Lesson 20: Understand What a Fraction Is

Standard 3.NF.1

• Understand that a unit fraction has a numerator of one and a non-zero denominator.

  1. Understand a fraction 1/b as the quantity formed by one part when a whole is partitioned into b equal parts.

  2. Understand a fraction a/b as the quantity formed by a parts of size 1/b. For example: 1/4 + 1/4 + 1/4 = 3/4.

Objectives:

• Understand what a fraction is

• Use a fraction to show equal parts of a whole

• Draw a model to show a fraction

Lesson 21: Understand Fractions on a Number Line

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

1. 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.

2. 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.

Objectives:

Lesson 22: Understand Equivalent Fractions

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

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

2. Recognize and generate simple equivalent fractions, such as 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent by using a visual fraction model, for example.

Lesson 23:  Find Equivalent Fractions

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

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

2. Recognize and generate simple equivalent fractions, such as 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent by using a visual fraction model, for example.

3. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. For example, 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.

Lesson 24: Understand Comparing Fractions

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

1. 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, for example, by using a visual fraction model.

Lesson 25: Comparing Fractions

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

1. 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, for example, by using a visual fraction model.