## Unit Overview

**Essential Questions: **

**Lesson Plans and Seeds**

Lesson Plan B.4: Greatest Common Factor

Lesson Plan B.2: Division of Whole Numbers

Lesson Seed B.3: Estimating Decimal Products

Lesson Seed B.4: Greatest Common Factor and Least Common Multiple

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

**Content Emphasis By Clusters in Grade 6**

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

### Unit Overview

This unit extends the understanding of decimals and fractions. During this unit students should be able to fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm. They will also find the greatest common factor and least common multiple of whole numbers. The distributive property will be used to express the sum of two whole numbers from 1 to 100.

**Teacher Notes:**

- Teachers should prepare students to be fluent in adding, subtracting, multiplying and dividing multi-digit decimals..
- Use the distributive property to express a sum of two whole numbers with a common factor.

**Enduring Understandings:**

At the completion of the unit on multiplication and division of fractions, the student will understand that:

- Using standard algorithms, the students will add, subtract, multiply, and divide whole number and decimals to solve problems.
- Develop understanding of factors and multiples, common factors and common multiples, and the relationships among them.

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

PARCC has no in-depth focus for computing fluently with multi-digit numbers and finding common factors and multiples.

**Possible Student Outcomes:**

The student will be able to:

- add, subtract, multiply and divide fluently with decimal numbers using the standard algorithm.
- identify and differentiate between common factors and common multiples.

**Evidence of Student Learning:**

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

**Common Misconceptions:**

Students may

- need more practice with the standard algorithm so they will be fluent when working on addition, subtraction, multiplication and division of decimals.
- need to know the differences between factors and multiples.
- need to differentiate between common factors and common multiples.
- lack complete conceptual understanding of the distributive property.

**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
The Number System: Compute Fluently with Multi-digit Numbers and Find Common Factors and Multiples **

* standard algorithm:* An algorithm is a systematic scheme for performing computations, consisting of a set of rules or steps.

** greatest common factor:** (GCF) The biggest number that will divide two or more other numbers exactly. It is sometimes called greatest common divisor. One way to find the GCF is: 9, 12, and 15 List the factors of each number.

** least common multiple:** (LCM) The smallest number that is the multiple of two or more other numbers. One way to find the LCM is: 3,4,and 6 List the multiples of each number.

3 is 3,6,9,12,15 4 is 4,8,12,16,20, 6 is 6,12,18,24,30 |
The LCM is 12 because it is the smallest number they all have in common. |

** distributive property:** The property of distributing one operation over another and the answer is the same.

Distributive Property of Multiplication over Addition a(b + c) = ab + ac 2(5 + 1) = 2×5 + 2×1 2(6) = 10 + 2 12 = 12 Distributive Property of Multiplication over Subtraction a(b – c) = ab – ac 2(5 – 1) = 2×5 - 2×1 2(4) = 10 - 2 8 = 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 problematic for instruction of the related standards.**