Modern math competition

Saw this brief exchange and thought it would be a good time to write down some ideas for a new type of math event:

There is a STEM Expo later this year w/ community partners and a 4th - 8th gr competition. Ideas on how to make comp more mathy? #MTBoS

— Jana Sanchez (@jsanchezmath) December 18, 2015

It will be clear below that these are all other people's ideas, I've really just added ideas for how you might score this.

Fold and Cut

Everyone gets a pair of scissors and three pages with a straight-line figure (a shape that has a boundary made up of polygons) in the middle of the page. For each shape, players try to find the smallest number of straight cuts they need to cut out each shape.

One example of a shape to cut out

Another example: cut the house and the tree at once (hard!)

Scoring for each shape:
10 points for least cuts
5 points for second
1 point for all who cut out the shape successfully, regardless of how many cuts it took

Reference: Fold and Cut Theorem.

Estimation

Set up an estimation challenge (number of marbles in a jar, weight of a collection of books, height of a blown-up picture of your favorite mathematicians, etc). All players write down:

1. Their estimate of the amount
2. An explanation of their reasoning
3. A value that they think is too low
4. A value that they think is too high

Scoring:

Each estimators performance is based on the absolute size of their error (|estimate - actual|) multiplied by the size of their low-to-high range, divided by 2 if the actual value is within their range. The lower the resulting value, the better.

20 points for best performance

10 points for second

5 points for third

1 point for everyone who estimates

Reference: Estimation180 has tons of great prompts for estimation.

Which one Doesn't Belong

Really simple: show players four things, then they figure out reasons why each of the figures could be the one that doesn't belong.

This is just a small sample of the ideas for Which One Doesn't Belong

Scoring:
1 point for every different reason + 5 bonus points if there is a reason given for each of the 4 shapes

Reference: Which One Doesn't Belong has a huge collection of great ideas for shapes, numbers, graphs.

Notice and Wonder

Pick a 3 to 5 math pictures, gifs, or videos to show on a large screen. Players write down the things that they notice ("I notice that ...") and wonder ("I wonder [what, why, when, how many, ...]..?").

From SolveMyMaths

Scoring (similar to WODB):
1 point for every notice or wonder + 3 bonus points for having both a notice and a wonder.

Reference: SolveMyMaths and MathHombre both have really nice collections. Mathematical Etudes has some excellent videos that don't seem to be as widely known among Anglophones. I'm sure there are others