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In this session, we will look at ways to interpret, model and work with rational numbers. We will examine various ways to determine the “unit” of the ratio we’re expressing with a rational number and to explore the basics of proportional reasoning.

For information on required and/or optional materials, see See Note 1 below.

**LEARNING OBJECTIVES:
**In this session, you will do the following:

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**Previously Introduced:**

**rational number**

Rational numbers are numbers that can be expressed as a quotient of two integers; when expressed in a decimal form they will either terminate (1/2 = 0.5) or repeat (1/3 = 0.333…)

**New in This Session:**

**absolute comparison**

An absolute comparison is an additive comparison between quantities. In an absolute comparison, 7 out of 10 is considered to be larger than 4 out of 5, since 7 is larger than 4.

**part-part interpretation**

Part-part interpretation of a fraction is the notion of comparing one quantity within a whole to another quantity within that whole. For example, if, on a field trip, there are 3 adults for every 10 students, the part-part interpretation of this relationship would be 3/10 (which could also be written as 3:10).

**part-whole interpretation**

Part-whole interpretation of a fraction represents one or more parts of a single unit. For example, the fraction 4/5 represents the part-whole relationship in the following phrase: “Four out of five dentists prefer Blasto toothpaste.”

**relative comparison
**

A relative comparison is a multiplicative, or proportional, comparison between quantities. In a relative comparison, 4 out of 5 is considered to be larger than 7 out of 10, since 4/5 is larger than 7/10.

**Materials Needed:**

- Cuisenaire Rods (optional)

You can use the cutouts of the rods from the Rod Template.