2017-2018 Curriculum Blueprint
Grade: 5
Course: Mathematics
Topic 8 – Apply Understanding of Multiplication to Multiply Fractions
Flexible Time
Line
10 days
Topic Overview
Topic 8 focuses on extending deep understanding of multiplication from whole numbers to fractions.
Vertical Progression
Coherence Map
4th Grade: The students add and subtract fractions with like denominators and multiply whole numbers and fractions.
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 multiply whole numbers and fractions, using models
What does it mean to multiply whole numbers and fractions?
and other strategies.
How can multiplication with whole numbers and fractions be shown
Topic 8 Scale
using models and symbols?
Deconstructed Standards
MAFS.5.NF.2.4 (DOK 2) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. [Conceptual
Understanding; Procedural Skill and Fluency]
a) Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For
example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In
general, (a/b) × (c/d) = ac/bd.)
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.
• Multiply fractions by whole numbers.
• Multiply fractions by fractions.
• Interpret the product of fractions times a whole number as total number of parts of the whole.
• Use visual models, including circles, tape/bar diagram, polygons, area models, etc, to show multiplication.
• Determine the sequence of operations that results in the total number of parts of the whole.
• Interpret the product of a fraction times a fraction as the total number of parts of the whole.
• Represent fraction products as rectangular areas.
• Justify multiplying fractional side lengths to find the area is the same as tiling a rectangle with unit squares of the appropriate unit fraction side
lengths.
• Find area of a rectangle with fractional side lengths using different strategies.
• Model the area of rectangles with fractional side lengths with unit squares to show the area of rectangles.
MAFS.5.NF.2.5 (DOK 3) Interpret multiplication as scaling (resizing), by: [Conceptual Understanding]
a) 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.
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×a)/(n×b) to the effect of multiplying a/b by 1.
• Know that scaling (resizing) involves multiplication.
• Know that multiplying whole numbers and fractions results in products greater than or less than one depending upon the factors.
• Compare 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.
• Draw a conclusion multiplying that a fraction greater than one will result in a product greater than the given number.
• Draw a conclusion that when you multiply a fraction by one, the resulting fraction is equivalent.
• Draw a conclusion that when you multiply a fraction by a fraction, the product will be smaller than the given number.
MAFS.5.NF.2.6 (DOK 2) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations
to represent the problem. [Application]
• Represent word problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations.
• Solve real world problems involving multiplication of fractions and mixed numbers by using visual fraction models or equations.
Math Practice Standard(s)
Link to Mathematical Practice Standards Rubric
MAFS.K12.MP.1.1 Make sense of problems and persevere in solving them.
MAFS.K12.MP.4.1 Model with mathematics.
Suggested Learning Progression
Recommended Instructional Sequence
The following learning progression provides students with an opportunity to
This instructional sequence is intended to provide a framework for student
construct meaning and create connections through the CRA Method: Concrete learning. Various options are listed below each step in the sequence.
Collaborative teams may adjust the sequence as necessary to meet the
– Representational – Abstract.
needs of their students.
*Collaborative teams should be selective in choosing standards-aligned tasks
Step 1: 5-Minute Spiral Review
for instruction and assessment. Teams may adjust the sequence and use
• Pearson Daily Review
additional resources based on the needs of their students.
Topic 8: Apply Understanding of Multiplication to Multiply Fractions
Sample Thinking Map of Models and Strategies to Multiply Fractions:
Teachers may use this map for professional development or as a teaching tool.
Teachers may build this map with their students as they learn the strategies
throughout the topic. Teachers should be selective in choosing strategies that
they feel will benefit their students’ understanding of the standard.
Topic Resource: Teaching Tools Centimeter grid paper pg. 9, Number Lines pg.
12, & Fraction strips pg. 13
• Common Misunderstandings or Errors
Step 2: Problem-Based Learning
• Solve and Share
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Math Formative Assessment System (MFAS) Tasks by Standard
• Illustrative Mathematics Tasks by Standard
Step 3: Focus Lesson & Opportunities for Practice
• Visual Learning Bridge
• Guided Practice
• Thinking Map/Graphic Organizer
• Collaborative work
• Interactive Notebook
• Independent Practice
• Whole Group i-Ready Lesson
• Task Oriented Instruction
(additional opportunities for PBL)
Step 4: Differentiated Instruction
• Small group instruction
• Guided Practice
• Intervention/Enrichment
*The following lessons are a review from 4th grade. Use these lessons only as
necessary so that you can focus on the 5th grade standards. Students should
have access to fraction strips as needed.
Lesson 8-1: Use Models to Multiply a Whole Number by a Fraction
Lesson 8-2: Use Models to Multiply a Fraction by a Whole Number
Lesson 8-3: Multiply Fractions and Whole Numbers
• Additional Resources:
o i-Ready Lessons (Numbers & Operations):
 Understand Products of Fractions
 Multiplying a Whole Number and a Fraction
o Georgia Units Unit 4 – Measuring for a Pillow
Problem-Based Learning Lesson: Suggested to be used as an introductory
lesson for Topic 8.
A Passion for Fractions Teaching Channel: Sign in to access the lesson plan and
student handout.
Lesson 8-4: Use Models to Multiply Two Fractions (NF.2.4a)
• Additional Resource: EngageNY - Module 4: Topic E: Lessons 13 & 14
Lesson 8-5: Multiply Two Fractions (NF.2.4a)
• Additional Resources:
o Georgia Units Unit 4 – Reasoning with Fractions
o EngageNY - Module 4: Topic E: Lesson 15
o i-Ready Lesson (Numbers & Operations): Multiplying Fractions
Lesson 8-6: Area of a Rectangle (NF.2.4b)
• Additional Resource: i-Ready Lesson (Number & Operations): Multiply
Fractions to Find Area
Lesson 8-7: Multiply Mixed Numbers (NF.2.6)
• Additional Resources: Georgia Units Unit 4 – Comparing MP3’s
Lesson 8-8: Multiplication as Scaling (NF.2.4a & NF.2.6b)
• Additional Resources:
o EngageNY - Module 4: Topic F: Lessons 22 & 23
o i-Ready Lesson (Number & Operations): Understand
Multiplication as Scaling
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Centers/stations (including iReady)
Step 5: Student Debrief
• Thinking Map/Graphic Organizer
• Exit Ticket
• Interactive Notebook
•
Reflection
o So what? What did you
learn?
o So why? Why is it
important?
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 decomposing fractions help us multiply fractions?
How can we use models to solve problems with fractions?
How can we model an area with fractional pieces?
How else can you model this problem?
How would you model this equation?
Interpret the product of a fraction.
Compare the size of a product to the size of a factor.
Examine how numbers change when we multiply by fractions.
What are some various strategies to solve word problems involving the
multiplication of a fraction by a mixed number?
Write to explain the strategy you used.
Lesson 8-9: Math Practices and Problem Solving: Make Sense and Persevere
(NF.2.6)
Professional Development
EngageNY Math Studio Talk: Common Core Instruction for
5.NF
This video segment focuses on strategies for performing
operations with fractions. (7:50 – 11:30)
* YouTube must already be opened on your browser
before clicking the link.
Marzano Proficiency Scales Bank
Common Core Flip Books: Provides additional information
and sample problems for every standard
FSA Test Item Specifications
Resources
Pearson enVisionMath2.0
Home-School Connection Page
Reteaching Pages
Daily Review
Florida Interim Assessment Item Bank and Test Platform
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.
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Essential Vocabulary
scaling
mixed number
factor
product