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 right rectangular prisms with whole number edge lengths,

• Use associative property of multiplication to find volume and relate it to packing a solid with unit cubes.
• Apply formula V = l × w × h, where V represents volume and l, w, and h represent the three dimensions of the prism (length, width, height) and relate the formula to a unit cube filled model.
• Apply formula V = B × h, where V represents volume, B is the base-area, and h represents the height (number of layers of the base-area) and relate the formula to a unit cube filled model.

• Given a solid figure composed of two or more right rectangular prisms in real-world or mathematical contexts, find the total volume by decomposing the figure into non-overlapping rectangular prisms and find the sum of the volumes.

Students know:

• Measurable attributes of area and how it relates to finding the volume of objects.
• Units of measurement for volume, specifically unit cubes.

Students are able to:

• Solve word problems involving volume.
• Use associative property of multiplication to find volume.
• Relate operations of multiplication and addition to finding volume.
• Apply formulas to find volume of right rectangular prisms.
• Find volume of solid figures composed of two rectangular prisms.

Students understand that:

• Volume is a derived attribute based on a length unit and can be computed as the product of three length measurements or as the product of one base area and one length measurement.
• Volume is an extension of area and can be found as the area of the base being repeated for a given number of layers.

Learning Objectives:
M.5.19.1: Define volume.
M.5.19.2: Recognize angle measure as additive.
M.5.19.3: Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.
M.5.19.4: Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.
M.5.19.5: Recognize the formula for volume.
M.5.19.6: Recall the attributes of three-dimensional solids.
M.5.19.7: Recall basic multiplication facts.
M.5.19.8: Fluently add.
M.5.19.9: Compare the unit size of volume/capacity in the metric system including milliliters and liters.
M.5.19.10: Measure and estimate liquid volumes.
M.5.19.11: Recall basic multiplication facts.
M.5.19.12: Compare the unit size of volume/capacity in the metric system including milliliters and liters.
M.5.19.13: Recognize the formula for volume.
M.5.19.14: Recall basic multiplication facts.
M.5.19.15: Describe attributes of three-dimensional figures.
M.5.19.16: Describe attributes of two-dimensional figures.
M.5.19.17: Identify solid figures.