![]() The next suggestion is that it has to be a right angle triangle. We disprove the conjecture to everyone's satisfaction. Someone suggests measuring the sides, which gives us a purposeful reason to show them how to measure lengths in GSP. Nathalie asks how they could verify this. The first suggestion is for equilateral triangles. After allowing them to play for a few minutes, Nathalie asks them under what conditions the point Q is inside the triangle. Almost immediately, oohs and aahs are audible, as Q (the orthocentre) moves much more wildly about than P did, well outside the triangle, even off the screen. ![]() We ask the students to manipulate the vertices again. There is a triangle with a mystery point Q in it. We close the file for P-triangle and open the one for the pre-made Q-triangle. We leave this concept for the time being and move on to the next sketch. Nathalie demonstrates this with a paper triangle. We introduce the idea of centre of gravity, and tell the students that the mystery point P is also called the centroid, because it is the centre of mass of a triangle. This leads into a discussion of what P might be. Jane suggests drawing another median and the intersection is indeed at P. Nathalie asks where P falls along the median. The students follow this set of instructions on their own screens. For this she must show them on the overhead how to select a segment and use the construct menu to get the midpoint, then the segment tool to draw in the median. Eventually, Zach's suggestion that she fold to find a median (of course, his terminology is not a precise) is taken up and Nathalie asks if the students can construct a median on the triangle they have in GSP. Many call out suggestions, so many, Nathalie can't follow them all. She holds a paper triangle and asks how we would go about finding the centre of it (i.e. Nathalie asks what it means to speak of the centre of a triangle. Another student conjectures that it stays in the centre of the triangle. One students observes that the point P seems to follow the movement of the vertex being dragged. Many comment that the point stays inside the triangle no matter what. With only one teacher in the lab, it would take longer to get through the learning stages for using GSP however, once the teacher has shown a student, this student can then show his/her neighbour and so on.Īfter the students have had a chance to play around with the sketch, Nathalie gathers the attention of the students and asks them what happens to the mystery point P as the vertices of the triangle are moved. Given that we have four instructors available, we are easily able to move about the room and assist students experiencing difficulties. We give them 5 minutes to manipulate the triangle shape and observe the movement of P. Most of the students are able to drag the vertices of the triangle intuitively to manipulate the triangles. How would you make the point P in your own triangle? Along with a triangle and a "mystery" point P inside the triangle, there are the following instructions:ĭrag the vertices of the triangle around. The students open a pre-made sketch called P-triangle. Classes are 72 minutes per day (semestered school). This is the first time the students have seen Geometer's Sketchpad (GSP). ![]() We have not done any introductory work with compass and ruler constructions. The class is just beginning a unit on geometry. There areĢ4 PCs (one per student), an Overhead projector connected to a PC, and Large Blackboards. ![]() The Setting: April 12th at the Computer Lab at KCVI in Kingston, Ontario. Three days Sketching madly with Grade 9 students Student Gallery Stories from the Classroom
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