U.S. National Standards
N.3. Geometry (NCTM)
3.4. Use visualization, spatial reasoning, and geometric modeling to solve problems.
3.4.4. Use geometric models to represent and explain numerical and algebraic relationships.
N.4. Measurement (NCTM)
4.2. Apply appropriate techniques, tools, and formulas to determine measurements.
4.2.2. Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.
4.2.3. Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.
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.