# What Is the Result When You Multiply Or Divide a Number by a Fractions

Content Area: Math

Unit Title: Multiply and Divide Fractions Unit: 2

**Target Course/Grade Level: Sixth Grade Timeline: 3 weeks**

Unit Summary: When describing real-world quantities, fractions are important because many quantities cannot be described using whole numbers. In this chapter, students learn how to multiply and divide fractions. The emphasis is on understanding the concepts and procedures used to perform the operations. Students first use models to find products and quotients. This method allows students to understand how numerators and denominators are related to the operations of multiplication and division. Then students learn and apply the multiplication and division algorithms. By moving from the concrete to the abstract, students will become proficient in multiplying and dividing fractions.

**Primary interdisciplinary connections:**Language Arts and Technology

**9.1 21st-Centuries Life & Career Skills**

Standard 9.1 All students will demonstrate the creative, critical thinking, collaboration, and problem-solving skills needed to function successfully as both global citizens and workers in diverse ethnic and organizational cultures.

**Strand: A. Critical Thinking and Problem Solving**

**B. Creativity and Innovation**

**C. Collaboration, Teamwork and Leadership**

**Content Statement:**

9.1.8: A The ability to recognize a problem and apply critical thinking skills and problem

solving skills to solve the problem is a lifelong skill that develops over time.

9.1.8: B Gathering and Evaluating knowledge and information from a variety of sources,

including global perspective, fosters creativity and innovative thinking.

9.1.8: C Collaboration and team work enable individuals or groups to achieve common goals

with greater efficiency.

Leadership abilities develop over time through participation in group and or teams that

that are engaged in challenging or competitive activities.

**21st Century themes and skills:**Critical Thinking and Problem Solving, Collaboration, Teamwork and

Leadership, Creativity and Innovation

**Mathematical Practices:**

6.MP.1 Make sense of problems and persevere in solving them.

6.MP.2 Reason abstractly and quantitatively.

6.MP.3 Construct viable arguments and critique the reasoning of others.

6.MP.4 Model with mathematics.

6.MP.7 Look for and make use of structure.

6.MP.8 Look for and express regularity in repeated reasoning.

**Learning Targets**

**Domain: Number System**

**Cluster: Apply and extend previous understandings of multiplication and division to divide fractions by fractions**

Standard # / Standards

6.NS.1 / Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.

9.1.8.A.1 / Develop strategies to reinforce positive attitudes and productive behaviors that impact critical thinking and problem-solving skills.

9.1.8.A.2 / Implement problem-solving strategies to solve a problem in school or the community.

9.1.8.B.2 / Assess data gathered to solve problems for which there are varying perspective (e.g., cross cultural, gender specific, generational, etc.) and determine how the data can best be used to design the multiple solutions.

9.1.8.C.1 / Determine an individual’s responsibility for personal actions and contributions to group activities.

9.1.8.C.2 / Demonstrate the use of compromise, consensus and community building strategies for carrying out different task, assignments and projects.

9.1.8.C.3 / Model leadership skills during classroom and extracurricular activities.

**Unit Essential Questions**

- What is the result when you multiply or divide a number by a fractions.
- How is multiplying two fractions similar to and different from adding two fractions? How is multiplying two fractions similar to and different from multiplying two whole numbers?

**Unit Enduring Understandings**

- To divide fractions, the rule is to multiply by the reciprocal of the divisor and write the quotient in simplest form.
- When dividing mixed numbers, rename any mixed numbers as improper fractions, and then divide as with fractions.

**Unit Learning Targets**

Students will ...

- Solve problems by drawing a diagram.
- Divide whole numbers by fractions.
- Divide fractions
- Divide mixed numbers

**Evidence of Learning**

**Summative Assessment**

- Estimate products and quotients of fractions and judge the reasonableness of the results.
- Multiply and divide fractions efficiently.
- Explain and justify procedures for multiplying and dividing fractions.
- Solve real-world problems that involve the multiplications and division of fractions.
- Use multiplication and division to solve problems.

Equipment needed: Number lines, base 10 models, Smart Board, white boards, calculators, Elmo

Teacher Instructional Resources: TBD

Study Island

Khan Academy Videos

Formative Assessments

- Skill sheets
- Quizzes/Tests
- Student workbook

- Homework
- Math games
- Study Island

Integration of Technology:

- Smart Board to play online games, utilize online resources, generate models with Smart Software.
- Kahn Academy Videos
- Elmo – for demonstration
- Study Island

Technology Resources:

– Interactive 2.0 instructional and practice site. Students can view instructional videos and complete practice modules for additional practice/remediation.

- Web-based instruction, practice, assessment and reporting built from NJ standards.

- IXL 6th grade online interactive activities for the students to complete

- AAA math 6th grade – online interactive activities and problems for the student to complete.

– Grade level material for practice, lessons, games, etc.

Opportunities for Differentiation:

Decelerate: Use grid paper to model fraction multiplication and division.

Accelerated: Students will work with complex fractions in division.

Multiply and simplify with algebraic fractions.

Teacher Notes:

When multiplying a whole number or a mixed number by a proper fraction the product gets smaller and when you are dividing a whole number or a mixed number by a proper fraction the quotient gets smaller.