Lesson 13 | Fraction Equivalence and Ordering | 4th Grade Mathematics

Objective

Compare two fractions using one whole as a benchmark.

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 fractions to 1.
Understand a benchmark fraction to be a common fraction.
Compare two fractions, one of which is less than a whole and the other of which is greater than a whole, using one as a benchmark (MP.3).
Compare two fractions that are both either greater than or less than a whole by reasoning about their proximity to one (MP.3).
Use the correct symbol (<, >, =) to record a comparison.

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Anchor Tasks

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

Problem 1

For each diagram:

Name a fraction the point represents.
Is that fraction greater than or less than 1?
How far is it from 1?

Guiding Questions

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References

Illustrative Mathematics Grade 4 > Unit 2 > Lesson 6 > Activity 1

Grade 4 > Unit 2 > Lesson 6 > Activity 1, accessed on Feb. 18, 2022, 9:43 a.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.

Problem 2

a. Ishmael says he knows $$\frac65$$ is greater than $$\frac78$$ because $$\frac65 \gt 1$$ and $$\frac78 \lt 1$$. Do you agree or disagree? Use the number lines from Anchor Task 1 to support your answer.

b. Use Ishmael’s strategy to compare the following fractions. Record your answer with $$\lt$$, $$\gt$$, or $$=$$.

$${{5\over3}}$$ and $${{9\over10}}$$
$${{4\over5}}$$ and $${{13\over12}}$$

Guiding Questions

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Problem 3

a. Now Joslyn is comparing $$\frac65$$ and $$\frac43$$. She says that she knows $$\frac65$$ is less than $$\frac43$$ because $$\frac65$$ is $$\frac15$$ more than 1 and $$\frac43$$ is $$\frac13$$ more than 1 and $$\frac13$$ is more than $$\frac15$$. Do you agree or disagree? Use the number lines from Anchor Task 1 to support your answer.

b. Use any strategy to compare the following fractions. Record your answer with $$\lt$$, $$\gt$$, or $$=$$.

$${{3\over4}}$$ and $${{9\over10}}$$
$${{7\over5}}$$ and $${{11\over9}}$$
$${{8\over11}}$$ and $${{13\over16}}$$

Guiding Questions

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Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

Which containers have enough soda in them to make the punch in #2? How could you tell?
How did you compare the fractions in #3?
Who ran the shortest distance in #4? How do you know?
What fraction did you come up with that is close to one? Did anyone else come up with a fraction that is close? Which one is closer? How do you know? Are there possible fractions that are even closer?

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. $${{2\over3}}$$ _____ $${{5\over4}}$$

b. $${{4\over5}}$$ _____ $${{5\over6}}$$

Student Response

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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

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Word Problems and Fluency Activities

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Lesson 12

Lesson 14

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

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

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