Lesson 16 | Fractions | 3rd Grade Mathematics

Objective

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 <.

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

Understand that given a fraction, when its whole is partitioned into more and more parts, the fractional pieces decrease in size and thus pieces of a whole that is partitioned into more pieces will be smaller than pieces of a whole that is partitioned into fewer pieces (i.e., when the denominator is larger, the pieces are smaller) (MP.7, MP.8).
Compare unit fractions by using the understanding that when the denominator is larger, the pieces are smaller, and thus a unit fraction with a denominator that is high in value is less than a unit fraction with a denominator that is low in value (MP.2).
Record the results of comparisons with the symbols >, =, or <.
Justify comparisons of unit fractions using the reasoning above and/or using an area model or number line (MP.3).
Recognize that comparisons are valid only when the two fractions refer to the same whole (MP.6).

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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

Kiana bought two Fruit-by-the-Foot snacks to share with friends. She splits one of them into 3 equal-sized pieces and the other into 8 equal-sized pieces. If Kiana were sharing a piece of Fruit-by-the-Foot with you, which snack would you take a piece from, the 3-piece snack or the 8-piece snack? Explain why.

Guiding Questions

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Problem 2

a. Locate and label the points $$\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, $$ and $$\frac{1}{5} $$ on the number line. You can use more than one number line if you wish.

b. What do you notice? What do you wonder?

Guiding Questions

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References

Illustrative Mathematics Locating Fractions Less than One on the Number Line — Part (c)

Locating Fractions Less than One on the Number Line, accessed on March 19, 2019, 11:10 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 3

Bryce drew this picture:

Then he said,

This shows that $$\frac{\mathbf{1}}{\mathbf{4}}$$ is greater than $$\frac{\mathbf{1}}{\mathbf{2}}$$.

a. What was his mistake? Draw a picture that shows why $$ \frac{1}{2}$$ is greater than $$\frac{1}{4}$$.

b. Which of these comparisons of $$\frac{1}{4}$$ with $$ \frac{1}{2}$$ are true?

i. $$\frac{1}{4}>\frac{1}{2}$$

ii. $$\frac{1}{4}<\frac{1}{2}$$

iii. $$\frac{1}{4}=\frac{1}{2}$$

iv. $$\frac{1}{2}>\frac{1}{4}$$

v. $$\frac{1}{2}<\frac{1}{4}$$

Guiding Questions

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References

Illustrative Mathematics Comparing Fractions with a Different Whole

Comparing Fractions with a Different Whole, accessed on March 28, 2018, 1:21 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.

Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

In #3, how could it be possible that Arnie ate more of his sandwich?
How did you decide where to place $$\frac{1}{2}$$ and $$\frac{1}{4}$$ on the number line in #4? Did your number line support or disprove Robert’s statement? Why?
What does area have to do with fractions in #6? How did you know the number of slices of pizza would result in pieces with the smallest area? How did you determine how many slices Casey’s pizza would have? How did you compare the slices?
What would it require to make Julian’s statement correct in #7?
Explain a general strategy for comparing unit fractions.

Target Task

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

Problem 1

Use <, >, or = to compare.

a. 1 half _____ 1 third

b. $$\frac{1}{8}$$ _____ $$\frac{1}{6}$$

Student Response

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Problem 2

Annie drank $$1\over 3$$ of a small juice. Enrique drank $$1\over 4$$ of a large juice. Who drank more? Explain your answer in words or pictures.

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

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Word Problems and Fluency Activities

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Lesson 15

Lesson 17

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

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

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

References

Problem Set

Discussion of Problem Set

Target Task

Problem 1

Student Response

Problem 2

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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