## 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

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

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

**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

**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 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

**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

**Day 5**:

**Session 1.5- Assessment**

5th. Centimeter Grid Paper

5th. Centimeter Grid Paper Spanish

5th. Assessment

5th. Assessment Spanish

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

**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****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 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.