2015-2016 Curriculum Blueprint
Grade: 5
Course: Mathematics
Topic 9 – Apply Understanding of Division to Divide Fractions
Flexible Time
Line
9 days
Topic Overview
Topic 9 focuses on extending a deep understanding of division from whole numbers to fractions.
Vertical Progression
4 Grade: The students add and subtract fractions with like denominators and multiply whole numbers and fractions.
th
6th Grade: The students will be able to use fraction computations to solve equations, use fraction computations to evaluate numerical expressions, and divide
fractions.
Learning Goal
Essential Question
The students will be able to relate fractions to division and divide with whole
How are fractions related to division?
numbers and unit fractions.
How can you divide with whole numbers and unit fractions?
Topic 9 Scale
Textbook Correlation
Recommended Instructional Sequence
Essential Vocabulary
*Be selective in choosing problems aligned to the standards
Step 1: Problem-Based Learning “Solve and Share”
 unit fraction
within the topic. Lessons and problems used for instruction
Problem-Based Learning Lesson Flow Map
and assessment should be determined through collaborative
Conceptual understanding is developed when mathematics is
unit planning.
introduced in the context of solving a real problem in which
ideas related to the new content are embedded. Conceptual
Topic 9: Apply Understanding of Division to Divide Fractions
understanding results because the process of solving a problem
Lesson 9-1: Fractions and Division
requires students to connect their prior knowledge with the new
Lesson 9-2: Fractions and Mixed Numbers as Quotients
concept or procedure (Charles, R., Bay-Williams, J., et al., 2016).
Lesson 9-3: Use Multiplication to Divide
Lesson 9-4: Divide Whole Numbers by Unit Fractions
Each lesson in the book begins with a Solve and Share. See the
Lesson 9-5: Divide Unit Fractions by Non-Zero Whole
links below for additional tasks to be used as needed:
Numbers
Lesson 9-6: Divide Whole Numbers and Unit Fractions
Math Formative Assessment System (MFAS) Tasks by Standard
Lesson 9-7: Solve Problems Using Division
Illustrative Mathematics Tasks by Standard
Lesson 9-8: Math Practices and Problem Solving: Repeated
Reasoning
Step 2: “Visual Learning Bridge”
Enhance student learning by connecting student thinking and
solutions from the Solve and Share to the new ideas of the
lesson through the use of the worked-out problem in the
textbook.
Deconstructed Standards
MAFS.5.NF.2.3 (DOK 2) Interpret a fraction 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, e.g., by using visual fraction models or equations to represent the problem. For
example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people
each person has a share of size 3/4. 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?
 Interpret a fraction as division of the numerator by the denominator.
 Interpret the remainder as a fractional part of the problem.
 Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.
MAFS.5.NF.2.7 (DOK 2) Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
a) Interpret division of a unit fraction by a non-zero whole number, 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) × 4 =
1/3.
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 × (1/5) = 4.
c) Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using
visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of
chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
 Know the relationship between multiplication and division.
 Interpret division of a unit fraction by a whole number and justify your answer using the relationship between multiplication and division, by creating
story problems, using visual models, and relationship to multiplication, etc.
 Interpret division of a whole number by a unit fraction and justify your answer using the relationship between multiplication and division, and by
representing the quotient with a visual fraction model.
 Solve real world problems involving division of unit fractions by whole numbers other than 0 and division of whole numbers by unit fractions using
strategies such as visual fractions models and equations.
Math Practice Standard(s)
Link to Mathematical Practice Standards Rubric
MAFS.K12.MP.5.1 Use appropriate tools strategically.
MAFS.K12.MP.8.1 Look for and express regularity with repeated reasoning.
Additional Resources & Links
Georgia Units
Unit 4 – Adding, Subtracting, Multiplying, and Dividing Fractions
Sharing Candy Bars
Dividing with Unit Fractions
Adjusting Recipes
Higher Order Questions & Writing Connections
Link to Webb’s DOK Guide
*Higher order questions should be utilized to foster a deep, conceptual
understanding of the topic. Encouraging students to express their
mathematical thinking in writing helps them solidify their learning.
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How can we use models to solve problems with fractions?
How would you model this equation?
EngageNY - Module 4
Topic B: Lessons 2-5
Topic G: Lessons 25-27
EngageNY Math Studio Talk: Common Core Instruction for 5.NF
This video segment focuses on strategies for performing operations with fractions.
(11:30 – end of video)
* YouTube must already be opened on your browser before clicking the link.
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Explain the relationship between multiplication and division.
What is the most efficient strategy for solving this problem?
How do fractions relate to division?
Generate a word problem representing division of a whole number
by a unit fraction.
www.PearsonRealize.com:
Home School Connection
Reteach to Build Understand Pages
Professional Development Videos
Marzano Proficiency Scales Bank
Math Formative Assessment System (MFAS) Tasks by Standard
CPALMS - MFAS includes tasks and rubrics that the teacher can implement with
their students.
Illustrative Mathematics Tasks by Standard
The site illustrates standards with impeccably crafted tasks, videos, lesson plans,
and curriculum modules.
Common Core Flip Books: Provides additional information and sample problems
for every standard
FSA Test Item Specifications
Spiral Review
*Consistent review of previously learned standards allows students multiple opportunities to master and build fluency with mathematical concepts and
procedures.
www.pearsonrealize.com
Daily Review 9-1 through 9-8