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.

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.

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)

Select image for lessons.

Print Resources:

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

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

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

Hands-On Standards, Common Core Fractions Grade 4
Equivalent Fractions and Decimals - Lessons 1 and 2
pagess 10-14

## 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.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.

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.

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

How do I know when fractions are equivalent?Essential Questions

equivalent, equivalent fractionsVocabulary (online dictionary, multilingual dictionary)

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.About the MathIllustrative Math Project

Illustrative Mathematics Project Example: Explaining Equivalence with Pictures

Illustrative Mathematics Project: Piggy Bank

Rich Tasks for Multiple Means of Engagement, Expression, and Representation (UDL)## Teaching Student-Centered Mathematics (Grades 3-5),

pgs. 144-146 Activities 5.7, 5.8, and 5.9pgs. 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)

Print Resources:Brain-Compatible Activities for Mathematics 4-5 pg 47-50

Hands on Standards (Grades 3-4), pgs. 50-51 (Comparing and Ordering Fractions)

Math Intervention: Building Number Power 3-5 (166-172)

Super Source, 3-4: Snap Cubes pg 62

Super Source: Cuisenaire Rods 3-4 pg 26

20 Thinking Questions for Fraction Circles 3-6

20 Thinking Questions for Geoboards 3-6

20 Thinking Circles for Rainbow Cubes 3-6

Equivalent Fractions and Decimals - Lessons 1 and 2

pagess 10-14

Web Resources:Lesson Seed

Virtual Manipulative

lesson plan

on-line game

Lesson Seed

(5 Lessons)

(4 eTool activities)

5 Lesson Series, NCTM

Virtual Manipulative

(online game)

5 Lesson Series, NCTM

NCTM exemplary lesson

Lesson Seed

Fraction Matching

Lesson Seed

NC Dept. of Public Instruction

NC Dept. of Public Instruction

MSDE Lesson Seeds

MSDE Lesson Seeds

MSDE Lesson Plan

MSDE Lesson Seeds

Connecting to Children's Literature:## Questions/Comments:

Contact John SanGiovanni at jsangiovanni@hcpss.org.Use and Sharing of HCPSS Website and ResourcesHoward County Public Schools Office of Elementary Mathematics Curricular Projects has licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.