Youth Curriculum

1. FUNCTIONS
AND LIMITS
CALCULUS FOR KIDS!

2. POP QUIZ
• What is the definition of calculus?
(remember, we talked about it last
time)
• Name one guy who invented calculus.
(spelling/nicknames does not matter)

3. KATHERINE JOHNSON
• Katherine Johnson was an American
mathematician
• Her calculations of orbital mechanics as a NASA
employee were critical to the success of the first
and subsequent U.S. crewed spaceflights.

4. DONEC QUIS NUNC
ORBITAL MECHANICS
E = Σ∞
n=1
M
n
3
n!
limθ→0
(
dn−1
dθn−1 (
θn
3
θ − sin(θ) ))
, ϵ = 1
E = Σ∞
n=1
Mn
n!
limθ→0
(
dn−1
dθn−1 (
θn
3
θ − ϵ ⋅ sin(θ) ))
, ϵ ≠ 1

5. WHAT THE MATH IS A FUNCTION?
• A function is like a vending machine.
You put your money in…and most of
the time you get candy out!
• A function works kinda in the same way

6. THE FUNCTION MACHINE
Input Function Output

7. LET’S LIST SOME COMMON FUNCTIONS
• Take out a sheet of paper and list 5 functions that you would see
every day.
• Like a vending machine.
• Another example is a quiz. You input the answers and get a grade
as output.

8. MATH FUNCTIONS
• Lets look how math people write functions:

9. THE FUNCTION MACHINE
Input Function Output
• Lets look how math people write functions:
• Y = x + 2
• , let’s talk about this.
• x - input (the letter x holds the place for any number you want!)
• - function (this is the vending machine turning the wheel so you get the tater chips!)
• Y - output (This is the number or chips you get out!)
y = x2
x2
You always input
a number
Like a calculator
the function
does some
calculations
Your output is a
number

10. VISUAL FUNCTIONS
• What is a coordinate
plane?
• We have an x and a y!
• The x and y always stay
together on a
coordinate plane.
• (x, y) is how you write a
coordinate.

11. VISUAL FUNCTIONS
• Functions are a way to figure out your y!
• This means if I know my x, and a function, then I
can know where to place a dot!
• Let’s try it out!
• Got to the computers and look up demos
graphing!

12. HOW TO GRAPH A FUNCTION
Your function should always start with
y = ________
Try to use the hat (^) or (shift+6) and then a number

13. LIKE REALLY…WHO CARES!!!
WHO CARES ABOUT FUNCTIONS
• Everyone! Lesson over. Just kidding.
• Functions help us describe our world in math
terms. They help us take real world problems.
Like video games!!!
• When you press left (input) on a joystick….it
moves left (output)…
• When you press the attack button (input)…
most of the time you character attacks (output)
—-Unless you just ate a peanut butter & jelly
sandwich and the controls are stuck!!!!!!—-

14. LIKE REALLY…WHO CARES!!!
WHO CARES ABOUT FUNCTIONS
• We can model real life!!!!
• Because modeling something gives us
the sense of what something does
without having to do that thing!!!
• How much you study (input) tells you
how well you will do in class (output)
• Temperature
• Height
• Speed of cars

15. MODELING
• The best example is when people like Einstein write math
equations that “model” the universe.
• There is no way we can understand and go out to check the
universe. We can model it with functions