Lesson 14
Situations Involving Factors and Multiples
Lesson Purpose
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 threedigit numbers in situations involving factors and multiples.
Student Facing
 Let’s interpret and solve division problems beyond 100.
Required Preparation
Lesson Timeline
Warmup  10 min 
Activity 1  20 min 
Activity 2  15 min 
Lesson Synthesis  10 min 
Cooldown  5 min 
Teacher Reflection Questions
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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Additional Resources
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