many students are actually needed to draw the circle?
           What are their roles?
           What did the rope represent?
           As they finish have them complete the questions on the worksheet.
      Ellipse
           If students need hints, tell them that fact that there are three people in the group is
              significant and to consider what they did to draw the circle. They should also
              reference the significant parts of an ellipse, from the vocabulary sheet, as well as
              question 1 and 2 from the worksheet.
           If students need further instruction: Two students are human foci, holding the
              ends of the rope at fixed points on the ground. These students should not hold the
              rope taut. The third student uses the chalk to pull the rope taut and sweeps out
              the locus of points. Not sure if a picture here would help???
      Questions
           As they finish, ask students to consider and discuss the questions on the activity
              sheet.
      Parabola
           Draw a focus approximately 4 feet from the directrix. This does not need to be
              precise.
           Assign roles to the three students in the group: F, D and A. Student D will be
              responsible for the directrix and will need a right angle measure, such as cardstock
              to approximate right angle measure. Student F will be responsible for the focus of
              the parabola. Student A will mark points on the parabola.
Source: NCTM-Illuminations, Human Conics
           Assign each student a point on the rope. Student A is at the marked midpoint of the
            rope. At equal distance from her, measured by the folding the rope, are F and D.
          F should hold her point of the rope at the focus of the ground. D should place the
            right angle measured on the directrix and guide the rope along side of the measure.
            She should move the card and the rope along the directrix, A pulls the rope taut.
            When the rope is taut and perpendicular to the directrix, A should mark the point
            on the parabola. A picture here also might be beneficial.???
          Students use the same rope length and repeat the procedure to draw a point on the
            other side of the parabola. Then, change the lengths and repeat for a total of at
            least ten points.
      Questions
          What is the shortest segment from the focus to the directrix?
          What is the midpoint of this segment?
          Why is it important to keep the rope perpendicular to the directrix?
          How can you find the vertex of the parabola using your rope right angle measure,
            and group members?

   D. Closing Questions for Students
          a. What effect does the length of the rope have on the shape of the conic? Is the rope
              ever too short?
          b. Why can you draw the circle with fewer people than the ellipse of the parabola?
          c. Which conics can you draw as a continuous line, without picking up your chalk?
          d. How could you use paper and pencil to draw or verify conics?
          e. Have the students complete the last column of the Vocabulary worksheet by
             writing the correct definition based from the activity and the discussion.

   E. Assessment options
         a. Give students a picture of an ellipse and a parabola with possible foci or directrix
            indicated. As them to sue a ruler and right angle measure to determine and
            explain whether or not the figure is actually the named conic.
         b. Give students two thumbtacks, string and a piece of cardboard to draw an ellipse.
            This is an individual reproduction of the chalk activity. Students may also be
            challenged to find a way to draw a parabola using these materials. LOVE THIS!!
         c. AS students to write a summary of either the ellipse or parabola constructions for
            the benefit of a classmate who has missed the lesson. The summary should include
            the definition and an explanation of how the drawing technique applies the
            definition.
         d. Students and teachers whoa re comfortable with the technology may construct
            these conics using geometry construction software.

   F. Extension
         a. Have the students construct a hyperbola.




Source: NCTM-Illuminations, Human Conics
                                 Human Conics
                          Vocabulary Worksheet
1. “soclu”
   What do you know?           Illustration / Example   Definition




2. “baaraplo”
   What do you know?           Illustration / Example   Definition




3. “pislele”
   What do you know?           Illustration / Example   Definition




4. “tceiixrid”
   What do you know?           Illustration / Example   Definition




5. “iocf”
   What do you know?           Illustration / Example   Definition



6. “lecric”
   What do you know?           Illustration / Example   Definition




7. “saruid”
   What do you know?           Illustration / Example   Definition




Source: NCTM-Illuminations, Human Conics
8. “recnet”
   What do you know?           Illustration / Example   Definition




9. “treexv”
   What do you know?           Illustration / Example   Definition




10. “scocin”
  What do you know?            Illustration / Example   Definition




11. “dipenreplacur”
  What do you know?            Illustration / Example   Definition




12. “tonidimp”
  What do you know?            Illustration / Example   Definition



13.
  What do you know?            Illustration / Example   Definition




14.
  What do you know?            Illustration / Example   Definition




Source: NCTM-Illuminations, Human Conics
                Human Circle                                    Human Ellipse
1. What is the definition of a Circle?           1. What is the definition of an Ellipse?




2. In the space below, draw a circle using the   2. Draw a sketch to illustrate the definition.
compass.




3. Working with a partner, sidewalk chalk, and   3. Working with 2 partners, sidewalk chalk and
a rope, draw a perfect circle on the pavement.   a rope, draw an ellipse on the pavement.
Explain how you were able to be a human          Explain the role that each person had in the
compass and complete the drawing of your         drawing. You may use a sketch to help
circle.                                          illustrate your explanation. ???




4. What does the rope represent in your human 4. What would happen if the foci of the ellipse
compass?                                      moved closed together or further apart?




                                                 5. What does the length of the rope represent?




Source: NCTM-Illuminations, Human Conics
                                      Human Parabola

   1. What us the definition of a parabola?




   2. Draw a sketch to illustrate the definition.




   3. Working with 2 partners, sidewalk chalk, a rope and a right angle measure, draw a
      parabola on the pavement. Explain the role that each person had in the drawing.




   4. How can you find the vertex of the parabola?




   5. What can you say about the distance between the parabola and the focus or directrix at
      the vertex?




   6. What would happen f the focus moved closer to the directrix?




   7. What would happen if the focus moved further from the directrix?




Source: NCTM-Illuminations, Human Conics

								
To top