Here are some better directions and help for the problems in this section.

Alternate Instructions for Pg. 72 2-58 evens

Problems 2,4

Looking at the blanks and knowing how the distributive property works, what do you think need to go into the blank(s)? Be sure to look at the other side of the equals.

Problems 6-14

We did 6 in class. First we need to decide what numbers we could rewrite as an addition or subtraction problem that would make it easier to solve using mental math. Next, use the distributive property to multiply the number on the outside to the new addition or subtraction problem. Simplify it and then add or subtract the two numbers and you will get your answer.

Ex. 7(48)

7(50 - 2) *rewrite*

7(50) - 7(2) *distribute*

350 - 14 *simplify*

336 *add or subtract*

Problems16-26

Use the distributive property to make a problem simpler by working backwards, or factoring out what is shared. We did number 16 as an example in class.

Ex. 2(9) - 3(9) Identify the number that both terms are multiplied by. In this case it is 9.

9(2 - 3) Factor out the nine to the front of the parenthesis or *un-distribute*

9( -1) Now use order of operations and simplify what is inside the parenthesis.

-9 Multiply to get the answer.

Problems 30-40

Disregard the ones saying use models and just do as you were shown in class. We did the example today of 2(4x - 1).

Ex. 2(4x - 1) Identify the number on the outside of the parenthesis that you need to distribute. (2)

2(4x) - (2)(1) Distribute the number outside to be multiplied to all the terms on the inside. Keep the sign in the middle the same.

8x - 2 Multiply the terms together and you are finished.

Problem 42

Refer to the notes we took in class and decide which property fits what happens between the two sides of the equals sign.

Problems 44 & 46

These two problems are like problems 6-14. Pick out the numbers that need multiplied and use the same method to do them.

Problem 48

Look at what your friend wrote. Pick out what is wrong with his answer. Hint: look at your distributive property notes.

Problem 50-54

Be sure to refer to your notes from 2-1 on all of the properties. Which property lets you move things around? Which one is about adding zero? Multiplying by 1?

Problem 56

Put t into the correct spot and follow your order of operations.

Problem 58.

Write an equation to solve. Remember that deposits are adding money to your account. Withdrawals and writing checks are taking money out of your account. How much money do you have left in your account?

# Mrs. Geiger's Pre-Algebra

## Wednesday, September 22, 2010

## Tuesday, September 21, 2010

### Grades and Assingments

We tested on Thursday and Friday of last week. Overall, most students did rather well.

Friday, there was a simple review assignment given after finishing the test. It was pg. 61

3-42 multiples of 3.

On Monday we covered the basic properties of commutative, associative, and identity as they relate to mathematics. Each student should have detailed notes written in their notebook about this section that we all wrote in class.

Today we did section 2-2 on the distributive property and there was no given assignment. We will continue this lesson tomorrow.

Grade slips were passed out today. Those students who have below a C- will be referred to study hall to bring up their grades. These grade slips are due back signed by a parent.

Many students have questions about their grades. Many may say that they have a zero on an assignment but they know that they turned it in. This is probably because they forgot to put their name on their paper. I have a box for all of my no name papers that I receive. Students are welcome to search for their work before and after school and get the credit they deserve. Thanks!

Friday, there was a simple review assignment given after finishing the test. It was pg. 61

3-42 multiples of 3.

On Monday we covered the basic properties of commutative, associative, and identity as they relate to mathematics. Each student should have detailed notes written in their notebook about this section that we all wrote in class.

Today we did section 2-2 on the distributive property and there was no given assignment. We will continue this lesson tomorrow.

Grade slips were passed out today. Those students who have below a C- will be referred to study hall to bring up their grades. These grade slips are due back signed by a parent.

Many students have questions about their grades. Many may say that they have a zero on an assignment but they know that they turned it in. This is probably because they forgot to put their name on their paper. I have a box for all of my no name papers that I receive. Students are welcome to search for their work before and after school and get the credit they deserve. Thanks!

## Tuesday, September 14, 2010

### Chapter 1 Test on Thursday!

We will be having a test in pre-algebra on Thursday. We will spend tomorrow reviewing. A couple of worksheets have been sent home to help students prepare for the test. For extra practice, feel free to do homework questions from past sections and also to do the cumulative review at the end of the chapter. Good luck!

### Sorry!

I apologize to those of you who have been faithfully following the blog and that there has not been a new post all week. We covered 1-8, 1-9, and 1-10 in the past few days.

1-8 was an extension of the inductive reasoning by using patterns to solve problems. The assignment for this was an orange worksheet.

1-9 was a lesson about multiplying and dividing integers. The hardest concept is remembering when the outcome will be positive or negative. The assignment for this section is pg. 47 3-51 multiples of 3.

1-10 was about the coordinate plane and ordered pairs. The assignment for this section was pg. 52 2-30 evens.

I will try to do better about updating the blog daily.

1-8 was an extension of the inductive reasoning by using patterns to solve problems. The assignment for this was an orange worksheet.

1-9 was a lesson about multiplying and dividing integers. The hardest concept is remembering when the outcome will be positive or negative. The assignment for this section is pg. 47 3-51 multiples of 3.

1-10 was about the coordinate plane and ordered pairs. The assignment for this section was pg. 52 2-30 evens.

I will try to do better about updating the blog daily.

## Tuesday, September 7, 2010

### Lesson 1-7 Inductive Reasoning

Inductive reasoning is when you use clues and patterns to make a conclusion.

A conjecture is the conclusion that you make.

You can look at patterns whether they are pictures or numbers and use inductive reasoning to determine the rule that they follow. Here are a couple of examples you can try.

2, 4, 6, 8,...... What is the rule? What are the next 2 terms?

4, 3, 5, 4, 6, 5, 7....... What is the rule? What are the next 2 terms?

Not all conjectures are true. Sometimes we make a conjecture about something and later find out it is incorrect. If it is incorrect, there is a counter example to prove it.

Here is an example.

All birds can fly. This is incorrect.

A counter example of this conjecture could be an ostrich or a penguin. Both are birds, but neither of them can fly.

The homework for this section is pg. 38 2-30 evens.

A conjecture is the conclusion that you make.

You can look at patterns whether they are pictures or numbers and use inductive reasoning to determine the rule that they follow. Here are a couple of examples you can try.

2, 4, 6, 8,...... What is the rule? What are the next 2 terms?

4, 3, 5, 4, 6, 5, 7....... What is the rule? What are the next 2 terms?

Not all conjectures are true. Sometimes we make a conjecture about something and later find out it is incorrect. If it is incorrect, there is a counter example to prove it.

Here is an example.

All birds can fly. This is incorrect.

A counter example of this conjecture could be an ostrich or a penguin. Both are birds, but neither of them can fly.

The homework for this section is pg. 38 2-30 evens.

### Lesson 1-6 Subtracting Integers

I apologize for not having this post up earlier. We learned how to subtract integers. We learned how to model them, but we also learned the little tricks and rules that make it easier to remember how to do. The two rules we learned were these:

When subtracting a positive, it is the same as adding a negative. (Add the opposite.)

Ex. 6 - 9

We can rewrite it as an addition problem.

6 + (-9) = -3

We then can add as we learned in the previous lesson to get the correct answer.

When subtracting a negative, it is the same as adding a positive. (Add the opposite.)

Ex. 6 - (-9)

We can rewrite it as an addition problem.

6 + 9 = 15

Once again, now we can just add them together.

Homework for this section was a worksheet that had both addition and subtraction of integers on it. If you need an extra copy, be sure to ask me for one. Thanks!

When subtracting a positive, it is the same as adding a negative. (Add the opposite.)

Ex. 6 - 9

We can rewrite it as an addition problem.

6 + (-9) = -3

We then can add as we learned in the previous lesson to get the correct answer.

When subtracting a negative, it is the same as adding a positive. (Add the opposite.)

Ex. 6 - (-9)

We can rewrite it as an addition problem.

6 + 9 = 15

Once again, now we can just add them together.

Homework for this section was a worksheet that had both addition and subtraction of integers on it. If you need an extra copy, be sure to ask me for one. Thanks!

## 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

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

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