1. So, let’s count in base 6 Digits allowed: 0, 1, 2, 3, 4, 5
There is no such thing as 6
When we read a number such as 2136, we don’t say “two hundred thirteen.” We say instead “two-one-three, base 6.”

2. Count! In base 6
1, 2, 3, 4, 5,
10, , 12, 13, 14, 15,
20, , 22, 23, 24, 25,
30, , 32, 33, 34, 35,
40, , 42, 43, 44, 45,
50, , 52, 53, 54, 55,
100, 101, 102, 103, 104, 105, 110

3. Compare base 6 to base 10 Digits 0 - 9
New place value after 9 in a given place
Each place is 10 times as valuable as the one to the right
243 = 2 • (10 • 10) + 4 • • 1
Digits 0 - 5
New place value after 5 in a given place
Each place is 6 times as valuable as the one to the right.
243base 6 = 2 • (6 • 6) + 4 • • 1
or 99 in base 10

4. In base 6, write the first five place values.
_____ _____ _____ _____ _____
cube flat long unit

5. Compare Base 6 to Base 10 312base 6 = 312 = 3 • 100 + 3 • 36 + 1 • 6 +
2 • 1 =
116 in base 10
312 = 3 • 100 +
1 • • 1

6. How to change from Base 10 to Base 6.
Suppose your number is 325 in base 10.
We need to know what our place values will look like.
_____ _____ _____ _____
6•6•6 6•
Now, 6•6•6 = = 1000 in base 6.

7. Base 10 to Base 6 ___1__ _____ _____ _____ 6•6•6 6•6 6 1
___1__ _____ _____ _____
6•6• •
Now, = Since 109 is less than 216, we move to the next smaller place value: 6 • 6 = 36.
= 73. Since 73 is greater than 36, we stay with the same place value.

8. Base 10 to Base 6 __1___ ___3__ _____ _____ 6•6•6 6•6 6 1
__1___ ___3__ _____ _____
6•6•6 6•
We had 109: = 1. We subtracted 36 three times, so 3 goes in the 36ths place.
We have 1 left. 1 is less than 6, so there are no 6s. Just a 1 in the units place.

9. Base 10 to Base 6 __1___ ___3__ __0___ __1___ 6•6•6 6•6 6 1
__1___ ___3__ __0___ __1___
6•6•6 6•
Check: 1 • • • 1 = 325

10. Count! In base 16
1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f
10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1a, 1b, 1c, 1d, 1e, 1f
20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 2a, 2b, 2c, 2d, 2e, 2f

11. In base 16, write the first five place values.
______ _____ _____ _____ _____
65,

12. In base 5, write the first five place values.
_____ _____ _____ _____ _____
cube flat long unit

13. In base 2, write the first five place values.
_____ _____ _____ _____ _____

14. Let’s Look at Adding and Subtracting in Alphabitia
If we use the Alphabitian numerals, do our rules for addition and subtraction hold true?
Warm up: tell me one more and one less of each AB
CAD
B0B
AA0 DD
Use manipulatives or drawings to explain your answers.

15. Let’s add in Alphabitia
BCD + DB
BCD is DB is BCD + DB is

16. You try:
B0B +ABC
Use the manipulatives or draw pictures to help explain your answer.

17. Let’s subtract
CBD ADC =
CBD is ADC is CBD - ADC is

18. You Try…
D00 -B0B
B0A -BD

19. You try: Use manipulatives or drawings to explain
BBC - A0C
A0A0D BCA

20. First Exam Scheduled Wednesday, February 13th Cover material from:
Textbook: 1.2, 1.3, 1.4, 1.7, 2.3, 3.1, 3.2
Explorations: 1.1, 1.4, 1.7, 2.8, 2.9, 3.1, 3.6
Notes/Problems from class
Sample test questions on line next Monday.

21. Homework for Monday Exploration 2.9:
Part 1: for Base 6, 2, and 16, do #2;
Part 3: #2, 3; Part 4: #1, 2, 4.
Read Textbook pp
Do Textbook Problems pp :
15b,c, 16b,d, 17a,i, 18b,f, 19, 29