Lesson 18 | Fractions | 3rd Grade Mathematics

Objective

Compare fractions with the same denominators by reasoning about their number of 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 denominator by using the understanding that when the denominator is the same, the pieces are the same size, and thus when comparing fractions with the same denominators, the fraction with a numerator that is high in value is greater than a fraction with a denominator that is low in value since there are more equal-sized pieces (MP.2).
Record the results of comparisons with the symbols >, =, or <.
Justify comparisons of fractions with the same denominator using the reasoning above and/or using an area model or number line (MP.3, MP.5).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

A number line is a very useful representation to compare fractions, i.e., “given two fractions—thus two points on the number line—the one to the left is said to be smaller and the one to the right is said to be larger” (NF Progression, p. 9). Thus, while Lessons 16 and 17 included tasks related to all models they’ve encountered throughout the unit, this lesson’s tasks include contexts or explicit referral to length models (namely, tape diagrams and number lines) in preparation for Lesson 19’s deeper analysis of the benefit of a number line to compare fractions.

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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 the class party, Robin and Shawn each made a loaf of banana bread. Their loaf pans were exactly the same size. Robin sliced her banana bread into 6 equal slices. Shawn also sliced his into 6 equal slices. After the party, Robin had more slices of banana bread left to take home than Shawn did. What fraction of the whole loaf pan might each person take home?

Guiding Questions

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References

San Francisco Unified School District Math Department 3.8 LS3 Day 3 Sharing Brownies Part II Student — Sharing Brownies Part II

3.8 LS3 Day 3 Sharing Brownies Part II Student is made available by the San Francisco Unified School District Math Department as a part of their SFUSD Math Core Curriculum under a CC BY 4.0 license. Accessed March 8, 2019, 4:42 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

a. Choose each statement that is true.

i. $$\frac{3}{4}$$ is greater than $$\frac{5}{4}$$.

ii. $$\frac{5}{4}$$ is greater than $$\frac{3}{4}$$.

iii. $$\frac{3}{4}>\frac{5}{4}.$$

iv. $$\frac{3}{4}<\frac{5}{4}.$$

v. $$\frac{5}{4}>\frac{3}{4}.$$

vi. $$\frac{5}{4}<\frac{3}{4}.$$

vii. None of these.

b. $$\frac{3}{4}$$ and $$\frac{5}{4}$$ 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 Denominator, Assessment Variation

Comparing Fractions with the Same Denominator, Assessment Variation, accessed on March 19, 2019, 11:14 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 parts, can you tell if fractions are equivalent? Why or why not?
In #1, where on the number line are the greater fractions compared to the lesser fractions? Do you think this relationship between a fraction’s size and its location on the number line is true of any pair of fractions? Why or why not?
What made the fractions in #2 different from the fractions in #1? Could you still use the same models to compare?
What made the fractions in #7 unique? What model did you use to compare them? Is one model more preferable to others? Why or why not?
Who was correct in #8? What was incorrect about Gabe’s drawing?
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.

$$\frac{\square}{6}<\frac{5}{6}$$

Problem 2

Compare $$\frac{2}{4}$$ and $$\frac{5}{4}$$ using <, >, or =. Draw a model to show your thinking.

Student Response

An example response to the Target Task at the level of detail expected of the students.

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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 17

Lesson 19

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

Tips for Teachers

Anchor Tasks

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

References

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Problem 2

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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