Key Concept: Fractions can be combined to make a 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.

IEP Goals

This topic contains lessons to reinforce basic concepts of the part/whole relationship of fractions. Student use previous experience to add and subtract like fractions that have sums and differences less than 1 whole. Estimation with benchmarks of 0, 1/2, and 1 help students build a deeper understanding of fractional amounts and assist in comparing fractions.

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

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.

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

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 an addition equation of two fractions 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 an addition equation of two fractions with common denominator 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.

3. Given three addition equations with common denominators, and a metacognitive strategy, the student will independently compare the sums of the equation using the appropriate sign (<, >, or =) with 80% accuracy for three consecutive sessions.

2. Given an addition equation of two fractions with common denominator 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.

3. Given three addition equations with common denominators, and a metacognitive strategy, the student will independently compare the sums of the equation using the appropriate sign (<, >, or =) with 80% accuracy for three consecutive sessions.

Unit Launcher

View Roberto's Trail Mix: Discussion Guide and KWL Chart

4.3-1-1 Add Unit Fractions |

View Guided Lesson Learn how to add unit fractions using models, models with numbers and then numbers only. (8-15 min)

4.3-1-2 Estimate Sums of Proper Fractions |

View Guided Lesson Estimate and place fractions and addition fraction expressions on a number line. (8-15 min)

4.3-1-3 Add Proper Fractions |

View Guided Lesson Learn how to add proper fractions using models, models with numbers and then numbers only. (8-15 min)

4.3-1-4 Compare Sums of Proper Fractions |

View Guided Lesson Use three strategies to compare and order fraction expressions with sums. (8-15 min)

Real World Investigation Part 1

View Roberto's Trail Mix: Roberto'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 to reinforce basic concepts of the part/whole relationship of fractions. Students subtract like fractions that have subtrahends less than 1 whole. They apply their understanding of numerator and denominator to compare and estimate the differences of one or more equation. Strategies such as comparing denominators, comparing numerators, and using benchmarks to determine location on a number line are reinforced.

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

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

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

4. Given a subtraction equation of two fractions with common denominators and a number line model with benchmark numbers, the student will select which benchmark number the fraction is closest to with 80% accuracy for four out of five sessions.

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

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

4. Given a subtraction equation of two fractions with common denominators and a number line model with benchmark numbers, the student will select which benchmark number the fraction is closest to with 80% accuracy for four out of five sessions.

4.3-2-1 Subtract Unit Fractions |

Lesson Plan

View Guided Lesson Learn how to subtract unit fractions using models, models with numbers and then numbers only. (8-15 min)

4.3-2-2 Estimate Differences of Proper Fractions |

Lesson Plan

View Guided Lesson Estimate and place fractions and subtraction fraction expressions on a number line. (8-15 min)

4.3-2-3 Subtract Proper Fractions |

Lesson Plan

View Guided Lesson Learn how to subtract like proper fractions using models, models with numbers and then numbers only. (8-15 min)

4.3-2-4 Compare Differences of Proper Fractions |

Lesson Plan

View Guided Lesson Use three strategies to compare and order fraction expressions with differences. (8-15 min)

Real World Investigation Part 2

View Roberto's Trail Mix: Create Some Data

Key Concept: Inverse relationships that occur in whole numbers also occur with fractions.

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.

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.

IEP Goals

This topic contains lessons in which students apply what they know about the inverse relationship of addition and subtraction to solve equations with unknowns. Students are also challenged to compare sums and differences of equations. Students learn to compare results by first considering the size represented by the denominators and then consider the number and size of the parts represented by the numerator.

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.1. Given an addition equation of fractions with common denominators and a missing addend, the student will apply subtraction of one addend from the sum to accurately determine the missing addend for five out of six examples by completion of this IEP.

2. Given a subtraction equation of fractions with common denominators and either a missing minuend or subtrahend and the use of models, the student will accurately determine the missing number with 80% accuracy for three consecutive sessions.

3. Given a set of mixed addition and subtraction equations each with fractions with like denominators and missing parts, the student will accurately apply a pre-taught strategy to correctly identify the missing number with 80% accuracy for five consecutive sessions.

4. Given a set of mixed addition and subtraction equations each with fractions with like denominators, the student will estimate the answers of each and use the symbols <, >, or = to show the relationship between the equations in five out of six trials by completion of the first marking period.

2. Given a subtraction equation of fractions with common denominators and either a missing minuend or subtrahend and the use of models, the student will accurately determine the missing number with 80% accuracy for three consecutive sessions.

3. Given a set of mixed addition and subtraction equations each with fractions with like denominators and missing parts, the student will accurately apply a pre-taught strategy to correctly identify the missing number with 80% accuracy for five consecutive sessions.

4. Given a set of mixed addition and subtraction equations each with fractions with like denominators, the student will estimate the answers of each and use the symbols <, >, or = to show the relationship between the equations in five out of six trials by completion of the first marking period.

4.3-3-1 Complete Addition Equations with Unknowns |

Lesson Plan

View Guided Lesson Learn how to find the value of a missing addend using models and numbers. (8-15 min)

4.3-3-2 Complete Subtraction Equations with Unknowns |

Lesson Plan

View Guided Lesson Learn how to find the value of a missing minuend or subtrahend using models and numbers. (8-15 min)

4.3-3-3 Complete Addition/Subtraction with Unknowns |

Lesson Plan

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

4.3-3-4 Compare Fraction Sums and Differences |

Lesson Plan

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

Real World Investigation Part 3

View Your Trail Mix: 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.

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.

#### 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.

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.

IEP Goals

Lessons in this topic require students to apply their understanding of part/whole relationships to solve problems. Students investigate the size of fractions when different shaded areas are designated as the whole. They identify the unit represented on a grid or as a design and express different shaded areas as fractional amounts.

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.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.1. Given an area created with pattern blocks, the student will use concrete or onscreen pattern blocks to cover areas that represent given fractional amounts of the design correctly in three consecutive sessions.

2. Given a geometric area, the student will place pattern block pieces together to cover a the region and then identify fractional relationships found among pattern block shapes with 100% accuracy in three out of five examples.

3. Given a unitizing grid with the whole identified, the student will tell how many parts are in the whole, and determine and write the fractions represented by other colors with no more than two prompts for three consecutive sessions.

4. Given a set of mixed addition and subtraction equations each with fractions with like denominators and missing parts, the student will accurately apply a pre-taught strategy to correctly identify the missing parts with 80% accuracy for five consecutive sessions.

2. Given a geometric area, the student will place pattern block pieces together to cover a the region and then identify fractional relationships found among pattern block shapes with 100% accuracy in three out of five examples.

3. Given a unitizing grid with the whole identified, the student will tell how many parts are in the whole, and determine and write the fractions represented by other colors with no more than two prompts for three consecutive sessions.

4. Given a set of mixed addition and subtraction equations each with fractions with like denominators and missing parts, the student will accurately apply a pre-taught strategy to correctly identify the missing parts with 80% accuracy for five consecutive sessions.

4.3-4-1 Compose/Decompose Numbers with Pattern Blocks |

Lesson Plan

View Guided Lesson Determine the value of a fractional part of a whole using pattern block models. (8-15 min)

4.3-4-2 Compose/Decompose Numbers with the Unitizing Grid |

Lesson Plan

View Guided Lesson Create shapes and/or write the fractions represented by the shapes in relation to the whole using the unitizing grid. (8-15 min)

4.3-4-3 Complete Proper Fraction Equations with Unknowns |

Lesson Plan

View Guided Lesson Find the value of a missing minuend or subtrahend using models and numbers. Use strategies and models and solve for the unknown in an addition or subtraction equation with two like fractions. (8-15 min)

This Big Idea focuses on addition and subtraction of fractions up to one whole using a variety of models. Students compare and estimate the relative size of fraction expressions and complete equations with unknowns using both models and 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.
a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

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.