First, show your students the 37 trick. Use fraction notation when demonstrating the trick. That is, use

$$\dfrac{777}{21} = 37$$instead of \(777 \div 21.\) Then challenge your students to explain why the trick always works. Here's both a demonstration of the trick, and explanation as to why it works.

Next, give your students this challenge:

Turning by NRICH

Conclude by leading this investigation:

Destroying Democracy! (counting, fractions, shapes)

by MathPickle