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

Count on it

What day is your birthday?

Think of the DATE you were born, but don’t say it out loud!

Card #1

1 3 5 7

9 11 13 15

17 19 21 23

25 27 29 31

Card #2

2 3 6 7

10 11 14 15

18 19 22 23

26 27 30 31Card #3

4 5 6 7

12 13 14 15

20 21 22 23

28 29 30 31Car

d #48 9 10 11

12 13 14 15

24 25 26 27

28 29 30 31

Card #5

16 17 18 19

20 21 22 23

24 25 26 27

28 29 30 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?

• 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 8 + 5 = 1?

10 digits

∞ (infinity)

Any symbol will work.

Yes!

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 2 3 4

5 6

7 8 9 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’s a few the Egyptians used

So what’s their value?

© Mark Millmore 1997 - 2004

A Few Mayan Math Symbols

In Mayan Math

Thanks to: http://www.michielb.nl/maya/math.html

This is 1 This is 2

But this is 21

The Mayans had up and down place value!

Could we count with lights?

How?

So….

• If this is one:

• And this is two:

• Then the sum is:

O O O O xx O O O xx O

O O O x xx x

(1)

(10)

(11)

Lights, Lights, Lights!

Binary Number Light 5 Light 4 Light 3 Light 2 Light 1 (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_____

What to remember:

1 is “on” 0 is “off”

What is the value of each 1?

1

Has a value of 1

What is the value of each 1?

Has a value of 2

One’s Place

10

What is the value of each 1?

Has a value of 4

One’s PlaceTwo’s Place

100

What is the value of each 1?

Has a value of 8

One’s PlaceTwo’s Place

Four’s Place

1000

So the value of this binary number would be

8

12

4

1111 = 8 + 4 + 2 + 1

= 15

So let’s double some numbers

101 11 111 100 1010

1010 110 1110 1000 10100

Is there a pattern?

Why does it work for doubling?

Is it similar to a pattern we use in our system?

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

Try writing these answers in binary --

3 x 24

4 x 23

7 x 25

13 x 23

= 11

= 100

= 111

= 1101

3 is 11 so with four zeroes it would be…

0000

00000000

000

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 #1

1 3 5 7

9 11 13 15

17 19 21 23

25 27 29 31

Birthday Cards

Card #1

1 3 5 7

9 11 13 15

17 19 21 23

25 27 29 31

Card #2

2 3 6 7

10 11 14 15

18 19 22 23

26 27 30 31Card #3

4 5 6 7

12 13 14 15

20 21 22 23

28 29 30 31Card #4

8 9 10 11

12 13 14 15

24 25 26 27

28 29 30 31

Card #5

16 17 18 19

20 21 22 23

24 25 26 27

28 29 30 31

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?

For Example

• 34 x 10 =• 723 x 104 =

• 9 x 107 =• 4,571 x 102 =• 500 x 103 =

• This is TOO easy!

340

7,230,000

90,000,000

457,100

500,000

Let’s look at a different number system --

Xmania

How do the Xmanians count?

Our Number System

Xmania

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.

• _________________

• _________________

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)?

Let’s sum up!

650,000

784,000

400,000

930

• Here’s a few for you to review:

• 65 x 104 =

• 784 x 103 =

• 4 x 105 =

• 93 x 10 =

Questions?

Good-bye!