(11) (12)

This activity it designed for fifth to seventh grade students. This activity deals with geometry concepts. Area of rectangles is the main topic of this activity. Perimeters are also explored. A graphing challenge is included at the end of the activity.

Materials (9)

Scissors for students

Graphing calculators (TI-83)

Paper with one unit square boxes sectioned off

Pre-activity exercise (2) (10)

Show overheads of rectangles of various areas. Each rectangle should have been sectioned into boxes of 1 square unit area (Samples for overhead at the end of this document). This is to allow the students to easily count the area of the rectangles. Have the students as a class count the area, length, and width of each rectangle. When you are certain that the students understand what is referred to as the area, length, and width of the rectangle, proceed.

Now, supply the students with paper that is sectioned into boxes of area one square unit (such as graph paper) (Sample piece of paper is at the end of this document). Tell the students to cut out multiple rectangles of area twelve.

(8) When the students have done this, compare their rectangles to the other students rectangles. The students should have produced rectangles of the same area (12 sq.units) but of different perimeters. You can use the students varying rectangles to emphasize that objects that have the same area do not necessarily have the same perimeter.

Generative activity (1) (15) (5) (6) (10)

Now, ask the students to make other rectangles by placing together their pre-cut rectangles from the pre-activity exercise. Ask the students to make atleast seven different rectangles. Have the students record the length, width, and area of each of their rectangles on a table.

Hand calculators to the students. Ask them if there is any sort of relationship in the information in their tables. Allow them to work in groups to "play" with the numbers in their tables.

(8) Now, gather the class into a group. Ask some students to write their favorite rectangle on the board. Lead a group discussion about the rectangles. Suggestions are as follows.

Take one of the students favorite rectangles dimensions. Recreate a rectangle of the same dimensions on the overhead for the class to view. Write the length and width dimensions next to their appropriate sides. Ask the class if anyone notices a relationship between the length and width dimensions and the area. If students do not notice a similarity it would be possible to refer to the area model of multiplication and see if the students notice a similarity between the area model and their rectangles. (This will only be appropriate if your students have used the area model for multiplication.)

This discussion can be followed with exercises, in the format of what is the area of a rectangle with:

Length:3 units Width:5 units

Length:2 units Width:10 units

Length:50 units Width:11 units

The students can use drawings to help them if needed.

Challenge Activity (13)

Now the students should have the knowledge that the area of a rectangle is equal to the length of the rectangle multiplied by the width. Now, a graphing calculator can be used to illustrate that there is an infinite possibility of combinations of lengths and widths that can be multiplied to make a rectangle of an area of twelve. On the graphing calculator, have the students type in what Y equals. Y can be pre-determined to equal the width of the rectangle. The students will have to enter the area in a form of what Y equals (i.e. Y = area/length). Now, graph this function. Have students pick random points off of their graph. Do these points (lengths and widths) when multiplied together equal twelve?

(8) You can also draw the students attention to the fact that the graph does not enter the negative quadrants. Why?

Examples of students' possible solutions (3) (4) (7) (14)

Pre-activity

Examples of rectangle cut outs