# Lesson 17

Fractions as Partial Quotients (optional)

### Lesson Purpose

The purpose of this lesson is for students to interpret sums of fractions as partial quotients.

### Lesson Narrative

Most of the quotients students have worked with in this unit have had whole number values. As seen in the previous lesson, sometimes the quotient has a remainder and fractions can be used to express the meaning of that remainder. The purpose of this optional lesson is to evaluate division expressions using fractions. Although the quotients students work with here are whole numbers, the fractions still highlight an important part of the partial quotients algorithm, namely that working with nice multiples of the divisor facilitates the calculation process. The new part of this lesson is that some of the multiples are fractions.

- Representation

### Learning Goals

Teacher Facing

- Make sense of partial quotients using fractions.

### Student Facing

- Let’s use fractions to help us divide whole numbers.

### Required Preparation

### Lesson Timeline

Warm-up | 10 min |

Activity 1 | 15 min |

Activity 2 | 20 min |

Lesson Synthesis | 10 min |

Cool-down | 5 min |

### Teacher Reflection Questions

What opportunities are you giving students to reflect on their understanding of the mathematical content?

### Suggested Centers

- Mystery Number (1–4), Stage 6: Decimals (Supporting)