“Enrichment beyond the classroom”
GREECE and ITALY
join a Mediterranean math-collaboration!
etwinning project 2015-2016
STEP1 ( Collaborate to decide a conic section to study and create an intresting motive to engage students in conic sections. Because math is fun!
At first our team decided to simply demonstrated the foci of the ellipse. Asthe italan students in our team attent a vocational school they present the foci using a construction and they filmed it.We used Skype and emails to make any arrangements and take decisions. See the amazing the first video that our team created. Click below to watch!
"The photo is from Greek team. We LOOOVED the video that italian friends prepared. We are not very fond of maths. Actually it is a hard lesson for us. But now at least we have a good reason to try harder for study conic sections! We have to schedule the next step for the activity."
STEP2 (post videos and study)
"As we planed the second step was to study about conic sections, especially about ellipses.
We tryied to undrstand the video that our italian partners prepared in the 1st part of thiw activity. then That is why we posted our comments and all together created a padlet to copy the videos we selected and then posted to the mail of the "Math Investigation". All are about conic sections"
BY gU.iTALY
" Conic sections is an activity that we decided to do it after the middle-evaluation. It was not in the schedule from the beginning. On the 11th grade (in greek educational system it is B Class of LYKEIO) students in maths have to face with the Conic sections in details. I watch the video at the right (you can watch it .I am sure that you will love it) and I was so impressed! Sometimes a little help from audios or videos get us in the imaginary world of learning! I loved the way the Doodling in Math Class (Connecting Dots) approaches units in maths as conic sections. We proposed to our teachers to include video activities in the eTwinning project "Math investigation". Our teachers are so flexible! They organized the activity and we had the help we needed". We think that in Greece and also in Italy, eTwinning let them involve with things according to the cirriculum using their imagination and their own special talents!" BY EL. sCHIMATARI
STEP 3 (collaborate to create a video )
Properties of an ellipse
Center A point inside the ellipse which is the midpoint of the line segment linking the two foci. The intersection of the major and minor axes.
Major / minor axis The longest and shortest diameters of an ellipse. Study Major Axisof an Ellipse . The length of the major axis is equal to the sum of the two generator lines (a and b in the diagram above).
Semi-major / semi-minor axisThe distance from the center to the furthest and closest point on the ellipse.
Half the major / minor axis. It is the same as Semi-major / semi-minor axis
Foci (Focus points) The two points that define the ellipse. Study the Foci of an ellipse.
Perimeter (circumference) The perimeter is the distance around the ellipse. Not easy to calculate. Study Perimeter of an ellipse
Area The number of square units it takes to fill the region inside an ellipse. Study Area enclosed by an ellipse.
Chord A line segment linking any two points on an ellipse.
Tangent A line passing an ellipse and touching it at just one point. Study Tangent to an Ellipse
Secant A line that intersects an ellipse at two points.
Relation to a circle
A circle is actually a special case of an ellipse. In an ellipse, if you make the major and minor axis the same length, the result is a circle, with both foci at the center. Study for Circle definition
How to draw an ellipse
There are some practical ways to draw an ellipse of a given size. Study for Drawing an ellipse with string and pins.
To be continued in the next project!!!
Ellipse
From Latin: ellipsis - "ellipse"
by EVI. VEL.sCHIMATARI
A curved line forming a closed loop, where the sum of the distances from two points (foci) to every point on the line is constant.
We watch this video in which we drag any orange dot. We change the position of the two focus points (F1, F2). Also we drag the point on the ellipse and
observe that the sum of the lengths of the lines that meet there is constant.
An ellipse looks like a circle that has been squashed into an oval. Like a circle, an ellipse is a type of line. Imagine a straight line segment that is bent around until its ends join. Then shape that loop until it is an ellipse - a sort of 'squashed circle' like the one above. Things that are in the shape of an ellipse are said to be 'elliptical'.
How ellipses are defined
An ellipse is defined by two points, each called a focus. (F1, F2 above). If you take any point on the ellipse, the sum of the distances to the focus points is constant. In the figure above, drag the point on the ellipse around and see that while the distances to the focus points vary, their sum is constant. The size of the ellipse is determined by the sum of these two distances. The sum of these distances is equal to the length of the major axis (the longest diameter of the ellipse).
The two lines a and b that define the ellipse are called generator lines . Each one is sometimes called a generatrix .
The position of the foci (plural of focus, pronounced 'foe-sigh') determine how 'squashed' the ellipse is. Drag F1 and F2 and see how this happens. If they are at the same location, the ellipse is a circle. A circle is, in fact, a special case of an ellipse. In the figure above, drag one focus until it is over the other.
The 3rd part of this activity is about to collaborate and write a senario . Then we took action and we created a video using avatars as it was.... more amusing! The script was created using ideas from both teams, we used..... to write te senario and an etool to make our avatars live. In addition we were going to upload the video in youtube so we used avatars as we keep in mind avoid to expose students. Our schools' concern is keep students safe.
Here is the senario in brief:
Deppie (Greece) and Guilio (Italy) are best friends. They take part in an Easmus+ project. They are in Greece.They help each other in school activities. Deppie is affraid of math even though she is good in math at aschool.Guillio is mechanics and electronics student.
They have to watch a video and explaine in plain math what is about.
Finally they find the answer and write down their presentation for the next day.
PROBABLY DEPPIE'S HOMEWORK START LIKE THIS...
