#### MAT-07.GM.AV.01

 7th Grade (MAT) Targeted Standard     (GM) Geometry and Measurement (AV) Area and Volume Learners will use visualization and spatial reasoning to solve problems involving the area, surface area, and volume of geometric figures.

## Progressions

Perimeter

• MAT-03.GM.M.06 Solve problems involving the perimeters of rectangles given the side lengths or when given the perimeter and unknown side length(s).
• MAT-04.GM.M.05 Apply the area and perimeter formulas for rectangles, including connected rectangular figures, in problems.
• MAT-05.GM.M.02 Find the area and perimeter of a rectangle, including connected rectangular figures, with fractional side lengths.
• MAT-07.GM.AV.01 Describe the relationship between the circumference and diameter of a circle (pi). Apply given formulas to calculate the area and circumference of a circle, including in authentic problems.
• MAT-10.GM.30 Compute perimeters of polygons and areas of triangles, parallelograms, trapezoids, and kites using coordinates.

Circle Measurements

• MAT-07.GM.AV.01 Describe the relationship between the circumference and diameter of a circle (pi). Apply the given formula to calculate the area and circumference of a circle, including in authentic problems.
• MAT-10.GM.22 Apply theorems about relationships between line segments and circles or angles and circles formed by radii, diameter, secants, tangents, and chords to find unknown lengths or angles.
• MAT-10.GM.25 Explain and use the formulas for arc length and area of sectors of circles.
• MAT-10.GM.26 Recognize that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.
• MAT-10.GM.31 Explain derivations of the formulas for the circumference of a circle, area of a circle, and volume of a cylinder, pyramid, and cone.
• MAT-12.GM.01 Write the equation of a conic section given its special features. Convert between the standard form and general form equations of conic sections.
• MAT-12.GM.02 Identify key features of a conic section given its equation. Apply properties of conic sections in context.
• MAT-12.AR.F.18 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.