## Unit Overview

**Essential Questions: **

**Lesson Plans and Seeds**

Lesson Plan B.3: Analyzing Patterns

Lesson Seed B.3: Analyzing Relationships

**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

Students build on their understanding of operations to create numerical patterns based on two given rules, as well as identify any relationships that may exist between two corresponding terms in the two patterns. Integrating new learning of how to plot points on a coordinate plane, students will form ordered pairs of values that correspond to the two rules, and graph them..

**Teacher Notes:**

- In order to identify and replicate two rules, students must be able to use the four operations.
- Students must be comfortable generating and analyzing patterns of values that follow one rule.

**Enduring Understandings:**

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

- Patterns and relationships can be represented numerically, graphically, symbolically, and verbally.
- Spatial relationships can be described using coordinate geometry.
- Patterns, relations, and functions can be recognized and understood mathematically.
- Change, in various contexts, both quantitative and qualitative, can be identified and analyzed.
- Patterns provide insights into potential relationships.

**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:

- Create numerical patterns based on two given rules.
- Identify obvious relationships between corresponding terms.
- Form ordered pairs comprised of corresponding terms from the two numerical patterns.
- Graph ordered pairs on the coordinate plane.

**Evidence of Student Learning:**

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

**Common Misconceptions:**

Students may

- fail to understand the meaning of the two rules and the resulting sequences of values.
- misinterpret the relationship between in quantities in relationships and thus might graph the corresponding terms incorrectly.

**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
Represent and Interpret Data Analyze Patterns and Relationships **

**corresponding terms:** Given a rule, generate a number pattern with two sets. For example given one rule to multiply the first number by 2 to get the second number and given a second rule to multiply the first number by 4 to get the second number. The second number in second rule should be twice the size of the second number in the first rule.

First rule: | (1,2) | (2,4) | (3,6) | (4,8)… |

↕ | ↕ | ↕ | ↕ | |

Second rule: | (1,4) | (2,8) | (3,12) | (4,16)… |

**
coordinate plane:
**

This is a coordinate plane. It can be called a coordinate grid or Cartesian plane. It has two axes and four quadrants. The two number lines form the axes. The horizontal number line is called the x-axis and the vertical number line is called the y-axis. The four quadrants are number counter clockwise. |

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

**
axis:
**

The two number lines form the axes. The horizontal number line is called the x-axis and the vertical number line is called the y-axis. |

**
quadrant:
**

The four quadrants are number counter clockwise. They are formed by the x-axis and y-axis. |