High School Math Guide

Measuring Circles, Angles, and Shapes

Unit 8

MATH CORE STANDARDS II.G.GMD.1 : Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. II.G.C.5 : Derive, using similarity, the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. II.G.GMD.3 : Use volume formulas to cylinders, pyramids, cones, and spheres to solve problems. II.A.SSE.1 : Interpret expressions that represent a quantity in terms of its context.

Critical Background Knowledge

• Know the area and circumference of a circle (7.G.4) • Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment (I.G.CO.1) • Use a variety of construction methods (I.G.CO.12, I.G.CO.13) • Know the formulas for the volume of cones, cylinders, and spheres (8.G.9) • Solve real-world and mathematical problems involving volume of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, and cubes, and right prisms (7.G.6) • Understand similarity (II.G.SRT) • Calculate circumference and area of a circle (7.G.4)