Inputs and Outputs

5 min

Teacher Prep
Setup
Groups of 2. 1 minute quiet work time followed by partner and whole-class discussion.

Narrative

The purpose of this activity is for students to see why an expression that contains the operation of dividing by zero can't be evaluated. They use their understanding of related multiplication and division equations to make sense of this.

Launch

Arrange students in groups of 2. Tell students to consider the statements and try to find a value for xx that makes the second statement true.

Give students 1 minute of quiet think time followed by 1 minute to share their thinking with their partner. Finish with a whole-class discussion.

Student Task

Study the statements carefully.

  • 12÷3=412 \div 3 = 4 because 12=4 312=4 \boldcdot 3.
  • 6÷0=x6 \div 0 = x because 6=x 06=x \boldcdot 0.

What value can be used in place of xx to create true statements? Explain your reasoning.

Sample Response

None. Sample explanation: There is no number that can be multiplied by zero to get something other than zero. Therefore, x0=6x \boldcdot 0=6 is never a true statement for any value of xx.

Activity Synthesis (Teacher Notes)

Select 2–3 groups to share their conclusions about xx.

As a result of this discussion, we want students to understand that any expression where a number is divided by zero can't be evaluated. Therefore, we can state that there is no value for xx that makes both equations true.

Standards
Building Toward
  • 8.F.1·Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
  • 8.F.A.1·<p>Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. <span>Function notation is not required in Grade 8.</span></p>

15 min

15 min