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.

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 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 equivalentfractions(online dictionary, multilingual dictionary)

The Illustrative Mathematics tasks below demonstrate expectation for this standard.

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.

## 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.

Increasing Rigor

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 includesAbout the MathIllustrative Math Project

equivalentandequivalentfractions(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)## 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)

Additional Lesson Sets from Learnzillion: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)

pg 108

Blocks pg 72

Beyond Pizzas and Pies pg 32-36

Hands-On Standards, Common Core Fractions Gr 4

Equivalent Fractions and Decimals - Lessons 1 and 2

pgs 10-14

Fractions with Pattern Blocks pg 72

3-4 p 46

Super Source, Snap Cubes

3-4 p 62

Super Source: Cuisenaire Rods

3-4 pg 26

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

Web Resources:(eTool)

(lesson seed)

(Virtual Manipulative)

(online game)

(lesson seed)

(Virtual Manipulative)

(4 eTool activities)

(5 lesson series, NCTM)

(online game)

(5 lesson series, NCTM)

(online game)

Teacher guideline for virtual manipulatives 4.NF.1

(NCTM exemplary lesson)

(online game)

(lesson Seed)

(lesson seed)

(NC Dept. of Public Instruction)

(NC Dept. of Public Instruction)

(MSDE lesson seeds)

(MSDE lesson seeds)

(MSDE lesson plan)

(MSDE lesson seeds)

## 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.