## Unit Overview

**Essential Questions: **

**Lesson Plans and Seeds**

Lesson Plan A.1: Evaluating Expressions

Lesson Seed A.1: Order of Operations

Lesson Seed A.2: Interpreting Numerical Expressions

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

**Content Emphasis By Clusters in Grade 5**

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

### Unit Overview

Students use their understanding of operations of whole numbers and apply this knowledge to order of operations with parentheses, brackets and braces. This unit has students develop their understanding of simple numerical expressions to prepare students for studying proportional relationships and functions in middle school. This unit also focuses on writing simple numerical expressions without focusing on evaluation.

**Teacher Notes:**

- Students have learned to simplify expressions by performing multiplication and division (left to right) before performing addition and subtraction (left to right). This is considered the conventional order of completing the four operations. In previous grades, students perform operations in the conventional order when there are no symbols of inclusion (also known as grouping symbols) to specify a different order.
- Students need fluency with the four basic operations in order to simplify numerical expressions.
- Students have been introduced to properties, including the distributive property, although they may not have used the formal names for these properties.

**Enduring Understandings:**

At the completion of the unit on addition and subtraction of fractions with unlike denominators, the student will understand that:

- Estimates help determine the reasonableness of an answer.
- Expressions are simplified using a predetermined order of operations.
- There are multiple representations for any number.

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

**Possible Student Outcomes:**

The student will be able to:

- Recognize that basic operations can be performed in a specific order in each expression.
- Understand that symbols of inclusion (grouping symbols) are used when an operation needs to be performed in a different order than the four basic operations specify.
- Write and interpret simple expressions without evaluating them.

**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

- Fail to do multiplication and division first instead of addition and subtraction.
- Not understand that you do parentheses first, brackets second and braces third.
- Not remember to work from the inside out as they use grouping symbols.

**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*

*Formative Assessment*

**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
Write and Interpret Numerical Expressions **

**parentheses: ** ( ) A grouping symbol. This is commonly used as the first grouping symbol. They indicate in which order the operations should be performed.

**brackets: ** [ ] A grouping symbol. Brackets are used when a second grouping symbol is needed.

**braces: ** { } A grouping symbol. Braces are used when a third grouping symbol is needed. Grouping symbols are often used in order of operation problems. Example:

**expressions: ** a mathematical phrase that has no equality or inequality signs. Examples:

7 × 5 2(3 + 4) 3 – 9 + 7 2 + 4 – 6 × 8

**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.**

**http://commoncoretools.files.wordpress.com/2012/06/ccss_progression_g**

_k6_2012_06_27.pdf

_k6_2012_06_27.pdf