Roads and Ramps: Slopes, Angles, and Ratios

In this unit, students work with concepts and skills involving angles, slopes, scale drawings, right triangles, proportions and the tangent ratio. Students begin by building a “slope-o-meter” to explore slope and angle relationships. This leads to work with the Pythagorean Theorem. Students then investigate slope as a ratio and use the idea of percent-grade of roads to study real-world slopes. They then work with tangent ratios and apply everything they have learned to design a road and build a 3-D model of it.

NCTM standard: Geometry

NCTM standard: Measurement

NCTM standard: Algebra

Primary Mathematical Goals