## Unit Overview

Essential Questions:

**Lesson Plans and Seeds**

Lesson Plan D.8: What is Perimeter?

Lesson Seed D.8: Same Perimeter Different Area

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

**Content Emphasis By Clusters in Grade 3**

**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

In this unit, students focus on solving real-world and mathematics problems involving perimeters of polygons. They find the perimeter of a polygon when the side lengths are given. They find the unknown side length. They display rectangles that have the same perimeter but different areas or the same area but different perimeters.

**Teacher Notes:**

_2012_07_21.pdf to see the development of the understanding of measurement as stated by the Common Core Standards Writing Team, which is also the guiding information for the PARCC Assessment development.

**Enduring Understandings:**

At the end of the unit on Perimeter, students will understand that:

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

**3.NF.A.2**Understand a fraction as a number on the number line; represent fractions on a number line diagram.

**3.MD.C.7**Relate area to the operations of multiplication and addition.

**3.MD.D.8**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.

**Possible Student Outcomes:**

The student will be able to:

**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:**

**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*

Topic |
Standards Addressed |
Link |
Notes |
---|---|---|---|

Shapes and Their Insides | 3.MD.D | http://www.illustrative-mathematics.org/illustrations/1514 | The purpose of this task is to help students differentiate between a polygon and the region inside of a polygon so that they understand what is being measured when the perimeter and area are being found. |

**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**

** measurement quantities: ** examples could include inches, feet, pints, quarts, centimeters, meters, liters, square units, etc.

** area: **the number of square units needed to cover a region. Examples:

** tiling: **highlighting the square units on each side of a rectangle to show its relationship to multiplication and that by multiplying the side lengths, the area can be determined. Example:

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

** partitioning: **dividing the whole into equal parts.

** partitioned: **the whole divided into equal parts.

Additional Resources:

**Free Online Resources:**

__Math Related Literature:__*Spaghetti and Meatballs for All! A Mathematical Story*

__References: __

*Principles and Standards for School Mathematics*. Reston, VA: National Council of Teachers of Mathematics.

*Math Misconceptions: From Misunderstanding to Deep Understanding.*

*About Teaching Mathematics: A K-8 Resource.*Sausalito, CA: Math Solutions Publications.

*Teaching Student-Centered mathematics, Grades K-3.*Boston, MASS: Pearson Education, Inc.