Objective The students will be able to derive and use formulas for area and volume.
Previous Material Studied Accelerated math students in the seventh grade should have mastered the use of simple formulas as well as the use of all four operations with whole numbers, fractions and decimals. Before this unit they also should be proficient in the uses of inverses to solve mulit-step equations. The geometry chapter which includes vocabulary, and properties of quadrilateral, triangles, and three-dimensional figures is included in prior knowledge.
Materials In order to use this unit, the classroom must be equipted with a computer, access to GSP, and an overhead projector connected to the computer. The students will need 1/4" grid paper on which to copy these constructions
Area of squares and rectangles In order to stress the concept of area, students will trace their hands on square centimeter grid paper and count the number of squares that their hands cover. The exercise needs to include how to handle partial squares. The same grid paper can then be used to make figures with a given area. Discussion of squares and rectangles, as to why they easiest figures to draw, need to include the concept of numbers of squares in each row times the number of rows. At this point, students should be ready to use the standard formulas for the areas of squares and rectangles.
Area of Parallelograms The first activity with the area of parallelograms is to compare the area of that of a rectangle. Each student is given a ruler and a large sheet of paper 8 1/2 by 14". They are directed to find the area and perimeter of this sheet of paper, some students can even divide it into square inches to count the squares.
Now the paper is torn, using the ruler or simply by repeated folding, diagonally within the long edges. By exchanging parts, the students now have a parallelogram. Have them compute the area and perimeter of this figure. When they finally realize that the area has not changed but the perimeter has, we can discuss the importance of perpendicular distance.
The following sketchpad illustration can be put on the overhead to demonstrate the concepts involved in the new formula. (Click here for the illustration.)