Architects in Action
Show students a map of the United States and point out the scale in the map key. Explain that sometimes we shrink objects or make them larger so they are easier to work with. The map is a scale model of an object that is too large to represent on paper. Other scale models represent objects that are too small, such as a diagram of an atom or a magnified view of a computer chip. Review the scale on the map. For example, the scale may say that 1 inch is equal to 50 miles. Explain that a scale is a ratio used to determine the size of a model of a real object. In this case, the map of the United States is the model.
Illustrate how to draw an object to scale. Use a ruler to draw a square on the board with sides that equal 10 inches in length. Ask students how they might use this square to draw another that is half its size. Now measure and draw a second square with 5-inch sides. Explain that when an object is scaled down, the length of its sides must be reduced by the same amount. Compare the corresponding sides of the two squares. The ratio of the small square to the larger is 5: 10. Show that a ratio can be expressed in three ways: 5: 10, 5 to 10, or 5/10, which is a fraction that reduces to 1/2.
- Explain that students will use ratio to make a scale drawing on graph paper of the classroom floor plan including the desks, tables, closets, and so on. Divide students into teams of four. The class may choose to use either metric or English measurements.
- Construct a class data table on the board with three columns labeled "object," "measurement," and "scaled measurement." Students should copy this table in their notebooks and fill in the answers as they measure the objects. Once teams have recorded all their data, they will decide on the scale of their floor plan.
- Students can determine their scaled equivalents by cross-multiplying. Students should recall that when both sides of an equation are multiplied by the same amount, the equation remains balanced.
- Have students use their scaled measurement, rulers, and graph paper to draw the floor plan their team measured. Remind them to include a title, labels, and a scale.
- As students complete their drawings, have them calculate the perimeter and area of their classrooms. What is the relationship between the drawing and the actual classroom? They should notice that the ratio of these areas is the square of the scale they chose. For example, if a scale of 0.5 inch = 1 foot was used, the ratio of areas of the drawing to the actual room will be (0.5 inches)2 = (1 foot)2 or 0.25 square inches = 1 square foot.
- Compare your classroom floor plan to that of another student. How are they similar and different? Which would be more useful to a construction worker trying to build a classroom in a new school? Why?
- List other instances in which you use ratio to compare objects in your daily life. Why is it important to maintain the same scale for each measurement you record when making your model?
- Debate the merits of using the metric system and the English system to measure lengths. Explain how to convert between the two systems.
- Using what you have learned about ratios, proportions, and scale models, create four word problems for other students in your class to solve. For example: A square carpet measures 8 feet x 4 feet. Suppose the scale of a drawing containing the carpet is 1 foot to 1/4 inch. What are the dimensions of the carpet in the drawing? The answer: 2 inches x 1 inch.