Transcript Xmania! - MathinScience.info

Count On
It!
What day is your birthday?
Think of the DATE you were born,
but don’t say it out loud!
Card #1
Card #2
1
9
17
3
11
19
5
13
21
7
15
23
2
10
18
3
11
19
6 7
14 15
22 23
25
27
29
31
26
27
30 31
Card #3
Card #4
4
5
6
7
12
20
28
13
21
29
14
22
30
15
23
31
Card #5
8
9
10
11
16
17
18
19
12
24
28
13
25
29
14
26
30
15
27
31
20
24
28
21
25
29
22
26
30
23
27
31
What to expect…
• Learn some new things about our number
system.
• Learn some stuff about other number
systems.
• Learn some cool short-cuts that work for
our number system.
• Learn how the Birthday cards work.
Let’s look at what we know:
• How many digits are
there? 10 digits
• How many numbers are
there? ‫א‬0 (infinitely many)
• Do we have to use 1,2,3…
or can we use something
else? Any symbol will work.
• Do we know any other
number systems? Yes!
• When is 8 + 5 = 1?
On a Clock!
So what is the value of --
34
Why is it not 7?
So we can count to 9 then we have to
use another digit for 10.
1
7
3
9
8
5
2
4
6
10
Back in the day…
• Different groups used
different symbols.
• Symbols could be a
single value or different
values (depending on
where they were).
• Here’s some examples:
Here are a few the Egyptians used
So what’s
their value?
© Mark Millmore 1997 - 2002
http://www.eyelid.co.uk/numbers.htm
© Mark Millmore 1997 - 2002
http://www.eyelid.co.uk/numbers.htm
A Few Mayan Math Symbols
Thanks to: http://www.michielb.nl/maya/math.html
In Mayan Math
This is 1
This is 2
The Mayans had up and
down place value!
But this
is 21
Thanks to: http://www.michielb.nl/maya/math.html
Could we count with lights?
How?
So….
• If this is one:
• And this is two:
• Then the sum is:
OOOOo
OOOoO
O O O oo
(1)
(10)
(11)
What to remember:
 1 is “on”
 0 is “off”
Lights, Lights, Lights!
Light 5 Light 4 Light 3 Light 2 Light 1
1. __
2. __
3. __
4. __
5. __
6. __
7. __
8. __
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
x
O
O
O
x
x
x
x
O
O
x
x
O
O
x
x
O
x
O
x
O
x
O
x
O
Binary Number
(1’s and 0’s)
____1_______
____10______
____11______
____100_____
____101_____
____110_____
____111_____
____1000____
What is the value of each 1?
Has a value of 1
1
What is the value of each 1?
Has a value of 2
10
One’s Place
What is the value of each 1?
Has a value of 4
100
One’s Place
Two’s Place
What is the value of each 1?
Has a value of 8
1000
Four’s Place
Two’s Place
One’s Place
So the value of this binary
number would be
8
1111
4
2
=8+4+2+1
1
= 15
So let’s double some numbers
 101
 11
 111
 100
 1010
 1010
 110
 1110
 1000
 10100
 Is there a pattern?
 Is it similar to a
pattern we use in
our system?
 Why does it work
for doubling?
Guess what uses the binary
system?
So back to the Birthday Cards
• What is so special about
the numbers on card #1?
• Look at your lights,
lights, lights sheet and
tell me if the numbers
have something in
common in binary.
• What about card #2? #3?
#4? And #5?
Card
Card
#4
#5
Card#1
#2
Card
#3
16
4821
17
59
3
10
18
65
19
11
7
12
10
12
20
9 13
13
21
11 14
13 15
22
23
20
17 21
18
24
19 22
25
21 23
26
27
28
25 29
26
28
27 30
29
29 31
Let’s look at a different
number system --
Xmania
How do the Xmanians count?
Our Number System
Xmania
Now it’s your turn to
Your system should have:
•
•
•
•
•
A name
A digit for “zero”
3 or 4 digits total
Place value
Multiplication shortcut (with explanation)
Let’s sum up!
• How are place valued
number systems alike?
• What are the major
differences?
• What are the shortcuts to
our number system?
• Do the number shortcuts
work with other number
systems (like Xmania)?
Questions?
Good-bye!