Students will learn two reasons why division by zero is undefined. First, if division is repeated subtraction, then we cannot reach zero by repeatedly subtracting zero from some number. Second, consider the fractions where the numerator is fixed, and the denominator shrinks. For example, 1/1, 1/0.1, 1/0.01, etc. This value is getting larger and larger, and we can see it approaches positive infinity. But if we define 1/0 to be positive infinity, then we reach the absurdity that 1 = 2. Here's a video on all this.

Next, give your students these challenges:

- Cows and Sheep by NRICH
- 2018 Math Kangaroo Levels 5-6 Problem #23 by STEM4all

Conclude by leading this investigation:

EKG Sequences – factorization

by MathPickle