Dear Parents, Grandma hopes she can finish the rest of the year with all your needs provided. Even though you may not carry out the day in lessons because it is Presidents Day, Grandma is still going to give you some lessons you can just carry the lessons throughout the rest of this years lessons. Grandma does not know if you conduct classes throughout the whole year, but she will be giving you only a little in the summer to do academically and ideas of fun things to do for the summer totally. Grandma wants you to keep up the good work of guiding the children in doing tasks and taking responsibility.
There is a great fear among parents of children forming relationships too soon and getting into trouble. Parents need to remember they were young once and even though there is chances of children getting into trouble; every person should obtain experiences as long as parents do the best guidance and direction that they can. Give each child the feeling that they are capable of doing the right things and that each parent lets their children know what things there are out there to harm them and how they can avoid them. Let them know what consequences are for each action. Also let them know that the world is with a lot of problems into today's age and that everyone is capable of mistakes because none of us are perfect. Just let them know that you feel they are very smart and can do the best they can to do the best they can. Let them know that they are loved and you will always be there for them if they might make a mistake. Also let them know that God loves them and forgives them in life also to the point he sent his only son to save them as long as they realize their mistakes, always love Jesus Christ, and make changes in their lives for the better.
Work on your tasks, Childrobotics, writing, words, alphabets, vocabulary, books assigned and reports, essay's, work they may need to finish especially on math papers. Do as much spelling as you can with your children, but you do not need to give them spelling like in the public schools. Just have them keep a record in a notebook or jotted in their journals of words to learn. Put them in sentences if you think of any. Be sure to find books as Dr. Sues books to learn sounds with. Cover various sounds each day or so, whenever you can.
some children going into 4th grade and up are beginning to learn about algebra. Some younger children are beginning to learn about multiplication and some are just beginning to learn to add and others are learning about place values. Others will be learning Geometry the next year.
The book that Grandma will give Algebra out of is called
Elementary Algebra for College Students by Allen R.
Angel 2004, 2000, 1996, 1992, 1988, 1985
Education, Inc. Grandma will call it Book (714). This book
will cover Real Numbers which any algebra starts with.
"Real Numbers" will cover Problem Solving ,Fractions, The Real Number system, Inequalities, Addition of Real Numbers, Subtraction of Real Numbers, Multiplication and Division of Real Numbers, Exponents, Parentheses, and the Order of Operations, Properties of the Real Number System.
The next unit will be "Solving Linear Equations and Inequalities" which will cover Combining Like Terms, The Addition Property of Equality, The Multiplication Property of Equality, Solving Linear Equations with a Variable on Only one side of the Equation, Solving Linear Equations with the Variable on Both Sides of the Equation, Ratios and Proportions, and Inequalities in One Variable.
The next unit will be "Formulas and Application of Algebra" coving Formulas, Changing Application Problems into Equations, Solving Application Problems, Geometric Problems, and Motion, Money, and Mixture Problems.
Unit 4 is "Exponents and Polynomials" with exponent, Negative Exponents, Scientific Notation, Addition
and Subtraction of Polynomials, Multiplication of Polynomials, and Division of Polynomials covered.
Unit 5 will be on "Factoring" covering Factoring a Monomial from a Polynomial, Factoring by Grouping,
Factoring Trinomials of the form ax² + bx + c, a=1, Factoring Trinomials of the form ax² + bx + c, a is not =1,Special Factoring Formulas and a General Review of Factoring, Solving Quadratic Equations Using Factoring, and Applications of Quadratic Equations.
Unit 6 is "Rational Expressions and Equations" covering Simplifying Rational Expressions, Multiplication and Division of Rational Expressions, Addition and Subtraction of Rational Expressions with a Common Denominator, Addition and Subtraction of Rational Expressions, Complex Fractions, Solving Rational Equations, Rational Equations: Applications and Problem Solving, and Variation.
Unit 7 is "Graphing Linear Equations" covering The Cartesian Coordinate System and Linear Equations in Two Variables, Graphing Linear Equations, Slope of a Line, Slope-Intercept and Point-Slope Farms of a Linear Equation, Graphing Linear Inequalities, and Functions.
Unit 8 is "Systems of Linear Equations" covering Solving Systems of Equations Graphically, Solving
Systems of Equations by Substitution, Solving Systems of Equations by the Addition Method, Systems of Equations: Applications and Problem Solving, and Solving Systems of Linear Inequalities.
Unit 9 is "Roots and Radicals" covering Evaluating Square Roots, Simplifying Square Roots, Adding, Subtracting, and Multiplying Square Roots, Dividing Square Roots, Solving Radical Equations, Radicals: Applications and Problem Solving, and Higher Roots and Rational Exponents.
The last unit of 10 is "Quadratic Equations" covering The Square Root Property, Solving Quadratic Equations by Completing the Square, Solving Quadratic Equations by the Quadratic Formula, Graphing Quadratic Formula, Graphing Quadratic Equations,and Complex Numbers.
Grandma will try to cover the other math concepts she pointed out above writing about this book. She will do her best to provide examples and Geometry to you that she can.
For today she will cover the first section of "Real Numbers" called Problem Solving.
In Problem Solving the first thing you will do is "Learn the five-step problem-solving procedure., then Solve problems involving bar, line, and circle graphs. Last you will learn to Solve problems involving statistics.
In the book, "we will be problem solving to real-life problems. The first things one must be able to do in
algebra is to express the problem in mathematical symbols. We will now give the general five-step
problem-solving procedure that was developed by George Polya and presented in his book How to Solve
It. You can approach any problem by following this general procedure.
Guidelines for Problem Solving
1. Understand the problem.
- Read the problem carefully at least twice. In the first trading, get a general overview of the problem. In the
second reading, determine (a)exactly what you are being asked to find and (b)what information the
- Make a list of the given facts. Determine which are pertinent to solving the problem.
- Determine whether you can substitute smaller or simpler numbers to make the problem more
- If it will help you organize the information, list the information in a table.
- If possible, make a sketch to illustrate the problem. Label the information given.
2. Translate the problem to mathematical language.
- This will generally involve expressing the problem in terms of an algebraic expression or equation. (We will explain how to express application problems as equations in Chapter 3.)
- Determine whether there is a formula that can be used to solve the problem.
3. Carry out the mathematical calculations necessary to solve the problem.
4. Check the answer obtained in step 3.
- Ask yourself. "Does the answer make sense?""Is the answer reasonable?" If the answer is not
reasonable, recheck your method for solving the problem and your calculations.
- Check the solution in the original problem if possible.
5. Make sure you have answered the question.
- State the answer clearly."
An algebraic expression used in step 2 sometimes just referred to as an expression, is a general term
for any collection of numbers, letters (called variables), grouping symbols such as parentheses ( ) or
brackets [ ], and operations (such as addition, subtraction, multiplication, and division). In this section we will not be using variables. We will discuss their use later.
Examples of Expressions are as follows:
3 + 4, 6(12 ÷ 3), (2)(7)
(In some problems it may not be possible or necessary to list every step in the procedure). In some of the examples the book uses, they use decimal numbers and percentages, so review procedures for adding, subtracting, multiplying, or dividing numbers, and using percentages.
"Example 1 Transportation Chicago's O'Hare airport is the busiest in the world with about 65 million
passengers arriving and departing annually. The airport express bus operates between the airport and
downtown, a distance of 19 miles. A particular airport express bus makes 8 round trips daily between the airport and downtown and carries an average of 12 passengers per trip (each way). The fare each way is $17.50.
a) What are the bus's receipts from one day's operation?
b)If the one-way fare is increased by 10%, determine the new fare.
a) Understand the problem--A careful reading of the problem shows that the task is to find the bus's total
receipts from one day's operation. Make a list of all the information given and determine which information is needed to find the total receipts.
Information Given Pertinent to Solving
65 million passengers arrive/depart annually no
19 miles from airport to downtown no
8 round trips daily yes
12 passengers per trip (each way) yes
$17.50 fare (each way) yes
To find the total receipts it is not necessary to know the number of passengers who use the airport or the distance between the airport and downtown. Solving this problem involves realizing that the total receipts depend on the number of one-way trips per day, the average number of passengers per trip, and the one-way cost per passenger. The product of these three numbers will yield the total daily receipts. For the 8 round trips daily, there are 2 x 8 or 16 one-way trips daily.
Translate the problem into mathematical language
receipts number of number of cost per
for one = one-way x passengers x passenger
day trips per day per trip each way
Carry out the calculations
= 16 x 12 x $17.50 = $3360.00
We could also have used 8 round trips and a fare of $35.00 per person to obtain the answer. Can you
Check the answer The answer $3360.00 is a reasonable answer based on the information given.
Answer the question asked The receipts for one day's operation are $3360.00.
b) Understand--If the fare is increased by 10%, the new fare becomes 10% greater than $17.50. Thus you need to add 10% of $17.50 to $17.50 to obtain the answer. When performing calculations, numbers given in percent are usually changed to decimal numbers.
Translate new fare= original fare + 10% of original fare
Carry Out new fare= $17.50, seems reasonable
= $17.50 + $1.75 = $19.25
Check The answer $19.25, which is a little larger than $17.50, seems reasonable.
Answer When increased by 10% the new fare is $19.25."
This is only one example but Grandma will have to give more problems tomorrow.
Three experiments from book (1) having to do with heat are as follows:
Pour some colored water into a bottle. Push a drinking straw through a hole bored in the cork so that
it dips into the water. Seal the cork with glue. If you place your hands firmly on the bottle, the water rises up
The air enclosed in the bottle expands on heating and presses on the water surface. The displaced water
escapes into the straw and shows the degree of heating by its position. You can fix a scale on the side of the
Roll paper napkin (not too salt material) into a tube and twist up the top. Stand it upright and light the tip.
While the lower part is still burning, the ash formed rises into the air. Take care! The air enclosed by the
paper is heated by the flame and expands. The light, balloon-like ash residue experiences a surprising
buoyancy because the hot air can escape, and the air remaining in the balloon becomes correspondingly
lighter. Very fine napkins are not suitable for the experiment because the ash formed is not firm enough.
Take an empty, corked wine bottle, push as long an aluminum knitting needle as you can find into the bottle
cork and let the other end project under slight pressure over the mouth of a second, uncorked bottle. Glue
a paper arrow on to a sewing needle, making sure that it is balanced, and fix it between the knitting needle
and the neck of the bottle. Place a candle so that the tip of the flame touches the middle of the needle and
watch the arrow.
The arrow turns quite quickly some way to the right because the knitting needle expands on heating like
other substances. With an ordinary steel knitting needle the arrow would only turn a little, because steel
only expands half as much as aluminum. Since the aluminum is longer as well, the difference is still
greater. The expansion is clearly visible in electricity power cables, which sag more in summer than in
winter. If you take the candle away from the knitting needle, the arrow moves back.
Grandma wanted to give some of the calendar history, but she will have to skip it till tomorrow.
To start giving the Bible out of Faith Alive Grandma wants to cover a few things out of John first.
In John 1:1-18 John writes about The Word Became Flesh. Faith Alive says in "Did You Know? 1:1
what is the "Word"? The "Word" is a special name for Jesus. It means that Jesus is the person who
reveals God, or tells us what God is like. The Bible says that Jesus existed forever and that he is God.
Read all of chapter 1. The next note that is written is Words to Remember 1:14 The Word became flesh
and made his dwelling among us. The next chapter to read is Jesus the Lamb of God. Read that chapter
and Did You know? 1:29 What does Lamb of God mean?
In Old Testament times lambs were offered as sacrifices when a person sinned. To call jesus the Lamb
of God meant that he would die as a sacrifice to take away our sins.
Read the rest of Chapter 1 and John 2:1-11 with a note pro the readers from Faith Alive of "Life In Bible
Times-Water Jars which is as follows
Water Jars-Water was stored in large stone jars and was used for washing and drinking. Jews at the time
of Jesus did much ceremonial washing of their hands before eating. These very large jars were the sort that this could be done.
Jesus asked it to be filled with water before he changed that water to wine."
This is all Grandma is giving for now. She will have more for Tuesday.