Math Circle 2.0 Sept 20, 2015: Graphs, Robots, Algebra, Cells, and Sun

Graphs, Robots, Algebra, Cells, and Sun 

Graphs

Similar to last week (four points, how many connecting lines), but with objects (round clay dishes are towns, below) and strings (pipe cleaners).

The story is that the king in his Lego castle has asked Bonita the Banjo player from Batesville to come play. Then asks Guy the Guitar player from Galax and .... Then Filament the fiddle player from Finland ... They each live in different places. How many ways can the musicians get to the castle.

• connect two towns. 
• define, find, and count: how many nodes (towns)? and edges (lines)?

• Now with three towns ...

• And with four?

Robots

Robots are going to walk from town to town.

• Create a 3 x 3 grid of points
• Pink pipe cleaner is robot, understands two commands: North and West
• students take turns instructing robot to get from bottom green square at SW to white square at NE

How many ways can robot get to NE corner? Students found NNWW, NWNW, WNWN, WWNN. 

Homework: Are there others? (Hint: yes)

Algebra

count the number of circles on one square Lego.

How many circles on two square Legos?

Experiments

1. Earth's movement: rotating on its axis and around the sun. 

note: we are starting at the fall equinox

Materials:

• cardboard + graph paper
• sticker
• south-facing window
• pencil

1. place sticker on window
2. paper so sun's shadow lands on it
3. mark the shadow location at 11 AM, 11:30 AM, 12 PM
4. Repeat each Sunday morning for one year.