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Xmania!.

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Presentation on theme: "Xmania!."— Presentation transcript:

1 Xmania!

2 What day is your birthday?
Think of the DATE you were born, but don’t say it out loud!

3 Card #1 Card #2 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 2 3 6 7 10 11 14 15 18 19 22 23 26 27 30 31 Card #3 4 5 6 7 12 13 14 15 20 21 22 23 28 29 30 31 Card #5 Card #4 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 8 9 10 11 12 13 14 15 24 25 26 27 28 29 30 31

4 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.

5 Let’s look at what we know:
How many digits are there? How many numbers are there? Do we have to use 1,2,3… or can we use something else? Do we know any other number systems? When is = 1? 10 digits א0 (infinitely many) Any symbol will work. Yes! On a Clock!

6 So what is the value of --
34 Why is it not 7?

7 So we can count to 9 then we have to use another digit for 10.
7 10 8 3 9 5 2 4 6

8 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:

9 Here are a few the Egyptians used
So what’s their value?

10 © Mark Millmore

11 A Few Mayan Math Symbols

12 The Mayans had up and down place value! But this is 21
In Mayan Math This is 1 This is 2 The Mayans had up and down place value! But this is 21 Thanks to:

13 Could we count with lights?
How?

14 So…. If this is one: O O O O x And this is two: O O O x O
Then the sum is: (1) (10) (11) O O O O x O O O x O O O O x x

15 Lights, Lights, Lights! Binary Number 1. __ O O O O x ____1_______
Light 5 Light 4 Light 3 Light 2 Light (1’s and 0’s) 1. __ O O O O x ____1_______ 2. __ O O O x O ____10______ 3. __ O O O x x ____11______ 4. __ O O x O O ____100_____ 5. __ O O x O x ____101_____ 6. __ O O x x O ____110_____

16 What to remember: 1 is “on” 0 is “off”

17 What is the value of each 1?
Has a value of 1 1

18 What is the value of each 1?
Has a value of 2 10 One’s Place

19 What is the value of each 1?
Has a value of 4 100 One’s Place Two’s Place

20 What is the value of each 1?
Has a value of 8 1000 Four’s Place One’s Place Two’s Place

21 So the value of this binary number would be
1111 8 = 4 1 = 15 2

22 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?

23 So to double over and over…
Add a zero each time you double So in our number system we would write 1 x 2 x 2 x 2 if we wanted to double the number 1 three times. The shortcut for that would be 1 x 23 In binary that number would be… 1000 (a zero for each double!) Exponent

24 Try writing these answers in binary --
3 x 24 4 x 23 7 x 25 13 x 23 = 11 = 100 = 111 = 1101 0000 3 is 11 so with four zeroes it would be… 000 00000 000

25 Guess what uses the binary system?

26 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 #1 Card #5 Card #4 Card #2 Card #3 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 8 9 10 11 12 13 14 15 24 25 26 27 28 29 30 31 2 3 6 7 10 11 14 15 18 19 22 23 26 27 30 31 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 4 5 6 7 12 13 14 15 20 21 22 23 28 29 30 31

27 So our base 10 system has shortcuts too…
If binary had a shortcut for doubling ( x 2) then our system has one for… x 10 So if I want to multiply a number by ten all I have to do is _______ ? And if I want to multiply by ten twice or three times?

28 For Example This is TOO easy! 34 x 10 = 723 x 104 = 9 x 107 =
340 7,230,000 90,000,000 457,100 500,000

29 Let’s look at a different number system --
Xmania

30 How do the Xmanians count?

31 Our Number System

32 Xmania

33 How is Xmania like our decimal system?
Has a digit for zero. Uses place value (except they add digits to the left instead of the right). Has shortcuts for multiplying. _________________

34 Create your own number system
Now it’s your turn to Create your own number system

35 Your system should have:
A name A digit for “zero” 3 or 4 digits total Place value Multiplication shortcut (with explanation)

36 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)?

37 Let’s sum up! Here are a few for you to review: 65 x 104 = 784 x 103 =
650,000 784,000 400,000 930

38 Questions? Good-bye!


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