Key Concept: Fractions can be combined to make more than a whole, and an amount larger than 1 whole can be separated into two fractions.

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

4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
#### Georgia

MGSE4.NF.3 Understand a fraction a/b with a numerator > 1 as a sum of fractions 1/b.

IEP Goals

This topic contains lessons in which students build on previous experiences with proper fractions to add and subtract like fractions that have sums, differences, or minuends greater than 1 whole. Estimation with benchmarks goes beyond 0, 1/2, and, 1 to include whole numbers such as 1, 2, and 3.

a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

1. Given an addition equation of two proper fractions with like denominators resulting in an improper fraction, the student will represent the problem using models and solve for the answer accurately for five out of six examples by the second marking term.

2. Given a set of 20 subtraction equations each with fractions with like denominators and a cognitive strategy, the student will apply the strategy and correctly solve for the answer with 80% accuracy for three consecutive sessions.

3. Given an addition equation of two proper fractions with like denominators resulting in a sum greater than one, and a number line with benchmark numbers, the student will select which benchmark number the sum is closest to with 80% accuracy for four out of five sessions.

4. Given two addition or subtraction equations with common denominators and a benchmark number, the student will estimate the sums or differences of each and use the symbols <, >, or = to show the relationship between the numbers for 5 out of 6 equations by completion of the first marking period.

2. Given a set of 20 subtraction equations each with fractions with like denominators and a cognitive strategy, the student will apply the strategy and correctly solve for the answer with 80% accuracy for three consecutive sessions.

3. Given an addition equation of two proper fractions with like denominators resulting in a sum greater than one, and a number line with benchmark numbers, the student will select which benchmark number the sum is closest to with 80% accuracy for four out of five sessions.

4. Given two addition or subtraction equations with common denominators and a benchmark number, the student will estimate the sums or differences of each and use the symbols <, >, or = to show the relationship between the numbers for 5 out of 6 equations by completion of the first marking period.

Unit Launcher

View Shawn's Swing Set: Discussion Guide and KWL Chart

4.4-1-1 Add Proper Fractions Across 1 Whole |

View Guided Lesson Add two like fractions that result in sums greater than 1 whole, first with models, then without. (8-15 min)

4.4-1-2 Estimate Fraction Sums Across 1 Whole |

View Guided Lesson Estimate the location of addition expressions with like fractions on a number line. (8-15 min)

4.4-1-3 Subtract Fractions with Minuends >1 |

View Guided Lesson Subtract like fractions with minuends greater than 1, first with models, then without. (8-15 min)

4.4-1-4 Compare Fraction Sums/Differences >1 |

View Guided Lesson Use 3 strategies to compare fractions and fraction expressions with like fractions. (8-15 min)

Real World Investigation Part 1

View Shawn's Swing Set: Shawn's Data

Key Concept: Since addition and subtraction are inverse operations, fractions can be used to show the difference between two quantities of the whole.

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

4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
#### Georgia

MGSE4.NF.3 Understand a fraction a/b with a numerator > 1 as a sum of fractions 1/b.

a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

IEP Goals

This topic contains lessons that require the addition and subtraction of improper fractions. Students build on their previous experiences with both proper and improper fractions to add and subtract improper fractions with common denominators. Students apply their understanding that a whole can be written as a fraction to assist them in comparing and estimating.

a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

1. Given a set of addition or subtraction problems with improper fractions with like denominators, the student will use models and a cognitive strategy to solve the equation converting the answer from an improper to mixed number for nine out of ten examples for five consecutive lessons.

2. Given a set of addition or subtraction equations of two improper fractions with like denominators, and a number line with benchmark numbers, the student will select which benchmark number the sum or difference is closest to with 80% accuracy for four out of five sessions.

3. Given an addition or subtraction equation of improper fractions fractions with common denominators with unknowns, and the use of models, the student will accurately determine the missing parts with 80% accuracy for three consecutive sessions.

4. Given three addition or subtraction equations of improper fractions with common denominators, the student will estimate the sums or differences of each and use the symbols <, >, or = to show the relationship between the numbers for 5 out of 6 equations by completion of the first marking period.

2. Given a set of addition or subtraction equations of two improper fractions with like denominators, and a number line with benchmark numbers, the student will select which benchmark number the sum or difference is closest to with 80% accuracy for four out of five sessions.

3. Given an addition or subtraction equation of improper fractions fractions with common denominators with unknowns, and the use of models, the student will accurately determine the missing parts with 80% accuracy for three consecutive sessions.

4. Given three addition or subtraction equations of improper fractions with common denominators, the student will estimate the sums or differences of each and use the symbols <, >, or = to show the relationship between the numbers for 5 out of 6 equations by completion of the first marking period.

4.4-2-1 Add/Subtract Improper Fractions |

Lesson Plan

4.4-2-2 Estimate Fraction Sums and Differences >1 |

Lesson Plan

View Guided Lesson Estimate the location of addition expressions with like improper fractions on a number line. (8-15 min)

4.4-2-3 Complete Equations with Improper Fractions |

Lesson Plan

View Guided Lesson Use strategies and models and solve for the unknown in an addition or subtraction equation with two like improper fractions. (8-15 min)

4.4-2-4 Compare Fraction Sums and Differences >1 |

Lesson Plan

View Guided Lesson Use strategies and benchmark numbers to compare expressions with improper fractions. (8-15 min)

Real World Investigation Part 2

View Shawn's Swing Set: Create Some Data

Key Concept: Whole numbers and proper fractions can be added to mixed numbers or subtracted from mixed numbers.

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

4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
#### Georgia

MGSE4.NF.3 Understand a fraction a/b with a numerator > 1 as a sum of fractions 1/b.

IEP Goals

This topic contains lessons that require addition and subtraction of mixed numbers. Students learn to convert improper fractions to mixed numbers and mixed numbers to improper fractions in isolation and when solving addition and subtraction equations.

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.

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.

1. Given an addition or subtraction equation of two mixed numbers with like denominators, the student will represent the problem using concrete manipulatives or computer models and solve for the answer accurately for five out of six examples by the second marking term.

2. Given a model for numbers greater than one whole, the student will write the amount as both a mixed number and improper fraction with 90% accuracy for seven consecutive sessions.

3. Given a set of addition problems with two mixed numbers with like denominators, the student will use models and a cognitive strategy to solve the equation, writing the sum as a mixed-number with the correct whole number and proper fraction for nine out of ten examples for five consecutive lessons.

4. Given a set of mix number subtraction problems in which the fractional part of the subtrahend is less than the minuend, the student will use models to assist in regrouping and subtracting with 80% accuracy for three consecutive sessions.

2. Given a model for numbers greater than one whole, the student will write the amount as both a mixed number and improper fraction with 90% accuracy for seven consecutive sessions.

3. Given a set of addition problems with two mixed numbers with like denominators, the student will use models and a cognitive strategy to solve the equation, writing the sum as a mixed-number with the correct whole number and proper fraction for nine out of ten examples for five consecutive lessons.

4. Given a set of mix number subtraction problems in which the fractional part of the subtrahend is less than the minuend, the student will use models to assist in regrouping and subtracting with 80% accuracy for three consecutive sessions.

4.4-3-1 Add/Subtract Mixed Numbers |

Lesson Plan

View Guided Lesson Add and subtract mixed numbers with common denominators with and without models. (8-15 min)

4.4-3-2 Convert to Mixed Numbers |

Lesson Plan

View Guided Lesson Learn how to convert improper fractions to mixed numbers using models. (8-15 min)

4.4-3-3 Add and Convert to Mixed Numbers |

Lesson Plan

View Guided Lesson Model addition problems with like improper fractions and convert the sums to mixed numbers. (8-15 min)

4.4-3-4 Convert to Improper Fractions |

Lesson Plan

View Guided Lesson Learn how to convert mixed numbers to improper fractions using models. (8-15 min)

4.4-3-5 Convert and Subtract Fractions |

Lesson Plan

View Guided Lesson Convert mixed number minuends to improper fractions to solve subtraction equations. (8-15 min)

Real World Investigation Part 3

View Your Swing Set: Your Data

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

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

3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

#### Georgia

MGSE3.NF.3 Explain equivalence of fractions through reasoning with visual fraction models. Compare fractions by reasoning about their size.

a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

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.

IEP Goals

Lessons in this topic require students to first determine the whole and then consider the size of the colored areas in relation to the whole. Students also explore the reciprocal relationship between addition and subtraction by determining unknowns in addition and subtraction equations involving proper fractions, improper fractions, and mixed numbers.

c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

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.

c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 6/2 (3 wholes is equal to six halves); recognize that 3/1 = 3; locate 4/4 and 1 at the same point of a number line diagram.

MGSE4.NF.3 Understand a fraction a/b with a numerator > 1 as a sum of fractions 1/b.b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

1. Given a graphic representation of a whole unit and additional units that are larger than the whole, the student will identify the value of the whole and write the improper fraction that represents the value of the remaining colors for three out of four colors on three out of five opportunities.

2. Given a graphic representation of a whole unit and additional units that are larger than the whole, the student will identify the value of the whole and write the mixed number that represents the value of the remaining colors for three out of four colors on three out of five opportunities.

3. Given a set of mixed addition and subtraction equations each with mixed numbers with like denominators and the use of models, the student will supply the missing number (addend, minuend, subtrahend) to accurately complete five out of six equations on three consecutive sessions.

2. Given a graphic representation of a whole unit and additional units that are larger than the whole, the student will identify the value of the whole and write the mixed number that represents the value of the remaining colors for three out of four colors on three out of five opportunities.

3. Given a set of mixed addition and subtraction equations each with mixed numbers with like denominators and the use of models, the student will supply the missing number (addend, minuend, subtrahend) to accurately complete five out of six equations on three consecutive sessions.

4.4-4-1 Create Improper Fractions with Pattern Blocks |

Lesson Plan

View Guided Lesson Color pattern block shapes and/or write the improper fraction represented by each color. (8-15 min)

4.4-4-2 Create Mixed Numbers with Pattern Blocks |

Lesson Plan

View Guided Lesson Color pattern block shapes and/or write the mixed number represented by each color. (8-15 min)

4.4-4-3 Complete Equations with Unknowns |

Lesson Plan

View Guided Lesson Use strategies and models and solve for the unknown in an addition or subtraction equation with like improper fractions and mixed numbers. (8-15 min)

This Big Idea focuses on addition and subtraction of fractions greater than one whole. Students begin with equations with proper fractions that result in improper sums and move onto adding and subtracting improper fractions and mixed numbers. Estimation and comparison lessons challenge students to think critically.

c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 6/2 (3 wholes is equal to six halves); recognize that 3/1 = 3; locate 4/4 and 1 at the same point of a number line diagram.

MGSE4.NF.3 Understand a fraction a/b with a numerator > 1 as a sum of fractions 1/b.