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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!