This is an outline to a lesson I did for my 5th grader’s math class during the NCAA tourney

#### Ask class to write down the answers to the following “Opening Questions”

**Assume all teams have a 50% chance of winning any game**

## How many games must a team win to get to the Final Four?

4

## What’s the chance a team make it to the Final Four?

1/16

## What’s the chance a team has to win the tournament?

1/64

#### Visualizing a Tree

#### Base-10 number system review

## How many digits do you need to represent 29,851?

5

#### Base-2 number system explanation

## Give example of how to represent 9

1001

## How many digits do you need to represent 25? Represent it

5 —> 11001

## Display the numbers 1 through 8 in binary

0: 0

1: 1

2: 10

3: 11

4: 100

5: 101

6: 110

7: 111

8: 1000

#### Binary in real life

- Computers use binary or base-2 number system because electricity is either on or off

- A letter like “X” in computer language is represented by ASCII 120. In binary that is 1111000

- A pixel on your computer screen can be any of a million colors.
- 16 characters are 0-9, A-F

**Color Name: (Decimal RGB), (Binary RGB), (Hexadecimal RGB)**Blue: (0,0,255), (00000000,00000000,11111111), (00,00,FF)

Cyan: (0,255,255), (00000000,11111111,11111111), (00,FF,FF)

## Hexadecimal is base-16 so there’s a ones place, a 16th place, a 32nd place and so on.

- A byte is 8 bits
- megabyte is 1mm bytes…how many bits? (8mm)
- gigabyte is 1000 megabytes
- terabyte is 1000 gigabytes

MP3 is about 5 MB.

- How many songs can a 1 gigabyte hard drive hold? (200)

- How about a 1 TB hard drive? (200,000)

4K movie is about 20 GB

- Every frame has 3840 pixels horizontally and 2160 pixels vertically —> about 8.2mm pixels!
- Each pixel is a color that requires several digits or bits to represent it (perhaps 1 byte per pixel)
- So there are about 8 MB per frame!
- Standard movie is 24 frames per second so need 192 MB/s
- Movies is 90 x 60s = 5400 seconds
- 192 MBs x 5400 seconds = 1mm MBs = 1 terabyte!
- Compression of 50 to 1 gets the movie down to 20 GB

#### Fun Stuff

## How high can you count if you use your fingers to represent numbers using binary notation?

1023

## How many fingers do you need to represent each letter of the alphabet?

5 using number to letter cipher