2015-2016 Curriculum Blueprint
Grade: 4
Course: Mathematics
Topic 8 – Fraction Equivalence and Ordering
Flexible Time
Line
8 days
Topic Overview
Students will use strategies such as area models, number lines, multiplication, and division to identify equivalent fractions. Students will use strategies such as
benchmark fractions, area models, and number lines to compare fractions.
Vertical Progression
3rd Grade:
 Students learn about the meaning of fractions and used various models to represent them.
 Students learn how to recognized and generate simple equivalent fractions and how to express whole numbers as fractions.
 They also compare two fractions with the same numerator or the same denominator.
5th Grade:
 Students will add and subtract fractions and mixed numbers with unlike denominators.
 They will multiply fractions.
 They will interpret a fraction as a division, and they will divide unit fractions and whole numbers.
Learning Goal
Essential Questions
Students will use strategies to identify equivalent fractions and compare and order What are some ways to name the same part of a whole?
fractions.
How can you compare fractions with unlike denominators?
Topic 8 Scale
Textbook Correlation
Recommended Instructional Sequence
Essential Vocabulary
*Be selective in choosing problems aligned to the standards within the
Step 1: Problem-Based Learning “Solve and Share”
 equivalent fractions
topic. Lessons and problems used for instruction and assessment should be
Problem-Based Learning Lesson Flow Map
 fraction
determined through collaborative unit planning.
Conceptual understanding is developed when mathematics is
 numerator
introduced in the context of solving a real problem in which
Topic 8: Extend Understanding of Fraction Equivalence and Ordering
 denominator
ideas related to the new content are embedded. Conceptual
Lesson 8-1: Equivalent Fractions: Area Model
 common factor
understanding results because the process of solving a problem
Lesson 8-2: Equivalent Fractions: Number Lines
requires students to connect their prior knowledge with the new  benchmark fraction
Lesson 8-3: Generate Equivalent Fractions: Multiplication
Lesson 8-4: Generate Equivalent Fractions: Division
Lesson 8-5: Use Benchmarks to Compare Fractions
Lesson 8-6: Compare Fractions
*Lesson 8-7: Math Practices and Problem Solving: Construct Arguments
*Lesson 8-7 provides few opportunities for the following comparisons,
however they are essential for developing strong fraction number sense:
 Comparing fractions with like denominators (same size pieces)
 Comparing fractions with like numerators (same number of pieces)
 Comparing fractions with a missing piece
Refer to Higher Order Questions for an explanation of each type of
comparison, and collaborate with your grade level PLC to develop
opportunities for students to explore these strategies.
concept or procedure (Charles, R., Bay-Williams, J., et al., 2016).
Each lesson in the book begins with a Solve and Share. See the
links below for additional tasks to be used as needed:
Math Formative Assessment System (MFAS) Tasks by Standard
Illustrative Mathematics Tasks by Standard
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.4.NF.1.1 (DOK 3) Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number
and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
 Recognize and identify equivalent fractions with unlike denominators.
 Explain why a/b is equal to (n x a)/ (n x b) by using fraction models with attention to how the number and size of the parts differ even though the two
fractions themselves are the same size.
 Use visual fraction models to show why fractions are equivalent.

Generate equivalent fractions using visual fraction models and explain why they can be called “equivalent.”
MAFS.4.NF.1.2 (DOK 2) Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or
numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole.
Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
 Recognize fractions as being greater than, less than, or equal to other fractions.
 Record comparison results with >, =, or <.
 Use benchmark fractions such as ½ for comparison purposes.
 Make comparisons based on parts of the same whole.
 Compare two fractions with different numerators or denominators.
 Justify the results of a comparison of two fractions by using a visual fraction model.
MAFS.4.OA.1.a Determine whether an equation is true or false by using comparative relational thinking. For example, without adding 60 and 24, determine
whether the equation 60 + 24 = 57 + 27 is true or false.
Math Practice Standard(s)
Link to Mathematical Practice Standards Rubric
MAFS.K12.MP.2.1 Reason abstractly and quantitatively.
MAFS.K12.MP.3.1 Construct viable arguments and critique the reasoning of others.
Additional Resources & Links
Higher Order Questions & Writing Connections
Georgia Units
Link to Webb’s DOK Guide
Unit 3
*Higher order questions should be utilized to foster a deep, conceptual
 Red Rectangles
understanding of the topic. Encouraging students to express their
 More or Less
mathematical thinking in writing helps them solidify their learning.
(All of Georgia Unit 3 pertain to this Topic)
 How can we use fair sharing to determine equivalent fractions?
 How do we know fractional parts are equivalent?
EngageNY - Module 5
 What happens to the value of a fraction when the numerator and
Topic B
denominator are multiplied or divided by the same number?
Topic C
 How can you compare and order fractions?
**Note: All of EngageNY Module 5 pertains to this Topic
 How do I compare fractions with unlike denominators?
 What can you do to decide whether your answer is reasonable?
EngageNY Math Studio Talk: Common Core Instruction for 4.NF
This video addresses strategies for developing fraction number sense. This
segment focuses on fraction equivalence and ordering. (Beginning of video – 7:45)
* YouTube must already be opened on your browser before clicking the link.
www.pearsonrealize.com
Home-School Connection Page
Reteach to Build Understand Pages
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Florida Interim Assessment Item Bank and Test Platform
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
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How can identifying factors and multiples of denominators help to
identify equivalent fractions?
How do we represent a fraction that is greater than one?
How do we locate fractions on a number line?
How can benchmark fractions be used to compare fractions? (Ex. I
know that 5/11 is less than 6/9 because 5/11 is les than one-half and
6/9 is greater than one-half.)
How can we compare fractions with the same denominator by
thinking of the fractions as having the “same size pieces”? (Ex. I
know that 3/8 is greater than 2/8 because both fractions have the
same size pieces, however the first fraction has three pieces, while
the second fraction only has two pieces.)
How can we compare fractions with the same numerator by
thinking of the fractions as having the “same number of pieces”?
(Ex. I know that 4/9 is less than 4/5 because each fraction has the
same number of pieces, but nineths are smaller than fifths, so fournineths is less than four-fifths.)
How can we compare two fractions using the “missing piece”
thought process? (Ex. I know 7/8 is greater than 5/6 since both
fractions have one piece missing, and eighths are smaller than sixths
so seven-eighths is closer to being a complete whole than fivesixths.)
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 8-1 through 8-7