In this unit, students explore relationships among fractions through work with the region 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.
This unit consists of five lessons designed to help the students understand
fractions when they are represented as a part of a region. Subsequent units
develop understanding of other fraction models (e.g., set, area, and length).
Representing fractions in a variety of ways helps students see relationships and
develop understanding of later fraction concepts. It is important that students
"see" a variety of concrete examples in addition to pictorial representations.
The following lessons incorporate the use of physical and virtual manipulatives.
Math Content
Concepts about fractions are basic to mathematics but can pose challenges for students. In elementary schools, the most frequently used fraction models are the region and set models. This unit exposes students to the region model and gives an opportunity for them to develop a thorough understanding of this model in multiple applications. 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 the relationships among them.
Individual Lessons
Lesson 1 - Investigating Fractions with Pattern Blocks
This lesson promotes problem solving and reasoning with fractions as students investigate the relationships between various parts and wholes. It also focuses on representation because students are given multiple opportunities to investigate the relative value of fractions. Students use communication skills as they work in pairs to articulate and clarify their understanding of fraction relationships.
Lesson 2 - Virtual Pattern Blocks
Students use virtual pattern blocks to problem solve and reason with fractions. They investigate relationships between parts and wholes using another representation of a region model, virtual fractions. Students use conversation to explain their understandings in order to extend and clarify their mathematical content knowledge.
Lesson 3 - Pattern Block Fractions
This lesson builds on the previous two lessons by focusing on the identification of fractional parts of a region and by recording them in standard form. Students continue to develop communication skills by working together to express their understanding of fraction relationships and to record fractions in written form.
Lesson 4 - Expanding Our Pattern Block Fraction Repertoire
In this lesson, the students expand the number of fractions they can represent with pattern blocks by increasing the whole. Instead of representing the whole with one yellow hexagon, the students explore fractional relationships when two, three, and four yellow hexagons constitute the whole.
Lesson 5 - Exploring the Value of the Whole
This lesson focuses on the relationship between parts and the whole. These relationships were developed earlier and require the students to consider the size or value of the same fraction when different "wholes" are compared (i.e., the value of x is relative to the whole; x of a small pie is not equivalent to x of a large pie). This lesson promotes problem solving and reasoning as the students compare similar fractions with different "wholes." Students develop communication skills as they work in pairs and share their understanding about the relationship between the value of a fraction and the whole.
