The scale factor is the ratio of two corresponding sides of two similar figures. If you have two squares, the first measuring 4 inches x 4 inches and the second measuring 8 inches x 8 inches, the scale factor is two. In other words, the second square is enlarged by a scale of two. Similarly, if a square measuring 3 inches x 3 inches is enlarged by a scale of five, the new square will measure 15 inches x 15 inches. The scale factor then is the number you multiply or divide to the length of a side to get the length of a corresponding side. Scale factor projects include making scale models of two-dimensional or three-dimensional figures.

## Two-dimensional Scale Factor Project

Making a scale model of a classroom is a simple and effective scale factor project. Students will appreciate how a given factor reduces or enlarges a two-dimensional figure, as they tackle the concept in a hands-on approach. To start, draw a simple sketch of the classroom and include the location of windows and doorways. Indicate the location of any furniture inside the classroom, such as desks, shelves and cabinets. Next, measure and note the actual lengths and widths of the classroom. You will have to measure the width of the windows and doorways, as well as the distance from the wall for each window and doorway. Similarly, measure the distance between each piece of furniture and the wall. Note the lengths and round all lengths to the nearest inch.

## Scaling Down A Classroom

With all measurements noted, calculate the area and perimeter of the floor. Suppose the length of the room is 400 inches and the width is 300 inches; the area of the room will be 120,000 square inches (length x width), and the perimeter will be 1,400 inches (sum of all sides). Once you have the actual measurements, you can draw the exact scale model of the room on a graph paper using a scale factor. Suppose your factor is 50:1. This means that for every 50 inches of actual length, you will draw 1 inch in your scale model. Since you are reducing from an actual size to a smaller scale model, you will have to divide the measurements by 50. This gives a length of 8 inches (400 / 50) and a width of 6 inches (300 / 50). So, your scale model will be 8 inches x 6 inches. Complete the scale by drawing the windows, doorways and furniture on the graph paper by dividing the actual distances by 50.

## Three-dimensional Scale Factor Project

A scale factor project can also be done on a three-dimensional object, such as a pyramid. For a three-dimensional scale model you will have to construct a miniature version of the object using readily available school supplies such as tape, glue and cardboard. First, find out the measurements of the pyramid and determine an appropriate scale factor for the project.

## Constructing a Scale Model Pyramid

Suppose the height of the pyramid is 145m (14,500cm) and your scale factor is 3,000:1. This means the height of the scale model will be 4.8cm (14,500 / 3,000). With the measurements of the scale model, construct the pyramid. Mark the lengths of the base and the sides on separate pieces of paper, and cut lengths of cardboard using the paper pieces as a guide. Bind the four sides together with tape and attach it to the base. The scale model will be 3,000 times smaller than the actual pyramid.

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