Key Concept: Fractions can be modeled in multiple ways.

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

2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

3.G.2. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

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

#### Georgia

MGSE2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

MGSE3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part is 1/4 of the area of the shape.

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.

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 very basic beginning lessons in which students partition models into equal parts, shade parts of a whole, and learn the terms numerator and denominator. Fraction numbers are not presented.

3.G.2. Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

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.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.b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

MGSE3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part is 1/4 of the area of the shape.

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.

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.

b. Recognize and generate simple equivalent fractions with denominators of 2, 3, 4, 6, and 8 (e.g., 1/2 = 2/4, 4/6 = 2/3), Explain why the fractions are equivalent, e.g., by using a visual fraction model.

1. Given pre-teaching, the student will divide a model into equal parts with no more than one teacher prompt for ten examples with 90% accuracy by the end of the first progress period.

2. Given a fraction verbally, the student will shade the correct number of parts of a model that has been divided into equal parts with 100% accuracy for three consecutive trials.

3. Given the number of parts in the whole and the number of shaded parts with prior teacher guidance and guided practice, the student will create an accurate model eight out of ten times for three consecutive sessions.

4. Given a number of parts, the student will shade parts to create a model of an equivalent fraction for one half or one whole with no more than one teacher prompt for ten examples with 90% accuracy.

2. Given a fraction verbally, the student will shade the correct number of parts of a model that has been divided into equal parts with 100% accuracy for three consecutive trials.

3. Given the number of parts in the whole and the number of shaded parts with prior teacher guidance and guided practice, the student will create an accurate model eight out of ten times for three consecutive sessions.

4. Given a number of parts, the student will shade parts to create a model of an equivalent fraction for one half or one whole with no more than one teacher prompt for ten examples with 90% accuracy.

Unit Launcher

View Alleah's School: Discussion Guide and KWL Chart

F.1-1-1 Make Equal Parts and Shade One Part |

F.1-1-2 Shade Some Parts |

F.1-1-3 Make the Model |

View Guided Lesson Divide models into equal parts and shade parts to show a fractional amount. (12-18 min)

F.1-1-4 Model Fractions for Half and Whole |

Real World Investigation Part 1

View Alleah's School: Alleah's Data

Key Concept: The fraction number shows the relationship between parts and the related whole; each numeral of the fraction shows a size or amount.

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

2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

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.

#### Georgia

MGSE2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

MGSE3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part is 1/4 of the area of the shape.

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. IEP Goals

This topic contains lessons that develop an understanding of each numeral in a fraction number. Students write numbers represented in models, create models, and count fractional parts. The terms numerator and denominator are introduced and reinforced throughout all lessons.

3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

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.

MGSE3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part is 1/4 of the area of the shape.

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.

1. Given a model of a fraction with prior teacher modeling and guided practice, the student will correctly write the fraction number eight out of ten times for three consecutive sessions.

2. Given a fraction verbally, the student will write the fraction 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.

3. Given pre-teaching of the terms numerator and denominator and a model of a fraction, the student will write the correct number for either the numerator or denominator in the correct location above or below the fraction bar with 100% accuracy for three consecutive trials.

2. Given a fraction verbally, the student will write the fraction 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.

3. Given pre-teaching of the terms numerator and denominator and a model of a fraction, the student will write the correct number for either the numerator or denominator in the correct location above or below the fraction bar with 100% accuracy for three consecutive trials.

F.1-2-1 Write the Denominator |

Lesson Plan

F.1-2-2 Write the Numerator |

Lesson Plan

F.1-2-3 Write the Fraction |

Lesson Plan

F.1-2-4 Count by Fractional Amount |

Lesson Plan

View Guided Lesson Write fraction numbers for models that are presented in a counting sequence. (8-15 min)

F.1-2-5 Make Models and Write Fractions |

Lesson Plan

View Guided Lesson Write the fraction number or create the model for a given fraction word.

(8-15 min)

(8-15 min)

Real World Investigation Part 2

View Alleah's School: Create Some Data

Key Concept: Understanding the size or amount of each numeral in a fraction will help you compare its size to other numbers and place it on a number line.

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

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

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.#### Georgia

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 in which students learn to identify fractions with common denominators and common numerators, and then apply strategies to compare those fractions. Lessons begin with making models, progress to using the greater than and less than signs, and culminate with ordering fractions on a number line.

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

b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

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.

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

b. Recognize and generate simple equivalent fractions with denominators of 2, 3, 4, 6, and 8 (e.g., 1/2 = 2/4, 4/6 = 2/3), Explain why the fractions are equivalent, e.g., by using a visual fraction model.

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 two fractions and the use of models or manipulatives, the student will compare fractions to determine which one is larger and/or smaller value with 80% accuracy for five consecutive sessions.

2. Given two fractions and a sequential process of first comparing denominators and then numerators, the students will identify which fraction is larger and indicate the answer using the correct sign (<, >) for four out of five examples on three consecutive sessions.

3. Given two fractions and a series of verbal prompts, 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.

4. Given a number line with tic marks and preteaching of a comparison strategy, the student will mark or place the model in the correct location on the number line with 80% accuracy for three consecutive trials.

2. Given two fractions and a sequential process of first comparing denominators and then numerators, the students will identify which fraction is larger and indicate the answer using the correct sign (<, >) for four out of five examples on three consecutive sessions.

3. Given two fractions and a series of verbal prompts, 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.

4. Given a number line with tic marks and preteaching of a comparison strategy, the student will mark or place the model in the correct location on the number line with 80% accuracy for three consecutive trials.

F.1-3-1 Compare with Common Denominators |

Lesson Plan

View Guided Lesson Compare fractions with common denominators by comparing the models and placing fractions into comparison bins. (8-15 min)

F.1-3-2 Order with Common Denominators |

Lesson Plan

F.1-3-3 Compare with Common Numerators |

Lesson Plan

View Guided Lesson Compare fractions with common numerators by comparing the models and placing fractions into comparison bins. (8-15 min)

F.1-3-4 Order with Common Numerators |

Lesson Plan

Real World Investigation Part 3

View Your School: Your Data

Key Concept: Benchmark numbers can be used to estimate the length and place of a fraction 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.

3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.#### 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 in which students learn to compare fractions with benchmarks. Using models and the number line, students compare fractions to 0, 1/2, and 1. The topic culminates with a lesson on comparing fractions to related fractions.

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 number line with markings for 0, 1/2, and 1, the student will estimate the placement of up to three fractions for three consecutive sessions.

2. Given a fraction number, a number line model, and a two-step routine, the student will estimate the value related to benchmark numbers in four out of five examples for five out of seven trials.

3. Given a model of a benchmark fraction, students will create a model of an equivalent fraction with no more than one teacher prompt for ten examples with 90% accuracy for three consecutive trials.

2. Given a fraction number, a number line model, and a two-step routine, the student will estimate the value related to benchmark numbers in four out of five examples for five out of seven trials.

3. Given a model of a benchmark fraction, students will create a model of an equivalent fraction with no more than one teacher prompt for ten examples with 90% accuracy for three consecutive trials.

F.1-4-1 Understand the 1/2 and 1 Benchmarks |

Lesson Plan

View Guided Lesson Make models of fractions that are equivalent to 1/2 and 1, and place those fractions on a number line. (8-15 min)

F.1-4-2 Estimate with the 0, 1/2 and 1 Benchmarks |

Lesson Plan

View Guided Lesson Determine whether a fraction is close to 0, 1/2 or 1 using models and the number line. (8-15 min)

F.1-4-3 Compare to the 1/2 Benchmark |

Lesson Plan

View Guided Lesson Determine whether a fraction is less than, greater than, or equal to 1/2 using models and the number line. (8-15 min)

This Big Idea is an introduction to fractions, where lessons focus on developing an understanding of part/whole relationships using a variety of models. Students are introduced to equivalence and magnitude in lessons in which they compare and estimate the relative size of fractional quantities.

same shape.

3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

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.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.

b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

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.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part is 1/4 of the area of the shape.

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.

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.

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

b. Recognize and generate simple equivalent fractions with denominators of 2, 3, 4, 6, and 8 (e.g., 1/2 = 2/4, 4/6 = 2/3), Explain why the fractions are equivalent, e.g., by using a visual fraction model.

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.