Lesson objective: Use the meaning of fractions to construct a whole given a fraction less than 1 or greater than 1.
Fluency and Procedural Skill Lesson: This lesson helps to build fluency with reasoning about fractions. Students work to construct one from a given fraction by applying their understanding that nonunit fractions are composed of unit fractions, as well as their understanding that it takes b pieces the size of 1/b to make one whole. Tape diagrams will support students’ identification and iteration of unit fractions. This work develops students' understanding that fractions are numbers that can be composed and decomposed for future work with addition and subtraction.
Students engage in Mathematical Practice 2 (Reason abstractly and quantitatively) as they use the tape diagrams to represent fraction lengths and wholes. They must reason about the size of the given fraction relative to the whole. Mathematical Practice 4 (Model with Mathematics) is also featured as students model lengths in order to create new lengths.
Key vocabulary:

unit fraction

nonunit fraction

decompose