Equations

In the midst, of homeschooling the children are learning more about equations. Although, teaching them can be interesting to see what they can get right with working with the equations. Most people do not believe that we use equations in everything that we do in our life. We use equations for a variety of things. Telling time, distant from one place to another, cooking in the kitchen, plotting out a garden, and many other things.

Of course, the equations that we are working on are simple. However, if you are good with math these are not challenging enough. One of the equations we are working on today is

(3x^2y^6)^7
3^7(x^2)^7 (y^6)^7
2,187x^14y^42

Simple for those who understand math equations however, when you are teaching math equations you have to do it step by step for the children to learn the process of finding their answer without the help of a calculator.

3a^n (a^n + a^n-1)
3a^n × a^n + 3a^n × a^n-1
3a^2n + 3a^2n-1

Math can be fun, and easy to learn when you have the right person teaching you the ropes of the equations. Enjoying math is not easy for most people because they think they are always going to get the wrong answer. However, when you second guess yourself you will always get the answer wrong because of the second guessing.

Second Week of Biology Homeschool

The second week of biology and the questions keep coming. Of course, this is going to be an interesting subject for the children to learn. Looking forward to the outcome  because this is going to be a wonderful course. You have to make up your own questions and sometimes that is better in the long run.

1. Who was involved in refining the production of lenses and made microscopes satisfactory for simple scientific observations?

2. When did intensive work on cells begin?

3. Who are the two German investigators of the first clear enunciation of cell theory?

4. What is cell theory?

5. Were Schleiden and Schwann the first people to enunciate the principle of cell theory?

6. Who observed the first nucleus? What year?

7. Who was Robert Hooke? What did he study?

8. Who was responsible for the extension of cell theory? When?

9. Who did experiments to prove Virchow’s theory of biogenesis?

10. What are two components of cell theory?

11. How long is a single human nerve cell?

12. What is the diameter of a human red blood cell?

13. What is the diameter of an ostrich egg?

14. What is a solution?

15. What happens when the sand is no longer agitated?

16. What are the factors that cause changes in Sol and Gel? Name six.

17. What is a protoplasm?

18. What is plasma membrane?

19. What is a angstrom?

20. who concluded that the membrane consists of inner and outer layers of protein? What year?

22. How many angstroms is a whole membrane?

23. Movement of particles from one place to another is called?

24. What is free energy?

25. What is the movement of water through a semipermeable membrane?

26. What is osmotic pressure?

27. What is phagocytosis?

28. What is pinocytosis?

29. What is the primary wall?

30. What is Pectin?

31. What is the middle lamella?

32. What is the secondary wall?

33. What is lignin?

34. What are chromosomes? What composes them?

35. What are genes? What do they do?

36. _________________are dark-staining, generally oval bodies.

37. Who developed endoplasmic reticulum? What year?

More to come with this chapter! They needed the book to do their schoolwork……

Evaluating Algebraic Equations

When we evaluate algebraic equations we substitute the variables with real numbers. When you know the value of the variables within the equation it becomes easier to find the correct answer that you are seeking.

For example: If you have an equation like w + c  when W = 8 and C = 9 you would replace the variables w and c with 8 and 9. You would then end up with 8 + 9 simple enough when you are just learning about algebra.

Another example would be 5xz if you put the numbers 8 and 9 into the equation you would end up with 5(8)(9); so in order to evaluate this equation you would first multiply 5 and 8 to get 40 then you would multiply 40 and 9 to come up with your final answer of 360.

Now, if y = 8 and t = 6 in the following equations what do you think the answer would be?

in y – t

and

in 8yt

By putting your numbers into the equation y – t you should come up with the equation 8 – 6 = 2; and in 8yt you should come up with  8(8)(6) = 64(6) = 384 you are just multiplying each of the numbers to come up with the end result.

Evaluating algebraic expressions is an easy concept to learn once you understand the variables, and insert the real numbers into your equation.

Here are some to evaluate

If a = 5, t = 7, c = 6, and d = 3

1. 6a + 9t

2. 8c + 6d

3. a3 + 7t

4. 8(a + d)

5. 15(c + a)

Another Great Year of Homeschooling

Just a bit of information to my reader’s! My children have passed mom’s exams and will head to the 10th grade next school year! They are excited and ready for the upcoming school year. It has turned out to be a long road but they did well.

Next, year they will be doing algebra II, Biology, Computer programming, American Literature, and History of the American Nation. Of course, they are all excited about all of the classes that they will take in the upcoming year.

A very proud moment to see that I have done my job as a mother, and teacher to my children. I am very glad that I chose to homeschool four years ago. It has turned out to be the best experience of my life.

Looking forward to the upcoming year as we learn more about a variety of things. I believe that the hardest part for them this year was English Literature however, they passed with no problems. I also learned quite a bit from teaching them in English Literature.

Algebra of course, they were surprised when I could solve the problem in my head without working it out on paper. They are getting to where they can do some problems like that but I told them that it takes time to be able to look at a problem and solve it without working it out.

In the month of May I will not be writing as much! I have to get final exam’s ready for the children. Homeschooling is not an easy task and they come first. I will try to post a few things here and there throughout this month. However, making sure that the children pass their final exams is the most important thing to me right now.

I know that everyone will understand! I am working on some articles right now but they are not finished and not ready to publish.

So here is hoping that the children pass their final exams and move onto the 10th grade!!!!!

Zero

The zero is used to determine the positional value of a certain number within the mathematics world and to indicate the absence of quantity. The zero is needed in the positional number system that is used by people today. When you think about the position of any number in the positional numeral system it determines the value of that position. For example, in 567 the 5 stands for five hundred, and the 6 stands for six tens (sixty) and the 7 stands for seven ones or six units. In order to write the number five hundred six dollars you would have to include a zero to show that there are no tens in the number.

In school you learn that when you add a number to zero you get the original number. When you subtract you also get the original number. Multiplying a number by zero will automatically give you a zero. By dividing a number by zero it becomes indefinable. Yes it is just common sense to know these things.

It is believed that the Maya Indians invented the concept of Zero before 300 A.D. Several years later the Hindus developed the concept of the zero independently a few hundred years later after the Maya Indians did.

This ends the A to Z challenge it has been  a fun experience, and I am looking forward to the next challenge of writing. Adding more articles to my blog for the viewer’s to enjoy.

Basic Algebra

In actual Junior high school she was never good at math it was not until she reached her Associate’s degree that she started enjoying math. Your associate’s degree is nothing more than rehashing the things that you learned in Junior high school and high school.

To many this is just common sense however, to other’s who have math anxiety, and issues understanding the concepts of basic algebra this might come in handy for them to understand the concepts of learning such algebraic expressions.

Basic algebra is using the same methods like addition, subtraction, multiplication, and division. However, algebra also uses letters to represent numbers in the algebraic equations.

x + y would mean the sum of x and y equals a certain number

For example: The sum of a and 5 would be written as a + 5

The sum of y and 8 would be written as y + 8

If L plus W it would be written as L + W

So in writing with symbols you could use the following examples to practice writing algebraic equations in addition.

The sum of x and 5    x + 5

9 more than Y     9 + y

a plus b     a + b

Z increased by 7   z + 7

Some problems for you to practice with on your own:

1. The sum of x and y

2. t plus z

3. b plus 9

4. The sum of b and n

5. 15 more than y

6. x increased by 5

7. 9 more than k

8. 100 increased by z

When you learn the words that are used within the algebraic equations it becomes easier to learn how to solve the problem to obtain the right answer.

Subtraction in Algebra

Subtraction is almost the same as addition but the words that you will see for subtraction our a little different.

Some writing expressions that would indicate subtraction would include:

w minus t would be written   w – t

w decreased by 9 would be written  w – 9

9 less than b would be written 9 – b

The difference of t and 15 would be written  t – 15

Some of the problems that you will see throughout your experience in algebra may not make sense to you in the beginning and learning the terms is something that you need to practice so that you do not have issues with the problems on tests or quizzes.

Therefore, here are some problems for you to work on your own:

1. 8 less than p

2. 10 less than t

3. y decreased by w

4. d minus l

5. y minus 9

6. z decreased by 7

7. c decreased by 4

8. t less than 15

I hope that you are still with me here in learning algebraic equations with addition and subtraction. Therefore, we will discuss multiplication, and division.

Multiplication in algebra

There are a variety of ways to write algebraic equations when you are using the multiplication symbol.

a ∙ b

(a)(b)

ab

These examples indicate that the product of a and b or a times b

Now, the words that you might see in multiplication expressions would include:

7 times b could be written like  7 ∙ b   (7)(b)   7b

twice c is written as 2c

6 more than the product of 8 and x would be written like 8x + 6

The product of 8, t, z would be written like 8tz

The product of 6 and the sum of x and w would be written as 6(x + w)

Therefore, here are some problems that you can work on your own.

1. t times z

2. The product of r and w

3. The product of 9, c, and d

4. The sum of twice t and z

5. The product of 8 and the sum of c and t

6.  9 times a

7. The product of 10 and the sum of z and r

8. twice the sum of t and z

Once, you learn the words that are involved with multiplication expressions it becomes easier to spot what you need to do to solve the algebraic equations.

Division in Algebra

w/t means that w divided by t or the quotient of w and y

Therefore, if you see these terms within an algebraic expression you need to divide the numbers.

y divided by 8 is written as y/8

the quotient of z plus t divided by 9 would be written like     z + t/9

The sum of r plus z divided by the difference of w minus a would be written like                   r + z/w-a

Furthermore, when you are just learning algebra and the meanings behind the expressions it becomes easier as you are learning. The problems become easier as you go along because you are understanding the meanings behind the words in the problems.

Therefore, here are some problems for you to work on your own.

1. w divided by 15

2. The quotient when x is divided by 9

3. The sum of s and 6 divided by 3

4. The difference of t and q divided by 8

5. The sum of t and x divided by the difference of a and 6

6. The difference of  y minus t divided by 4

7. The quotient of c plus r divided by 9

8. The sum of y and 5 divided by the difference of y and 5

Within these examples, and problems I hope that you have understood some of the information that I have provided. Homeschooling children can be a fun experience or it can be a total flop. Understanding the information that is before you is the main key to succeeding in learning algebraic expressions.

More to come! The problems will get more complex but I believe that this type of information is good for our children to understand what they are learning in Basic algebra….

Any questions feel free to email me at tammyhopkinson@aol.com