Content Standard(s):
Mathematics 18. Identify volume as an attribute of solid figures, and measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised (non-standard) units.
a. Pack a solid figure without gaps or overlaps using n unit cubes to demonstrate volume as n cubic units.
Unpacked Content
Evidence Of Student Attainment:
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. Teacher Vocabulary:
Volume
Cube
Cubic unit
Unit cube
Space
Three-dimensional
Attribute Knowledge:
Students know:
strategies or the formula to find the area of a rectangle. Skills:
Students are able to:
Count unit cubes to find volume.
Demonstrate volume by packing a solid figure with unit cubes. Understanding:
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. Diverse Learning Needs:
Essential Skills:
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.
Prior Knowledge Skills:
Count unit cubes to find volume.
Demonstrate volume by packing a solid figure with unit cubes.
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.
Alabama Alternate Achievement Standards
AAS Standard:
Mathematics 19. Relate volume to the operations of multiplication and addition, and solve real-world and mathematical problems involving volume.
a. Use the associative property of multiplication to find the volume of a right rectangular prism and relate it to packing the prism with unit cubes. Show that the volume can be determined by multiplying the three edge lengths or by multiplying the height by the area of the base.
b. Apply the formulas V = l x w x h and V = B x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world and mathematical problems.
c. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the two parts, applying this technique to solve real-world problems.
Unpacked Content
Evidence Of Student Attainment:
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. Teacher Vocabulary:
Volume
Unit cube
Rectangular prism
Base
Base-area
Dimensions
Face
Length
Width
Height
Layers
Edge
Equivalent
Conservation of volume
Attribute
Composition
Decomposition
Formula Knowledge:
Students know:
Measurable attributes of area and how it relates to finding the volume of objects.
Units of measurement for volume, specifically unit cubes. Skills:
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. Understanding:
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. Diverse Learning Needs:
Essential Skills:
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.
Prior Knowledge Skills:
Count unit cubes to find volume.
Demonstrate volume by packing a solid figure with unit cubes.
Convert measurement units.
Solve mulit-step word problems involving measurement conversions.
Alabama Alternate Achievement Standards
AAS Standard:
