# Open ended problem: Boarding passengers onto planes

This might be an interesting conversation starter for a class: what’s the best way to board an airplane?

The students will probably have lots of ideas to discuss, and best of all, every single one of them will be better than what the airlines actually do.

# Ten-frames to explore decimals

Chris Hunter writes on his blog about a student explaining how they would express 0.500 using ten-frames:

One student expressed this as 500/1000 and 0.500. I assumed he was just extending the pattern(s). “Yeahbut where do you see the 500 and 1000?” I asked challenged. “I imagine that inside every one of these *points to a dot* there is one of these *holds up a full ten-frame*,” he explained. As his teacher and I listened to his ideas, our jaws hit the floor.

Showing 500/1000 or 0.500 using ten-frames

Have you seen examples where students come up with innovative ways of representing numbers?

# Exploring a digital block game

Screen-shot from one of the puzzles included in the block game.

I wrote this puzzle/game last year with  the hope it could be used to help generate some thinking about area, multiplication, and addition.

Here are some questions you could use with the game.

Try solving the problems, if possible, in a variety of different ways. Which ways give you the most points? How much is each piece worth? What is a general strategy you can use to get as many points as possible? How do you know your general strategy is effective?

Note: This game does not currently work in Internet Explorer.

# Open-ended problem: Do groups of people follow predictable patterns?

My sister and I were walking our kids back from a trip to Science World, when we passed a park sparsely filled with people. My sister looked at the people sitting in the park, and wondered aloud, “I wonder if you can use mathematics to figure out how far apart people will sit on a lawn?” I looked carefully at the park too, and noticed that everyone seemed to be carefully at an maximal distance apart from anyone else on the field. I am particularly excited about my sister’s question, because she has always described herself as “not a math person.”

I decided to generalize her question, to “do groups of people follow predictable patterns?” This would allow for exploration in a wide variety of ways, for example:

• Do people tend to follow the same paths when crossing open-space, like a field or in the meeting room of a train station?
• How random is the motion of people as they sit waiting in a theatre?
• Can you track use of phrases of language through groups of people?
• What similarities exist, if any, between the networks of relationships each person has?