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## Measuring Volume using Customary Units

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Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).  Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.

## Measuring Volume - Metric Units

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Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).1 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.

## 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.

## Volume of a Sphere

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

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

## Volume of a Cone

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Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.G-GMD.A.3, CCSS.Math.Content.8.G.C.9

## Volume of a Pyramid

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

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

## Volume of a Cylinder

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

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

## Volume of a Rectangular Prisms

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Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

## Metric Units of Mass and Liquid Volume

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Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).17 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.