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.

Increasing Rigor

  • What are 3 fractions equivalent to 3/4?
  • How can 4/5 and 8/10 be equivalent if the numerator and denominator in each is different?
  • Represent the value of 1 ½ in 3 different ways.
  • Andy, Lee, and Val each ate ½ of pizza. The pizzas were the same size, but Andy at one piece, Lee ate 3 slices, and Val ate four slices. How is this possible? (Andy cut his in halves, Lee cut his in sixths, and Val cut her pizza into eighths.)
  • Show how 5/15 is equivalent to 1/3 rather than 1/5.
  • Write the statement 10/12 is twice as large as 5/6 on the board. Ask students if they agree or disagree with the statement. Can they use a model to defend their answer?
  • Why is 3/5 the same as 6/10 when the two fractions have different numbers?

About the Math
illustrative_math_4nf1.png
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. Essential vocabulary for this standard includes equivalent and equivalent fractions (online dictionary, multilingual dictionary)



The Illustrative Mathematics tasks below demonstrate expectation for this standard.





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

VDW3-5.png

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.



Additional Lesson Sets from Learnzillion:
Print Resources:
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Brain-Compatible Activities for Mathematics 4-5 pg 47-50
hands-on_standards.pngHands 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.pngNimble With Numbers 4-5
pg 108
fractions_with_pattern_blocks.jpgFractions with Pattern
Blocks pg 72
beyond_pizzas_and_pies.jpeg
Beyond Pizzas and Pies pg 32-36
hands_on_standards_cc_fractions_4.jpg
Hands-On Standards, Common Core Fractions Gr 4


Equivalent Fractions and Decimals - Lessons 1 and 2

pgs 10-14
20_thinking_questions.png
Fractions with Pattern Blocks pg 72
supersource_all.pngSuper Source Color Tiles
3-4 p 46

Super Source, Snap Cubes
3-4 p 62

Super Source: Cuisenaire Rods
3-4 pg 26
building_number_power3-5.pngMath Intervention: Building Number Power 3-5 (153-158)

Math Intervention: Building Number Power 3-5 (166-172)
numbersense.pngNumber Sense 4-6 pg 59-61, 92-93, 99-101


Web Resources:

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lessons.jpg
student_resources.jpg
video_segments.jpg
Games and Centers
Lessons
Student Resources
Video Segments
Equivalent Fractions
(eTool)
Creating Equivalent Fractions
(lesson seed)
Fraction Bars
(Virtual Manipulative)

Equivalent Fraction Bingo
(online game)
Thirteen Ways of Looking at one-half
(lesson seed)
12 Fraction Activity Tools
(Virtual Manipulative)

Equivalent Fractions
(4 eTool activities)
Pattern Block Fractions
(5 lesson series, NCTM)
Reducing Fractions

Matching Equivalent Fraction Game
(online game)
Fun with Fractions
(5 lesson series, NCTM)
Fraction Patterns

Equivalent Fractions Modeling
(online game)
Make Equivalent Fractions
Virtual Manipulatives

Teacher guideline for virtual manipulatives 4.NF.1

Fraction Wall Call(game/center)
Fraction Clothesline
(NCTM exemplary lesson)


Equivalent Fractions Triplets
(online game)
Fraction Wall
(lesson Seed)



Their Fair Share



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)







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.