Beckie Zheng
720
10/18/13
Math (Ms.Anthony)
In this unit, I had learned many new things such as; what rational and integer
numbers are, and how you use them. We also worked with number string, number
lines, and chip models so prove what we think. But for this project, we are focusing on
pemdas (order of operations). The game dealing down helps improve our thoughts in
this unit because we have to include proof. We need to include a detailed explanation to
prove what we think using anything. This is what we were working on for part of the
unit. Dealing Down also improves our overall knowledge in operations. We are using
operations to find the smallest quantity. We are making expressions, which helps us
feel comfortable in creating number sentences and when we are solving it, it helps
build our math muscles.
____________________________________________________________
-In this game, you will need a partner.
-Your objective of this game is to find an expression with the least quantity
using: Order of operations, whole numbers (negative or positive numbers, and
zero) fractions, and decimals.
-You have to deal out four cards and you must use those numbers you drew to
make an equation that you think will have the smallest answer possible,
independently.
-You may not use negative exponents.
-And you must prove why the answer to your equation is smaller than your
opponent’s answer using a number line, a brief but detailed explanation, etc
STRATEGIES FOR DEALING DOWN:
One strategy I used was changing the
operations. I compare each operation to see
which one is largest. Basically, which
operation is biggest out of all of them and
try to make a number sentence with it. For
STRATEGIE FOR DEALING DOWN:
The second strategy I used was if all the
numbers were positive, to get the
smallest number, I would subtract all of
the numbers starting with the smallest
example, exponents are the largest. But I
number to the biggest.
have to make sure that the negative number
Example: 9, 3, 5, 7 Smallest-Largest: 3, 5,
is the one that is being multiplied (base) and
then the largest number out f all four
7, and 9
Equation: 3-5-7-9=x (x=-18)
numbers would be on the top (exponent).
But you can also subtract the smallest
Example: -10, 5, 3, 0
multiply it with the rest.
I would use -10 and 5. If I had the idea of
using exponents then it would look like this:
-10
number from the largest and then
Example: (3-9)(3)(7)
1.3-9=-6 2.-6(3)=-
18 3.-18(7)=-112
STRATEGIE FOR DEALING DOWN:
STRATEGIE FOR DEALING DOWN:
If all the numbers are negative, then some
If all the numbers are in a decimal,
dividing wouldn’t be your best bet of
getting the smallest number possible but
multiplying would. Same goes for
fractions. The reason why dividing a
decimal would get you a larger, is because
it is the same things as multiplying by a
whole number.
people think that you would add all of them to
get the smallest number. But does it get you
the smallest number? I decided that you
should use exponents the numbers to get the
smallest. Using exponents isn’t always going to
give you the smallest number but in some
cases, they do. But you should keep in mind
the exponent above the base because the
number has to be odd. When you multiply it
the base, the exponent determines if the
Example:
-Dividing by a decimal: 2/0.5=4
result will be positive or negative.
-Multiplying by a decimal: 2x0.5=1
Example: Even number: -5 to the power of 4
As a result, when dividing a decimal, the
quotient will be larger than multiplying a
decimal.
= -5x-5x-5x-5x-5= +725
0dd number: -5 to the power of 5 = -5x-5x5x-5x-5= -3625
4<1
Rules for Adding, Multiplying, Dividing, and Subtracting
positive and negative numbers:
If you are multiplying, then here are
some rules:
-Positive x Positive = Positive
If you are adding, then here are some rules:
-Positive - Positive = Positive, Zero, and Negative
-Negative – Positive = Negative, Zero and -
-Negative x Positive = Negative
Positive
-Positive x Negative = Negative
-Positive – Negative = Zero, Negative, Positive
-Negative x Negative = Positive
-Negative – Negative = Negative and Zero
If you are adding, then here are some
rules:
-Positive + Positive= Positive
-Negative + Negative = Positive, Negative,
If you are dividing, then here are some rules:
-Positive/Positive = Positive
- Positive/Negative = Negative
and Zero
-Negative/Positive = Negative
-Negative + Positive = Positive and Zero
-Negative/Negative = Positive
-Positive + Negative = Positive and Zero
How do negative exponents work?
What is order of operations? Why does it exist?
Order of operations is also known as P. E.M.D.A.S.
P =PARENTAHSES ( ) E = EPONENTS X M/D = MULTIPLICATION AND DIVISION
X OR / A/S =ADDITION AND SUBTRACTION + OR --
Order of operations exist because
How does commutative Properties of Addition and Multiplication help
you add and multiply rational numbers?
When it comes to commutative properties, order doesn’t matter. When
you are adding, and you switch the sentence around, the sum will be the
same. If you multiply, and you switch the equation around, the product will
be the same.
Example: Commutative property of addition: 5+6=11 6+5=11
Example: Commutative property of multiplication: 5x6=30 6x5=30
They help you with adding or multiplying with rational
numbers because rational numbers are basically decimals, fractions,
and integers. So, if you know what 3/4 x 6/4= 18/16 = 1 2/16 = 1
1/8, and then the next question is 6/4 x 3/4 commutative property of
multiplication kicks in. It helps you because since ORDER DOESN’T
MATTER, then if you switch it around, the equation will be the same
as the first and you can solve it like that. The answer will ALWAYS be
the same. That is why it’s so helpful. Same thing goes for addition.