Key Concept: Fractions can be rewritten so they have the same denominator, which does not change their value.

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 discover that when fractions are related, changing one to an equivalent results in two fractions divided into the same number of equal parts or having the same common denominator. Lessons progress from developing the conceptual understanding of finding a common denominator for two related fractions to applying the procedure without models to solve addition and subtraction equations.

1. Given models of two related fractions and guided practice, the student will change one of the models, so that the fractions have common denominators, with 90% accuracy for five out of seven consecutive sessions.

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

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

Unit Launcher

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5.4-1-1 Model Common Denominators for Related Fractions |

View Guided Lesson Manipulate two models linked to numbers so that two related fractions have a common denominator. (8-15 min)

5.4-1-2 Add/Subtract Related Fractions Using Models |

View Guided Lesson Use models to find a common denominator for two related fractions in order to complete addition or subtraction equations. (8-15 min)

5.4-1-3 Model/Write Common Denominators-Related Fractions |

View Guided Lesson Use models and the “one” fraction procedure to find a common denominator for two related fractions. (8-15 min)

5.4-1-4 Add/Subtract Related Fractions Using "1" Fraction |

View Guided Lesson Use models and the “one” fraction procedure to solve addition and subtraction equations with related fractions (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 move beyond the use of models only to apply the procedure to find equivalent fractions that have a common denominator. Students then apply their ability to solve addition and subtraction examples with related fractions to estimate and solve equations with unknowns.

1. Given two related fractions and no more than one verbal prompt, the student will explain and complete the procedure using the “one” fraction to find an equivalent fraction with a common denominator for the other with 80% accuracy by the end of the second marking period.

2. Given an equation with two related fractions, the student will find a common denominator and solve for the sum or difference, with 80% accuracy for five consecutive sessions.

3. Given an expression and a number line with benchmarks, the student will estimate the sum or difference and show it on the number line for five out of six examples in five consecutive trials.

4. Given a set of ten addition and subtraction equations containing related fractions and at least one 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 two related fractions, the student will find a common denominator and solve for the sum or difference, with 80% accuracy for five consecutive sessions.

3. Given an expression and a number line with benchmarks, the student will estimate the sum or difference and show it on the number line for five out of six examples in five consecutive trials.

4. Given a set of ten addition and subtraction equations containing related fractions and at least one 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.

5.4-2-1 Find Common Denominators for Related Fractions |

Lesson Plan

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

5.4-2-2 Add/Subtract Related Fractions Using Equations |

Lesson Plan

View Guided Lesson Use the “one” fraction procedure to solve addition and subtraction equations with related fractions without using models. (8-15 min)

5.4-2-3 Estimate Sums/Differences of Related Fractions |

Lesson Plan

View Guided Lesson Estimate the placement of addition and subtraction expressions with related fractions on a number line. (8-15 min)

5.4-2-4 Add/Subtract Related Fractions with Unknowns |

Lesson Plan

View Guided Lesson Solve addition and subtraction equations containing related fractions with missing unknowns without models. (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 discover that when fractions are unlike, they must change both models to equivalent forms to find a common denominator. Lessons progress from developing the conceptual understanding of finding a common denominator for two unlike fractions to applying the procedure without models to solve addition and subtraction equations.

1. Given models of two unlike fractions and guided practice, the student will change both of the models, so that the fractions have common denominators, with 90% accuracy for five out of seven consecutive sessions.

2. Given an addition or subtraction equation with two unlike fractions, the student will solve five out of six examples correctly for five consecutive lessons with no more than one prompt.

2. Given an addition or subtraction equation with two unlike fractions, the student will solve five out of six examples correctly for five consecutive lessons with no more than one prompt.

5.4-3-1 Model Common Denominators for Unlike Fractions |

Lesson Plan

View Guided Lesson Manipulate two models linked to numbers so that two unlike fractions have a common denominator. (8-15 min)

5.4-3-2 Add/Subtract Unlike Fractions Using Models |

Lesson Plan

View Guided Lesson Use models to find a common denominator for two unlike fractions in order to complete addition or subtraction equations. (8-15 min)

5.4-3-3 Find Common Denominators for Unlike Fractions |

Lesson Plan

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

5.4-3-4 Add/Subtract Unlike Fractions |

Lesson Plan

View Guided Lesson Solve addition and subtraction equations containing unlike fractions with missing unknowns without models. (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.

1. Given a set of ten addition and subtraction equations containing unlike fractions and at least one 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 two addition and subtraction equations with uncommon denominators, the student will estimate the sums or differences of each and use the symbols <, >, and = to show the relationship between the two equations for five out of six equations by completion of the first marking period.

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

5.4-4-1 Compare Sums/Differences of Uncommon Fractions |

Lesson Plan

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

5.4-4-2 Complete Fraction Equations with Unknowns |

Lesson Plan

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

This Big Idea introduces students to addition and subtraction of fractions with uncommon denominators. Lessons introduce the use of the “one” fraction procedure to find equivalents with common denominators, first by changing only one fraction and then changing both fractions within an equation. Initial lessons use models to support learning the procedure while final lessons consist of equations with numbers only.