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?
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
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.
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
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.
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
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!
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!
Algebra Course Disclosure
http://bit.ly/bh0Qyd
Mrs. Geiger's Classroom Procedures
http://bit.ly/9xaIrO
See you in class!
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