Lesson objective: Understand that the meaning of division does not change when dividing a unit fraction by a whole number, and that the name of the quotient is based on the whole.

Students have worked with division for a few years, most recently in 5.NBT.6, in which they worked exclusively with whole numbers. This prior knowledge is extended to include fractions as students divide unit fractions by whole numbers, and later in the unit, when they divide whole numbers by unit fractions. A conceptual challenge students may encounter is understanding that a unit fraction can be subdivided into smaller equal parts, and then naming those parts. Students may also confront the limitations of the idea that "division makes smaller," which is not the case when the divisor is greater than the dividend.

The concept is developed through work with number lines which provide a visual model to show how a unit fraction can be divided into equal parts that represent smaller parts of the whole. The vertical number lines used with the liquid quantities helps students see how the name of the quotient is based on the whole.

This work helps students deepen their understanding of numbers because it builds on the understanding that, like whole numbers, a fraction is a number that can be operated on and represented on a number line.

Students engage in Mathematical Practice 3 (construct viable arguments and critique the reasoning of others) as they work to convince Helen of her mistake. The use of number lines and tape diagrams helps students see how a unit fraction can be divided into equal parts and supports them in justifying the result of the division.

**Key vocabulary:**

- dividend
- divisor
- quotient