Intro Question: Alpacas Along a River.
Consider the picture in our shared folder. How much area can we make for Alphonse if we have a river on one side, as shown? How does it change? How can we verify our answer?
Go over homework:
Blades of grass:
what questions did you have to answer before you could answer your question (assumptions)
did we have to be as precise as we were?
what calculations did you have to do in order to answer your question (function)
how can we refine our answer if we so chose? What information might be useful for us to answer this question?
Order of operations:
so what it the order that you know?
PEMDAS
BODMAS
GEMS
How did it come about?
because. seriously.
that being said, let's think what the structure DOES:
grouping (parenthesis)--"hey, this is more important! look over here!"
exponents (I represent multiplication--which you are going to next--but don't use the number. Let's uncomplicate that"
multiplication and division. Same thing, really. though multiplication can be considered iterated addition
what is division? how is it different than a fraction?
addition and subtraction ... same thing again!
Possible Issues With Fractions
Dividing by zero (not a great idea)
Multiplying Fractions
the key word here is "of". Start with whole numbers:
3x2 = Three of two ... 2 + 2 + 2
3x(1/2) = Three of (1/2) = 1/2 + 1/2 + 1/2
(2/3) x (1/2) = ....
Dividing Fractions
We've got 7 cups of food -- my puppy eats 2/3 of a cup per meal. How many meals do we have for the dog?
Show how you know before watching the video. How can we think about the problem?
...now we have 60 cups, and my dog eats 3/4 of a cup at each meal. How do we get there?
https://www.youtube.com/watch?v=mUKbL_OL_-Q&feature=youtu.be
Adding/Subtracting Fractions
Solving Literal Equations
Start with an easy equation: 3x+5=11 . This even ends in a whole number to make you happy.
Now let's go to 3x+y=11