On June 2nd 2009, IMPOME Students studied mathematics about What a teacher can explain by roof? That class was lectured by Prof. Zulkardi, M.Sc and attended by 13 students. Students divided into 6 group to facilitate learning process and discussion. Each student was given 1 roof which is divided 12 sides, and they have same length. After that, Professor had students use their roofs as a learning model.
There are some subjects which can be used roof as learning model like number theory, Triangle, Quadrilateral, Hexagon, and Symmetry.
A teacher can use roof (figure 1) to explain number line, positive-negative number, addition-division number and comparison number. For example, Students can discuss how to calculate 3 + 2 or 4 – 6 base on figure 1. They must understand number line first, so they can also understand other subjects. A teacher is only hoped to guide his/her students find concept so they can use that to answer many question about number.
There are three triangles can be made in roof. First, right triangle which sides 3,4, and 5 is in figure 2. Students are hoped to understand about Pythagorean theorem, which states in any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the two other sides. Second, equilateral triangle which is in figure 3 sides 4,4, and 4. all sides are the same length. An equilateral triangle is also a regular polygon with all angles equal to 60°. Students can find it because they make it by themselves. Last, isosceles triangle which sides 5,5, and 2 is in figure 4. two sides are equal in length. An isosceles triangle also has two equal angles: the angles opposite the two equal sides. A teacher only guides his/her students to reinvent triangle, and they must develop their ability to analyze triangle theory.
figure 2 figure 3 figure 4
Students can make many kinds of Quadrilateral such as square, rectangle, parallelogram, rhombus, and kite. First, Students make square which sides 4 in Figure 5.They can calculate that area by dividing it and perimeter by summing its sides. all four sides are of equal length (equilateral), and all four angles are right angles. the diagonals perpendicularly bisect each other, and are of equal length. Second, Students are able to make two different size rectangle. In Figure 6 is rectangle which sides 5 length-1 wide and 4 length-2 wide in figure 7. So, students can know that all four angles are right angles. Equal conditions are that opposite sides are parallel and of equal length, or that the diagonals bisect each other and are equal in length. There are two model of rectangle. They can compare figure 6 with figure 7 about those area and perimeter. Third, There are two parallelogram which are different area but same perimeter. They side 5,1 in figure 8 and 4,2 in figure 9. Students can compare that parallelogram and make conclusion that parallelogram is a quadrilateral with two sets of parallel sides. Equal conditions are that opposite sides are of equal length; that opposite angles are equal; or that the diagonals bisect each other. Next, Students can make rhombus that sides 3 in figure 10. It is a parallelogram in which adjacent sides are of unequal lengths and angles are oblique (not right angles). “A pushed-over rectangle. Finally, Students invent kite that is two adjacent sides are of equal length and the other two sides also of equal length. This implies that the angles between the two pairs of congruent sides are equal, and also implies that the diagonals are perpendicular.
Figure 5 Figure 6 Figure 7
Figure 8 Figure 9 Figure 10 Figure 11
Using that roof, students can make hexagon which sides 2 units, and they can also analyze its figure. Each angle is more than 900, and if they divide it, they can get 6 equilateral triangle. So, there is some relation between hexagon and triangle.
There are 2 kinds of symmetries that students can find from roof media by making letters. First, They can make some letters like in figure 12 – letter M, figure 13 – letter C, and figure 13 – letter U, and find definition about reflection symmetry. They have to know what mirror symmetry is and also know other figures which have that symmetry in their life. Second, Rotational symmetry which is an object that looks the same after a certain amount of rotation is in figure 14 – letter Z and figure 15 – letter S.
Figure 12 Figure 13 Figure 14
Figure 15 Figure 16
Roof is a media which can be use to explain some mathematics subjects such as Number theory, Triangle, Quadrilateral, Hexagon and Symmetry. First, Students study about natural number and number line from it. Second, They study about equilateral triangle, isosceles triangle, and right triangle and square, rectangle, parallelogram, rhombus, and kite. Next, Hexagon is one of figure which students can make and study. Finally, By making letters students can study about reflection symmetry and rotational symmetry. So, students are able study many things by using roof as media.