Essential Strategy 2. Provide opportunities for students to investigate, assess, and refine mathematical “rules” and generalizations.

A fraction is the relationship between two numbers. When comparing fractions, students need to consider the size of the wholes and interpret each fraction as a single number defined by the relationship between the numerator and the denominator.

### Specific Strategies

##### #1: More of the Same Sized Parts

Tool Example: Finding Common Denominators

The Finding Common Denominators Tool can be used to model and compare two fractions. To do this, simply hide the equation and/or the fraction number. The teacher can lead a discussion in which students use a strategy of determining if the each of the same-sized wholes is divided into the same amount of equal parts, they can then determine the number of parts selected or shaded to determine which is larger. This allows students to explore the rule, “if the denominators are the same then the larger numerator is the larger fraction.”

Finding Common Denominators
Note: be sure to hide the equivalence portion in the middle row.

##### #2: Same Number of Parts, But Parts of a Different Size

Tool Example: Finding Common Denominators

The Finding Common Denominators Tool can be used to compare two fractions. The teacher hides the equation, and can choose to either hide or show the fraction number. NOTE: the Check Work button should not be used.

Finding Common Denominators. In this example, only the models are displayed.

##### #3: Closeness to One Whole

Tool Example: Order Fractions on a Number Line

The Order Fractions on a Number Line tool allows students to determine which fraction is larger by determining which one is closer to one whole.

Order Fractions on a Number Line displaying two fractions with values close to one.

##### #4: Determine the Distance from 0 on a Number Line

Tool Example: Finding Common Denominators

The Number Line model found in the Finding Common Denominators tool lets students see each number on a number line and compare which one is farther from zero and therefore longer in length.

Finding Common Denominators Tool with Number Lines Displayed.

##### #5: Using a Shaded Part of an Area

Tool Example: Finding Common Denominators

See Specific Strategies #1 and #2 above using the Finding Common Denominators tool. Additional examples can be created by the teacher that compares fractions with uncommon denominators using a variety of models that are available in the tool.

### Classroom Activities

Below is an example of how the tools can be used to create some of the sample activities from the book that are designed to help students understand that “knowing the denominator of a fraction is a very important aspect of understanding its value, but it is only part of the information that is necessary”.

##### Activity 1: Various.

Tool: Order Fractions on a Number Line

The Order Fractions on the Number Line tool can be used to set up many of the Questions to Help Students Reason About Fractions as Numbers as they appear in #6. Entering fractions 2/4, 5/10 and 3/6 and placing them on the number line illustrates, “what other numbers are the same as one-half?” The tool can be used to illustrate the creation and placement of numbers that answer the question, “what number is one-fourth more than one-half?”