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## Expanded Form

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Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

## Derive Volume formula for Pyramid

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Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Give informal arguments for the formula of the volume of a cylinder, pyramid, and cone using Cavalieri’s principle.

## Derive Volume formula for Cylinder

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Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.

Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

## Derive the Law of Sine for Problem Solving

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Prove the Laws of Sines and Cosines and use them to solve problems.

Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

## Slope Condition for Perpendicular Lines in Coordinate Plane

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Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

## Slope Condition for Parallel Lines in Coordinate Plane

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Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

## Finding the Area of Polygons using Distance Formula

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Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

## Proving Midpoint Theorem for 2 Sides of a Triangle

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Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

## Appropriate Tools for Measurement

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Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

## Derive the Formula A=½ ab Sin(c) from the Area of a Triangle

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Derive the formula A = ½ ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.