# Lesson 14

Situations Involving Factors and Multiples

### Lesson Purpose

The purpose of this lesson is for students to solve division problems that involve finding unknown factors. They do so by reasoning with partial quotients and by decomposing a dividend into familiar multiples of the divisor. In the problems, the dividends are greater than 100 and the divisions result in whole numbers with and without a remainder.

### Lesson Narrative

In this lesson, students relate problems about factors and multiples to division. To solve the problems, they rely on the relationship between multiplication and division, and their understanding of division as a way to find an unknown factor.

Students continue to interpret division in terms of finding the number of groups (“If we write multiples of 5, how many numbers will we need to write to get to 105?”) and the size of a group (“What number are we finding multiples of if we get to 112 after writing 7 numbers?”). They may solve the problems by multiplying in parts (finding partial products) or by dividing in parts (finding partial quotients). Through repeated reasoning, they notice that it helps to decompose a dividend into familiar multiples (MP2, MP8).

In these materials, division that results in a whole number with a remainder—for example $$145 \div 7$$—is not expressed with an expression such as “20 R 5.” Instead, students will relate this result to a multiplication equation, in that $$145 = 7 \times 20 + 5$$.

In future lessons, students will more formally investigate partial quotients as a strategy dividing numbers.

• Engagement
• MLR8

### Learning Goals

Teacher Facing

• Reason about division of two- and three-digit numbers in situations involving factors and multiples.

### Student Facing

• Let’s interpret and solve division problems beyond 100.

Building On

### Lesson Timeline

 Warm-up 10 min Activity 1 20 min Activity 2 15 min Lesson Synthesis 10 min Cool-down 5 min

### Teacher Reflection Questions

Which questions that you asked today would you rephrase to improve students’ ability to make connections or to help them better consolidate what they did? How would you rephrase them?

### Suggested Centers

• Compare (1–5), Stage 4: Divide within 100 (Supporting)
• Rolling for Fractions (3–5), Stage 2: Multiply a Fraction by a Whole Number (Supporting)

### Print Formatted Materials

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