5th Grade
Volume
Geometric measurement: understand concepts of volume.
CCSS.MATH.CONTENT.5.MD.C.3
Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
CCSS.MATH.CONTENT.5.MD.C.3.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.
CCSS.MATH.CONTENT.5.MD.C.3.B
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.
CCSS.MATH.CONTENT.5.MD.C.4
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
CCSS.MATH.CONTENT.5.MD.C.5
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
CCSS.MATH.CONTENT.5.MD.C.5.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.
CCSS.MATH.CONTENT.5.MD.C.5.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.
CCSS.MATH.CONTENT.5.MD.C.5.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.
CCSS.MATH.CONTENT.5.MD.C.3
Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
CCSS.MATH.CONTENT.5.MD.C.3.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.
CCSS.MATH.CONTENT.5.MD.C.3.B
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.
CCSS.MATH.CONTENT.5.MD.C.4
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
CCSS.MATH.CONTENT.5.MD.C.5
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
CCSS.MATH.CONTENT.5.MD.C.5.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.
CCSS.MATH.CONTENT.5.MD.C.5.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.
CCSS.MATH.CONTENT.5.MD.C.5.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.
Curricular Resources:
Investigations Unit 2: Prisms and Pyramids
Investigations Common Core Supplemental Book
Investigations Unit 2: Prisms and Pyramids
Investigations Common Core Supplemental Book
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Volume Supplements:
These supplements may be used in conjunction with the volume lessons and/or as spiral review.
Finding Volume of Prisms
Finding Volume with Unit Cubes
Name Each Prism (Suggestion: This can be done whole class before Day 1 lesson study)
Prism Pile Up Game Instructions (Suggestion: Students can play this game during the volume unit and/or as spiral review)
Pile Up Game Instructions Spanish
Prism Pile Up Hoja de Registro
Prism Pile Up Card Deck #1
Prism Pile Up Card Deck #2
Volume Exit Slip English
Volume Exit Slip Spanish
These supplements may be used in conjunction with the volume lessons and/or as spiral review.
Finding Volume of Prisms
Finding Volume with Unit Cubes
Name Each Prism (Suggestion: This can be done whole class before Day 1 lesson study)
Prism Pile Up Game Instructions (Suggestion: Students can play this game during the volume unit and/or as spiral review)
Pile Up Game Instructions Spanish
Prism Pile Up Hoja de Registro
Prism Pile Up Card Deck #1
Prism Pile Up Card Deck #2
Volume Exit Slip English
Volume Exit Slip Spanish
Week 1:
Day 1: Introduction to Volume using Geo Solids.
Lesson Study
PowerPoint for Introduction
Volume Exit Slip
Materials Needed
Geo Solids (Found in A124)
Rice, Cubes, cups, plates, weight scales
Day 1: Introduction to Volume using Geo Solids.
Lesson Study
PowerPoint for Introduction
Volume Exit Slip
Materials Needed
Geo Solids (Found in A124)
Rice, Cubes, cups, plates, weight scales
Day 2: Session 1.1- How Many Cubes?
Blackline Masters
Quick Images
Quick Images-Spanish
Packaging Factory
Packaging Factory-Spanish
Three-Quarter-Inch Grid Paper
Three-Quarter-Inch Grid Paper-Spanish
Blackline Masters
Quick Images
Quick Images-Spanish
Packaging Factory
Packaging Factory-Spanish
Three-Quarter-Inch Grid Paper
Three-Quarter-Inch Grid Paper-Spanish
Day 4: Session 1.3 and 1.4- Doubling the Number of Cubes and How Many Packages?
Note: For time purposes, you can condense these two lessons in one day.
Blackline Masters
How Many Packages?
How Many Packages? Spanish
Note: For time purposes, you can condense these two lessons in one day.
Blackline Masters
How Many Packages?
How Many Packages? Spanish
Day 5: Session 1.5- Assessment
5th. Centimeter Grid Paper
5th. Centimeter Grid Paper Spanish
5th. Assessment
5th. Assessment Spanish
Day 6: Session 1.5a- Finding the Volume of Solids
Note: This lesson is found in the Supplemental Book
5th. Centimeter Grid Paper
5th. Centimeter Grid Paper Spanish
5th. Assessment
5th. Assessment Spanish
Day 6: Session 1.5a- Finding the Volume of Solids
Note: This lesson is found in the Supplemental Book
Day 7: Session 1.6 and 1.7- Finding Volume and Designing Boxes
Note: You can combine these lessons or skip if necessary.
Blackline Masters
How Many Packages? Pattern for Box 2
How Many Packages? Pattern for Box 2 Spanish
Note: You can combine these lessons or skip if necessary.
Blackline Masters
How Many Packages? Pattern for Box 2
How Many Packages? Pattern for Box 2 Spanish
Day 7: Session 2.1- Finding Cubic Centimeters
Blackline Masters
5th. Pattern for a Closed Box
5th. Pattern for a Closed Box Spanish
Blackline Masters
5th. Pattern for a Closed Box
5th. Pattern for a Closed Box Spanish
Blackline Masters
Assessment: Measuring Volume in Cubic Centimeters
Assessment: Measuring Volume in Cubic Centimeters in Spanish
2.4a End of Unit Assessment (Lesson found in Supplemental Book)
2.4a End of Unit Assessment in Spanish (Found in Supplemental Book)
Prism Pile-Up Game
Assessment: Measuring Volume in Cubic Centimeters
Assessment: Measuring Volume in Cubic Centimeters in Spanish
2.4a End of Unit Assessment (Lesson found in Supplemental Book)
2.4a End of Unit Assessment in Spanish (Found in Supplemental Book)
Prism Pile-Up Game
Note: Investigation 3 of Unit 2 was not included because it goes beyond 5th grade standards.