1. Welcome to the World of Algebra
mathematical A
thinking race!

2. Two aliens, Xigmat and Yancy have just arrived on Earth
Two aliens, Xigmat and Yancy have just arrived on Earth. Xigmat and Yancy disagreed about the answer to:
7 + 5  2
What answers do you think they got?
Which answer is correct?

3. 7 + 5  2 By the Order of Operations is equal to 7 + 2.5 which is 9.5
Explain to X & Y, how the mnemonic PEMDAS will help them!
“Please Excuse My Dear Aunt Sally”

4. The Order of Operations P  Parentheses & Grouping Symbols
E  Exponents
MD  Multiply & Divide from left to right
AS  Add & Subtract from left to right
“Please Excuse My Dear Aunt Sally”

5. What number times itself
Remember Parentheses are not the only grouping symbol:
If a = 3 and b = 4, simplify:
Square Root symbol:
What number times itself
results in this value?
“Please Excuse My Dear Aunt Sally”

6. the positive distance from zero.
Recall : Absolute Value is
the positive distance from zero.
| -5.2 | and | 5.2 | are both equal to 5.2
since they are each 5.2 units from the origin. 2 4 6 -4 -6 -2
-5.2
5.2
Both distances equal 5.2
Origin

7. Remember Parentheses are not the only grouping symbol:
Recall : Absolute Value is the positive distance from zero.
Simplify: | |
| -4 |  4
Notice that you must simplify INSIDE
the absolute value bars first!
It would be wrong to do abs. value first:
| -7 | + | 3 |   10
“Please Excuse My Dear Aunt Sally”

8. His answer was 6.5 5 + 3/2 gives 6.5 (5 + 3)/2 gives 4
Remember Parentheses are not the only grouping symbol:
Xigmat used his calculator to simplify:
His answer was 6.5
What did he do wrong?
He forgot the division line in a fraction is a grouping symbol!
5 + 3/2 gives 6.5
You must enter parentheses in your calculator!
(5 + 3)/2 gives 4
“Please Excuse My Dear Aunt Sally”

9. Solve to find x: 2 x = 64 x must equal 6
Xigmat was stumped by this problem.
Can you explain it?
Solve to find x: x = 64
exponent
base
Since 2  2  2  2  2  2 = 64 or 26 = 64
x must equal 6
That is, 2 times itself six times will give 64.
More
Examples: 32 = = 100, = 81

10. If you triple Xigmat’s age and subtract 2, the result is 601.
Yancy needs to learn how to translate problems into algebra symbols.
If you triple Xigmat’s age and subtract 2, the result is 601.
How old is Xigmat?
Let x represent Xigmat’s age.
3x – 2 = 601
3x = 603
x = 201
Xigmat is 201 years old.

11. X & Y also need to learn how to graph.
Complete the table, plot the points and connect the dots to graph the equation : x -6 -3 3 6 9 -1 1 2 3 4

12. There must be an easier way than listing all the possible orders:
Xigmat & Yancy have to visit 7 earth friends,
(Alpha, Beta, Cee, Delta, Epsiplon, Fred & Gamma),
one each day for the next week.
In how many ways, could they arrange their visits?
There must be an easier way than listing all the possible orders:
ABCDEFG or DEABCGF or GDCABEF...
Look for a mathematical shortcut:
Day 1: they have 7 friends to choose from
Day 2: they have 6 friends left to choose from
Day 3: they have 5 choices left :
Day 7: only 1 choice left by elimination

13. Xigmat & Yancy have to visit 7 earth friends,
Alpha, Beta, Cee, Delta, Epsiplon, Fred & Gamma,
one each day for the next week.
In how many ways, could they arrange their visits?
Looking for a Mathematical Shortcut:
Day 1: they have 7 friends to choose from
Day 2: they have 6 choices left :
Day 7: only 1 choice left
Simply MULTIPLY to get the total number of different orders:
Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7
7  6  5  4  3  2  1 = 5,040 ways
In math symbols this is written as: 7! = 5,040
The exclamation point is read “FACTORIAL”

14. In how many different orders could you do homework for four classes:
Want another example?
In how many different orders could you do homework for four classes:
Algebra, Biology, Civics and Drawing?
You could list all the orders, if you are careful:
ABCD BACD CABD DABC
ABDC BACD CADB DACB = 24 ways
ACBD BCAD CBAD DBAC
ACDB BCDA CBDA DBCA
ADBC BDAC CDAB DCAB
ADCB BDCA CDBA DCBA
But there has to be a mathematical shortcut using the COUNTING PRINCIPLE we saw previously!

15. In how many different orders could you do homework for four classes:
Algebra, Biology, Civics and Drawing?
What HW do you do first? 4 subjects to choose from
What HW do you do second? 3 subjects left to choose from
What HW do you do third? 2 subjects left to choose from
What HW do you do fourth? Only 1 subjects left to complete!
HW 1 HW 2 HW 3 HW 4
4  3  2  1 = 24 different orders
This is written as 4! = Read: “4 factorial is 24.

16. Welcome to Algebra Quick Review:
| -5 | is read “Absolute Value of negative 5”
| -5 | = 5 since it is five units away from the origin (zero)
5! is read “5 Factorial” which is used in Counting Principles
5! = 5  4  3  2  1 = 120
8! = 8  7  6  5  4  3  2  1 = 40,320
35 is read “3 to the 5th power.” 35 = 3  3  3  3  3=243
52 = 25 which can also be read as “five squared.”
43 = 64 which can also be read as “four cubed.”
PEMDAS (Please Excuse My Dear Aunt Sally) is a mnemonic for the
Order of Operations:
Parentheses & Grouping Symbols 3. Multiply & Divide
Exponents Add & Subtract