Learning goals: Teacher Facing Interpret radian measure as the constant of proportionality between an arc length and a radius. Justify (in written language) why the formula $\frac12 r^2 \theta$ gives the area of a sector with central angle $\theta$ radians and radius $r$ units. Full lesson plan (warm-up, activities, synthesis, cool-down prompt) from Geo.7 Circles, Geometry.