MD-Geometric+measurement-understand+concepts+of+volume+&+relate+volume+to+multiplication+and+to+addition

5.MD.3.Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. a. A solid figure which can be packed without gaps or overlaps using //n// unit cubes is said to have a volume of //n// cubic units. 5.MD.4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. 5. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. a. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication. b. Apply the formulas //V// = //l// × //w// × //h// and //V// = //b// × //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. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. || ===‍‍‍‍‍‍‍‍‍‍**Anchor Standard/Mathematical Practice**=== 5. Use appropriate tools strategically 2. Reason abstractly and quantitatively 4. Model with mathematics 6. Attend to precision 7. Look for and make use of structure 5. Use appropriate tools strategically 4. Model with mathematics 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning 1. Make sense of problems and persevere in solving them. 7. Look for and make use of structure 5. Use appropriate tools strategically 4. Model with mathematics 3. Construct viable arguments and critique the reasoning of others || 5.TT.1 Use technology tools and skills to reinforce and extend classroom concepts and activities **. ** || ===‍‍‍‍‍‍‍‍‍‍**Revised Bloom's Level of thinking**=== <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.MD.3a I can recognize that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume.
 * ===**Common Core Standard**===
 * 5.MD.3a**
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">5.MD.3b **
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">5.MD.4 and 5.MD.5 **
 * ===‍‍‍‍‍‍‍‍‍‍**Information Technology Standard**===
 * 5.MD.3a Understand**
 * 5.MD.3b Create**
 * 5.MD.4 Create**
 * 5.MD.5 Create** ||
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Explore attributes of cubic objects including nonstandard units
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Identify benchmark volume units of cm3 in3 ft3 meter3
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Explain why a cubic unit (unit3 cm3 in3) is the standard unit for measuring volume

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.MD.3b I can recognize that volume is packing a figure with cubic units without gaps or overlaps.


 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Explain the connections between volume and area
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Create various rectangular solids using cubic units
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Recognize that in order for volume measurement to be precise, unit cubes need to fill the spaces without gaps or overlaps. (e.g. iteration)
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Decompose rectangular solids into layers of arrays of cubes.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Explain why a <span style="color: black; font-family: 'Arial','sans-serif'; font-size: 13px;">figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.MD.4 I can measure volume.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.MD.5a I can find the volume of a right rectangular prism.

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.MD.5b I can apply the formulas for volume of rectangular prisms (volume = length x width x height and volume=base x height)

<span style="font-family: 'Times New Roman','serif'; font-size: 16px;">5.MD.5c I can find volume by adding the non-overlapping parts.


 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Measure volume of a rectangular prism using cubic units.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Generalize a rule for measuring the volume of a rectangular prism by analyzing the relationship between the number of cubes in an array and the number of arrays needed to fill the prism.


 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Connect the associative property of multiplication with the volume of a rectangular prism.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Explain the relationship between V= l x w x h and the visual model of a rectangular prism.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Connect the equivalent formulas of V= area of the base x height and

<span style="font-family: 'Arial','sans-serif'; font-size: 13px;">V=l x w x h


 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Calculate the volume of various right rectangular prisms using formulas
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Determine the various dimensions of all possible rectangular prisms when given “n” cubic units.
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Estimate the volume of a rectangular prisms
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Apply formulas for volume to solve real world and mathematical problems
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Create real world problems involving volume of rectangular prisms
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Create composite shapes using multiple rectangular prisms without overlaps
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Decompose composite shapes into rectangular prisms to find the total volume
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Generalize a rule for calculating the composite shapes
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Explain the relationship of addition and multiplication in the calculation of the volume of composite shapes
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Apply the formula of volume and understanding of addition to solve real world problems involving composite shapes

‍‍‍‍‍‍‍‍‍‍**Essential Vocabulary**
<span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Attribute <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Volume <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Cubic unit (unit3) <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Length <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Capacity <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Volume <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Rectangular prism <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Overlap <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Gap <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Area <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Layers <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Multiplication <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Decompose <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Edge <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Length <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Width <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Height <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Array <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Unknown variable || 5.MD.4 and 5.MD.5 <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Volume <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Area of base <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Dimensions <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Length <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Width <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Height <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Measurement <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Solid figure <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Right rectangular prism <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Unit <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Gaps <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Layer <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Multiplication <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Additive <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Composite figure <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Associative property <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Non-overlapping <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Decompose <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Formula <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">3-D figure ||  ||
 * **5.MD.3a** <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">Measurement
 * <span style="font-family: 'Arial','sans-serif'; font-size: 13px;">5.MD3b **

‍‍‍‍‍‍‍‍‍‍**Sample Assessments**
softschools.com/quizzes/math/geometry/quiz148.html internet4classrooms.com/skill_builders/geometry_math_fifth_5th_grade.htm www.ixl.com

‍‍‍‍‍‍‍‍‍‍**Instructional Resources**
www.mathguide.com/lessons/**Volume**.html /www.k-5mathteachingresources.com/geometry-activities-2.html www.apples4theteacher.com/math.html#geometrygames

[|Volume by Detail]
===‍‍‍‍‍‍‍‍‍‍**Notes and Additional Information**===