Unit Overview
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:
http://www.purplemath.com
http://www.khanacademy.org – Interactive 2.0 instructional and practice site. Students can view
instructional videos and complete practice modules for additional practice/remediation.
http://www.studyisland.com/ - Web-based instruction, practice, assessment and reporting built from NJ
standards.
http://www.ixl.com/math/grade-6 - IXL 6th grade online interactive activities for the students to
complete
http://www.aaamath.com/grade6.html - AAA math 6th grade – online interactive activities and
problems for the student to complete.
http://www.adaptedmind.com/Math-Worksheets.html?type=hstb – 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.