Ellipse (string and optical properties) Ms. Edge 2016-06-22 | This video uses the string property of an ellipse to help you construct an ellipse. To keep the definition simple, if you pick any point on the the ellipse, the sum of the distance of that point to the foci will be the same as 2a, or the length of the ellipse along the major axis. http://ggbm.at/Km3uQ6cC Materials needed: paper, marker, corkboard, string, 2 pins Instructions:1. Draw two points, label them F1 and F2. (You definitely do not have to put them on a specific axis, I used this activity to help students derive other equations, so we needed to have it set up as you see in the video.)2. Place pins in at both points.3. Take your string, tie it into a loop, and, keeping the string taut, complete your ellipse as shown. 4. Try measuring your ellipse along the axis and pick a point X on the ellipse to see if it really matches the definition.OPTICAL PROPERTY:geogebra.org/o/TwYEtRbG A ray of light (or sound) emanating from one foci will bounce off the side and hit the other foci.(Again, I don't have any audio for these videos, since I use them to enrich my instruction. You can say what you want with these videos!)**If you have any requests for videos, let me know in the comment section.**
Hyperbola (String Property) Ms. Edge 2016-06-22 | If you've seen my videos for a parabola and ellipse, you will understand that we're looking at the geometric properties of conic sections. For example, in this video, we're experimenting with a ruler and string to match the definition that if I pick any point on my hyperbola, measure the distance from the point to both of my foci, the difference (subtraction) between the distances will be the same as 2a.Here is a geogebra worksheet to play around with: http://ggbm.at/m3E5MTB7 This construction can be very frustrating for students, so approach it with a happy attitude and open mind. It's contagious. I promise.Materials needed: tape, ruler, corkboard, two pins, marker.Instructions:1. Draw two points to represent your foci.2. Place tape on one end of your ruler where you can put your pin through it and pivot the ruler.3. Tape the string to the other end. (There will be some trial and error here, figuring out just how long the string has to be before it will give you the right shape. Great for a discussion!)4. Pin your string into one of the foci, and pin the ruler into the other focus. Keeping the string taut against the ruler, construct the upper (or lower) half of one of the branches of your hyperbola. 5. To get the other half of the branch, you will need to unpin the ruler, turn it over, and pin it back into the same focus, and repeat the process.6. To get the other branch, switch the string and ruler pins.7. Be patient with yourself!!!OPTICAL PROPERTIES: This one is pretty cool. Basically, if you shine a light from one focus to the opposite branch, it will reflect so that it looks like it's coming from the other focus.geogebra.org/o/knGStem2 (There is no audio in my videos, since I feel that teachers know what they want to focus on/say, so have at it!)**If you want a specific video for a specific concept, feel free to enter into the comments below. I'll do my best.**
Parabola (String and Optical Properties) Ms. Edge 2016-06-22 | This video opens with a typical way of constructing a parabola given a focus and directrix: simply line up the directrix with the focus, and make a fold. Move to a different point on the directrix, and repeat the process until you have many tangent lines to your parabola.The string property of a parabola is written on the blue paper: It's simply a fancy way of saying that if I pick any point on my parabola, the distance from that point to the focus will be the same distance from the point to the directrix. **If you want to play around with this definition of a parabola, you can use this geogebra worksheet: http://ggbm.at/ERJhm75N **This is a possible way to construct a parabola using that definition. You could have a class discussion/brainstorming session of why this method works/matches the string property.Materials needed for construction: String, ruler, tape, marker, pin, corkboard. Instructions:1. Draw a line to be your directrix. Draw a point to be the focus. Measure the halfway point between the directrix and focus. Make a little mark.2. Tape a string to your ruler, and pin the other end in the focus.3. Start by looping your string until the bottom of the string is at the halfway point between the directrix and focus. Place your pen in this loop. 4. Keeping your ruler perpendicular to the directrix, gently slide it to the right, and keep your string tight next to the ruler.5. To get the left half, flip the ruler over, and repeat the process.To consider the special optical property associated with parabolas, you can try doing this geogebra activity: geogebra.org/o/ArkDus9h Yes, I don't have any sound with my videos, but that's because I use them for instruction. I talk what I want to talk about as I show my students the video.**If you have any requests for a specific video, you can write a comment, and I'll try to make one just for you!**
Tangent Lines Art Ms. Edge 2015-05-05 | I made this video a looong time ago. I forgot I even made it. I don't remember what I said. Cool.
Conicopia of fun narration Ms. Edge 2015-05-01 | This is the activity my students did April 29/30, 2015. The intention is to to help the students who were absent this day to complete the activity.
Intro to Sliceforms (Hyperbolic Paraboloids) Ms. Edge 2015-05-01 | Sliceforms are a fun sneaky way to get kids to start thinking along the lines of calculus. I have my freshmen work on this and roughly calculate the volume by making some measurements with a ruler.Resources: http://papercraftetc.blogspot.co.uk/2013/07/the-coolest-sliceform-hyperbolic.htmlhttp://www.cutoutfoldup.com/972-hyperbolic-paraboloid-from-parabolic-cross-sections.php
