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## 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).

## 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.

## 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.

## 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.

## 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).

## 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).

## Calculating the Intersection Points for 2 Equations

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Graphing Calculator Lesson (TI-84)

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x² + y² = 3.

## Choosing a Unit of Measurement for Time

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Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

## Choosing a Metric Unit of Measurement for Length

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Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...