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.

Note: Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Quarter 1
Quarter 2
Quarter 3
Quarter 4
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.
Revisit to make connections with other fraction concepts in this quarter.

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.
Revisit to make connections with other fraction concepts in this quarter.

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.
Revisit to make connections with other fraction concepts in this quarter.

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.

Enduring Understanding

The same fractional amount can be represented by an infinite set of different but equivalent fractions.

Essential Questions

How do I know when fractions are equivalent?

Vocabulary (online dictionary, multilingual dictionary)

equivalent, equivalent fractions

About the Math
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Illustrative Math Project

Understanding equivalent fractions is an important concept when comparing fractions, ordering fractions and adding and subtracting fractions. Equivalent fractions are fractions that represent equal value. They are numerals that name the same fractional number. When we say that fractions are equivalent there is an underlying assumption that the wholes are the same size. Students need to understand this concept. A focus question should be “Are the wholes the same size?” Fraction manipulatives should be used when first introducing the concept of equivalency. Students should explore using fraction strips or pattern blocks which fractions are equivalent before moving to a procedure to find equivalent fractions.

Illustrative Mathematics Project Example: Explaining Equivalence with Pictures
Illustrative Mathematics Project: Piggy Bank



Rich Tasks for Multiple Means of Engagement, Expression, and Representation (UDL)

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Teaching Student-Centered Mathematics (Grades 3-5),

pgs. 144-146 Activities 5.7, 5.8, and 5.9
pgs. 151-156 Activities 5.14 - 5.19, * Figure 5.20
pages 140-141 activites 5.4 and 5.5


Students should be provided time to explore how to rename improper fractions and mixed numbers through manipulatives such as fraction bars, Cuisenaire rods, snap cubes, or fraction circles prior to introducing the algorithm to them. In Teaching Student-Centered Mathematics page140-141, you will find a variety of activities to complete with students to build understanding of this concept.

Learnzillion Video Resources (5 Lessons)

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Select image for lessons.

Print Resources:
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Brain-Compatible Activities for Mathematics 4-5 pg 47-50
Hands on Standards (Grades 3-4), pgs. 52-53 (Mixed Numbers)

Hands on Standards (Grades 3-4), pgs. 50-51 (Comparing and Ordering Fractions)
Nimble With Numbers 4-5 pg 108
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Math Intervention: Building Number Power 3-5 (153-158)
Math Intervention: Building Number Power 3-5 (166-172)
Number Sense 4-6 pg 59-61, 92-93, 99-101
Super Source, 3-4: Color Tiles pg 46
Super Source, 3-4: Snap Cubes pg 62
Super Source: Cuisenaire Rods 3-4 pg 26
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Fractions with Pattern Blocks pg 72
20 Thinking Questions for Pattern Blocks 3-6 pg 42-46
20 Thinking Questions for Fraction Circles 3-6
20 Thinking Questions for Geoboards 3-6
20 Thinking Circles for Rainbow Cubes 3-6
Beyond Pizzas and Pies pg 32-36
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Hands-On Standards, Common Core Fractions Grade 4
Equivalent Fractions and Decimals - Lessons 1 and 2
pagess 10-14



Web Resources:

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Games and Centers
Lessons
Student Resources
Video Segments
Equivalent Fractions eTool
Creating Equivalent Fractions
Lesson Seed
Fraction Bars
Virtual Manipulative
Simplifying Fractions (Discovery Ed)
Tony's Fraction Pizza Shop
lesson plan
on-line game
Fraction Wall Call
Lesson Seed
Equivalent Fractions Virtual Manipulative
Learnzillion Video Resources
(5 Lessons)
Equivalent Fractions
(4 eTool activities)
Pattern Block Fractions
5 Lesson Series, NCTM
12 Fraction Activity Tools
Virtual Manipulative

Matching Equivalent Fraction Game
(online game)
Fun with Fractions
5 Lesson Series, NCTM
Reducing Fractions

Comparing Fractions eTool

Fraction Patterns

Fractions Concentration
Fraction Clothesline
NCTM exemplary lesson


Equivalent Fraction Bingoonline game
Fraction Wall
Lesson Seed


Thirteen Ways of Looking at one-half
Their Fair Share


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Fraction Matching
A Bowl of Fruit
Lesson Seed



Pattern Block Puzzles



Design of Fractions (4.NF.1 & 4.NF.3)
NC Dept. of Public Instruction



Race to One
NC Dept. of Public Instruction



Equivalent to Half
MSDE Lesson Seeds



Painted Wall
MSDE Lesson Seeds



Exploring Equivalent Fractions of a Region
MSDE Lesson Plan



Equivalent Sets
MSDE Lesson Seeds







Connecting to Children's Literature:



Questions/Comments:

Contact John SanGiovanni at jsangiovanni@hcpss.org.


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Howard County Public Schools Office of Elementary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.