Key Concept: Fractions greater than or equal to 1 whole can be written as mixed numbers, compared to other numbers, and placed on a number line.

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

3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

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

MGSE3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts (unit fraction); understand a fraction a/b as the quantity formed by a parts of size 1/b. For example, ¾ means there are three ¼ parts, so ¾ = ¼ + ¼ + ¼.

MGSE4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by using visual fraction models, 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.

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

IEP Goals

This topic contains lessons that introduce mixed numbers. Students create models to illustrate given mixed numbers or write the mixed number for a given model. The final lesson builds on and is similar to lessons in topic three of Big Idea 1 in which two mixed number models are compared and sorted by size.

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

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.

d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

4.NF.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.MGSE4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by using visual fraction models, 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.

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

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.

d. Compare two fractions with the same numerator or the same denominator by reasoning about their size, Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

1. Given a model of a mixed number and guided practice, the student will write and read the mixed number for five out of six examples on two consecutive sessions.

2. Given a mixed number, the student will read the number and create a model with no prompts or cues with 90% accuracy for three consecutive sessions.

3. Given either a model of a mixed number or the numeral, the student will identify the whole and the fractional parts remaining without hesitation for three consecutive trials.

4. Given a mixed number verbally, the student will write the number and create a corresponding model with no more than one teacher prompt for ten examples with 90% accuracy by the end of the first progress period.

5. Given either models of two mixed numbers or the numerals, the student will identify which is larger or smaller and explain his/her reasoning using appropriate language (e.g., denominator, equal parts, larger) with 100% accuracy for three consecutive trials.

2. Given a mixed number, the student will read the number and create a model with no prompts or cues with 90% accuracy for three consecutive sessions.

3. Given either a model of a mixed number or the numeral, the student will identify the whole and the fractional parts remaining without hesitation for three consecutive trials.

4. Given a mixed number verbally, the student will write the number and create a corresponding model with no more than one teacher prompt for ten examples with 90% accuracy by the end of the first progress period.

5. Given either models of two mixed numbers or the numerals, the student will identify which is larger or smaller and explain his/her reasoning using appropriate language (e.g., denominator, equal parts, larger) with 100% accuracy for three consecutive trials.

Unit Launcher

View Mrs. Patterson's Reading Class: Discussion Guide and KWL Chart

F.2-1-1 Model Mixed Numbers |

View Guided Lesson Students will make mixed number models by dividing whole shapes and number lines into equal parts and shading some parts to represent more than 1 whole. (8-15 min)

F.2-1-2 Write Mixed Numbers |

View Guided Lesson Students will write the whole number, numerator, and denominator of mixed numbers based on models. (8-15 min)

F.2-1-3 Model and Write Mixed Numbers |

View Guided Lesson Students will make models and write mixed numbers for values greater than 1 whole. (8-15 min)

F.2-1-4 Compare Mixed Numbers |

View Guided Lesson Students will compare mixed numbers with the same denominator using models, numbers, and inequality symbols. (8-15 min)

F.2-1-5 Order Mixed Numbers |

View Guided Lesson Students will compare and order mixed numbers with the same using models, numbers, and inequality symbols. (8-15 min)

Real World Investigation Part 1

View Mrs. Patterson's Reading Class: Mrs. Patterson's Data

Key Concept: Fractions greater than or equal to 1 whole can be written as fractions, compared to other numbers, and placed on a number line.

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

3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.

#### Georgia

MGSE3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.

IEP Goals

This topic contains lessons using the number line model. Students work with benchmark numbers to estimate the size of mixed numbers or place the numbers on the number line. Students apply their understanding of the relationship between the numerator and denominator to determine quantity and placement on the number line.

a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

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.

a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b. Recognize that a unit fraction 1/b is located 1/b whole unit from 0 on the number line.

b. Represent a non-unit fraction a/b on a number line diagram by marking off a lengths 1/b (unit fractions) from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the non-unit fraction a/b on the number line.

a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

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.

1. Given a mixed number 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 number line model with a metacognitive routine, the student will place mixed numbers with 90% accuracy for three consecutive sessions.

2. Given a number line model with a metacognitive routine, the student will place mixed numbers with 90% accuracy for three consecutive sessions.

F.2-2-1 Model Improper Fractions |

Lesson Plan

View Guided Lesson Students will make improper fraction models by dividing whole shapes and number lines into equal parts and shading some parts to represent more than 1 whole. (8-15 min)

F.2-2-2 Write Improper Fractions |

Lesson Plan

View Guided Lesson Students will write the numerator and denominator of improper fractions based on models. (8-15 min)

F.2-2-3 Model and Write Improper Fractions |

Lesson Plan

View Guided Lesson Students will make models and write improper fractions for values greater than 1 whole. (8-15 min)

F.2-2-4 Estimate Fractions Greater Than 1 with Benchmarks |

Lesson Plan

View Guided Lesson Students will estimate the location of improper fractions and mixed numbers on a number line by estimating with whole numbers, numerators, denominators, and benchmarks, including fractions that name the same point. (8-15 min)

Real World Investigation Part 2

View Mrs. Patterson's Reading Class: Create Some Data

This Big Idea is an introduction to mixed numbers and improper fractions, where lessons focus on identifying, writing, and representing the numbers using a variety of models. Students compare and estimate the relative size of fractional quantities greater than one whole. Converting from improper fractions to mixed numbers and mixed numbers to improper fractions is introduced.

3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.

a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

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.

d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

4.NF.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.MGSE3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.

a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b. Recognize that a unit fraction 1/b is located 1/b whole unit from 0 on the number line.

b. Represent a non-unit fraction a/b on a number line diagram by marking off a lengths 1/b (unit fractions) from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the non-unit fraction a/b on the number line.

MGSE3.NF.3 Explain equivalence of fractions through reasoning with visual fraction models. Compare fractions by reasoning about their size.a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

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.

d. Compare two fractions with the same numerator or the same denominator by reasoning about their size, Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

MGSE4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by using visual fraction models, 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.