Consider Supplemental Math Programs For Children

Parents of school-aged children might want to think of giving their children an enduring holiday gift this year: enrollment in a supplemental mathematics program. While it can cost anywhere from $80 to $110 a month, the results of practicing mathematics nearly daily is rewarding to both students and parents. In fact, parents might be even bigger recipients of this gift than their children. While their children gain self-esteem and confidence, the parents very likely will feel a sense of relief and pride in their children's accomplishment.

Singapore, Saxon and Kumon are three popular such programs. Many home-school practitioners use the first two, and Kumon, which involves daily practice and some tutoring, is popular with parents who feel their schools might be letting them down.

Dan Kimura, Ph.D., a senior professor of computer science and engineering at Washington University in St. Louis, opened St. Louis' first Kumon center in 1984, in large part because of his disappointment in the math education that his sons were getting. Mathematics is a major foundation of computer science, and Kimura, whose specialty is software programming, took action.

Begun in Kimura's hometown, Moriguchi, Japan, in 1958 by the late Toru Kumon, a math teacher who invented it to help his sons, Kumon math has more than four million students enrolled worldwide in 43 countries, nearly 180,000 in the United States. The method stresses repetition, speed, accuracy, individual pace, hard work and goal orientation in teaching mathematics.

Finding their level, then advancing

Students begin at a comfortable learning level, having been tested to determine that level, working with paper and pencil on series of calculations devised to reinforce what they learn; they master a learning phase at their own pace, pass a timed test and go onto another level. They do their problems at home daily for 15 to 30 minutes and meet weekly with their Kumon instructors for a half hour to 45 minutes. Gradually, after much positive reinforcement, Kumon practitioners gain self-confidence and, if they stick with the program, their mathematics progress invariably improves greatly, said Kimura.

Kimura said the reason that many parents are seeking supplemental help for their children in mathematics is the American method of teaching and the contents taught.

"The philosophy in American schools is a bottom-up approach, where the basic assumption is that every child has the innate ability to learn, the purpose of education is to help kids grow, that the direction they take is rooted in their DNA and that cannot be altered, and that teachers and parents should facilitate this growth process," said Kimura. "There is a sense that you can't force students to learn, that it stifles creativity. The best a teacher can do is to suggest that students learn certain things, but students shouldn't be forced."

What's missing, Kimura said, is the concept of training.

"The Kumon method is based on training, and is a top-down approach that stresses achieving goals," he said. "The process of practice and training is very painful. Top-class athletes and musicians will tell you that, too. Kids may not like it, but kids don't see the goals. They do, however, feel the satisfaction of achieving a goal. Parents are the immediate beneficiaries of Kumon math. They see the goals, and they see the progress."

Kimura runs two suburban Kumon math centers, one in a well-to-do suburb that services 350 students. A newer one in a blue-collar suburb, where schools have lost accreditation from No Child Left Behind, has about 60 students.

Thinking vs. knowing

Kimura said that there are two stages in acquiring knowledge: thinking and knowing. For example, 3+2=5. Students trained in Kumon math or exposed to the training concept in another context, once they are in the knowing stage, know that automatically. In contrast, he said the way that the simple calculation is taught in schools today is to attach icons, such as apples, to the numbers so that students supposedly grasp the concept.

"From the beginning, American students are exposed to the applications of mathematics," Kimura said. "In my humble opinion, that is not teaching mathematics, rather the applications of mathematics. The philosophy in Kumon is that you have to learn mathematics before applying it."

The transition to the knowing stage is speed, Kimura said, calling it perhaps the most vital tenet of the method.

"The Kumon method stresses the syntax of mathematics, not the semantics, which is opposite of the way mathematics has been taught in America for several decades," said Kimura. "In the schools today, learning revolves around student-centered curricula: the teacher creates a social environment that stresses education, citizenship and self-esteem, which are, indeed, worthy learning components. From this environment, the student is expected to construct his own body of knowledge. But this is like teaching a child to play tennis by telling him to create his own method. It de-emphasizes the concept of training.

"If you do not know how to read, write and compute, how can you construct your own body of knowledge? More and more parents and teachers are beginning to see that learning cannot be achieved without training."

With Kumon, the basics become as automatic as a piano player practicing the scales, laying the foundation for higher level reasoning skills.

Kumon parents marvel over improved attention spans, mathematics grades, test-taking skills and overall attitude of their children. It's not just for remedial students, either. Kimura says nearly 45 percent of his Kumon students are performing well beyond their grade levels. "It's not uncommon for elementary school children to advance into algebra and trigonometry with the Kumon method," he said.

Some even take it to prepare for the SAT and ACT tests.

Note : Nah, bagimana dengan anda...?

Taket from : www/sciencedaily.com

Why Women Shy Away From Careers In Science And Math

Girls steer away from careers in math, science and engineering because they view science as a solitary rather than a social occupation, according to a University of Michigan psychologist.

"Raising girls who are confident in their ability to succeed in science and math is our first job," said Jacquelynne Eccles, a senior research professor at the U-M Institute for Social Research (ISR) and the U-M Institute for Research on Women and Gender.

"But in order to increase the number of women in science, we also need to make young women more interested in these fields, and that means making them aware that science is a social endeavor that involves working with and helping people."

Eccles gave an invited address on how parents and teachers influence children's academic and career choices April 9, 2005, in Atlanta at the biennial conference of the Society for Research in Child Development.

For the talk, she drew upon data from decades of research, funded by a variety of agencies and foundations, including the National Science Foundation and the National Institute of Child Health and Development. One of the studies Eccles used for the analysis was the Michigan Study of Adolescent and Adult Life Transitions, a longitudinal study she started in 1983 that has followed approximately 1,200 predominately white, working-class young men and women from early adolescence into adulthood. The last interviews were conducted in 2002 when participants were 30 years old.

In 7th-grade, the occupational aspirations of girls had little to do with their abilities as indicated by their grades and the opinions of both their parents and their teachers, Eccles and colleagues found. The girls' perception of the career potential of advanced or honors math and science classes in high school was a stronger predictor of their selection of such courses than was their actual ability in those subjects.

Eccles and colleagues have repeatedly found that parents provide many types of messages to daughters that undermine both their daughters' confidence in their math and science abilities and their interest in pursuing careers in these fields.

Even though girls got better math grades than boys, parents of daughters reported that math was more difficult for their child than parents of sons. "Parents of daughters also said their girls had to work harder to do well in math than parents of sons, even though teachers told us this was not true," she said.

Girls said that they worked harder in math than in English, and parents reported that is true, too. But student time diaries told a different story, with boys and girls both reporting that they spent more time on language arts than on math.

"Parents also gave very different reasons for the math success of girls and boys," Eccles said. "Parents of boys rated talent and effort as equally important, while parents of girls said hard work was much more important than math talent."

Eccles urged teachers to tell parents that their daughters are talented in math and science, and to provide girls and their parents with vocational and intellectual reasons for studying math or science.

Eccles and colleagues also analyzed gender differences in college majors and occupations, finding that sex differences in general self-concepts and values at age 20 had a long-term influence on the college courses and jobs young men and women picked.

Young women were more likely than young men to place a high value on occupations that permitted flexibility and did not require them to be away from their family. The women also valued working with people. Even though young women had higher college GPAs than young men, young men were more likely to have a higher opinion of their abilities in math and science, and in their general intellectual abilities. They were also more likely to value jobs that required them to supervise other people.

"In addition to improving the confidence of girls, we need to show them that scientists work in teams, solving problems collaboratively. And that as a result of their work, scientists are in a unique position to help other people.

"We as a culture do a very bad job of telling our children what scientists do. Young people have an image of scientists as eccentric old men with wild hair, smoking cigars, deep in thought, alone. Basically, they think of Einstein. We need to change that image and give our children a much richer, nuanced view of who scientists are, what scientists do and how they work."

Taken from : www/sciencedaily.com

Calculators Okay In Math Class, If Students Know The Facts First, Study Finds

Calculators are useful tools in elementary mathematics classes, if students already have some basic skills, new research has found. The findings shed light on the debate about whether and when calculators should be used in the classroom.

“These findings suggest that it is important children first learn how to calculate answers on their own, but after that initial phase, using calculators is a fine thing to do, even for basic multiplication facts,” Bethany Rittle-Johnson, assistant professor of psychology in Vanderbilt’s Peabody College of education and human development and co-author of the study, said.

The research is currently in press at the Journal of Experimental Child Psychology and is available on the journal’s Web site.

Rittle-Johnson and co-author Alexander Kmicikewycz, who completed the work as his undergraduate honors thesis at Peabody, found that the level of a student’s knowledge of mathematics facts was the determining factor in whether a calculator hindered his or her learning.

“The study indicates technology such as calculators can help kids who already have a strong foundation in basic skills,” Kmicikewycz, now a teacher in New York City public schools, said.

“For students who did not know many multiplication facts, generating the answers on their own, without a calculator, was important and helped their performance on subsequent tests,” Rittle-Johnson added. “But for students who already knew some multiplication facts, it didn’t matter – using a calculator to practice neither helped nor harmed them.”

The researchers compared third graders’ performance on multiplication problems after they had spent a class period working on other multiplication problems. Some of the students spent that class period generating answers on their own, while others simply read the answers from a calculator. All students used a calculator to check their answers.

The researchers found that the calculator’s effect on subsequent performance depended on how much the students knew to begin with. For those students who already had some multiplication skills, using the calculator before taking the test had no impact. But for those who were not good at multiplying, use of the calculator had a negative impact on their performance.

The researchers also found that the students using calculators were able to practice more problems and had fewer errors.

“Teachers struggle with how to give kids immediate feedback, which we know speeds the learning process. So, another use for calculators is allowing students to use them to check the answers they have come up with by themselves, giving them immediate feedback and more time for practice,” Rittle-Johnson said.

And, for many of the students, using calculators was simply fun.

“Kids enjoyed them. It’s one way to make memorizing your multiplication facts a more interesting thing to do,” Rittle-Johnson said.

“So much of how you teach depends on how you market the material – presentation is very important to kids,” Kmicikewycz added. “Many of these students had never used a calculator before, so it added a fun aspect to math class for them.”

“It’s a good tool that some teachers shy away from, because they are worried it’s going to have negative consequences,” Rittle-Johnson said. “I think that the evidence suggests there are good uses of calculators, even in elementary school.”

Rittle-Johnson is an investigator in the Learning Sciences Institute and the Vanderbilt Kennedy Center for Research on Human Development.

Note : Why we make consider to allow our students use calculator as a help-tool in counting...?

Taken from : www.sciencedaily.com

Full-day Kindergarteners' Reading,

Children in full-day kindergarten have slightly better reading and math skills than children in part-day kindergarten, but these initial academic benefits diminish soon after the children leave kindergarten. This loss is due, in part, to issues related to poverty and the quality of children's home environments.

Those are the findings from a new study by researchers at the University of Pittsburgh and Loyola University Chicago. The study sheds light on policy discussions as full-day kindergarten programs become increasingly common in the United States.

Using data on 13,776 children from the Early Childhood Longitudinal Study--Kindergarten Class of 1998-1999, a study of a nationally representative group of kindergartners, the researchers measured children's academic achievement in math and reading in the fall and spring of their kindergarten and first-grade years, and in the spring of their third- and fifth-grade years. The researchers also looked at the type and extent of child care the children received outside of kindergarten, the quality of cognitive stimulation the children received at home, and the poverty level of the children's families.

Overall, the study found that the reading and math skills of children in full-day kindergarten grew faster from the fall to the spring of their kindergarten year, compared to the academic skills of children in part-day kindergarten.

However, the study also found that the full-day kindergarteners' gains in reading and math did not last far beyond the kindergarten year. In fact, from the spring of their kindergarten year through fifth grade, the academic skills of children in part-day kindergarten grew faster than those of children in full-day kindergarten, with the advantage of full-day versus part-day programs fading by the spring of third grade. The fade-out can be explained, in part, by the fact that the children in part-day kindergarten were less poor and had more stimulating home environments than those in full-day programs, according to the study.

"The results of this study suggest that the shift from part-day to full-day kindergarten programs occurring across the U.S. may have positive implications for students' learning trajectories in the short run," notes Elizabeth Votruba-Drzal, assistant professor of psychology at the University of Pittsburgh and the study's lead author. "They also highlight that characteristics of children and their families play noteworthy roles in why the full-day advantages fade relatively quickly."

http://www.sciencedaily.com/releases/2008/07/080715071444.htm

Student Motivation

Some students study because they do well with their marks or because they like learning. Many more become cynical about the value of education. How do we help them?

An advisor should not give direct advice. The advisor instead offers open or multi-choice problems for others, interested parties, students, sons or daughters, to solve. Then they have a say in what to do. No one likes to be told.

Here are a few questions or problems for your teen to consider.

D What to do in School and Why
E. How to Study Mathematics

While some teenagers may skip the terrible teens and remain polite and serious, the terrible teens arrive sooner or later for most. During that period parents can do no right. And during that period if not before, school may become less attractive. Elementary students may be motivated by the notion that school attendance helps them grow-up or mature, but after several years of schooling from ages 6 to 13 say, school loses it appeal. It is compulsory, parent and teachers may not be say clearly why school is necessary except for bureaucratic need for a high school graduation as a ticket to further studies if not employment.

Compulsory instructions may seem pointless for some students. The question of why go or why stay does not have a clear nor immediate answer. The reward if any lies in the future.

One way to motivate students is to say that studying is a job and to support that view with pay or pocket money for performance and attitude. That is, students could be given an immediate reward for their effort. (As an instructor, I would not object to informing students that their pay in my class depends on their work habits and work presentation - In the presence of a demanding and rigourous curriculum, students may not see point of the long preparation. Some way to get students to behave in class with motivation would be welcome.

My subject properly taught can be rather dry despite efforts on my part to lighten the subject and provide a context for it. Kid who lack motivation slow learning for themselves and will sooner or later not cooperate in their own education,. and may even rebel.

Students in the past and today have been expected to bring their own motivation. That motivation may be inherited from parents. Students with motivation, regardless of source, will go further than students with out. The will to learn is important.

Teachers and school may provide encouragement. Instruction in not leading to definite ends, but in leading to general ends cannot say to a student in concrete terms why he or she should work at their studies and take those studies seriously. General statements of the importance of education may lack specifics. So education itself may mean following a dream or path with no definite aims nor ends. And in those circumstances, loss of interest in school may be a sign of intelligence. Parents and Course Designers need to consider the question of leadership, the question of how to provide motivation for learning.

Attempt to provide motivation are provided by the appendices in site volume three skills for algebra on what to do in school and why, and on how to study mathematics and why. Besides those appendices, parents may give their teens and younger charges a message, namely that mastery of logic and arithmetic (fraction sense) is provides the intelligence needed to follow multi-step methods in many arts and disciplines at school, home and work. The knowledge that an error in one step makes all that follow wrong or likely to be wrong is a sign of intelligence and application provided by the mastery of logic and arithmetic.

Taken from : http://whyslopes.com/ParentCenter/Student_motivation.html

Patience Please

In mathematics, logic and perhaps other subjects, there are some ideas which are easily described and understood. Identifying them and explaining them may help your child's education. Patience is required. There is no need to rush. You may remember how long it took for your child to walk, to talk, to listen (a skill yet to form or one that may be temporary), to swim, to ride, and so on. A gentle persistence may be required. You have several years. You can test your child by presenting advance ideas, but if the reaction is not as hoped, retreat to material he or she can learn or accept more easily, and with each such retreat aim to build confidence.

It is important not to criticize or put down a subject area. (In teaching mathematics, I once found a student in my class with an poor attitude to the subject. He reported that his mother said that mathematics after arithmetic was nonsense and not important. This report came out after I asked halfway through the term why he disliked mathematics. No other teacher had challenged him on this matter before. Unfortunately, as a transient instructor with no expectations of continued employment, I did not get involved further in providing extra help for this student.

Taken from : http://whyslopes.com/ParentCenter/patience_please.html

Grade Nine Problems

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1)

Elizabeth visits her friend Andrew and then returns home by the same route. She always walks 2km/h when going uphill, 6km/h when going downhill and 3km/h when on level ground. If her total walking time is 6 hours, then what is the total distance she walks in km?

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2)

Joyce was decorating her store window for a going out of business sale. She wanted to make a figure that looks like the following. The shaded piece is made of a different material. How much material does she need in metres squared?


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3)

In # 2 Joyce needed to find the material she would need for the shaded region. How much material would she need for the unshaded region in m²?

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4)

George and Phil were playing with their fish tank again. They had a difficult time keeping their fish alive. The fish tank is 100cm long, 60 cm wide and 40 cm high. They tilted the tank, as shown, resting on a 60 cm edge, with the water level reaching the midpoint of the base. When they rest the tank down to a horizontal position, what is the depth of the water in cm?


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5)

Alex, Fred and Thomas run at constant rates. In a race of 1,000m, Alex finished 200m ahead of Fred and 400m ahead of Thomas. When Fred finished, how far was he ahead of Thomas? (in m)

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6)

If ABCD is a square and ABE is an equilateral triangle, then what is the measure of <>


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7)

An unusual die has six faces labelled 1,2,3,5,7 9. If two of these dice are rolled, and the numbers showing on the upper faces are added, what is the number of possible different sums?

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8)

The Quinpool family decided to build a pool of the following shape. The sides of their 12 * 9 yard are trisected. What is the perimeter of the shaded pool?


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9)

A classroom contained an equal number of boys and girls. Eight girls left to play hockey, leaving twice as many boys as girls in the classsroom. What was the original number of students present?

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10)

Flora had an average of 56% on her first 7 exams. What would she have to make on her eighth exam to obtain an average of 60% on 8 exams?

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11)

I have a broken fan belt on my car. The belt goes around 2 pulleys, whose centers are 15cm apart and each pulley is 4 cm in diameter. How long should the belt be?

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12)

Coming out of the grocery store, Ebree has eight coins, of which none is a half-dollar, that add up to $1.45. Unfortunately, on the way home she loses one of them. If the chances of losing a quarter, dime or nickel are equal, which coin is most probably lost?

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13)

Joe gives Nick and Tom as many peanuts as each already has. Then Nick gives Joe and Tom as many peanuts as each of them then has. Finally, Tom gives Nick and Joe as many peanuts as each has. If at the end each has sixteen peanuts, how many peanuts did each have at the beginning?

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14)

After a Math test, each of the twenty-five students in the class got a peek at the teacher's grade sheet. Each student noticed five A's. No student saw all the grades and no student saw his or her own grade. What is the minimum number of students who scored A on the test?

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15)

Bart Simpson goes to the corner store and buys an equal number of 35 cent and 30 cent candies for $22.75 (that's a lot of candy!!) How many candies did he buy?

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16)

The Band Committee of 100 people wishes to set up a telephone call system. The initial contact person calls three other people, each of whom call three others and so on, until all the people in the Band Committee have been contacted. What is the maximum number of people they need to make the calls.

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17)

Students in an elementary class decided to spend D dollars for a present for their favourite teacher, Mrs. Ballentine, each contributing an equal amount. Because fifteen students refused to contribute, each of those remaining agreed to contribute an additional, equal amount. What was the additional amount each had to contribute, in dollars?

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18)

Ian was entering a Math contest for Grade 9. He was working on this particular problem. He was having difficulty with the answer. This was the problem: The integers greater than 1 are arranged, four in each row, in 5 columns, as follows:

 a b c d e

2 3 4  5

 9 8 7 6

10 11 12 13

 17 16 15 14

If he followed the pattern what column would the number 1002 fall in?

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19)

Three grade nine Math students were given the following problem:
A three digit number 2A4 is added to 329 and gives 5B3. If 5B3 is divisible by 3, then what is the largest possible value of A? One student thought A could be 1. Another student thought A was 5. The last student thought A was 4. Who was correct?

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20)

Joy, Noella and Holly were playing jump rope. Joy and Noella at points B and C were twirling the skipping rope waiting for Holly at point A to jump into the middle of the rope (at point D). The three girls formed a 90 degree angle. Holly was 1m away from Noella and 1m away from Joy. How far does she have to jump into the middle of the skipping rope? AD is perpendicular to BC.


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21)

You are given this graph of a triangle DEF and you are asked its area. What do you think it is?


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22)

Constable Bob is driving along the Trans-Canada Highway at 100 km/h. He is passed by Melissa who is driving in the same direction at a constant speed. Ten seconds after Melissa passed Bob, their cars are 100m apart. What is the speed of Melissa's car in km/h?

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23)

Triangle ABC is an isosceles right angled triangle with BC = AB = 2. A circular arc of radius 2 with centre C meets the hypotenuse at D. A circular arc of radius 2 with center a meets the hypotenuse E. What is the area of the shaded region?

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24)

Fred picked four numbers out of a hat. The average of the four numbers is 9. If three of the numbers are 5, 9 and 12, then what is the fourth number?

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25)

Stephanie wasn't very keen on Algebra. Her teacher gave her an Algebra problem and told Stephanie to solve it. She was having problems, can you help her?

3x + 7 = x² + k = 7x + 15 What is the value of k?

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26)

Chris asked Loretta her age and she said:
"My age?" she asked, "you'll have to guess!"

"Just let me think, AH!, that's it: yes!!"

"Reverse my age, divide by three, add thirty-four, my age you'll see!"

How old was Loretta?

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Answer

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27)

George Jefferson plans to drive from his home to Edmonton, a trip of 2200km. His car has a 24 gallon tank and gets 27km to the gallon. If he starts out with a full tank of gasoline, what is the fewest number of stops he will have to make for gasoline to complete his trip to Edmonton?

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28)

Can you guess this number?
• The number is not an odd number.
• It has exactly four factors.
• If you reverse the digits, a prime number is formed.
• The sum of the digits is a two digit prime number.
• The number is less than the square root of 10⁴.
• One of the digits is a square number.

What number are we thinking of?

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29)

"Was that your bike Mom?" asked Charlene in awe. Her mother looked at the faded old photo and replied, "My first, and I earned it. I got a job that summer with a cycle dealer and he was to pay me thirty dollars and this new bike for seven weeks of work. But I didn't enjoy the job so I quit after four weeks. He gave me three dollars and I kept the bike." How much was the bike worth?

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30)

A cubic metre of water weighs 1000kg. What is the weight of a waterbed mattress that is 2 metres by 3 metres by 20cm if the casing of the mattress weighs 1kg?

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31)

Melissa and Craig were doing their math homework. They had a disagreement on one of the problems. The problem read, "What is the value of (4)(2¹⁹⁹⁶)? Melissa found it to be (8¹⁹⁹⁶), but Craig disagreed and felt it was (2¹⁹⁹⁸). Were either of them right? If so, who was right?

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32)

A farmer found an advertisment for a plot of land with very good soil and an asking price of $12500.00. The plot of land looked like this:


Why didn't the farmer buy the land?

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33)

In a recent survey, 40% of houses contained two or more people. Of those homes containing only one person, 25% contained a male. What is the percentage of all houses which contain exactly one female and no males?

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34)

In a recent election at the Dr. John Hugh Gillis High School, Susie Cook received 542 votes, Greg MacDonald received 430 votes and Travis Austen received 130 votes. If 90% of those eligible to vote did so, what was the number of eligible voters?

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35)

If the figure shown is folded to make a cube, then what is the letter opposite the S?


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36)

Jill loves math but she hates this problem. Can you help her? The sum of four numbers is 64. If you add 3 to the first number, 3 is subtracted from the second number, the third is multiplied by 3 and the fourth is divided by three, then all the results will be equal. What is the difference between the largest and the smallest of the original numbers?

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Answer

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37)

If the five expressions 2x + 1, 2x - 3, x + 2, x + 5, and x - 3 can be arranged in a different order so that the first three have a sum 4x + 3, and the last three have a sum 4x + 4, what would the middle expression be?

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38)

In our volleyball league, the numbers on the jerseys may be formed using one or two digits chosen from 1, 2, 3, 4, 5. Numbers with repeated digits are allowed but the single digit numbers are not allowed. What is the total number of possible jersey numbers for each team?

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39)

Mark has $4.50 and Jean-Martin has $3.00. Mark spends twice as much as Jean-Martin and now sees that he has half as much money left as Jean-Martin has left. How much money did Mark spend? How much money did Jean-Martin spend? How much do each of them have left?

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Answer

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40)

A motorcycle and a truck left a roadside diner at the same time. After travelling in the same direction for one and a quarter hours, the motorcycle had travelled 25km farther than the truck. If the average speed of the motorcycle was 60km/hour, find the average speed of the truck.

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41)

Similar rectangles are constructed on the sides of a right triangle as shown. Find their areas and a relationship among those areas. Have you seen a similar relationship?


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42)

Triangle PQR is equilateral. QR = 30 units, B is the midpoint of QA. QA is perpendicular to PR. What is the length of PB?


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43)

I have sold 2/3 of my pencils for $0.15 each. If I have 8 pencils left, how much money did I collect for the pencils I sold?

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44)

The minute hand of a clock is 6cm long. To the nearest centimeter, how far does the tip of the minute hand move in 35 minutes?

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45)

The numerator of a certain fraction is 3 less than the denominator. If the numerator is tripled and the denominator is increased by 7, the value of the resulting fraction is 3/2. What was the original fraction?

x = denominator

x-3 = numerator

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46)

Darryl ate 100 peanut butter cups in five days. Each day he ate six more than he ate the previous day. How many peanut butter cups did Darryl eat on the first day?

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47)

What is the next term in the sequence?

2, 10, 202, ______.

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48)

A Roman boy was given this puzzle:

Take one hundred one, and to it affix the half of a dozen, or if you please six; Put fifty to this, and then you will see what every good boy to others should be.

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49)

Solve the magic square:

         42 |    | 40
     ----+----+----
         |    |
     ----+----+----
      38 | 43 | 36

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Answer

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50)

Lilly had a math project to do for her geometry class. Her teacher wrote, "A cuboctohedren is a polyhedron that can be formed by slicing a cube at the midpoints of its edges." Lilly had to find the surface area of the cuboctobedren formed by a cube having a side of length 4cm?

Need A Hint?

Answer

Exploring Pascal's Triangle

Elementary Level

Working with a partner, study the numbers in the balloons. What patterns do you see in the arrangement of the numbers? Describe each pattern using words and symbols.

As you look for patterns, try to answer the following questions:

1. Can you predict the next row of numbers?
2. Add the numbers in each row. Is there a pattern in the sums of these numbers?
3. Do any numbers repeat?
4. Can you find a pattern in the diagonal numbers?

Share your discoveries with your class.

Taken from : http://mathforum.org/workshops/usi/pascal/pascal_elemdisc.html

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Exploring Pascal's Triangle

Elementary Level

Working with a partner, study the numbers in the balloons. What patterns do you see in the arrangement of the numbers? Describe each pattern using words and symbols.

As you look for patterns, try to answer the following questions:

1. Can you predict the next row of numbers?
2. Add the numbers in each row. Is there a pattern in the sums of these numbers?
3. Do any numbers repeat?
4. Can you find a pattern in the diagonal numbers?

Share your discoveries with your class.

Taken from : http://mathforum.org/workshops/usi/pascal/pascal_elemdisc.html

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Maths and home educated teenagers

How many people say, 'I couldn't possibly teach my teenager any algebra or geometry. I never understood them myself at school.'?

Seems a fair comment. But wait! If you didn't understand these concepts in school, why do you suppose that your child might do any better? Your child has some of your genetic make-up, and problems with mathematical concepts may just run in the family.

Moreoever, if you didn't understand your high-school maths classes, did you enjoy them? Did they inspire you to find out more about the mathematical world... or did they engender in you a hatred of the subject? More likely the latter.

How much maths do you really need?

As an adult, have you needed geometry and algebra and so on? Have you even needed to do complex long division or to multiply fractions? I doubt it! The only reason you would need to know these things is if you're going to teach them in school.

I happen to be someone who DID like school maths - I loved algebra and calculus and all those things, but I knew well that I would never use them in real life. I even studied maths at university, and worked for some years as a computer programmer. I needed to think logically - but I never needed any of those maths skills I had enjoyed so much in my high school years. When I've needed to calculate prices and sizes of carpets, or balance my bank account, I use a calculator or computer software. Yes, I need a conceptual awareness of numbers and accounting at a basic level, but those were skills which weren't covered in my school, or my degree. I learned them in about five minutes when I opened my first bank account.

So...

If you're panicking about home educating your teenager because you don't have much of a grasp of high school maths, stop right now. Brainstorm with your teen just what kind of maths he might need for his chosen career - if he's thought about that. Discuss what kinds of things he would like to know. Think about the kinds of problems he might need to solve, either now or when he's older. Help him with strategies for problem-solving and involve him in your budgeting, baking, shopping and house decorating.

The more he thinks of maths as a part of everyday life, the more likely he is to be intrigued and want to know more. It's only when we become afraid - or bored - or totally bemused - that we back away from something and become unable to learn.

Many ways of learning maths with home education

And if your teenager does enjoy maths, and already knows more than you do? Well then, whatever you have been doing so far is obviously working for him. No two children learn in the same way. There are several different maths curricula available, and text-books of the kind used in schools. If your child is learning algebra from one of these, or from a TV programme, or a web-site devoted to this, or a game such as 'Algebra-blaster' - then encourage him, and ask him to teach you! If he reaches an impasse, and is struggling to understand a new concept, do one of two things: put it aside for later (see below), or find a friend or relative - or even pay a tutor - who can help.

What happens when - out of the blue - your teen (or younger child) suddenly asks, 'Mum, how do you do simultaneous equations?' - or, as happened to me - 'What are sines and cosines?' Yes, these questions do occur even in a totally unstructured, unschooling environment. Your child might read something about these things, or find a relevant puzzle in a magazine, or get stuck on some concept in quite a different concept.

I thought, when we started home education, that it would be helpful that I have a good background in maths. But it's not necessarily an advantage when my children have difficulties understanding. Some things which seem 'obvious' to me are not at all obvious to others. We have different learning styles, and different personalities - it might have been better if I were able to understand why maths is so difficult for some people.

If, incidentally, your child - at any age - DOES ask about simultaneous equations, and you've no idea where to start, try this page where I outline the concept and go step-by-step through a simple example.

Learn maths together, or browse the Internet

So when your child asks a question, don't worry if you don't know the answer. If you have a good maths text book, you should be able to find the relevant section. If you don't understand the topic, see if you can learn together. Home education should be educational for the parents as well as the children! When your child asks the question, then is the time to try and help him find the answer because he has the motivation to learn. Alternatively there are some excellent web sites devoted to this topic - I have listed a few below. Or you can call your friendly local maths expert. But take your child's question seriously, and don't tell him it's far too complicated!

Drill and busywork do more harm than good

Do children need continual drill in order to learn? No. Extensive drill does nothing, other than making students angry and bored. Nobody ever learned from busywork. If your child understands a mathematical concept, he can work one or two examples to show that he understands. Working fifty examples won't teach him anything else, other than the idea that maths is boring. If he works one or two examples and gets them wrong, he needs to look back at the teaching material, or find another book that explains in a way he understands, or re-think his strategy. Then perhaps he can try a couple more examples.

But whether he understands or not, working through dozens of the same kind of question will not help. If he cannot understand a topic after several attemps and different approaches, it may simply be that he's not ready for it. Put it aside, work on something else, and come back to it a few months later. What seemed impossibly difficult may suddenly 'click' and become easy. Coming to it freshly may provide the inspiration that's needed, which months of drill would destroy.

So... your teen will not necessarily learn maths if he goes to school, and he will - if he doesn't have much aptitude for the subject - most likely learn to dislike and avoid it if coerced to take classes, or do multiple examples. If he isn't learning from one method, try another - or put it aside for a while. Browse your library for interesting books that cover different angles of maths. Perhaps you would enjoy puzzle books, or high level model-building. Or take a programming course. Or look at maths in music and art. All education should be fulfilling and worthwhile, and also enjoyable, fitting in with the child's interests and motivation, as well as his abilities and aptitudes.

If all else fails, but your teenager needs maths skills for his future career - or perhaps a qualification in maths in order to go to the college of his choice - he can learn what he needs when he's older. He can take an adult education course when he's 16 or 18, do an extensive 'maths skills' class with other people who find it difficult, and probably learn more than he would have learned in several years at high school anyway.

Taken from : http://home-ed.info/maths/maths_HEteen.htm

Mathematics as Problem Solving, Communication, and Reasoning

Helping your child learn to solve problems, to communicate mathematically, and to demonstrate reasoning abilities are fundamental to learning mathematics. These attributes will improve your child's understanding of and interest in math concepts and thinking. Before beginning the activities in this book, let's first look at what it means to:

Be a Problem Solver,
Communicate Mathematically, and
Demonstrate Reasoning Ability.

A problem solver is someone who questions, investigates, and explores solutions to problems; demonstrates the ability to stick with a problem to find a solution; understands that there may be different ways to arrive at an answer; considers many different answers to a problem; and applies math to everyday situations and uses it successfully. You can encourage your child to be a good problem solver by involving him or her in family decisionmaking using math.

To communicate mathematically means to use words, numbers, or mathematical symbols to explain situations; to talk about how you arrived at an answer; to listen to others' ways of thinking and perhaps alter their thinking; to use pictures to explain something; and to write about math, not just give an answer. You can help your child learn to communicate mathematically by asking your child to explain a math problem or answer. Ask your child to write about the process she or he used, or to draw a picture of how he or she arrived at an answer to a problem.

Reasoning ability means thinking logically, being able to see similarities and differences about things, making choices based on those differences, and thinking about relationships among things. You can encourage your child to explain his or her answers to easy math problems and to the more complicated ones. As you listen, you will hear your child sharing his or her reasoning.

Important Things To Know

1. Problems Can Be Solved in Different Ways While some problems in math may have only one solution, there may be many ways to get the right answer. Learning math is not only finding the correct answer, it's also a process of solving problems and applying what you have learned to new problems.

2. Wrong Answers Can Help! While accuracy is always important, a wrong answer could help youand your child discover what your child may not understand. The wrong answer tells you to look further, to ask questions, and to see what the wrong answer is saying about the child's understanding. It is highly likely that when you studied math, you were expected to complete lots of problems using one, memorized method and to do them quickly. Today, the focus is less on the quantity of memorized problems and memorized methods and more on understanding the concepts and applying thinking skills to arrive at an answer.

• Sometimes, a child may arrive at the wrong answer to a problem, because the child misunderstands the question being asked. For example, when children see the problem 4+____ = 9, they often respond with an answer of 13. That is because they think the problem is asking, "What is 4+9?" instead of "4 plus what missing number equals 9?"
  
• Ask your child to explain how a math problem was solved. The explanation might help you discover if your child needs help with the procedures; the number skills, such as addition, subtraction, multiplication, and division; or the concepts involved. In working with your child, you may learn something the teacher might find helpful. A short note or call will alert the teacher to possible ways of helping your child learn math more easily.
  
• Help your children be risk takers. Help them see the value of trying to do a problem even if it is difficult for them. Give your child time to explore the different approaches to solving a problem. Your child's way might differ from yours, but if the answer is correct and the strategy or way of solving it has worked, it may be a great alternative. By encouraging children to talk about what they are thinking, we help them to have stronger math skills and become independent thinkers.

3. Doing Math in Your Head Is Important

• Have you ever noticed that today very few people take their pencil and paper out to solve problems in the grocery store, restaurant, department store, or in the office? Instead, most people estimate in their heads, or use calculators or computers.
  
• Using calculators and computers demands that people put in the correct information and that they know if the answers are reasonable. Usually people look at the answer to determine if it makes sense, applying the math in their heads (mental math) to the problem. This, then, is the reason mental math is so important to our children as they enter the 21st century. Using mental math can make children become stronger in everyday math skills.

4. It's Okay to Use a Calculator

• It's okay to use calculators and computers to solve math problems. In fact, students are taught to use calculators at young ages and are often required to use them to do homework and take tests. The Scholastic Assessment Test (SAT), for example, permits the use of calculators for its timed tests. Many schools teach computer courses that include how to do spread sheets, statistical display, and computer-assisted designs for mechanical drawing and graphics. Schools often sell calculators to families at a low cost or supply them for all students to use. Knowing how to use a calculator and computer is a benefit for all students.

How Do I Use This Book?

This book is divided into introductory material that explains the basic principles behind the current approaches to math, sections on activities you can do with your children, and lists of resources.

The activities are arranged by levels of difficulty. Look for the suggested grade levels on each page that indicates the level of difficulty. The activities you choose and the level of difficulty depend on your child's ability. If your child seems ready, you might want to skip the easier exercises and go straight to the more challenging ones. Each activity includes a tip box with a simple explanation of the mathematical concept behind the activity, so that when your child asks, "Why are we doing this?" you can explain.

Let's Go and Explore Math!

Mathematics is everywhere, and every day is filled with opportunities to help children experience it. So flip through the pages, find an activity, and get ready to help your child explore math and have fun at the same time.

Taken from : http://www.ed.gov/pubs/parents/Math/intro.html

Helping Your Child Learning Math

As our children go about their daily lives exploring and discovering things around them, they are exposed to the world of mathematics. And since mathematics has become increasingly important in this technological age, it is even more important for our children to learn math at home, as well as in school.

This second edition of Helping Your Child Learn Math is for parents of children in kindergarten through fifth grade. It has been revised to include a variety of activities that will help children learn and apply mathematical concepts such as geometry, algebra, measurement, statistics, and probability in a useful and fun way. All of the activities in this book relate math to everyday life and complement many of the math lessons that children are learning in school. These fun activities use materials that are easy to find. They can be done in the home, at the grocery store, while traveling, or just for the fun of it.

Attitude Counts

How do you feel about math? Your feelings will have an impact on how your children think about math and themselves as mathematicians. Take a few minutes to answer these questions:

Do you think everyone can learn math?
Do you think of math as useful in everyday life?
Do you believe that most jobs today require math skills?

If you answer "yes" to most of these questions, then you are probably encouraging your child to think mathematically. Positive attitudes about math are important for your child's success. This book will help reinforce these positive attitudes about math.

Taken from : http://www.ed.gov/pubs/parents/Math/intro.html

The Problem Study Math in Indonesia

So many problems learning Math in Indonesia. Students I teach or I meet, many times say to me that learning Math is boring, learning Math is very..very...difficult to understand.
Let's we see one by one about the condition...
1. Many teachers in Basic School, didn't teach them more patiently, or press the pupil how but they teach them outside their mind. They don't push the pupils look for how, why, but teach them "these are the rules ....or .... these are something you cannot ask me.."
2. The teacher have problem with time and the subject must be learnt to their student, so they must give more time to their students to understand what they teach.
3. If this conditions is play around, so the student just know about the skin of the subject, they don't know what the point is, until they study at the higher level, e.g. Elementary School or University.
4. They need to understand the subject, but they don't have time or change to explore with experiment in their life, to apply the subject the teachers teach them.So they can solve the exam, or homework by they are drilled with many exercises or homeworks. (poor are they..)
5. They aren't learned increase their skill in counting or understand the point in Math, so they are built worse habit like always or easy to give up (if they meet difficult exercise), they didn't have fighting spirit to solve the problems themselves.
6. Many factor that I can't explore one by one here...

So, how to solve this conditions...? That's the big and good question, I think...

In my eyes as a teacher and a parents, I suggest that we (not just a teacher or parents, but we are together) must hand in hand, with good coordination to make revolution study math :

1. Renew the Teaching Method
Not just this is the rules.....not just say these are exercise you must do or these are you r homework...But, teach them with funny Math and Create the condusive situation to study math with HOW, WHY, and finally they can summary they experiment....

2. Give the exercises level by level, start from the easy, medium, and hard level in the exercises...Test they comprehensive understanding...

3. Don't teach too fast, louder your voice, make them enjoyable.....
4. Give them motivation that they are not stupid, they can solve the problems in Math,they can understand more ....
5. Let them study in group, so they can help one and another....

There's many ways to change motto : Math is difficult...
Now we can say "Study Math is Fun ......"

The Indonesian scholarship: Trisakti Scholarship

The Indonesian scholarship: Trisakti Scholarship

Legendary Chinese Dragon

The Chinese Dragon has been part of the Chinese culture for generations and it is said that the first figure of a Chinese Dragon, formed from shells, was found in the ruins of a tomb from 6000 years ago. Ever since the first emperor of the Han Dynasty, the Chinese Dragon has been associated with the emperor of China, and it was only the emperor who could own a Chinese Dragon with five claws; the 'common' dragon having four claws.

The Chinese Dragon is said to have had nine sons, the first born being named 'Bixi', and his image is usually seen carved on the base of tablets, as he was good at carrying weights. The ninth son of the Chinese Dragon, named Jiaotu, was fond of closing things, so his image can be seen on gates. The remaining sons of the Chinese Dragon, bore the names, Haoxian, Yazi, Chiwen, Baxia, Pulao, Qiuniu, and Suanmi. The Nine Dragon Walls seen in different locations in China, show images of the nine sons of the Chinese Dragon, formed from glazed tiles.

Many statues of Chinese Dragons seen in public places, bear shiny patches on them where the surface has been worn smooth by touching hands. These are due to the fact that the Chinese Dragon is said to have the ability to bring good fortune and give protection from many evils. The authorities concerned have decided that in certain circumstances, the Chinese Dragon itself needs to be protected from the people! Some models of Chinese Dragon will be seen surrounded by fencing, and some Dragons covered with wire mesh. One such mesh-covered Dragon had not escaped the attention of the people, for in a small gap in the mesh, hands had been forced through to touch the foot of the standing dragon; part of the foot was all smooth and shiny!

During recent construction work at the Shaolin Temple, many sculptured stone heads of Chinese Dragons were salvaged from demolished buildings; these were stored in one part of the grounds and near to these stone heads, were stacked carved wood heads of the Dragon ready to be fitting to the roof top of new halls in the course of construction. New sculptured stone models of Bixi, said to be the first son of the Chinese Dragon, were also positioned ready to carry the weight of stone tablets. Bixi, with his shell back does not have the usual appearance of a Chinese Dragon, but he is still subjected to the touching hands of visitors, seeking his help and protection.

ATOMIC STRUCTURE PERIODIC SYSTEM AND [OF] ELEMENT

Atom
Atom [is] smallest particle [is] which still measure up to unsure which compiling of. Atom own very small size measure so that cannot be seen with naked eye. But all man of science able to determine size measure and nature of atom [of] pursuant to research which they [do/conduct]. Estimate hit atom picture referred [as] [by] a atom model. Because research hit atom model [done/conducted] step by step, hence model this atom experience of several times the completion or experience of growth.


Growth Model Atom

Model atom made to water down in learning the nature of atom. Model atom always experience of renewal. This [is] happened [by] because science hit atom non-stoped to expand. Can be said that [by] model of atom [do] not emerge at once, but always there [is] completion [of] along with science growth.
Model acceptable atom by erudite society if supported with data [of] result of experiment. This data have to can just be repeated by whom, just where, and any time. Become the data unattached by space and time.
One who first make model of atom [is] John of Dalton so that the model which he propose referred [as] [by] model of Dalton atom. [Is] hereinafter completed by Thomson, Rutherford, Bohr.

Model Dalton Atom
Atom Word [is] first time proposed by so called Greek philosopher [of] Democritus ( 460-370 SM). According to Democritus, items which cannot dibelah continuously. [His/Its] intention, items bisection will reach a[n storey;level [of] where the items indiscrete again. indiscrete again That shares referred [as] with Atom. This Word come from Greek atomos; a = [do] not and atom tomos = divisible.
Concept [of] soft rice [of] atom Democritus [of] during some century forgotten [by] a people. In the year 1803, John Dalton ( 1776-1844) proposing postulate hit atom. This postulate [is] proposed [by] pursuant to quantitative measurement from chemical reaction. Fill Dalton postulate shall be as follows

a. Items lapped over [by] for a number of indiscrete small particle again. That particle [is] referred [as] [by] a atom
b. Atom [of] a[n unsure identik in all matter, good [of] volume, form, and also [his/its] mass and differ from compiler unsure atom [of] other;dissimilar
c. In chemical change, happened [by] [of] atom dissociation or affiliation. Hereinafter that atom [is] re-arranged so that form certain composition
d. Atom can joint forces with other;dissimilar atom to form a[n molecule with circular comparison number and modestly.

First Dalton Postulate assure opinion Democritus expressing items division will reach a[n particle which cannot be redistributed. That particle [is] so-called with atom
Postulate of Second represent new idea from Dalton. According to Dalton, atom represent smallest shares from a[n element which still measure up to that unsure.
Relied on [by] Third postulate [of] hokum convert mass from Lavoisier, that is in chemical reaction [of] mass of Iihat vitamin [do] not change. [His/Its] intention [is] mass of Iihat vitamin [of] before and hereafter react [is] of equal. So that the atom nothing that disappear or created in a[n chemical reaction. Equally, change that happened only in the form of dissociation and affiliation [of] [among/between] atom.
Fourth postulate represent molecule concept, that is [among/between] atom can join to form molecule. Atom joining to earn of a kind or [do] not of a kind. If affiliation with atom of a kind will form element molecule. If joining atom which [do] not of a kind will form compound molecule. In everyday use, term of molecule of element and molecule of compound [is] enough writed [by] element and compound.

Carl Friedrich Gauss

Carl Friedrich Gauss
from Wikipedia bahasa Indonesia, ensiklopedia bebas

Johann Carl Friedrich Gauss (Gauß) (30 April 1777 - 23 Februari 1855) is a Mathist, astronomist, dan Physcist from German who is given many contribution; he is one of the most Mathist other Archimedes and Isaac Newton.

He was born at Braunschweig, German, when he was not 3 years,he had corrected yhe foult of salary list his father's employee. According the history, when he was 10, he made his teacher was surprisingly when he gave the formula for counting aritmatimatical progression there is counting from 1+2+3+...+100. Altough this story almost is right, the exercises which given from the teacher is more difficult . [1]

Gauss is a scientist in many categories: Math, Physics, and astronomy. In analys and geometry he contibutes many brainstorming contribution in Maths. Calculus (include limit) is one of analyse that he was concerned .

Gauss was died at Göttingen.

Logarithm Exercises

Responsing Exercise about Logarithm, I upload Logarithm exercises to everybody who wants download or for my colega Math's Teacher.....
I hope it can help you al or enrich for exercises about Logarithm.....

Please Download :
Logarithm 2
Logarithm 1