Prior to this unit, in Grades 1 and 2, students work with partitioning shapes. They have some familiarity with vocabulary related to partitioning shapes from those grades, espically "halves", "thirds", and "fourths", but have yet to name those parts using numbers. This unit marks the first time third graders are officially introduced to fractions as numbers (and their numerical representations).
In this unit, students will come to understand unit fractions and use them to build other fractions. This idea is tightly connected to what students know about using "1" to build other whole numbers. Students are likely to struggle with understanding that fractions are one number, rather than two. They will use number lines to explore how fractions are numbers that live on the number line with the whole numbers they already know.
Key Concepts:
 Fractions are numbers that describe a quantity that results from partitioning a whole.
 Just as whole numbers denote a collection of whole units, fractions denote a collection of unit fractions.
 When a whole is partitioned into \(b\) equal sized pieces, each piece is \(\frac1b\) of the whole. It takes \(b\) of these pieces to make the whole. When we take \(a\) of those pieces, the result is \(\frac ab\).
 Fractions live on the number line denoting a distance from 0, just as whole numbers do.
Prior Knowledge Needed:
 Partition shapes into fair shares; (Grade 1, Unit 17; 1.G.A.3)
 Partition shapes into fair shares; (Grade 2, Unit 10; 2.G.A.3)
Units on the Horizon:
 Using Fractions in Measurement and Data; (Grade 3, Unit 5)
 Understanding Equivalent Fractions; (Grade 3, Unit 10)
 Comparing Fractions; (Grade 3, Unit 11)
 Understanding Fraction Equivalence and Comparison; (Grade 4, Unit 5)
Lessons

Lesson objective: Extend understanding that shapes can be equally shared by partitioning a whole, and begin to understand that fractions describe the partitioning of a whole and can be written as numbers. Students bring prior knowledge of partitioning a...

Lesson objective: Identify unit fractions. This lesson helps to build procedural skill with identifying unit fractions. Tape diagrams and number lines are used here because they support an understanding of the importance of unit fractions for creating n...

Lesson objective: Practice building nonunit fractions from unit fractions. This lesson helps to build skill with building and naming nonunit fractions from fractions. Tape diagrams and number lines are used here because they support students' understa...

Lesson objective: Apply understanding of unit fractions and partitioning to make and defend claims about fractions of wholes. This lesson provides an opportunity for students to apply their knowledge and understanding of partitioning shapes and naming u...

Lesson objective: Extend students' understanding of unit fractions to using unit fractions to find one whole. Students bring prior knowledge of unit fractions and their relationship to the whole. Previously students started with a whole, and created and...

Lesson objective: Practice using unit fractions to create a whole. This lesson helps to build skill with iterating unit fractions to create a whole. Tape diagrams and number lines are used here because they support reasoning about the size and number of...

Lesson objective: Apply understanding of how to create and name unit fractions to solve a problem about a whole partitioned into differentsized pieces. This lesson provides an opportunity for students to apply their knowledge and understanding that uni...

Lesson objective: Use named points on a number line to name other points on the line. Students bring prior knowledge about whole number distances on number lines. This prior knowledge is extended to understanding that fractions also represent a distance...

Lesson objective: Locate and name distances on a number line. This lesson helps to build procedural skill with locating and naming distances on a number line. Number lines are used here because they highlight that fractions are numbers that tell us abou...

Lesson objective: Apply understanding of fractions as distances from zero to solve a problem. This lesson provides an opportunity for students to apply their knowledge and understanding of fractions as numbers that name a distance from zero. Students ar...