In this unit, students explore relationships among fractions through work with the set model. This early work with fraction relationships helps students make sense of basic fraction concepts and facilitates work with comparing and ordering fractions and working with equivalency.
Math Content
This unit exposes students to the set model and provides an opportunity for
them to develop a thorough understanding of this model in multiple applications.
In the set model, the unit is represented by the entire set, and subsets of
the unit make up the fractional parts. For example, in a set of 12 eggs, 4 eggs comprise one-third of the set of 16 eggs. The set of 12 in this
example represents the whole, or 1.
This notion of referring to a collection of objects makes studying the set
model difficult for young children. As students work with a variety of fraction
models in contexts that promote reasoning and problem solving, they develop a
more thorough understanding of fractions and their relationships.
Individual Lessons
Lesson 1 - Eggsactly with a Dozen Eggs
Students begin to examine fractions as part of a set. This lesson helps students develop skill in problem solving and reasoning as they examine relationships among the fractions used to describe part of a set of 12.
Lesson 2 - Eggsactly with Eighteen Eggs
Students continue to examine fractions as part of a set. This lesson helps students develop skill in problem solving and reasoning as they examine relationships among the fractions used to describe part of a set of eighteen.
Lesson 3 - Eggsactly Equivalent
Students use twelve eggs to identify equivalent fractions. Construction paper cutouts are used as a physical model to represent various fractions of the set of eggs, for example, 1/12, 1/6, and 1/3. Students investigate relationships among fractions that are equivalent.
Lesson 4 - Another Look at the Set Model using Attribute Pieces
The previous lessons focused on the set model where all objects in the set are the same size and shape. Students also need work with sets in which the objects “look” different. In the real world, we are often faced with fraction situations where the objects in the set are not identical. For this lesson, students use fractions to describe a set of attribute pieces. Students develop skill in problem solving and reasoning as they think about their set and how to create new sets given specific fractional characteristics.
Lesson 5 - Class Attributes
During this lesson, students create their own classroom survey or use previously generated questions to study the class and describe the set [class] in fractional parts. This lesson requires that students identify fractions in real-world contexts from a set of items that are not identical. This lesson is integrated with other areas of the math curriculum, including data analysis and statistics.
Lesson 6 - Another Look at Fractions of a Set
This lesson gives students another opportunity to explore fractions using the set model. This lesson is integrated with other areas of the math curriculum including data analysis and statistics.
