Start with estimating the area of a triangle when first introducing the topic with students. Provide students with graph paper or geoboards, which are square shaped peg boards, and rubber bands. Have the students create a triangle. For example, tell the students to make a triangle with a base of 3 and a height of 2. Once the students have created the triangles, have them estimate the area of the triangle by counting the number of squares inside the triangle. For partial squares, have the students estimate whether it is 1/2 or 1/4th of the square. Add them together to find the estimated area.
Continue using the graph paper or geoboards to find the exact area of the triangle. Instead of estimating, the students will find the exact area of the triangle by using squares or rectangles around the triangle. The area of a square and rectangle is easy to find, base multiplied by the height. On graph paper, the area is also easy to count. In this method, students use subtraction by first finding the area of a square or rectangle which surrounds thee triangle. The students then subtract the outside squares which are inside the square or rectangle but are not part of the triangle from the total area of the square or rectangle.
Have the students experiment with different triangles, focusing on the base, height and the area of the triangle using one of the techniques of addition or subtraction. Have the students record their findings. The class as a whole should share some of their answers listing the base, the height and the area of the triangle. Work as a class to find a pattern within the graph. You will get many variations on the traditional equation 1/2 height times the base. For example, 1/2 base times the height or base multiplied by height divided by 2 are both equivalent equations for the area of a triangle.
Break the class into groups of three or four. Provide the students with graph paper and a sheet of instructions. The instructions should include directions on creating and finding the area of certain triangles. For example, "Draw a triangle with a base of 5 and a height of 6. Find the area of the triangle." Other instructions should use the equation in a different way such as, "Draw a triangle with an area of 4." The group that gets the most correct answers, both in drawing the correct triangle and finding the correct area of the triangles, wins.