Ordering games involve estimation and comparison, two essential skills for mathematics.

Here are some ordering games I gave to groups of students at Greenwich High School. Teams raced to arrange the slips of paper from smallest to largest. (No calculator)

Some groups were very enthusiastic about this game; others not so much. In the future it might help to do one “practice” round with numbers like 1,2,3,4,5, so that each group could get a feel for what they are trying to do and what a successful ordering looks like.

Each ordering game below is geared to a different skill level. The cards are not necessarily in order as pictured.

A little bit of trig:

Finding areas enclosed by curves. I gave this to students in a calculus class, but it could also be great for eager students who haven’t learned calculus yet. It can be completed without any calculus.

I feel I have only scratched the surface of what can be done with ordering games. It would be cool to create decks of cards (several different decks) like this. You’d need an ordering game of 13 items. The concept of suits (clubs, diamonds, hearts, spades) would be preserved. Just as in a normal deck, there would be 4 copies of every number. However, math skills would be required to sort the cards. For instance, instead of relationships like “a jack is higher than a 10” you’d have relationships like “a card with log(11) is higher than a card with sin(89 degrees).” Students could then play classic card games with each other, using the mathematical card decks. They’d have to swap out decks periodically to avoid getting too familiar with one deck and memorizing the orderings.

Eventually students could design decks for each other. This would involve thinking of 13 numbers that are obscure enough to make people think, but “easy” enough that no laborious calculations would be needed to compare them to one another.