Lesson 17 | Fractions | 3rd Grade Mathematics

Objective

Compare fractions with the same numerators by reasoning about the size of their units. Record the results of comparisons with the symbols >, =, or <.

Common Core Standards

Core Standards

The core standards covered in this lesson

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.

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.

Foundational Standards

The foundational standards covered in this lesson

2.MD.A.2

Measurement and Data

2.MD.A.2 — Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.

Criteria for Success

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

Compare fractions with the same numerator by using the understanding that when the denominator is larger, the pieces are smaller, and thus when comparing fractions with the same numerators, the fraction with a denominator that is high in value is less than a fraction with a denominator that is low in value (MP.2).
Record the results of comparisons with the symbols >, =, or <.
Justify comparisons of fractions with the same numerator using the reasoning above and/or using an area model or number line (MP.3, MP.5).

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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

LaTonya has 2 equal-sized candy bars. She cut the first candy bar into fourths after lunch and eats three pieces. Later, she cut the second candy bar into sixths after dinner and eats three pieces. Did LaTonya eat the same amount of the first candy bar and second candy bar? If not, did she eat more of the first candy bar or the second one? Show or explain how you know.

Guiding Questions

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References

EngageNY Mathematics Grade 3 Mathematics > Module 5 > Topic F > Lesson 28 — Application Problem

Grade 3 Mathematics > Module 5 > Topic F > Lesson 28 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

a. Who correctly compares the numbers $$\frac{2}{3}$$ and $$\frac{2}{5}$$?

i. Ben said that $$\frac{2}{3}$$ is greater than $$\frac{2}{5}$$.

ii. Lee said that $$\frac{2}{3}$$ is equal to $$\frac{2}{5}$$.

iii. Mia said that $$\frac{2}{3}$$ is less than $$\frac{2}{5}$$.

b. Compare $$\frac{2}{3}$$ and $$\frac{2}{5}$$ using symbols:

$$\frac{2}{3}$$ _____ $$\frac{2}{5}$$

c. Choose the two pictures that best compare $$\frac{2}{3}$$ and $$\frac{2}{5}$$.

Guiding Questions

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References

Illustrative Mathematics Fraction Comparisons with Pictures, Assessment Variation

Fraction Comparisons with Pictures, Assessment Variation, accessed on March 19, 2019, 11:11 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.

Problem 3

a. Choose each statement that is true.

i. $$\frac{9}{8}$$ is greater than $$\frac{9}{4}$$.

ii. $$\frac{9}{4}$$ is greater than $$\frac{9}{8}$$.

iii. $$\frac{9}{8}>\frac{9}{4}.$$

iv. $$\frac{9}{8}<\frac{9}{4}.$$

v. $$\frac{9}{4}>\frac{9}{8}$$.

vi. $$\frac{9}{4}<\frac{9}{8}.$$

vii. None of these.

b. $$\frac{9}{8}$$ and $$\frac{9}{4} $$ are shown on the number line. Which is correct?

ii.

iii. Neither of these.

Guiding Questions

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References

Illustrative Mathematics Comparing Fractions with the Same Numerators, Assessment Variation

Comparing Fractions with the Same Numerators, Assessment Variation, accessed on March 19, 2019, 11:12 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.

Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

If you only know the number of shaded parts, can you tell if fractions are equivalent? Why or why not?
Look at the models in #1─4. When comparing fractions, why is it so important that the wholes are the same size?
Tell a partner how you used the models in #1─4 to determine greater than, less than, or equal to.
Explain a general strategy for comparing fractions with the same numerators.

Target Task

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

Problem 1

Fill in the blank to make the statement true.

$$\frac{3}{4}>\frac{3}{\square}$$

Problem 2

a. Compare $$5\over 6$$ and $$5\over 8$$. Use <, >, or = to record your comparison.

b. Explain how you know your answer in Part A is correct. Draw a picture or a number line to support your reasoning.

Student Response

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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

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Word Problems and Fluency Activities

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Lesson 16

Lesson 18

Lesson Map

Topic A: Understanding Unit Fractions and Building Non-Unit Fractions

Partition a whole into equal parts using area models, identifying fractional units.

3.G.A.2 3.NF.A.1

Partition a whole into equal parts using tape diagrams (i.e., fraction strips), identifying and writing unit fractions in fraction notation.

3.G.A.2 3.NF.A.1

Partition a whole into equal parts using area models and tape diagrams, identifying and writing non-unit fractions in fraction notation.

3.NF.A.1

Identify fractions of a whole that is not partitioned into equal parts.

3.NF.A.1

Draw the whole when given the unit fraction.

3.NF.A.1

Identify a shaded fractional part in different ways, depending on the designation of the whole.

3.NF.A.1

Topic B: Fractions on a Number Line

Partition a number line from 0 to 1 into fractional units.

3.NF.A.2

Place any fraction on a number line with endpoints 0 and 1.

3.NF.A.2

Place any fraction on a number line with endpoints 0 and another whole number greater than 1.

3.NF.A.2

Place any fraction on a number line with endpoints greater than 0.

3.NF.A.2 3.NF.A.3.C

Place various fractions on a number line where the given interval is not a whole.

3.NF.A.2 3.NF.A.3.D

Topic C: Equivalent Fractions

Understand two fractions as equivalent if they are the same point on a number line referring to the same whole. Use this understanding to generate simple equivalent fractions.

3.NF.A.3.A 3.NF.A.3.B

Understand two fractions as equivalent if they are the same sized pieces of the same sized wholes, though not necessarily the same shape. Use this understanding to generate simple equivalent fractions.

3.NF.A.3.A 3.NF.A.3.B

Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

3.NF.A.3.C

Explain equivalence by manipulating units and reasoning about their size.

3.NF.A.3.A 3.NF.A.3.B 3.NF.A.3.C

Topic D: Comparing Fractions

Compare unit fractions (a unique case of fractions with the same numerators) by reasoning about the size of their units. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <.

3.NF.A.3.D

Compare fractions with the same numerators by reasoning about the size of their units. Record the results of comparisons with the symbols >, =, or <.

3.NF.A.3.D

Compare fractions with the same denominators by reasoning about their number of units. Record the results of comparisons with the symbols >, =, or <.

3.NF.A.3.D

Compare and order fractions using various methods.

3.NF.A.3

Understand fractions as numbers.

3.NF.A

Topic E: Line Plots

Measure lengths to the nearest half inch.

3.MD.B.4

Measure lengths to the nearest quarter inch.

3.MD.B.4

Generate measurement data and represent it in a line plot.

3.MD.B.4

Create line plots (dot plots).

3.MD.B.4

Fractions

Objective

Common Core Standards

Core Standards

Number and Operations—Fractions

Foundational Standards

Measurement and Data

Criteria for Success

Anchor Tasks

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

References

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Problem 2

Student Response

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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