ALEX Classroom Resource

Students:

• Measure volume of rectangular solids by packing the figure and counting the number of same-sized unit cubes needed to completely fill the figure.

Students know:

• strategies or the formula to find the area of a rectangle.

Students are able to:

• Count unit cubes to find volume.
• Demonstrate volume by packing a solid figure with unit cubes.

Students understand that:

• volume represents the amount of space enclosed in a three-dimensional figure and is measured by the number of same-size cubes that exactly fill the interior space of the object.

Learning Objectives:
M.5.18.1: Define volume including the formulas V = L × W x h, and V = B x h.
M.5.18.2: Define solid figures.
M.5.18.3: Define unit cube.
M.5.18.4: Recognize that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).
M.5.18.5: Describe attributes of three-dimensional figures.
M.5.18.6: Describe attributes of two-dimensional figures.
M.5.18.7: Compare the unit size of volume/capacity in the metric system including milliliters and liters.
M.5.18.8: Define cubic inches, cubic centimeters, and cubic feet.
M.5.18.9: Compare the unit size of volume/capacity in the customary system including fluid ounces, cups, pints, quarts, gallons.
M.5.18.10: Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
M.5.18.11: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).
M.5.18.12: 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.
M.5.18.13: Recall basic multiplication facts.
M.5.18.14: Fluently add.

Students:
Given a right rectangular prism with fractional edge lengths within a real-world or mathematical problem context,

• Find and justify the volume of the prism as part or all of the problem's solution by relating a cube filled model to the corresponding multiplication problem(s).

Given cubes with appropriate unit fraction edge lengths,

• Create and explain rectangular prism models to show that the volume of a right rectangular prism with fractional edge lengths l, w, and h is represented by the formulas V = l w h and V = b h.

Students know:

• Measurable attributes of objects, specifically volume.
• Units of measurement, specifically unit cubes.
• Relationships between unit cubes and corresponding cubes with unit fraction edge lengths.
• Strategies for determining volume.
• Strategies for finding products of fractions.

Students are able to:

• Communicate the relationships between rectangular models of volume and multiplication problems.
• Model the volume of rectangles using manipulatives.
• Accurately measure volume using cubes with unit fraction edge lengths.
• Strategically and fluently choose and apply strategies for finding products of fractions.
• Accurately compute products of fractions.

Students understand that:

• The volume of a solid object is measured by the number of same-size cubes that exactly fill the interior space of the object.
• Generalized formulas for determining area and volume of shapes can be applied regardless of the level of accuracy of the shape's measurements (in this case, side lengths).

Learning Objectives:
M.6.28.1: Define volume, rectangular prism, edge, and formula.
M.6.28.2: Recall how to multiply fractional numbers.
M.6.28.3: Evaluate the volumes of rectangular prisms in the context of solving real-world and mathematical problems.
M.6.28.4: Use models and volume formulas (V=lwh and V=Bh) to find volumes in the context of solving real-world and mathematical problems.
M.6.28.5: Calculate the volume of a rectangular prism using fractional lengths.
M.6.28.6: Test the formula V= lwh and V=Bh with the experimental findings.
M.6.28.7: Experiment with finding the volume using a variety of sizes of rectangular prisms manipulatives.

Students:

• Find efficient ways to determine surface area of right prisms and right pyramids by analyzing the structure of the shapes and their nets.
• Use the formulas for volume of prisms and pyramids to solve multi-step real-world problems.
• Use the formula for volume to find missing measurements of a prism.

Students know:

• that volume of any right prism is the product of the height and area of the base.
• The volume relationship between pyramids and prisms with the same base and height.
• The surface area of prisms and pyramids can be found using the areas of triangular and rectangular faces.

Students are able to:

• find the area and perimeter of two-dimensional objects composed of triangles, quadrilaterals, and polygons.
• Use a net of a three-dimensional figure to determine the surface area.
• Find the volume and surface area of pyramids, prisms, or three-dimensional objects composed of cubes, pyramids, and right prisms.

Students understand that:

• two-dimensional and three-dimensional figures can be decomposed into smaller shapes to find the area, surface area, and volume of those figures.
• the area of the base of a prism multiplied by the height of the prism gives the volume of the prism.
• the volume of a pyramid is 1/3 the volume of a prism with the same base.

Learning Objectives:
M.7.22.1: Define volume, surface area, triangles, quadrilaterals, polygons, cubes, and right prisms.
M.7.22.2: Discuss strategies for solving real-world mathematical problems.
M.7.22.3: Recall formulas for calculating volume and surface area.
M.7.22.4: Identify the attributes of triangles, quadrilaterals, polygons, cubes, and right prisms.

Students:

• Find efficient ways to determine surface area of right prisms and right pyramids by analyzing the structure of the shapes and their nets.
• Use the formulas for volume of prisms and pyramids to solve multi-step real-world problems.
• Use the formula for volume to find missing measurements of a prism.

Students know:

• That volume of any right prism is the product of the height and area of the base.
• The volume relationship between pyramids and prisms with the same base and height.
• The surface area of prisms and pyramids can be found using the areas of triangular and rectangular faces.

Students are able to:

• Find the area and perimeter of two-dimensional objects composed of triangles, quadrilaterals, and polygons.
• Use a net of a three-dimensional figure to determine the surface area.
• Find the volume and surface area of pyramids, prisms, or three-dimensional objects composed of cubes, pyramids, and right prisms.

Students understand that:

• Two-dimensional and three-dimensional figures can be decomposed into smaller shapes to find the area, surface area, and volume of those figures.
• The area of the base of a prism multiplied by the height of the prism gives the volume of the prism.
• The volume of a pyramid is 1/3 the volume of a prism with the same base.