Division as an Unknown Factor

10 min

Narrative

The purpose of this Warm-up is to elicit the idea that multiplication and division are related, which will be useful as students learn to understand division as an unknown factor problem. While students may notice and wonder many things about these equations, ideas about how multiplication and division are alike and different are the important discussion points.

Students have seen division expressions, but this will be their first time seeing division equations.

Launch

  • Groups of 2
  • Display the equations.
  • “What do you notice? What do you wonder?”
  • 1 minute: quiet think time
Teacher Instructions
  • “Discuss your thinking with your partner.”
  • 1 minute: partner discussion
  • Share and record responses.

Student Task

What do you notice? What do you wonder?

3×?=123 \times {?} = 12

12÷3=?12 \div 3 = {?}

Solution Steps (3)
  1. 1
    Examine equations: 3 × ? = 12 and 12 ÷ 3 = ?
    →Both use 3, 12, and an unknown
  2. 2
    Notice relationship
    →Unknown is 4 in both equations
  3. 3
    Understand connection
    →Division finds the unknown factor from multiplication

Sample Response

Students may notice:
  • The 12 is being broken into 3 groups or groups of 3.
  • Both equations have a 3, a 12, and a question mark, but they are not in the same places.
  • Putting 4 for the question mark would make sense for both equations.
  • One equation uses multiplication, and the other uses division.
Students may wonder:
  • Is the unknown number the same in both equations?
  • What is the unknown number?
  • Are the two equations related?
Activity Synthesis (Teacher Notes)
  • “Today, we are going to work more with multiplication and division equations like these.”
Standards
Addressing
  • 3.OA.6·Understand division as an unknown-factor problem. <em>For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.</em>
  • 3.OA.B.6·Understand division as an unknown-factor problem. <span>For example, find <span class="math">\(32 \div 8\)</span> by finding the number that makes <span class="math">\(32\)</span> when multiplied by <span class="math">\(8\)</span>.</span>

15 min

20 min