Monday, August 30, 2010

Lesson 1-5 Adding Integers

Yesterday we talked about integer opposites and how they are the opposite signs of each other, such as 3 and -3. Today we will learn about the term additive inverses. This is just another name for the opposite. The rule states that when you add two opposites or additive inverses together, you get zero. Let's see if this is true.

Ex. 3 and -3

3 + -3 = 0

This is true. It is also the same if we were to use variables such as x.

x + (-x) = 0

When we add one negative to one positive, we get what is called a zero pair.
In a way, they cancel each other out.


There are a couple of rules you need to remember when adding integers. Since integers can be either positive or negative, it is very important that we follow the rules with their signs.

When adding integers of the same sign, the sum of two positive integers is positive. The sum of two negative integers is negative. When they are different signs, you can find the difference of their absolute values. The sum has the same sign of the integer with the greater absolute value.

Ex.

(-2) + (-5)

Since they both have the same sign, we just add them together and they keep the negative sign.
The answer to this example would be (-7).

Ex.

(-12) + 8

Since they are of different signs, we take the absolute value of each one and then subtract the smaller one from the larger one.

12 - 8 = 4

Now, since the one with the larger absolute value was -12, our answer will still have to be negative. So the answer to this example is -4.

We will discuss this more in class.

Homework for this section is Pg. 26 14-50 evens

Lesson 1-4 Integers and Absolute Value

On Monday the students received their books that they are to keep at home in order to finish assignments and study. They will not need to bring these back until the end of the school year.

Integers are any number that is a reduced non-decimal/fraction number. They can be both positive and negative. I like to refer to them as "pretty numbers" because they are the kind that we like working with most of the time.

Absolute value is the distance a number is away from zero. The absolute value will always be positive.

We covered this in class, but the idea is very simple. Whenever a number or expression is within the absolute value symbols, the outcome will always be positive.

The homework for this section was Page 19, 12 -50 evens, 54, 58, and 63-68 all.

Thursday, August 26, 2010

Lesson 1-3 Evaluating Expressions

We already learned about what expressions are. We will now learn how to evaluate expressions. All this means is to use a value or number in place of a variable and solve.


Ex. 1 Evaluate 2y - 3 when y = 4

We plug in 4 where the y is in the expression. From there you must use the order of operations to solve.

2(4) - 3

8 - 3

5


Some of the problems may get more intense as more variables are added.

Ex. 2

Evaluate 2a + 4b -8 when a = 4 and b = 7

You just need to make sure that you place the right numbers in for the correct variables

2(4) + 4(7) - 8

8 + 4(7) - 8

8 + 28 -8

36 -8

28

You can also use this to solve story problems. We will learn more in class tomorrow.

Here is a copy of the assignment.

Evaluating Expressions

Tuesday, August 24, 2010

Thursday Lesson 1-2 Order of Operations

On Thursday we will start with the order of operations. For a fun way to remember the order of operations, you might want to memorize one of the following phrases.

Please Excuse My Dear Aunt Sally

Penguins Eat Many Donuts After School

Parenthesis
Exponents
Multiply and Divide (left to right in the order they appear)
Add and Subtract (left to right in the order they appear)

In mathematic equations, it is important to ALWAYS remember these important steps when solving any equation.

Here is a fun video to help you remember the order of operations.

Order of Operations Video


Here is an example:

(2 - 3*4) - 2(72/8) + 7*2 - 6

First, we do what is inside of the parenthesis. The order of operations still applies inside the parenthesis. In this set we must do the multiplication first.

(2-12) - 2(9) + 7*2 - 6

Now we have done the multiplication inside the parenthesis, we can finish off the other operations inside of the parenthesis.

6 - 2(9) + 7*2 - 6

Now we move on to exponents. Since there are no exponents in this equation, we will move on to the next step which is multiply and divide left to right.

6 - 18 + 14 - 6

The last step is to add or subtract in the order they appear left to right.

-12 + 14 - 6

2 - 6

-4

The final answer to this equation is -4.

You will use the order of operations throughout your math classes through high school. This is a very important concept to get down. Be sure to practice as much as you need to.

Sunday, August 22, 2010

Lesson 1-1 Variables and Expressions

Today we will begin actually learning math. No more testing!!! (at least for a little while) We will be learning about how to use variables and expressions.

Variables and expressions are the basic building blocks of algebra. It is very important to understand these key concepts as we move on into a little higher math.

Vocabulary:

Variables: these are the symbols such as x, y, or any other letter or picture we use to express a number that we do not know the value of. We call them variables because they could mean many different numbers

Expressions: these are the mathematical representations of a sentence dealing with values.

Numerical Expressions: these are expressions that only involve numbers

Variable Expressions: these are expressions that involve both variables and numbers


It is important that we can change these sentences into expressions and expressions into sentences. It is very hard to apply them into every day life if you don't know how to use them.

Here is an example of turning a sentence into a numerical expression:

Ex.1 5 groups of 7 and 2 more

In math, we use symbols such as +, -, *, and / to show what we are trying to say with words.

There are key words that allow us to understand what we need to do. In the example above, "groups of" lets us know we are talking about multiplication and the word "and" and "more" tells us that we need to add.

5 groups of 7 and 2 more

Our numerical expression would be this:

5*7 + 2


We can do the same thing with a variable expression. we just have to use a variable in place of a number.

Ex. 2. one less than twice the value of b

Once again, we pick out the key words but we also pick out the variable. In this example, b will be the variable because we do not know what b is. The key words from this is " less" meaning to take away or subtract, and "twice the value" meaning that it is multiplied by 2.

One less means minus one. Twice the value of b tells us that b is multiplied by 2. If we put this together mathematically it would look something like this.

2b -1

We will have lots of practice with this tomorrow.

Here is the homework worksheet for Wednesday.

Variables and Expressions

Friday, August 20, 2010

I know they aren't everyone's favorite thing to do, but we will be testing for the next couple of days to get a benchmark of where the students will be starting their year off in math. We will use these scores to calculate the growth of each student over the course of the year.

Parents: If you could make sure that your child gets a good breakfast before coming to school, this will help them to focus better on these tests. Thank you!

Tuesday, August 17, 2010

Welcome to Mrs. Geiger's Pre-Algebra Class!

I am so excited to start this school year. We will learn a lot and have fun this year in Pre-Algebra. Below you can find a link to the course disclosure for this class. I will also be handing these out the first day of class. There is also a link to my classroom procedures. We will be reviewing both of these the first day of class.

Algebra Course Disclosure
http://bit.ly/bh0Qyd

Mrs. Geiger's Classroom Procedures
http://bit.ly/9xaIrO

See you in class!