Lesson 11 | Fraction Operations | 4th Grade Mathematics

Objective

Compare and order fractions greater than 1 using various methods.

Common Core Standards

Core Standards

The core standards covered in this lesson

4.NF.B.3.C — Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Number and Operations—Fractions

4.NF.B.3.C — Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Foundational Standards

The foundational standards covered in this lesson

4.NF.A.1

Number and Operations—Fractions

4.NF.A.1 — Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
4.NF.A.2

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.

Criteria for Success

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

Compare two fractions greater than 1 written as mixed numbers or as fractions by choosing the strategy that would be most efficient, such as comparing to a benchmark, finding a common numerator, or finding a common denominator.
Order a set of fractions greater than 1 written as mixed numbers or as fractions using various strategies by comparing two fractions in the set at a time.
Use the correct symbol (< , >, =) to record a comparison.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Now that students have converted back and forth between fractions and mixed numbers, this lesson returns to the comparison work students did in Unit 4 to compare and order fractions greater than 1 written in various forms. Because today’s lesson isn’t directly aligned to the unit’s focus of fraction operations, though, you may decide to cut this lesson and instead put similar tasks into previous and upcoming lessons to ensure they are able to generalize the work of Unit 4 to fractions greater than 1 without dedicating additional instructional time to it.
Before the Problem Set, you could have students play a fraction comparison game "Making Fractions" described in the Georgia Standards of Excellence Curriculum Frameworks GSE Fourth Grade Unit 3: Fraction Equivalents on page 75. This game is similar to the one played in Unit 4.

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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

Alex, Barbara, Caroline, and Damien need flour for their cookie recipes. They know that the amount of flour in a recipe will change what the cookies are like, according to the picture they found online:

Alex’s recipes calls for $${{19\over8}}$$ cups of flour, Barbara’s calls for $${2{3\over4}}$$ cups of flour, Caroline’s calls for $${2{1\over3}}$$ cups of flour, and Damien’s calls for $${{13\over4}}$$ cups of flour. Which recipe calls for the most flour? Which recipe calls for the least? Show or explain your work.

Guiding Questions

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References

Wikimedia Commons Photo: Chocolate Chip Cookie by Renee Comet

Chocolate Chip Cookie by Renee Comet is made available on Wikimedia Commons under the CC0 1.0 license. Accessed July 18, 2018, 11 a.m..

Wikimedia Commons Photo: A Nantucket Pepperidge Farm Chocolate Chip Cookie by Evan-Amos

A Nantucket Pepperidge Farm Chocolate Chip Cookie by Evan-Amos is made available on Wikimedia Commons under the CC0 1.0 license. Accessed July 18, 2018, 11:02 a.m..

Problem 2

Compare. Record your comparison with symbols <, >, or =.

a. $${{19\over8}}$$ _____ $${{11\over4}}$$

b. $${4{2\over5}}$$ _____ $${4{6\over17}}$$

c. $${{16\over3}}$$ _____ $${5{5\over15}}$$

Guiding Questions

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Problem 3

Compare. Record your comparison with symbols <, >, or =.

a. $${2{5\over8}}$$ _____ $${2{1\over3}}$$

b. $${{13\over5}}$$ _____ $${{20\over6}}$$

c. $${{35\over8}}$$ _____ $${4{7\over12}}$$

d. $${6{1\over11}}$$ _____ $${{41\over7}}$$

Guiding Questions

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Problem Set

Problem Set

Answer Keys

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Discussion of Problem Set

In what way is #1(c) easier than #1(d)?
Who converted to a mixed number or a fraction greater than 1 before finding like units for #1(e)? Was it easier to compare mixed numbers or fractions greater than 1 for this particular problem?
In #1(i), the denominators had no common factors. What strategy did you use to solve? Did you solve by finding like numerators or by drawing a model to find like denominators?
At first glance, #3(j) looks really difficult. What makes it easier to solve?
Were there any problems in #1 or #3 that you could compare without renaming or without drawing a model? How were you able to mentally compare them?
When comparing the mixed numbers and fractions on the Problem Set, which strategies did you use? Were some strategies easier than others? Was it helpful to think about benchmark fractions?
Why is it often easier to compare mixed numbers than to compare fractions greater than 1?
How does this lesson relate to earlier lessons? How did earlier lessons help you to understand this lesson?

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 =.

a. $${{22\over5}}$$ _____ $${4{2\over7}}$$

b. $${3{1\over4}}$$ _____ $${3{7\over12}}$$

c. $${5{7\over12}}$$ _____ $${{23\over4}}$$

d. $${{29\over8}}$$ _____ $${{12\over3}}$$

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 10

Lesson 12

Lesson Map

Topic A: Building, Adding, and Subtracting Fractions Less Than or Equal to 1

Decompose fractions as a sum of unit fractions and as a multiple of a unit fraction.

4.NF.B.3.B 4.NF.B.4.A

Decompose fractions as a sum of fractions with the same denominator in more than one way.

4.NF.B.3.B 4.NF.B.4.A

Add and subtract fractions within 1 with the same units.

4.NF.B.3.A 4.NF.B.3.C

Solve word problems that involve the addition and subtraction of fractions where the total is less than or equal to one.

4.NF.B.3.D

Topic B: Building, Adding, and Subtracting Fractions Less Than 2

Decompose non-unit fractions less than 2 as a sum of unit fractions, as a sum of non-unit fractions, and as a whole number times a unit fraction.

4.NF.B.3.B 4.NF.B.4.A

Add and subtract fractions that require regrouping where the total is less than 2.

4.NF.B.3.A 4.NF.B.3.C

Add two fractions where one denominator is a multiple of the other using the denominators 2, 3, 4, 5, 6, 8, 10, and 12.

4.NF.B.3.A 4.NF.B.3.C

Topic C: Building, Adding, and Subtracting Fractions Greater Than or Equal to 2

Decompose and compose non-unit fractions greater than two as a sum of unit fractions, as a sum of non-unit fractions, and as a whole number times a unit fraction.

4.NF.B.3.B

Convert fractions greater than 1 to mixed numbers.

4.NF.B.3.B 4.NF.B.3.C

Convert mixed numbers to fractions greater than 1.

4.NF.B.3.B 4.NF.B.3.C

Compare and order fractions greater than 1 using various methods.

4.NF.B.3.C

Add fractions and mixed numbers where the total is greater than or equal to 2.

4.NF.B.3.C

Subtract fractions and mixed numbers where the total is greater than or equal to 2.

4.NF.B.3.C

Add and subtract mixed numbers using a variety of mental strategies.

4.NF.B.3.C

Solve word problems involving addition and subtraction of fractions.

4.NF.B.3.D

Topic D: Multiplication of Fractions

Multiply a whole number by a fraction.

4.NF.B.4.B

Multiply a whole number by a mixed number.

4.NF.B.4.B

Solve word problems involving multiplication of fractions.

4.NF.B.4.C

Solve word problems involving addition, subtraction, and multiplication of fractions.

4.NF.B.3.D 4.NF.B.4.C

Topic E: Line Plots

Make a line plot (dot plot) representation to display a data set of measurements in fractions of a unit.

4.MD.B.4

Solve problems using information presented in line plots.

4.MD.B.4

Fraction Operations

Objective

Common Core Standards

Core Standards

Number and Operations—Fractions

Foundational Standards

Number and Operations—Fractions

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

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