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# Grade 3 Common Core State Standards for Fractions

## Develop understanding of fractions as numbers

### Note: This lesson begins with students becoming familiar with models for fractions and describing part-to-whole relationships verbally using whole numbers rather than fraction symbols. The lesson concludes with the introduction of unit fractions, that is, fractions of the form 1/b, where the whole is partitioned into b equal parts.

• Lesson: Fractions for Regions and Sets
• Worksheet #3
• Worksheet #4
• Worksheet #5
• Worksheet #6

### Note: Fractions a/b are introduced as a parts out of a whole with b equal parts. Fractions are illustrated by showing parts of region models and parts of sets (collections). Further illustrations of fractions for regions and sets with visual models can be seen at Basic Concepts Step 2 TeachingFractionBarVideos

• Lesson: Fraction Terminology and Names
• Worksheet #7
• Worksheet #8

### Note: This lesson provides a gradual introduction to the names of fractions. It is suggested that names such as "three-fourths" also be referred to as "3 over 4" in the early stages to be less threatening and to reinforce the part-to-whole language of "3 out of 4." The words "numerator" and "denominator" are also introduced in this lesson, but for  simplicity in the early stages are also called the "top number" and the "bottom number."

• Lesson: Solving Problems - Regions and Sets
• Worksheet #9
• Worksheet #10

### 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.

• Lesson: Fraction Number Line
• Worksheet #1
• Worksheet #2

### 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

• Lesson: Equality of Fractions
• Worksheet #1
• Worksheet #2
• Worksheet #3

### Note: In this lesson, regions having the same whole and same amount of shading provide a visual model for equality of fractions. By comparing the resulting equalities and looking for patterns, rules for generating equal fractions and writing fractions in simplified form can be formulated. These demonstrations provide a visual illustration of the rule a/b = (n × a)/(n × b). This rule can also be seen at Equality Step 1 TeachingFractionBarVideos

• Lesson: Solving Problems - Equality of Fractions
• Worksheet #6
• Worksheet #7

### Note: Visual models illustrate inequality of fractions in this lesson. If one bar has a greater amount of shading than another bar, the fraction for the first bar is greater than the fraction for the second bar. Examples of bars having the same number of equal parts and different amounts of shading provide evidence to help students formulate a rule for inequality of fractions having the same denominator. The model is also used to address student misconceptions that larger numbers in the numerator and denominator of a fraction means larger fractions. For example, one such visual shows that 3/12 is less than 1/3.

• Lesson: Inequality and the 1/2 Benchmark
• Worksheet #10
• Worksheet #11

### Note: Various bars are compared to bars that are half shaded. This visual model leads to the conclusion that when a bar is less than half shaded, its numerator is less than half of its denominator; and when a bar is half shaded, its numerator is half its denominator; and when a bar is more than half shaded, its numerator is more than half its denominator. Also see Inequality Step 1 TeachingFractionBarVideos

• Lesson: Decreasing and Increasing Fractions
• Worksheet #12
• Worksheet #13

### Note: In this lesson, bars with decreasing shaded amounts lead to two important observations: (1) The fractions for the bars get closer and closer to 0; and (2) The more equal parts something is divided into, the smaller the fraction for one of these parts.

• Lesson: Solving Problems - Inequality of Fractions
• Worksheet #14
• Worksheet #15