Clapping, Number line, Counting coins, and Roboths Math Circle Nov 1 2015

Clapping Patterns

Right and left hands clap on table

First identify right and left hands. 

Then write R and L on hands to help students

Then try to clap against table 

R-L-R-L-

4/4 time, "-" = 1/8 rest

One at a time 

Then 

R-L-RRL-

Number Line; 

What is it? And what do the arrows mean?

Write 1 then 2,3,4,5 on line, starting at the third mark

Coins: 

Place the number of coins on each number to Link counting to numerals 

What numbers are bigger and smaller? 1 vs 2, 3 vs 4, Etc

What is smaller than 1? How many pennies is that?

What is smaller than 0?

Chess board: ranks and files with numbers and letters

Homework 

How many pennies is -1?

If the king is on 1d, what spaces could he reach in one move? In two moves?

Patterns, Rhythm, and a visit to the Store Math O 2.0 18 Oct 2015

Patterns

Finish the pattern. Starting with a few shapes, repeat the shapes

Music

Inspired by Steve Reich's Clapping Music

What is a nickel and a penny worth?

How can you buy a 5c banana?

Robots in the wild

Kids are robots. What instructions are required to get from Ellie's to  Dizas house

Patterns, Clapping Patterns, Addition and Subtraction, Coney, Magnets. Math O 2.0 25 Oct 2015

Clapping

this means 'right left left right'

Blue = Clap, White = no clap

(Too confusing)

Blue = Right hand, White = Left Hand

Lego patterns in sets of 4

Addition and subtraction 

Many variations of:
* Addition
  * We have two blue legos and two white. How many total?
* Subtraction:
  * 6 legos, take away 2, how many are left?
  * Start with 6 legos. Look over there! I hid some legos, how many did I hide?

Buying food

Each kid gets 5 pennies and two nickels.

We have many different items. How many pennies do they cost?

A carrot costs 4c for 1/2. How much is a whole?

Experiment 

Which items are magnetic?
What makes an item magnetic? (remains unanswered, may return to this next time)

oct 25

• Proportions:
• Blob ate three times as many mushrooms as Glob, and Clob ate two times as many as Blob. Together they ate 40 mushrooms. How many each ate?
• Pete had $3, and Paul $4. They bought together 14 rabbits. How many each gets?
•  Find three (or more ways) to cut a square - with straight lines - into two equal parts.
• Do they always intersect at the same point?
• What about a triangle? 
• Learning to count auf Deutsch:
• Funf-und-zwanzig - 25
• Sieben-und-dreißig - 37
• Zwei-und-zwanzig - 22
• Ein-und-zwanzig - 21
• Ein-und-vierzig - 41
• Mayan numbers

• Cut and fold...
• Can one wrap a 1x1x1 cube into 3x3 piece of paper?
• Old puzzle:
  
  

Experiments: sliding magnets

Homework:

Alice and Bob drove 500 miles. Alice drove 3 hours, and Bob 7 (with the same speed) - how many miles each of them drove?  

What numbers are Sieben-und-vierzig, Drei-und-dreißig, Vier-und-vierzig, Funf-und-funfzig?

Find at least three ways to cut by a straight line this triangle into two parts of equal area:

oct 18

• Continue with the areas of the lattice polygons. Work on Pick's formula. 

Reminders: 

Pick's formula for the area of lattice polygons - polygons with vertices in the nodes of a lattice - is:  Area=(number of nodes inside the polygon)+  (number of nodes on the boundary)/2 -1

Cavalieri principle asserts that the area of a figure - viewed as as stack of parallel intervals - does not change if one slides these intervals back and forth. 

• Padlock puzzle
• Linguistics
• Work with compasses; measure distances
• Proportions:
• Split 9 apples so that A gets 2 times as much as B; 
• split 8 pears so that A and C gets the same, B gets 2 times as much as A;...

Experiments
Laser- conical sections

Homework

• How to split 21 peaches between Anne, Amy and Aman so that Aman gets twice as many as Amy, but half as much as Anne?
• M. Argan takes three kinds of pills, one of each each day. He left for a week long travel with 7 pills of each kind. Unfortunately, in the box they all got mixed together, and they all look the same. How M. Argan can still make sure he takes one of each pill each day?
• Find the areas of each of these three figures:

Robots, Coins, Patterns, and a Prism. Math Circle 2.0 Oct 10 2015

Robots

Last week we re-programed the robot so that it could backwards.

Now, the robot not only understands North and West, but also South and East.

Furthermore, now instead of giving one instruction at a time, we give the robot all commands. To do so, first we write out the steps, then have the robot read the steps, and then see what the robot does 

Can we get the robot back from the NW to SE?

Coin Algebra

How many pennies in a nickel? How many in two nickels?

What is a dime worth in terms of pennies? In terms of nickels?

Started with a dime, a nickel, and a penny

trade nickel for five pennies. How many pennies?

Trade dime for ten pennies, how many pennies?

How many nickles can we get

Patterns

Lego chains

Drawing zigzags

1. What is the core pattern? How many times can we repeat this pattern given the pile of legos below?

Draw Triangle, circle square, and repeat. 

Experiments 

Split light into colors with a prism

What color is sunlight? Where do the colors of the rainbow come from?

If we split into ROYGBIV, where do brown, grey, and black come from? Why is the table brown, but we only get ROYGBIV from the prism?

And look at the Sun. How has the shadow changed in 3 weeks since solstice?

Homework 

Continue the patterns:

oct 10

• Continue with the areas of the lattice polygons: introducing half-integer areas. Are integers and half-integers all what we can encounter?
• We'll do a few more tree-climbing caterpillars... Where are the leaves hanging?
• Four German phrases and their translations are given (in a wrong order):

Er liest die Nachrichten     He reads a newspaper

Sie liest eine Zeitung       She eats a sandwich

Sie isst ein Butterbrot      He reads the news

Er liest eine Zeitung        She reads a newspaper

   Find which sentence translates which, and translate into German: Peter eats a sandwich.

• Proportions:
• More pizza: split it into four parts, give three to Alice, Bob and Clara, and continue: split the remaining piece into 4 parts etc. How much each is getting?

Experiments

• 2D version of Chasles theorem using optical illusions...

Homework

• Cut and fold from a single piece of paper (no glueing!):

• Four German phrases and their translations are given (in a wrong order):
Peter fährt sein Fahrrad    Lisa sees her brother
Lisa sieht ihr Bruder       Lisa likes her bike
Peter sieht sein Fahrrad    Peter rides his bike
Lisa mag ihr Fahrrad        Peter sees his bike

Find which sentence translates which, and translate into German: 
She sees her brother.




• Find areas of these polygons:
  




• Caterpillar crawls around the tree. Show the graph of his height, and show where he gets some leaves to munch on: