2015-2016 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
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 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?
Textbook Correlation
Recommended Instructional Sequence
Essential Vocabulary
*Be selective in choosing problems aligned to the standards
Step 1: Problem-Based Learning “Solve and Share”
 scaling
within the topic. Lessons and problems used for instruction
Problem-Based Learning Lesson Flow Map
 mixed number
and assessment should be determined through collaborative
Conceptual understanding is developed when mathematics is
 factor
unit planning.
introduced in the context of solving a real problem in which
 product
ideas related to the new content are embedded. Conceptual
Topic 8: Apply Understanding of Multiplication to Multiply
understanding results because the process of solving a problem
Fractions
requires students to connect their prior knowledge with the new
Lesson 8-1: Use Models to Multiply a Whole Number by a
concept or procedure (Charles, R., Bay-Williams, J., et al., 2016).
Fraction
Lesson 8-2: Use Models to Multiply a Fraction by a Whole
Each lesson in the book begins with a Solve and Share. See the
Number
links below for additional tasks to be used as needed:
Lesson 8-3: Multiply Fractions and Whole Numbers
Lesson 8-4: Use Models to Multiply Two Fractions
Math Formative Assessment System (MFAS) Tasks by Standard
Lesson 8-5: Multiply Two Fractions
Illustrative Mathematics Tasks by Standard
Lesson 8-6: Area of a Rectangle
Lesson 8-7: Multiply Mixed Numbers
Step 2: “Visual Learning Bridge”
Lesson 8-8: Multiplication as Scaling
Enhance student learning by connecting student thinking and
Lesson 8-9: Math Practices and Problem Solving: Make Sense solutions from the Solve and Share to the new ideas of the
and Persevere
lesson through the use of the worked-out problem in the
textbook.
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.
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.
 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:
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.
 Represent word problems involving multiplication of fractions and mixed numbers.
 Solve real world problems involving multiplication of fractions and mixed numbers.
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.
Additional Resources & Links
Georgia Units
Unit 4 – Adding, Subtracting, Multiplying, and Dividing Fractions
Comparing MP3’s
Measuring for a Pillow
Reasoning with Fractions
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.
EngageNY - Module 4
Topic E: Lessons 13-16
Topic F: Lessons 21-23
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.
www.PearsonRealize.com:
Home School Connection
Reteach to Build Understand Pages
Professional Development Videos
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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.
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 8-1 through 8-9