A more clickbait headline would be Pinterest Greatest Hits. For whatever reason, these activities pop up time and time again in the list of things people pin from me.
With the end of the semester approaching, it's likely you might have a random dead day here and there. You might not think these activities are something high school kids would enjoy, but believe me, they eat these up.
Something I do as an actual lesson is Hotel Snap. But it's good any time. Fawn provides a set of rules, but you can modify them to suit your needs. It's an interesting discussion in optimization.
An old classic. I keep a few thousand coffee straws in my cabinet. It came in handy this year when a nasty thunderstorm rolled in a 7am and a bunch of kids couldn't get to school.
The number of straws is up to you, typically 20-30. Usually I have them support a tennis ball and the structure can't be attached to the table. I generally set a height requirement of 18 inches off the table surface. I give them anywhere between 25-30 minutes to do this. You can even try bridges or whatever really. It's interesting to see the variety of designs that will work.
Something I stole from my own 6th grade teacher. Hand out a forest (a blank grid really) and give each forest a key related to the roll of a die (1 = tree, 2 = blank, etc) but create a few different sets. I have four cards, ranging from 33 - 66% chance that a tree will be planted on the roll. The students roll the dice, and if it comes up tree, they color in the square. I have them complete two forests. It takes a while and is very LOUD.
After the forest is planted, have them light the left-most column on fire. Fire spreads left, right, up, and down but not diagonally. I have them spread the fire to its natural conclusion and count up the percentage of dead trees. The cards with the highly probability of planting a tree are more likely to burn everything to the ground. Imagine that. Tree survival rates are all over the place.
Simple premise, with all levels of difficulty. Given four numbers and a set of operations (for the set I use, addition, multiplication, subtraction, and division), use each number once to make a total of 24.
I hand out about half a deck to each table, set a timer for 20 minutes and see how many they can solve as a group. The cards vary in difficulty. They get 1 point for the 1 dot, 2 pts for 2 dots, and 3 pts for 3 dots. Someone at each table keeps score and I put them on the honor system as far as the solutions go. You could require them to write them down if you wanted to.
I had a pair of 2 kids manage 17 points on their own and a set of 4 manage 50. For some kids, this is their jam.