Math 6 Honors Periods 6 & 7 (Thursday)

Subtracting Integers 11-3

Isn't it true that if you want to have a little less negativity, you just need to add a little positiveness!! What works in life-- works in math as well.


Rule

For all integers a and b, a- b = a + (-b)

Instead of subtracting-- ADD THE OPPOSITE

4 - (-5) = 4 + +5 = 9

We used Algebra tiles to prove this using Zero Pairs

+1 - 1 = 0 ( ZERO PAIR)

-3 - (-8) = - 3 + +8 = 5

5 - (-5) = 5 + + 5 = 10

-6 - -6 = -6 + + 6 = 0

Algebra Period 3

Using Equations that Factor 6-9

Word Problems

Problem Solving Guidelines

Phase 1: Understanding the problem
Ask yourself:

What am I trying to find?
What data am I given?
Have I ever solved a similar problem?

Phase 2: Develop and carryout a PLAN

Ask yourself:

What strategies might I use to solve the problem?
How can I correctly carry out the strategies I selected?

Phase 3: Find the ANSWER and CHECK

Ask Yourself:

Does the proposed solution check?
What is the answer to the problem?
Does the answer seem reasonable?
Have a stated the answer clearly? ( labeled??)


Practice translating some of these word problems:

The product of one more than a number and one less than the number is 8.
Find the number.

Start with a let statement. It can be as simple as
Let x = the number.

the product... means it will be a multiplication problem
one more than a number x + 1
one less than the number x - 1

so (x +1)(x- 1) = 8

in order to solve you must use FOIL or the box method
but just looking at ( x + 1) (x -1) you know that is the difference of 2 squares... so
x² - 1 = 8 move the eight to the other side setting the equation equal to 0

x² - 9 = 0 and now it is also the difference of two squares or
(x-3)(x+3) = 0

so x - 3 = 0 and x + 3 = 0 so x = + 3 OR x = -3



The square of a number minus twice the number is 48. Find the number

Let x = the number

the square of a number x²
minus twice the number -2x

so x² -2x = 48

again it becones x² -2x - 48 = 0

factor and you get (x -8)(x+6) = 0 Using the principle of Zero products
x = 8 or x = -6

Pre Algebra Periods 1, 2, & 4

Dividing Powers with Like Bases

m⁸
___ = m ^{8 - 5} = m³
m⁵


m³
__ = m ^{3 - 5} = m^-2
m⁵


1
__

m²




5⁶
_____ = 5 ^{6 - 8} = 5^-2 =
5⁸


1
__
5²



1
__

25

b³
__
b⁹

written without a fraction bar is

b^3-9 = b ^-6

Any number raised to the ZERO POWER is equal to 1

PROOF:

aⁿ
____
aⁿ

= 1 but it also equals a^n-n or a⁰
for every a , except a cannot equal zero!!

Math 6 Honors Periods 6 & 7 (Tuesday & Wednesday)

Negative Numbers 11-1

On a horizontal number line we use negative numbers for the coordinates of points to the left of zero. We denote the number called ‘negative four’ by the symbol -4. The graphs of 4 and -4 are the same distance from 0—but in opposite directions. Thus they are opposites. -4 is the opposite of 4.

The opposite of 0 is 0

Absolute Value is a distance concept. Absolute value is the distance of a number from 0 on a number line. The absolute value of -4 is 4. l-4l = 4

The absolute value of 5 is 5. l5l= 5

Counting numbers: 1, 2, 3, 4, ….

Whole numbers 0, 1, 2, 3, 4….

Integers are whole numbers and their opposites.

…-4, -3, -2, -1, 0, 1, 2, 3, 4….

The opposite of 0 is 0.

The integer 0 is neither positive nor negative.

The farther we go to the right on a number line--- the bigger the number. We can compare two integers by looking at their position on a number line.

if x <0>

Adding Integers 11-2

Rules: The sum of two positive integers is a positive integer.

The sum of two negative integers is a negative integer.

So- if the two numbers have the same sign, use their sign and just add the numbers.

-15 + -13 = - 28 -10 + -4 = -14

Rules: The sum of a positive integer and a negative integer is :

POSITIVE… IF the positive number has a greater absolute value

NEGATIVE… IF the negative number has a greater absolute value

ZERO… IF both numbers have the same absolute value

30 + -16 … ask yourself the all important question… “WHO WINS? in this case the positive and then ask “BY HOW MUCH?” take the difference so 30 + -16 = 14

14 + - 52… “WHO WINS?” the negative… “BY HOW MUCH?”

38 so 14 + -52 = -38

(-2 + 3) + - 6 you can work this 2 ways

(-2 + 3) + - 6 = 1 + -6 = -5 or

using all the properties that work for whole numbers

Commutative and Associative properties of addition

can change expression to (-2 + -6) + 3 or -8 + 3 = -5 you still arrive at the same solution.