by Derelle McFarland

*To use compass and straight edge to make constructions
*To use GSP to make constructions
*To use the properties of polygons
*To construct a portfolio containing your constructions
Day 1
On the board I will have listed the following figures, equilateral triangle, obtuse triangle, isoceles triangle, rhombus, trapezoid, isoceles trapezoid, kite, parallelogram, rectangle, square, and circle.
As a class we will brainstorm the properties of these figures. The students should remember the characteristics from middle school, but if they don't they are in their geometry book. When we finish discussing, and the students have taken notes on these I will explain the next two weeks assignment. They are to create a portfolio of the constructions we will be constructing for the next two weeks. Some days we will use GSP and others we will use compass and straight edge. Their portfolio will be worth a test grade and will be broken into presentation (15pts), organization (15pts), disc (15 pts), reflection (20pts) and contents (35pts). Today and tomorrow they will construct the figures we discussed using compass and straight edge. I will allow them to work in groups but they must do their own construction. For homework each night they are to describe any observations they made about their constructions, difficulties they had or things they enjoyed to be their reflections included in their portfolio.
Day 2
Continue constructions using compass and straight edge.
Day 3
Today we will go to the computer lab to do our constructions using GSP. I will give each student a disc for their use. I will explain that the disc must be organized and turned in for 15 points of the portfolio grade. The students have used GSP briefly before. I expect lots of questions so I will refresh their memory of using GSP. I will go over the icons on the left bar on the computer which projects onto the screen, but I will require the students follow along on their computer. I will explain the proper GSP construction that does not "move" and the improper ones that don't "stick". There are exactly enough computers for each student to have their own. Once we have reviewed the use of GSP, I will allow them to begin constructing the same constructions from our discussion on Monday. Each student will have a disc to use that I will keep at the end of the day. This will ensure that students who have the technology at home are staying on task in class.
Day 4
Continue constructions using Geometers Sketch Pad.
Day 5
Today we will construct inscribed figures. There will be eight constructions to be done on both GSP and compass and straight edge. We will go to the lab to do the GSP part and the compass and straight edge part will be homework. The eight constructions are:
1) square inscribed in a triangle
2) circle inscribed in a triangle
3) triangle inscribed in a triangle
4) square inscribed in a square
5) circle inscribed in a square
6) triangle inscribed in a square
7) triangle inscribed in a circle
8) square inscribed in a circle
Day 6
Today I am going to teach the students how to construct the altitude, medians, angle bisectors and perpendicular bisectors of a triangle to find the orthocenter, centroid, incenter and circumcenter of a triangle. I will bring the computer into my room and show my work on the overhead screen. I will allow students to come up and help with the constructions. Here is what I will show.

This should take most of the period, so I will allow them the end of the period to begin their compass and straiht edge construction of these points for equilateral, isoceles and obtuse triangles. They are to reflect upon the different postitions of these points depending on the type of triangle.
Day 7
Today they will construct the orthocenter, centorid, incenter and circumcenter for an equilateral, isoceles and obtuse triangle in the lab using GSP.
Day 8
We will be in the lab again today. We will use the previous lessons to construct the nine point circle, eight point circle, Euler line and Pedal triangle. After I demonstrate how to construct the nine point circle (and they follow along on their computer), I will give the students the following ditto describing the characteristics of each, and allow them to explore them on GSP.

Eight point circle: Let ABCD be a quadrilateral with perpendicular diagonals. The midpoints of the sides determine a parallelogram with sides parallel to the diagonals. The eight point circle passes through the four midpoints and the four feet of hte perpendiculars from the opposite sides.

Euler Line: The euler line is the line on which the orthocenter, centroid, circumcenter and nine point center lie. Investigate what kind of triangle has a Euler line that also contains the incenter. Be sure to write about this in your reflections.

Pedal Triangle: Given a point P, the pedal triangle of P is the triangle whose vertices are the feet of the perpendiculars from P to the sides. What do you think the second and third pedal triangles would be like. Investigate and explain in your reflection for today.

Day 9
Today we will be in the lab to allow students to complete any unfinished constructions. They should have all of their constructions on paper for their portfolio, but their disc should also be neatly organized so that I can be sure that their GSP constructions "stick".
Day 10
Today is the last day of the unit. The students will break into groups of 5 and share their portfolios. As they leave class they are to turn in their portfolios.
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