Students will learn how to solve Menseki Meiro puzzles, also known as area mazes. Teachers should watch at least this, then this. The puzzles in the second video are hard to see, so I have drawn them below:
Here's another easy puzzle:
And here's its solution. More puzzles can be found here. Students can use algebra to justify their answers, although algebra isn't strictly necessary. The same conclusions can be drawn by cutting rectangles into equivalent parts. For example, if one rectangle has area 13 and another has area 26, yet the rectangles have the same height, then one must be twice as wide as the other. That could be justified algebraically, but it doesn't have to be.
TODO: Are there other sources for these puzzles online (YouTube or elsewhere)?