Unit Overview
Content Area: Math
Unit Title: Multiplication/division of fractions
Unit: 4
Target Course/Grade Level: Fifth Grade
Timeline: 3 weeks
Unit Summary: Students will demonstrate their understanding using concrete manipulatives, drawing
models and explaining their thinking when working with fractions in multiple contexts. They will
multiply fractions including proper fractions, improper fractions and mixed numbers. They will multiply
fractions efficiently and accurately as well as solve problems in both contextual and non-contextual
situations. They will experience division problems with whole numbers divisors and unit fraction
dividends or with unit fraction divisors and whole number dividends. They will extend their
understanding of the meaning of fractions, how many unit fractions are in a whole and their understanding
of multiplication and division as involving equal groups or shares and the number of objects in each
group/share.
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
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: 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.
st
21 Century themes and skills: Critical Thinking and Problem Solving, Collaboration, Teamwork and
leadership
Mathematical Practices:
5.MP.1 Make sense of problems and persevere in solving them.
5.MP.2 Reason abstractly and quantitatively.
5.MP.3 Construct viable arguments and critique the reasoning of others.
5.MP.4 Model with mathematics.
5.MP.5 Use appropriate tools strategically.
5.MP.6 Attend to precision.
5.MP.7 Look for and make use of structure.
5.MP.8 Look for and express regularity in repeated reasoning.
Learning Targets
Domain: Number and Operations – Fractions
Cluster: Apply and extend previous understandings of multiplication and division to multiply and
divide fractions.
Standard #
5.NF.3
Standards
Interpret a fractions as division of the numerator by the denominator (a/b = a/b). Solve
word problems involving division of whole numbers leading to answers in the form of
fractions or mixed numbers, eg. by using visual fraction models or equations to represent
the problem. For example, interpret ¾ as the result of dividing 3 b 4, noting that ¾
multiplied by 4 equals 3 and that when 3 wholes are shared equally among 4 people each
person has a share of size ¾. If 9 people want to share a 50-pound sack of rice equally by
weight, how many pounds of rice should each person get? Between what two whole
numbers does your answer lie?
5.NF.4.a
Interpret the product (a/b) x q as a parts of a partition of q into b equal parts; equivalently,
as the result of a sequence of operations a x q / b. For example, use a visual fraction
model to show (2/3) x 4 = 8/3, and create a story context for this equation. Do the same
with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd)
5.NF.4.b
Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the
appropriate unit fraction side lengths, and show that the area is the same as would be found
by multiplying the side lengths. Multiply fractional side lengths to find areas of
rectangles, and represent fraction products as rectangular areas.
5.NF.5.a
Interpret multiplication as scaling (resizing) by: comparing the size of a product to the
size of one factor on the basis of the size of the other factor, without performing the
indicated multiplication.
5.NF.5.b
Explaining why multiplying a given number by a fraction greater than 1 results in a
product greater than the given number (recognizing multiplication by whole numbers
greater than 1 as a familiar case); explaining why multiplying a given number by a fraction
less than 1 results in a product smaller than the given number; and relating the principle of
fraction equivalence a/b = (n x a)/ (n x b) to the effect of multiplying a/b by 1.
5.NF.6
Solve real world problems involving multiplication of fractions and mixed numbers, eg. by
using visual fraction models or equations to represent the problem.
5.NF.7.a
Interpret division of a unit fraction by a non-zero whole number, (Students able to multiply
fractions in general can develop strategies to divide fractions in general, by reasoning
about the relationship between multiplication and division. But division of a fraction is
not a requirement at this grade) and compute such quotients. For example, create a story
context for (1/3) / 4, and use a visual fraction model to show the quotient. Use the
relationship between multiplication and division to explain that (1/3) / 4 = 1/12 because
(1/12) x 4 = 1/3.
5.NF.7.b
Interpret division of a whole number by a unit fraction, and compute such quotients. For
example, create a story context for 4 / (1/5) and use a visual fraction model to show the
quotient. Use the relationship between multiplication and division to explain that 4 / (1/5)
= 20 because 20 x (1/5) = 4.
5.NF.7.c
Solve real world problems involving division of unit fractions by non-zero whole numbers
and division of whole numbers by unit fractions, eg. by using visual fraction models and
equations to represent the problem. For example, how much chocolate will each person
get if 3 people share ½ lb of chocolate equally? How many 1/3 cup servings are in 2 cups
of raisins?
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.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
 How do operations affect numbers?
 What makes a computational strategy both
effective and efficient?
 How can we decide when to use an exact answer
and when to use an estimate?
Unit Enduring Understandings
 Computational fluency includes understanding not
only the meaning, but also the appropriate use of
numerical operations.
 The magnitude of numbers affects the outcome of
operations on them.
 In many cases, there are multiple algorithms for
finding mathematical solution, and those
algorithms are frequently associated with different
cultures.
 Context is critical when using estimation.
Unit Learning Targets
Students will ...
 Multiply fractions or whole numbers by a fraction.
 Divide a unit fraction by a whole number and a whole number by a fraction.
 Calculate area of a rectangle with fractional sides.
 Estimate a product by understanding when multiplying less than a whole number, the product will be
less than the other factor. If it is greater than one, the product will be more than the other factor.
(Scaling or resizing)
 Understand a fraction is a division problem, as numerator (dividend) over denominator (divisor).
 Solve real world problems with modeling.
 Find the reciprocal of a number.
 Develop strategies to divide fractions by using the relationship between multiplication and division.
Evidence of Learning
Summative Assessment
 Solve a multiplication equation of fraction by fraction, fraction by whole numbers, and mixed numbers.
 Solve division equation of unit fractions by whole numbers and whole numbers by unit fractions, using
reciprocals.
 Given the fractional dimensions of a rectangle, find the area. (Unit fractions and mixed numbers)
 When given an appropriate array, create a multiplication model using shading or tiling to demonstrate
the product. (Students must have LCM/LCD and multiplication array of whole numbers, and estimation
to the nearest whole number)
 When given a simple multiplication word problem where one factor is a fraction (unit or mixed),
students will predict the product will be larger or smaller than the given whole number.
 When given a visual fraction model (completed array) of a non-zero whole less then ten and a unit
fraction, students will rewrite the division problem as a multiplication problem.
.
Equipment needed: Smart Board, white boards, computers, number lines, fraction cubes, calculators
Teacher Instructional Resources: Scott Foresman and Addison Wesley
Study Island
Khan Academy Videos
Formative Assessments
 Skill sheets
 Student workbook
 Homework
 Quizzes/Tests
 Drawing model
 Study Island
Integration of Technology:
 Smart Board to play online games and utilize online resources.
 Kahn Academy Videos
 Elmo – for demonstration
 Scott Foresman – Pearson Success Net - https://www.pearsonsuccessnet.com/snpapp/login/login.jsp
 Study Island
Technology Resources:
Click the links below to access additional resources used to design this unit:
http://www.math-play.com/soccer-math-multiplying-fractions-game/multiplying-fractionsgame.html - game for practice of multiplication of fractions
http://www.math-play.com/math-basketball-dividing-fractions-game/math-basketball-dividingfractions-game.html - game for practice of division of fractions
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-5 - IXL 5th grade online interactive activities for the students to
complete
http://www.aaamath.com/grade5.html - AAA math 5th grade – online interactive activities and
problems for the student to complete.
http://www.adaptedmind.com/Fifth-Grade-Math-Worksheets-And-Exercises.html -5th grade math
worksheets and lessons on operations with fractions
Opportunities for Differentiation:
Decelerate: Student will only multiply and divide fractions by fractions, whole numbers by fractions and
fractions by whole numbers.
Accelerated: Students will multiply and divide all types of fractions and mixed numbers. They will also
be required to use cross reduction prior to completing the operation.
Teacher Notes:
Will need to know area of a figure (whole numbers)
Will need to be able to calculate the area of several types of quadrilaterals prior to introducing finding the
area of quadrilaterals with fractional parts. Use modeling and manipulates prior to math computation.