2015-2016 Curriculum Blueprint
Grade: 4
Course: Mathematics
Topic 10 – Extend Multiplication Concepts to Fractions
Flexible Time
Line
7 days
Topic Overview
Students will use strategies such as models, symbols, and equations to multiply a fraction by a whole number.
Vertical Progression
3rd Grade:
 Students strengthen their understanding of the meaning of fractions and use various models to represent them.
 Students learn how to recognize and generate simple equivalent fractions and to express whole numbers as fractions.
5th Grade:
 Students will add and subtract fractions and mixed numbers with unlike denominators.
 They will multiply fractions.
 They will divide fractions and whole numbers.
Learning Goal
Essential Questions
Students will multiply a fraction by a whole number.
How can you describe a fraction using unit fractions?
Topic 10 Scale
How can you multiply a whole number by a mixed number?
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 10: Extend Multiplication Concepts to Fractions
understanding results because the process of solving a problem
Lesson 10-1: Fractions as Multiples of Unit Fractions: Use
requires students to connect their prior knowledge with the new
Models
concept or procedure (Charles, R., Bay-Williams, J., et al., 2016).
Lesson 10-2: Multiply a Fraction by a Whole Number: Use
Each lesson in the book begins with a Solve and Share. See the
Models
links below for additional tasks to be used as needed:
Lesson 10-3: Multiply a Fraction by a Whole Number: Use
Symbols
Math Formative Assessment System (MFAS) Tasks by Standard
Lesson 10-4: Multiply a Whole Number and a Mixed
Illustrative Mathematics Tasks by Standard
Number*
Lesson 10-5: Solve Time Problems**
Step 2: “Visual Learning Bridge”
Lesson 10-6: Math Practices and Problem Solving: Model with Enhance student learning by connecting student thinking and
solutions from the Solve and Share to the new ideas of the
Math
lesson through the use of the worked-out problem in the
*Lesson 10-4 is an extension lesson only
textbook.
**Sequence of Lesson 10-5 may be adjusted by grade-level
PLC’s. If moved to Topic 13, please omit or replace question 3
on Topic Assessment (page 583 of student book)
Deconstructed Standards
MAFS.4.NF.2.3. (DOK 2) Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
a) Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
b) Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify
decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
c) Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of
operations and the relationship between addition and subtraction.
d) Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual
fraction models and equations to represent the problem.
 Understand accumulating unit fractions (1/b) results in (a/b), where a is greater than 1.
 Recognize multiple representations of one whole using fractions with the same denominator.
 Replace mixed numbers with equivalent fractions, using visual fraction models.
 Replace improper fractions with a mixed number, using visual fraction models.
 Using fraction models, reason that addition of fractions is joining parts that are referring to the same whole.
 Using fraction models, reason that subtraction of fractions is separating parts that are referring to the same whole.
 Using visual fraction models, decompose a fraction into the sum of fractions with the same denominator in more than one way.
 Record decompositions of fractions as an equation and explain the equation and explain the equation using visual.
 Add and subtract mixed numbers with like denominators by using properties of operations and the relationship between addition and subtraction.
 Add and subtract fractions with like denominators.
 Add and subtract mixed numbers by replacing each mixed number with an equivalent fraction.
 Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators by using visual fraction
models and equations to represent the problem.
MAFS.4.NF.2.4 (DOK 2) Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
a) Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion
by the equation 5/4 = 5 × (1/4).
b) Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction
model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
c) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the
problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast
beef will be needed? Between what two whole numbers does your answer lie?
 Represent a fraction a/b as a multiple of 1/b (unit fractions)
 Multiply a fraction by a whole number.
 Apply multiplication of whole numbers to multiplication of a fraction by a whole number using visual fraction models.
 Explain that a multiple of a/b is a multiple of 1/b (unit fractions) using a visual fraction model.
 Multiply a fraction by a whole number by using the idea that a/b is a multiple of 1/b.
 Use fraction models and equations to represent the problem.
 Solve word problems involving multiplication of a fraction by a whole number.
*MAFS.4.MD.1.2 (DOK 2) Use the four operations to solve word problems involving distances, intervals of time and money, including problems involving
simple fractions or decimals. Represent fractional quantities of distance and intervals of time using linear models.
 Express measurements given in a larger unit in terms of a smaller unit.
 Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
 Solve word problems involving distances, intervals of time and money.
 Solve world problems involving measurement that include simple fractions or decimals.
 Solve word problems that require expressing measurements given in a larger unit in terms of a smaller unit.
Math Practice Standard(s)
Link to Mathematical Practice Standards Rubric
MAFS.K12.MP.4.1 Model with mathematics.
MAFS.K12.MP.7.1 Look for and make use of structure.
Additional Resources & Links
Higher Order Questions & Writing Connections
Georgia Units
Link to Webb’s DOK Guide
Unit 4
*Higher order questions should be utilized to foster a deep, conceptual
 How Many CCs
understanding of the topic. Encouraging students to express their
 Area Models
mathematical thinking in writing helps them solidify their learning.
Engage NY - Module 5
Topic G: Repeated Addition of Fractions as Multiplication
EngageNY Math Studio Talk: Common Core Instruction for 4.NF
This video addresses strategies for developing fraction number sense. This
segment focuses on multiplication of fractions. (10:17 – 12:40)
* YouTube must already be opened on your browser before clicking the link.
CPALMS:
Multiply Fractions and Whole Numbers with Models
Modeling Multiple Groups of Fractions
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Home-School Connection Page
Reteach to Build Understand Pages
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Florida Interim Assessment Item Bank and Test Platform
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Marzano Proficiency Scales Bank
Write a story problem that requires multiplication of fractions.
Write to explain how you solved the problem.
How do you know your answer is reasonable?
What real life situations require multiplication of fractions?
How do we apply our understanding of fractions in everyday life?
How can I model the multiplication of a whole number by a fraction?
How can I multiply a whole number by a fraction?
How can we model answers to fraction problems?
How is multiplication of fractions similar to division of whole
numbers?
How is multiplication of fractions similar to repeated addition of
fraction?
What does it mean to take a fractional portion of a whole number?
What strategies can be used for finding products when multiplying a
whole number by a fraction?
Which problem solving strategies can we use to solve this problem?
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.
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Daily Review 10-1 through 10-6