## Unit Overview

**Essential Questions: **

**Lesson Plans and Seeds**

Lesson Plan C.3-5: Determining Volume

Lesson Seed C.3: Understanding Concepts of Volume

**Download Seeds, Plans, and Resources (zip)**

**Content Emphasis By Clusters in Grade 5**

**Progressions from Common Core State Standards in Mathematics**

Lesson seeds are ideas that can be used to build a lesson aligned to the CCSS. Lesson seeds are not meant to be all-inclusive, nor are they substitutes for instruction. When developing lessons from these seeds, teachers must consider the needs of all learners. It is also important to build checkpoints into the lessons where appropriate formative assessment will inform a teachers instructional pacing and delivery.

### Unit Overview

This unit recognizes volume as an attribute of solid figures and applies this knowledge to the volume of a right rectangular prism. Modeling plays a significant role in developing students’ understanding of volume. Students develop proficiency with volume through working with authentic situations.

The students will compare three-dimensional prisms using attributes. Students will find volume of right rectangular prisms and non-overlapping right rectangular prisms. They develop proficiency with number concepts and operations through working with authentic situations.

**Teacher Notes:**

- Students will need to draw on their background knowledge of area.
- Make sure that students understand the difference between a two-dimensional figure and a three-dimensional figure.
- Know how to relate volume to addition and multiplication.
- Students should know that volume in fifth grade is limited to the right rectangular prism.

**Enduring Understandings:**

At the completion of the unit on Geometric Measurement: Understand Concepts of Volume and Relate Volume to Multiplication and to Addition, the student will understand that:

- Attributes of geometric figures help us identify the figures and find their measures.
- Three-dimensional shapes can be described and classified by their properties.
- Geometry requires visualization, spatial reasoning, and geometric modeling to solve problems.

**Focus Standards (Listed as Examples of Opportunities for In-Depth Focus in the PARCC Content Framework document):
**

**5.MD.5 **Students work with volume as an attribute of a solid figure and as a measurement quantity. Students also relate volume to multiplication and addition. This work begins a progression leading to valuable skills in geometric measurement in middle school.

**Possible Student Outcomes:**

The student will be able to:

- Find the volume of right rectangular prisms using unit cubes.
- Develop the volume formula.
- Solve real world and mathematical problems using the volume formula.

**Evidence of Student Learning:**

*The Partnership for Assessment of Readiness for College and Careers (PARCC) has awarded the Dana Center a grant to develop the information for this component. This information will be provided at a later date. The Dana Center, located at the University of Texas in Austin, encourages high academic standards in mathematics by working in partnership with local, state, and national education entities. Educators at the Center collaborate with their partners to help school systems nurture students' intellectual passions. The Center advocates for every student leaving school prepared for success in postsecondary education and in the contemporary workplace.*

**Fluency Expectations and Examples of Culminating Standards:**

**Common Misconceptions:**

Students may

- Not understand how to find area of a two-dimensional figure.
- Not understand measurement units.

**Interdisciplinary Connections:**

Interdisciplinary connections fall into a number of related categories:

*Literacy standards within the Maryland Common Core State Curriculum*

*Science, Technology, Engineering, and Mathematics standards*

*Instructional connections to mathematics that will be established by local school systems, and will reflect their specific grade-level coursework in other content areas, such as English language arts, reading, science, social studies, world languages, physical education, and fine arts, among others.*

**Sample Assessment Items: ***The items included in this component will be aligned to the standards in the unit and will include:*

*Items purchased from vendors*

*PARCC prototype items*

*PARCC public release items*

*Maryland Public release items*

**Interventions/Enrichments/PD: ***(Standard-specific modules that focus on student interventions/enrichments and on professional development for teachers will be included later, as available from the vendor(s) producing the modules.)*

**Vocabulary/Terminology/Concepts: ***This section of the Unit Plan is divided into two parts. Part I contains vocabulary and terminology from standards that comprise the cluster, which is the focus of this unit plan. Part II contains vocabulary and terminology from standards outside of the focus cluster. These “outside standards” provide important instructional connections to the focus cluster.*

**
Part I – Focus Cluster
Geometric Measurement: Understand Concepts of Volume and Relate Volume to Multiplication and to Addition **

**Right rectangular prism: **A solid figure that has all right angles where opposite faces are congruent rectangles.

**Part II – Instructional Connections outside the Focus Cluster**

**NOTE: None of the vocabulary, terminology, and concepts in this cluster are new, nor should they be particularly problematical for instruction of the related standards.**