Lesson 11 | Fraction Equivalence and Ordering | 4th Grade Mathematics

Objective

Compare two fractions where one numerator or denominator is a factor of the other by replacing one fraction with an equivalent one.

Common Core Standards

Core Standards

The core standards covered in this lesson

4.NF.A.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.

Number and Operations—Fractions

4.NF.A.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.

Foundational Standards

The foundational standards covered in this lesson

3.NF.A.3.D

Number and Operations—Fractions

3.NF.A.3.D — Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Compare two fractions with the same numerators or denominators using visual models (MP.3, MP.5).
Understand that fractions are said to have a common numerator when they have the same number of units. Fractions are said to have a common denominator when they have the same sized units.
Compare two fractions where one numerator is a factor of the other numerator by replacing one fraction with an equivalent one to compare them with like numerators (MP.3).
Compare two fractions where one denominator is a factor of the other denominator by replacing one fraction with an equivalent one to compare them with like denominators (MP.3).
Use the correct symbol (< , >, =) to record a comparison.
Understand that comparisons are valid only when the two fractions refer to the same whole.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

The supporting work of gaining familiarity with factors and multiples (4.OA.4) supports this major work of comparing fractions with related numerators or denominators by finding common units or number of units, since students must recognize that the fractions’ numerators or denominators share a common factor to be able to utilize this strategy.
As mentioned in Lesson 5, there are no problems in this Problem Set, or any hereafter, that are related to the idea that “comparisons are valid only when the two fractions refer to the same whole” (4.NF.2). This is because this is also part of the third-grade expectations regarding fraction equivalence and comparison, so students should understand this idea already. However, if they would benefit from some additional practice, a list of potential resources can be found in the Tips for Teachers for Lesson 5.

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Tasks

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Problem 1

Below are measurements of ribbon in feet. For each pair of ribbons, determine which one is longer. Show or explain how you know.

a. $${{3\over4}}$$ ft. and $${{1\over4}}$$ ft.

b. $${{5\over12}}$$ ft. and $${{5\over6}}$$ ft.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Illustrative Mathematics Grass Seedlings — Comparing Fractions

Grass Seedlings, accessed on Feb. 8, 2018, 12:51 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic C > Lesson 14 — Concept Development

Grade 4 Mathematics > Module 5 > Topic C > Lesson 14 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

Compare the following fractions. Record your answer with $$\lt$$, $$\gt$$, or $$=$$.

a. $${{2\over3}}$$ and $${{7\over9}}$$

b. $${{7\over10}}$$ and $${{3\over5}}$$

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 3

Compare the following fractions. Record your answer with $$\lt$$, $$\gt$$, or $$=$$.

a. $$\frac35$$ and $$\frac13$$

b. $${{2\over3}}$$ and $${{4\over5}}$$

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem Set

Problem Set

Answer Keys

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

Discussion of Problem Set

How did the tape diagrams help you to determine which statements were true in #1?
What values did you choose to support Phil’s claim? What about to show that it’s not always true? Was there more than one correct choice for either or both parts?
#4a, 4d, and 4f can be compared using different types of reasoning. Explain the reasoning you used for each.
How did you determine whether the first comparison in #5 was true or false?
How can you determine whether you can make common numerators or common denominators when comparing fractions?

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Compare the following fractions by writing $${<}$$, $${>}$$, or $$=$$ in the blank.

a. $${{4\over5}}$$ _____ $${{2\over3}}$$

b. $${{3\over4}}$$ _____ $${{10\over12}}$$

Student Response

Create a free account or sign in to view Student Response

Additional Practice

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

Extra Practice Problems

Answer Keys

Answer keys for Problem Sets and Extra Practice Problems are available with a Fishtank Plus subscription.

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Lesson 10

Lesson 12

Lesson Map

Topic A: Factors and Multiples

Identify multiples and determine if a whole number is a multiple of another number.

4.OA.B.4

Explore patterns in multiples of various whole numbers.

4.OA.B.4

Find factor pairs for numbers to 100 and recognize that a whole number is a multiple of each of its factors.

4.OA.B.4

Determine whether a given number is prime or composite.

4.OA.B.4

Topic B: Equivalent Fractions

Recognize and generate equivalent fractions with smaller units using tape diagrams.

4.NF.A.1

Recognize and generate equivalent fractions with smaller units using number lines.

4.NF.A.1

Recognize and generate equivalent fractions with smaller units using area models.

4.NF.A.1

Recognize and generate equivalent fractions with smaller units using multiples.

4.NF.A.1

Recognize and generate equivalent fractions with larger units using visual models.

4.NF.A.1

Recognize and generate equivalent fractions with larger units using factors.

4.NF.A.1

Topic C: Comparing and Ordering Fractions

Compare two fractions where one numerator or denominator is a factor of the other by replacing one fraction with an equivalent one.

4.NF.A.2

Compare two fractions by replacing both fractions with equivalent ones.

4.NF.A.2

Compare two fractions using one whole as a benchmark.

4.NF.A.2

Compare two fractions using one half as a benchmark.

4.NF.A.2

Compare and order fractions using various strategies.

4.NF.A

Fraction Equivalence and Ordering

Objective

Common Core Standards

Core Standards

Number and Operations—Fractions

Foundational Standards

Number and Operations—Fractions

Criteria for Success

Tips for Teachers

Anchor Tasks

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Discussion of Problem Set

Target Task

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

Request a Demo

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Any other information you would like to provide about your school?

Effective Instruction Made Easy