MORE ON AREA AND MULTIPLICATION
Introduction and Background
As you now know, the area of a rectangle is determined by finding out how many unit squares it takes to cover the rectangle.
You have also discovered that the area of a rectangle can be computed by using multiplication. This activity will build on that discovery.
For this activity, you are going to use the Unit Square to measure both area and length. The length of any side of the unit square is equal to 1 unit.
Step 1. Construct Rectangles of a Given Area
On the GeoGebra page are four rectangles (A, B, C, and D) labeled with their height, width, and area. Use the MOVE GRAPHICS VIEW tool as needed to see all four rectangles.
Use the MOVE (pointer) tool to modify these rectangles so they each have an area of 24 unit squares.
However, each of the four rectangles you create should have a different height and width.
Use the GRID to check that your rectangles do have an area of 24 square units.
Step 2. A Problem
Mr. Jones has 12 carpet tiles that he wants to arrange into a rectangle on his basement. How many rectangles having different heights and widths can he make with his 12 carpet tiles?
Pull down the FILE menu and open a new GeoGebra page.
Use the POLYGON tool to construct all of the different rectangles Mr. Jones can make with his 12 carpet tiles.
Use the GRID to check that your rectangles do have an area of 12 square units.
Step 3. Print and Reflect
Print your constructions. On the printout, write a paragraph describing how multiplication and area are connected: