U.S. National Standards
N.1. Number and Operations (NCTM)
1.3. Compute fluently and make reasonable estimates.
1.3.4. Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.
N.3. Geometry (NCTM)
3.1. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
3.1.2. Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.
3.1.3. Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.
N.4. Measurement (NCTM)
4.2. Apply appropriate techniques, tools, and formulas to determine measurements.
4.2.5. Solve problems involving scale factors, using ratio and proportion.
N.12. Connections to the Grade 7 Focal Points (NCTM)
12.1. Measurement and Geometry: Students connect their work on proportionality with their work on area and volume by investigating similar objects. They understand that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related, and the cube of the scale factor describes how corresponding volumes are related. Students apply their work on proportionality to measurement in different contexts, including converting among different units of measurement to solve problems involving rates such as motion at a constant speed. They also apply proportionality when they work with the circumference, radius, and diameter of a circle; when they find the area of a sector of a circle; and when they make scale drawings.