Key Concept: If two fractions are related, then an equivalent form of one fraction can be written so that its denominator is the same as the second fraction.

Topic Overview | Standards Alignment | #### Common Core

5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)#### Georgia

MGSE5.NF.1 Add and subtract fractions and mixed numbers with unlike denominators by finding a common denominator and equivalent fractions to produce like denominators. IEP Goals

This topic contains lessons in which students build on their understanding of related proper fractions to work with related improper fractions. Lessons progress from developing the conceptual understanding of finding a common denominator for two related improper fractions to applying the procedure without models to solve addition and subtraction equations. Students also review converting improper fractions to mixed numbers, a skill introduced in Big Idea 4.

1. Given two models of related improper fraction and guided practice, the student will enter a “one” fraction to find an equivalent for one fraction so that both have a common denominator for nine out of ten examples in five consecutive sessions.

2. Given an addition or subtraction equation with two related improper fractions and the use of models, the student will solve five out of six examples correctly for five consecutive lessons with no more than 1 prompt.

3. Given an improper fraction and pre-teaching with models, the student will rewrite the fraction as a mixed number with 80% accuracy for five consecutive lessons.

2. Given an addition or subtraction equation with two related improper fractions and the use of models, the student will solve five out of six examples correctly for five consecutive lessons with no more than 1 prompt.

3. Given an improper fraction and pre-teaching with models, the student will rewrite the fraction as a mixed number with 80% accuracy for five consecutive lessons.

Unit Launcher

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5.5-1-1 Find Common Denominators for Improper Fractions |

View Guided Lesson Use the “one” fraction procedure to find a common denominator for two related improper fractions with and without models. (8-15 min)

5.5-1-2 Add/Subtract Related Improper Fractions |

View Guided Lesson Use models and the “one” fraction procedure to find a common denominator for two related improper fractions in order to complete addition or subtraction equations.. (8-15 min)

5.5-1-3 Review How to Convert Improper Fractions |

View Guided Lesson Convert improper fractions to mixed numbers with and without the use of models. (8-15 min)

5.5-1-4 Add Related Improper Fractions: Convert Sum |

View Guided Lesson Add related improper fractions and convert the sum to a mixed number with the help of models. (8-15 min)

Real World Investigation Part 1

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Key Concept: If two fractions are related, then an equivalent form of one fraction can be written so that its denominator is the same as the second fraction.

Topic Overview | Standards Alignment | #### Common Core

5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)#### Georgia

MGSE5.NF.1 Add and subtract fractions and mixed numbers with unlike denominators by finding a common denominator and equivalent fractions to produce like denominators. IEP Goals

In this topic students find a common denominator for two unlike mixed numbers. Students apply this skill to add and subtract mixed numbers in which the fractional parts are unlike. These lessons build on skills covered in Big Idea 4 in which students convert sums containing improper fractions to mixed numbers with a proper fractional part.

1. Given two models of related or unlike mixed numbers and guided practice, the student will enter a “one” fraction to find an equivalent for one fraction so that both have a common denominator for nine out of ten examples in five consecutive sessions.

2. Given an addition or subtraction equation with two related mixed numbers and the use of models, the student will solve five out of six examples correctly for five consecutive lessons with no more than one prompt.

3. Given a subtraction equation of two related mixed numbers and a cognitive strategy prompting routine, the student will independently use the routine to accurately find a common denominator, convert the subtrahend to a mixed number with an improper fraction, and solve the equation for five out of six examples by the end of the second progress report period.

4. Given an addition equation of two mixed numbers in which the fractional part of the sum is an improper fraction, the student will correctly convert the sum to a mixed number with a proper fraction with 90% accuracy for five consecutive sessions.

2. Given an addition or subtraction equation with two related mixed numbers and the use of models, the student will solve five out of six examples correctly for five consecutive lessons with no more than one prompt.

3. Given a subtraction equation of two related mixed numbers and a cognitive strategy prompting routine, the student will independently use the routine to accurately find a common denominator, convert the subtrahend to a mixed number with an improper fraction, and solve the equation for five out of six examples by the end of the second progress report period.

4. Given an addition equation of two mixed numbers in which the fractional part of the sum is an improper fraction, the student will correctly convert the sum to a mixed number with a proper fraction with 90% accuracy for five consecutive sessions.

5.5-2-1 Find Common Denominators for Related Mixed Numbers |

Lesson Plan

View Guided Lesson Use the “one” fraction procedure to find a common denominator for two related mixed numbers with and without models. (8-15 min)

5.5-2-2 Add/Subtract Related Mixed Numbers |

Lesson Plan

View Guided Lesson Use models and the “one” fraction procedure to find a common denominator for two related mixed numbers in order to complete addition or subtraction equations.. (8-15 min)

5.5-2-3 Convert to Add Related Mixed Numbers |

Lesson Plan

View Guided Lesson Add related mixed numbers and convert the sum to a mixed number with the help of models. (8-15 min)

5.5-2-4 Convert to Subtract Related Mixed Numbers |

Lesson Plan

View Guided Lesson Convert mixed number minuends of related mixed numbers to improper fractions in order to complete subtraction equations. (8-15 min)

Real World Investigation Part 2

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Key Concept: If two fractions are not related, then equivalent forms will be needed for both fractions before you can add or subtract the fractions.

Topic Overview | Standards Alignment | #### Common Core

5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)#### Georgia

MGSE5.NF.1 Add and subtract fractions and mixed numbers with unlike denominators by finding a common denominator and equivalent fractions to produce like denominators. IEP Goals

This topic contains lessons in which students apply previously learned skills for finding common denominators and converting fractions to unlike fractions. Addition and subtraction examples include proper, improper, and mixed numbers.

1. Given two unlike improper fractions or mixed numbers and guided practice, the student will enter a “one” fraction to find an equivalent for each fraction so that both have a common denominator for nine out of ten examples in five consecutive sessions.

2. Given an addition or subtraction equation with two unlike improper fractions or mixed numbers and pre-teaching with models, the student will independently find a common denominator and solve the equation for nine out of ten examples in three consecutive practice sessions.

3. Given a subtraction equation with two unlike fractions for mixed numbers and the use of models, the student will find a common denominator, convert the subtrahend, and find the differences for five consecutive examples in three consecutive trials.

4. Given an addition equation of mixed numbers with unlike denominators in which the fractional part of the sum is an improper fraction, the student will correctly convert the sum to a mixed number with a proper fraction with 90% accuracy for five consecutive sessions.

2. Given an addition or subtraction equation with two unlike improper fractions or mixed numbers and pre-teaching with models, the student will independently find a common denominator and solve the equation for nine out of ten examples in three consecutive practice sessions.

3. Given a subtraction equation with two unlike fractions for mixed numbers and the use of models, the student will find a common denominator, convert the subtrahend, and find the differences for five consecutive examples in three consecutive trials.

4. Given an addition equation of mixed numbers with unlike denominators in which the fractional part of the sum is an improper fraction, the student will correctly convert the sum to a mixed number with a proper fraction with 90% accuracy for five consecutive sessions.

5.5-3-1 Model/Write Common Denominators-Unlike Fractions |

Lesson Plan

View Guided Lesson Use the “one” fraction procedure to find a common denominator for two unlike fractions or mixed numbers with and without models. (8-15 min)

5.5-3-2 Add/Subtract Unlike Fractions |

Lesson Plan

View Guided Lesson Use the “one” fraction procedure to find a common denominator for two unlike fractions or mixed numbers with and without models. (8-15 min)

5.5-3-3 Add Unlike Improper Fractions-Convert Sum |

Lesson Plan

View Guided Lesson Add related mixed numbers and convert the sum to a mixed number with and without the use of models. (8-15 min)

5.5-3-4 Convert to Subtract Unlike Mixed Numbers |

Lesson Plan

View Guided Lesson Convert mixed number minuends of unlike mixed numbers to improper fractions in order to complete subtraction equations. (8-15 min)

Real World Investigation Part 3

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Key Concept: Addition and subtraction of fractions can be used to solve a variety of problems.

Topic Overview | Standards Alignment | #### Common Core

5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)#### Georgia

MGSE5.NF.1 Add and subtract fractions and mixed numbers with unlike denominators by finding a common denominator and equivalent fractions to produce like denominators. IEP Goals

Lessons in this topic require students to apply their understanding of related and unlike fractions to solve higher order tasks. They compare equations and explore the reciprocal relationship between addition and subtraction by determining unknowns in addition and subtraction equations without the use of models. Lessons include examples with proper, improper, and mixed numbers.

1. Given equations of two fractions with uncommon denominators and a benchmark number, the student will estimate the sums or differences of each and use the symbols <, >, and = to show the relationship between the numbers for five out of six equations by completion of the first marking period.

2. Given an equation with improper fractions and mixed numbers with uncommon denominators and the option to use models, the student will use given numbers in the equation to find the unknown numbers for five out of six equations for three consecutive sessions.

3. Given a set of ten addition and subtraction equations containing unlike fractions (proper, improper, or mixed numbers) and at least 1 unknown number along with a cognitive strategy, the student will apply the strategy and correctly solve for the answer with 80% accuracy for three consecutive sessions.

2. Given an equation with improper fractions and mixed numbers with uncommon denominators and the option to use models, the student will use given numbers in the equation to find the unknown numbers for five out of six equations for three consecutive sessions.

3. Given a set of ten addition and subtraction equations containing unlike fractions (proper, improper, or mixed numbers) and at least 1 unknown number along with a cognitive strategy, the student will apply the strategy and correctly solve for the answer with 80% accuracy for three consecutive sessions.

5.5-4-1 Compare Equations of Uncommon Fractions |

Lesson Plan

View Guided Lesson Use 4 strategies to compare fractions and fraction expressions with uncommon denominators. (8-15 min)

5.5-4-2 Add/Subtract Uncommon Fractions With Unknowns |

Lesson Plan

View Guided Lesson Solve for the unknown in an addition or subtraction equation of unlike fractions with and without the use of models. (8-15 min)

This Big Idea introduces students to addition and subtraction of mixed numbers and improper fractions with uncommon denominators. They learn how to use the “one” fraction procedure to find equivalents with common denominators, first by changing only one fraction and then by changing both fractions within an equation.