A New Way to Learn Math- The Magical Math Story

Some students struggle with math. These are the students who are usually out in the hall for misbehaving, quiet and withdrawn because they don't know the answers or complaining of headaches or stomach problems from the suffering of learning math. The signs of poor math skills come in many forms, but the message is always the same. These students don't understand numbers.

There is a way to reach these students. To help these students a teacher or parent needs to be patient, energetic and above all willing to think outside of the box. Traditional ways of teaching math simply will not work with these students. Here you will find an example of one the methods you can use to reach a student in elementary school. It is a method that has been refined over many years and has worked with hundreds of students.

There is a story, one of several stories, which actually changes how a child looks at math. Although it is an easy story to learn, it is very specific in design. It reaches auditory, kinesthetic and visual learners and includes mnemonic devices to make numbers easy to remember. It can reach students that have struggled with math for years. It is actually more effective with younger students as it helps create an understanding of math before bad habits like finger counting develop.

The story is simple: Your mother is chasing a spider around the house when she swings and accidentally breaks the window.

For parents, this story is one you can teach to a child anywhere such as in the car on your way to soccer practice, in the living room during a commercial or while taking a walk to the corner store. You can embellish the story and make it more personal, laughing about how much Mom freaks out about the spider. You can even have the child imagine the story in great detail, talking about how big the spider is and how loud it is when the window shatters. Although the core of the story can't be changed, it is a story that will taught uniquely by each individual teacher or parent who will add their own style and energy.

This story includes several mnemonic devices. Each image represents a specific part of a math fact, for example the number eight is represented by a spider which has a body that looks like an eight and has eight legs. It includes personal connections (Mom), imagery (a black spider), and actions (breaking the window) which will make the story stick in both the short term and long term memory. It also uses tangible images like a golf club and a spider that can be remembered more easily than abstract concepts. In short, it is a story that can be easily remembered.

The usual way for a student to learn eight times nine is to add nine together eight times. Not only is this time consuming, it is also boring. By nature this method creates confusion with other math facts as none are distinct from the others. It is easy to mix up seven times eight with six times nine. The traditional method of drill and practice takes many hours and often only reaches a few of the students in a class.

In contrast, teaching math by using vivid images of a memorable story will produce markedly different results. When asked what eight times nine is a student will recall the image for eight (a spider has eight legs and a body that looks like an eight) and nine (a golf club looks like a nine, comes in sets of nine and is called a nine iron) and the story that goes with these images. They will easily remember that the house (the bigger image) represents seventy (as the roof is shaped like a seven) and the window (the smaller image) represents two (since it has two curtains). This connects all the numbers, making it easy to remember that eight times nine is seventy two. It will work for the reverse (division) just as easily. With less than twenty unique but specific stories to learn, learning the times tables can be a fun adventure.

Though some traditional methods have been successful for some students, there is a way to reach those it hasn't worked for.

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Video and Computer Games that Sharpen Math Skills

Working with numbers improves concentration, problem solving skills, memory, focus and general clarity of thought. And there is great news for gamers young and old! Video and computer games are rich with numbers! I have done some research to hone in on the games that utilize math skills to a greater extent.

Computer Games are generally less expensive and a bit more versatile. They are usual sought after by a slightly younger audience. By younger I am referring to school age children. being that a very large portion of video game users are adult males! So I will start with a review of a couple of math focused computer games that I feel are of good quality. Math Munchers Deluxe by The Learning Company reinforces math skills by encouraging problem solving through gaming in areas of whole numbers, decimals, factors and simple geometry. Mighty Math by Edmark teaches geometry concepts using math and and problem solving-solving skills. Students explore attributes of shapes and solids, constructions and transformations, 2D and 3D coordinates, and the relationships between length, perimeter, area, and volume. Teaching Pro: Middle and Highschool Math by Mathsoft has comprehensive coverage to insure students learn math concepts and understand how math is utilized in the real world. The program includes focus in Basic Math, Pre-Algebra, Algebra, Algebra II, Geometry, and Trigonometry. It meets mandated curriculum standards in all states!

There are many math focused games readily available online. Suduko revolves around attempting to fill in a grid so that each line contains the numbers one through nine only once. This games is a widely known addictive brain teaser. It is a great game for sharpening math skills and is available for free on numerous websites and downloadable for your cell phone! Timez Attack is real video game created by the same engineers who have worked on Play Station games. The object of the game is to your way through the dungeon maze and foil those who would get in your way. You will develop your math skills while defeating a host of challenging obstacles and characters. The base version of this game is free at big online. The full length version is also available.

Nintendo offers a game called Math Play for the DS. This game encourages the player to create equations in four different game modules by arranging numbered cards. There are a variety of difficulty levels. There is also competitive multiplayer action and addictive puzzle play.

Donkey Kong Jr. Math has received mixed reviews. By mixed I mean not so great. It is one of the only math specific games however, that my search turned up for GameCube or Wii. When dealing with the game consoles, such as PS2, Gamecube or Wii I would choose puzzle games which are more abundant and tend to require math skill.

Working with numbers keeps many of our skills sharp including problem solving and improves general clarity of thought. Video and computer games [http://www.thesoftwarespot.com/default.asp?S=500&A=F&SearchText=&CategoryID=1695863&NID=6372614] are rich with numbers whether they are geared to be a math games or not. Research has brought a few games that focus on math to the surface so they might catch your eye more easily in the future!

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The Importance of Math in Higher Education

There are countless jobs in today's fast paced labor industry that requires an advanced application and understanding of mathematics or science background. Math and Science has always been the backbone of technological advances and remain at the forefront of innovation, and those with extensive math and science experience will be the highest paying workers. So how important is mathematics in higher education? Read on to find out.

Taking algebra, geometry, statistics, probability, and physics classes in high school might have seemed like a drag but there's a reason why it was required. Today, many jobs like accounting, computer science, engineering, and business incorporates mathematical applications on a daily basis. Many jobs that once require very basic understanding in mathematics now have heightened that standard, even for entry level jobs. This is reflected in the growth of computer technology, information technology, and allied health professions. Most science and math heavy programs require students to build upon a strong mathematical background and master advance topics like calculus and number theory.

Regardless, there is no denying the importance of mathematics in today's job market. A strong mathematics specialization involves complex calculations along with logical reasoning, axioms, and theorems that are applicable to professional real world problems. The best careers and degrees for mathematic lovers are broad but include Actuarial Science, Computer Science, Software Development, Mathematics Teacher, and Professional Accounting. A higher education degree online may also prepare you for the computing and logical reasoning skills you will need in business, science, and engineering occupations.

In fact, to highlight the importance of math in the real world and in secondary education programs, analytical skills are highly sought after in the professional world. The fastest growing and most stable jobs are those that require a specialized skill, and analytical, mathematical applications are equally as important. For example, financial examiners is a profession with requires precise accounting skills and is expected to grow by 41% in the next 5 years. Network systems and data communications analysts implement vast and complicated network and communications systems and need a strong algorithmic background in computer science. This profession is expected to grow by 53% by 2018.

If you're lacking mathematical skills, the best and fastest way to get trained and hone your skills is through an accredited online degree program with a heavy math foundation. You will be able to learn and pace yourself according to your own strengths and move on once you've mastered a math concept. Building on what you know is core to mathematical learning and with the right math degree online, doors of opportunity will open for you.

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Does Your Child Need Tuition?

It's approximately three months before the start of an exciting and enriching time for a group of children who are entering Primary school next year. Yet, the nail-biting anxiety has begun for their parents.

Very often, we hear the desperate cries from concerned parents: "Will my child cope well in school?" "My daughter doesn't know how to write an essay!" "My son didn't learn multiplication in kindergarten! Should I send him for lessons?" "Should I send my daughter for enrichment classes? She dislikes Math to the core..." Sounds familiar? If you are a parent, you might have heard these questions before, or are having these worries now.

Tuition, otherwise known as enrichment classes, has become part and parcel of almost every student's learning journey. Due to the ever-increasing standard of exam questions set by the Ministry of Education, and the challenging syllabus that is revised every five years, it has become a steep uphill task for most students to excel in their academics. In order to improve their grades, parents pay for supplementary classes that claim to have that 'extra something' for their kids to outperform others.

Although my business is affiliated to a tuition agency, it is my responsibility to tell you that you may not need to burn that hole in your pocket. Extra-curricular lessons should be necessary and appropriate.

The necessity of tuition or enrichment classes should be considered before enrolling your child for them. When I was a form teacher in a Primary school, I remember an instance when a student, who consistently did well in her tests and exams, failed to maintain her grades when she advanced to Primary 5. Concerned and puzzled over her sudden deterioration in grades, I asked her mother during our regular parent-teacher meeting for a possible explanation. Her mother said that she was as confused as I am regarding her daughter's performance, considering that she now sends her for extra classes during the weekends. That answer jumped out at me instantly for I realized that the student had been deprived of her rest days to recharge in preparation for the school week ahead. Thankfully, her mother heeded my advice to withdraw her daughter from the extra classes (since they weren't working anyway) and her grades were back on track after that.

Another factor to consider before registering your child for lessons in tuition centres is the suitability factor. I had another student, Jack (fictitious name to protect the identity), whose mother sent him for classes in a tuition centre which claimed to improve one's chances of getting into the Gifted Education Programme (GEP). To her disappointment, not only did her son fail to enter the GEP, he barely passed his Math end-of-year exams. Apparently, Jack could not fully grasp the basic concepts in class, and the tuition centre's accelerated programme only demoralized him further.

If, after mulling over these two factors, you still believe that your child would be better off with tuition, then proceed to look for a private home tutor who can give your child individual attention. Good tutors are hard to come by and a tuition agency is a superb channel through which you can find one quickly and conveniently. However, that would mean having to choose a reliable tuition agency in the first place. With the numerous tuition agencies online, how would one know which tuition agency to request a tutor from? Does size matter? Does experience matter? These issues shall be left for another page.

What matters most after reading this article is that as a parent, you make an informed choice about sending your child for additional classes, be it at home or at a tuition centre. Counter-intuitive as it may seem, relieving your child of extra-curricular lessons may be the key to improving your child's grades. Also, forcing your child to learn at too fast a pace will only cause him/ her to lose interest and confidence altogether. And I'm sure that will be the last thing you want to see happen.

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Online Tools for Differentiated Instruction

Differentiated instruction is a teaching model based around the idea of providing every student with an optimal learning environment. By tracking and assessing progress throughout the school year, teachers can then adjust both curriculum and teaching methods to better serve the personal needs of the kids in their classrooms. Online tools such as math games can help in this undertaking, as a virtual environment can provide detailed real-time feedback on the progress of every child who uses it.

Addressing Variables for Academic Success

Differentiated instruction addresses the fact that every child comes to the classroom with different educational needs. While some children thrive through reading textbooks and listening to lectures, others require a more hands-on, visual approach to learning. Despite this, today's teachers are expected to impart a specific subset of knowledge to children at each grade level. This mix of a common curriculum and variable learning styles can put a teacher in a difficult position. In order to provide the proper individualized educational environment, it's necessary to know where each student's strengths and weaknesses lie. Progress monitoring is an essential part of this process. However, traditional monitoring methods such as benchmark testing can take a lot of time away from instruction, which is frustrating for teachers and can have a negative effect on student progress.

Incorporating Online Tools

The use of technology in the classroom isn't a new thing. As the years go by, more and more schools are beginning to incorporate technological aspects into everyday instruction. This is a particularly valuable trend when it comes to differentiated instruction. Through the use of an online environment that includes games, virtual manipulatives and personalized progress summaries, teachers and administrators can more easily track how students are doing at any grade level. And since online games are hosted on a remote server rather than individual computers around the school, progress reports can be accessed from anywhere, anytime, making it easier for teachers to share information and better adapt their classroom environments to provide an optimal educational experience.

Implementing an Adaptive Environment in the Classroom

Since the current classroom model isn't conducive to intense, individualized instruction for every student, teachers who wish to implement a differentiated instruction model must mix group instruction with individual attention to create the proper learning environment. Organization and planning are key to this, which is where online learning tools come in handy. Getting comprehensive feedback about students' progress at the push of a button or click of a mouse saves time and gives teachers the information that they need to adapt the current curriculum to best serve their particular class. Adaptive online educational tools also provide students with an alternative method of learning, so teachers can offer those with different learning styles an easier environment in which to grasp and master new concepts. 

Using differentiated instruction in the classroom helps to ensure that each student receives the amount and type of attention that they need to succeed academically. Adding online games to everyday instruction provides students with an interactive learning environment that moves at their own pace while tracking progress in a way that teachers can use to better serve each child.

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How Can Instructional Technology Make Teaching and Learning More Effective in the Schools?

In the past few years of research on instructional technology has resulted in a clearer vision of how technology can affect teaching and learning. Today, almost every school in the United States of America uses technology as a part of teaching and learning and with each state having its own customized technology program. In most of those schools, teachers use the technology through integrated activities that are a part of their daily school curriculum. For instance, instructional technology creates an active environment in which students not only inquire, but also define problems of interest to them. Such an activity would integrate the subjects of technology, social studies, math, science, and language arts with the opportunity to create student-centered activity. Most educational technology experts agree, however, that technology should be integrated, not as a separate subject or as a once-in-a-while project, but as a tool to promote and extend student learning on a daily basis.

Today, classroom teachers may lack personal experience with technology and present an additional challenge. In order to incorporate technology-based activities and projects into their curriculum, those teachers first must find the time to learn to use the tools and understand the terminology necessary for participation in projects or activities. They must have the ability to employ technology to improve student learning as well as to further personal professional development.

Instructional technology empowers students by improving skills and concepts through multiple representations and enhanced visualization. Its benefits include increased accuracy and speed in data collection and graphing, real-time visualization, the ability to collect and analyze large volumes of data and collaboration of data collection and interpretation, and more varied presentation of results. Technology also engages students in higher-order thinking, builds strong problem-solving skills, and develops deep understanding of concepts and procedures when used appropriately.

Technology should play a critical role in academic content standards and their successful implementation. Expectations reflecting the appropriate use of technology should be woven into the standards, benchmarks and grade-level indicators. For example, the standards should include expectations for students to compute fluently using paper and pencil, technology-supported and mental methods and to use graphing calculators or computers to graph and analyze mathematical relationships. These expectations should be intended to support a curriculum rich in the use of technology rather than limit the use of technology to specific skills or grade levels. Technology makes subjects accessible to all students, including those with special needs. Options for assisting students to maximize their strengths and progress in a standards-based curriculum are expanded through the use of technology-based support and interventions. For example, specialized technologies enhance opportunities for students with physical challenges to develop and demonstrate mathematics concepts and skills. Technology influences how we work, how we play and how we live our lives. The influence technology in the classroom should have on math and science teachers' efforts to provide every student with "the opportunity and resources to develop the language skills they need to pursue life's goals and to participate fully as informed, productive members of society," cannot be overestimated.

Technology provides teachers with the instructional technology tools they need to operate more efficiently and to be more responsive to the individual needs of their students. Selecting appropriate technology tools give teachers an opportunity to build students' conceptual knowledge and connect their learning to problem found in the world. The technology tools such as Inspiration® technology, Starry Night, A WebQuest and Portaportal allow students to employ a variety of strategies such as inquiry, problem-solving, creative thinking, visual imagery, critical thinking, and hands-on activity.

Benefits of the use of these technology tools include increased accuracy and speed in data collection and graphing, real-time visualization, interactive modeling of invisible science processes and structures, the ability to collect and analyze large volumes of data, collaboration for data collection and interpretation, and more varied presentations of results.

Technology integration strategies for content instructions. Beginning in kindergarten and extending through grade 12, various technologies can be made a part of everyday teaching and learning, where, for example, the use of meter sticks, hand lenses, temperature probes and computers becomes a seamless part of what teachers and students are learning and doing. Contents teachers should use technology in ways that enable students to conduct inquiries and engage in collaborative activities. In traditional or teacher-centered approaches, computer technology is used more for drill, practice and mastery of basic skills.

The instructional strategies employed in such classrooms are teacher centered because of the way they supplement teacher-controlled activities and because the software used to provide the drill and practice is teacher selected and teacher assigned. The relevancy of technology in the lives of young learners and the capacity of technology to enhance teachers' efficiency are helping to raise students' achievement in new and exciting ways.

As students move through grade levels, they can engage in increasingly sophisticated hands-on, inquiry-based, personally relevant activities where they investigate, research, measure, compile and analyze information to reach conclusions, solve problems, make predictions and/or seek alternatives. They can explain how science often advances with the introduction of new technologies and how solving technological problems often results in new scientific knowledge. They should describe how new technologies often extend the current levels of scientific understanding and introduce new areas of research. They should explain why basic concepts and principles of science and technology should be a part of active debate about the economics, policies, politics and ethics of various science-related and technology-related challenges.

Students need grade-level appropriate classroom experiences, enabling them to learn and to be able to do science in an active, inquiry-based fashion where technological tools, resources, methods and processes are readily available and extensively used. As students integrate technology into learning about and doing science, emphasis should be placed on how to think through problems and projects, not just what to think.

Technological tools and resources may range from hand lenses and pendulums, to electronic balances and up-to-date online computers (with software), to methods and processes for planning and doing a project. Students can learn by observing, designing, communicating, calculating, researching, building, testing, assessing risks and benefits, and modifying structures, devices and processes - while applying their developing knowledge of science and technology.
Most students in the schools, at all age levels, might have some expertise in the use of technology, however K-12 they should recognize that science and technology are interconnected and that using technology involves assessment of the benefits, risks and costs. Students should build scientific and technological knowledge, as well as the skill required to design and construct devices. In addition, they should develop the processes to solve problems and understand that problems may be solved in several ways.

Rapid developments in the design and uses of technology, particularly in electronic tools, will change how students learn. For example, graphing calculators and computer-based tools provide powerful mechanisms for communicating, applying, and learning mathematics in the workplace, in everyday tasks, and in school mathematics. Technology, such as calculators and computers, help students learn mathematics and support effective mathematics teaching. Rather than replacing the learning of basic concepts and skills, technology can connect skills and procedures to deeper mathematical understanding. For example, geometry software allows experimentation with families of geometric objects, and graphing utilities facilitate learning about the characteristics of classes of functions.

Learning and applying mathematics requires students to become adept in using a variety of techniques and tools for computing, measuring, analyzing data and solving problems. Computers, calculators, physical models, and measuring devices are examples of the wide variety of technologies, or tools, used to teach, learn, and do mathematics. These tools complement, rather than replace, more traditional ways of doing mathematics, such as using symbols and hand-drawn diagrams.

Technology, used appropriately, helps students learn mathematics. Electronic tools, such as spreadsheets and dynamic geometry software, extend the range of problems and develop understanding of key mathematical relationships. A strong foundation in number and operation concepts and skills is required to use calculators effectively as a tool for solving problems involving computations. Appropriate uses of those and other technologies in the mathematics classroom enhance learning, support effective instruction, and impact the levels of emphasis and ways certain mathematics concepts and skills are learned. For instance, graphing calculators allow students to quickly and easily produce multiple graphs for a set of data, determine appropriate ways to display and interpret the data, and test conjectures about the impact of changes in the data.

Technology is a tool for learning and doing mathematics rather than an end in itself. As with any instructional tool or aid, it is only effective when used well. Teachers must make critical decisions about when and how to use technology to focus instruction on learning mathematics.

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Effective Way to Teach Mathematics - A Guide For Tutors

Mathematics can be considered as the most problematic subject area among average students. Not all students are able to grasp the concept of their math subjects as easily as how brilliant student are able to do so. This is the reason why home tuition will mostly cover math subjects. Thus, private tutors must develop a skill on how they will be able to deliver the concept of the subject matter in a manner that can be understood by their student easily.

In order to make teaching mathematics effective, teachers must follow the most important principle of teaching math to keep them on the right track. Teachers need to make everything about the concept make sense. Let's face it math can really be very complex. Your teacher can teach you the steps and procedures on how to solve a certain math equation but fails to make you understand why these steps actually work.

More often than not, math teachers will only focus on the how of the concept rather than the why. Meaning, the students may grasp the procedure and solve certain problems but loose on the concept or their ability to understand why the procedure is working. For instance, a child may be able to learn the procedure or the how to multiply but is not able to understand the concept or why the formula works. This kind of learning is very superficial and can be forgotten over time. But, if the teacher is able to let the student understand the concept behind the formula, then it can be considered as learning the subject matter as whole. The understanding of the procedures and the concept may vary from one student to another. Thus, the teacher must be flexible with how he relays the subject matter.

Teaching tools is another factor that needs to be considered to. Making use of different tools to make teaching more effective must also be given priority. With the innovations in technology, so many teaching tools have been developed. From abacus to calculators, textbooks to e-books, even games are utilized to make understanding easier. However, teachers must effectively use the resources efficiently and effectively. Teachers can start from the basics. As time goes by, they can now add more tools to aid them in their teaching strategies. You need not grasp every tool all at once. You can utilize each tool one at a time, taking in to consideration how your students are benefiting from each tool.

You see, every child has a unique learning potential. Thus, it is very important for educators to identify how their students are responding to their way of teaching. Thus to make teaching effective, it is the responsibility of the teacher to use variations on their styles and they must be flexible enough to adapt on the learning capacity of their student. This goes especially true among those who are providing home tuition. They must be very keen in observing whether their manner of delivering the subject matter is effective or not.

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Mistakes in Kids' Math - The Vehicle of Learning

Making mistakes is part of growing up and learning, but in kids' maths they are too often overlooked as a source of development for the child. Children need to be encouraged to take risks with their learning. They need to push themselves out of their comfort zone and tackle problems that they are uncertain of how to proceed with. This will give them increased confidence to tackle new concepts and will advance their education not only in maths but in general.

One indication of a child's preparedness to venture into unknown territory with confidence in maths is the appearance of their workbook. Generally, the child who is prepared to leave a mistake on the page and tackle the same problem again will be a child who is more confident in their work. This child views the attempt at the question as valid work, worth keeping. If the child has a greater awareness, he or she will understand that the process of making the mistake and then correcting it with another attempt is the key to learning in this subject.

The child who feels the need to remove the mistake and only have the perfectly correct solution in their book will have a narrower, less flexible approach to the topic. This second child will be less willing to tackle strange or difficult problems, as they view success as the completed, correct answer. Many times a child with this mindset will erase all their attempts to answer a question on a test, preferring to leave the page blank than risk having an error on it.

Several years ago I taught a particular year 7 student whose work made an impression on me. When I first collected his book, it was filled with what looked like complete nonsense. This work was done by a child from an non-English speaking background who had had very little exposure to education. While the work itself made no sense, the child had taken the numbers and symbols we had been working with in class and had attempted to use these to complete the homework task. This child had toiled away for over two pages in his exercise book making what looked like sums.

To me, that was an excellent effort. That child took a risk. He was prepared to be wrong, but took a risk and did his very best to complete the task he was given and in fact did far more work than was asked of him. That student went on to make excellent progress in math that year. By the end of the academic year he was competent with the basic operations, could handle simple fractions and equations and had memorized his 1 - 15 times tables.

Risks need to be taken by children and they need to be rewarded, regardless of the outcome. Math students need to be told frequently that since they are doing unfamiliar work they must expect to make mistakes, and that these mistakes are an essential part of their learning. If a child hears this often enough and is regularly rewarded for attempting work they are unfamiliar with, they have the opportunity to develop a positive approach to risk taking in the classroom.

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How to Teach Young Children to Love Math

Numbers and counting, it is the beginning of math. We want to instill a love of math at an early age so children will learn to excel in math. Let's teach our young children to love and have fun with numbers, which can turn into a love of math. Math is the language of counting and quantifying things, count with your children to show them different ways. Math is a language with symbols, sets of numbers, and rules. So many studies prove that languages are easiest acquired at a young age. So let's get started teaching them to love math.

Always try to make it fun with young children. Make everyday actions a fun word problem. While cooking breakfast ask your child, "we had 6 eggs, I cooked 2, how many do we have left for breakfast tomorrow?" Count, count, count everything! Introduce them to an abacus, play with marbles, and pennies. Ask questions like how many windows do we have in our house, how many stairs? Then go and count the windows and stairs together. Share your findings with the family at dinner. Count everything, the steps you take to get to the kitchen, to their bedroom, and to the car. Count the members of the child's family, then ask all together in our family how many legs, how many arms, ears, etc. Make it fun, draw pictures and count the people, legs, and arms again together.

Identify a "number for the day," and look for that number throughout the day. Look for the daily number on clocks, household items, food containers, and in books. Also, have a "shape of the day" and identify objects that fit that shape. Keep a running tally of how many circles or triangles you find each day. Count how many octagons or stop signs you see on the way to the supermarket.

While shopping let them help weigh the fruits and vegetables. Show them the price per pound or the unit price for different items. Then ask them to help you figure out the best buy for your money, which is cheaper, or more expensive. With older children let them help select coupons, and tell you how much you will save if you use that particular coupon and the item costs $2.00.

Have your child pick something they want to buy, for example a new toy. Give them chores and an allowance to work towards that toy. As they complete their chores and receive their allowance, have them document how much money they have and how much more they need to reach their goal.

While doing everyday chores, offer to time them. Each day encourage them to strive to beat their previous time. With older children introduce percentage change, increase or decrease.

Have a coin jar and allow the child to group all of the pennies, dimes, nickels, and quarters. Go over the value of each coin and then create pattern games. For example, with pennies and dimes on a table: penny, penny, dime, penny, penny, dime, penny, penny, and ask the child what comes next. With all of the pennies introduce addition and subtraction. Take two pennies and start with 1 + 1 =2. Give additional problems and let them use the pennies as a visual aid.

Teach them to tell time on a standard clock. Start with counting by fives, then together make a homemade clock with a movable long hand and short hand. Have them color and decorate their clock and then show them 1:00, 1:05, etc.

Bake with your children, let them help you measure the flour, sugar or water. Introduce degrees when you
set the oven, and go over time again when you set the timer. Order a pizza and introduce fractions. Show them that 4/8 is the same as ½ after dad has eaten half of the pizza.

If possible, learn to play a musical instrument. Research has shown that when children are trained in music at a young age, they tend to do well in math. It's amazing how when children start to do well or excel in a certain subject they start to love it!

Lastly introduce and memorize the old fashioned times tables. Put away the calculators and just learn the basics, go over them daily. Make the times tables into a song, children love to memorize song lyrics, so make it fun!

Let them see you making numbers and math problems fun. Encourage them to make up their own word problems, then get excited about their numerical creativity. We want children to constantly think of ways to show us that math and numbers are everywhere. We want to teach our children to love math and realize that math is awesome!

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Music and Mathematics - There Are Many Connections

If you thought music was not a mathematical language, then think again. In fact, music and mathematics are very much intertwined, so much so that I guess you could say one could not live without the other. Here we examine a relationship that clearly demonstrates the strength of this tie. Let the music begin.

For those with a rudimentary knowledge of music, the diatonic scale is something quite familiar. To understand why certain pairs of notes sound good together and others do not, you need to look into the sinusoidal wave patterns and the physics of frequencies. The sine wave is one of the most basic wave patterns in mathematics and is depicted by smoothly alternating crest-trough regularity. Many physical and real-world phenomena can be explained by this basic wave pattern, including many of the fundamental tonic properties of music. Certain musical notes sound well together (musically this is called harmony or consonance) because their sinusoidal wave patterns reinforce each other at select intervals.

If you play the piano, then how each of the different notes sounds to you is dependent on how your instrument is tuned. There are different ways to tune instruments and these methods depend on mathematical principles. These tunings are based on multiples of frequencies applied to a given note, and as such, these multiples determine whether groups of notes sound well together, in which case we say such notes are in harmony, or poorly together, in which case we say such notes are out of harmony or dissonant.

Where these multiples come from depend on criteria set by the instrument maker and today there are certain standards that these fabricators follow. Yet criteria notwithstanding, the multiples are inherently mathematical. For example, in more advanced mathematics, students study series of numbers. A series is simply a pattern of numbers determined by some rule. One famous series is the harmonic series. This comprises the reciprocals of the whole numbers, that is 1/1, 1/2, 1/3, 1/4... The harmonic series serves as one set of criteria for certain tunings, one notably called Pythagorean Intonation.

In Pythagorean intonation, notes are tuned according to the "rule of the perfect fifth." A perfect fifth comprises the "musical distance" between two notes, such as C and G. Again without trying to turn this article into a treatise on musical theory, the notes between C and G are C#, D, D#, E, F, F#, and G. The "distance" between each of these notes is called a half-step. Thus a perfect fifth comprises 7 half-steps, C-C#, C#-D, D-D#, D#-E, E-F, F-F#, and F#-G. When we number the notes in a musical harmonic series, the number ascribed to the C note and that ascribed to the G note will always be in the ratio of 2:3. Thus the frequencies of these notes will be tuned so that their ratios correspond to 2:3. That is the C-note frequency will be 2/3 the G-note frequency, or vice versa, the G note frequency will be 3/2 the C note frequency, in which frequency is measured in cycles per second or Hertz.

Now, continuing by tuning according to perfect fifths, the fifth above G is D. Applying the perfect fifth ratio, the D note will be tuned to a frequency which is 3:2 the G frequency, or looking at this from below, the G note is 2/3 the frequency of the D note. We can continue in like manner until we complete what is called the Circle of Fifths, bringing us back to a C note by applying successive ratios of 3/2 to the previous note in the cycle. This takes twelve steps and when complete, the frequency of the second C, or the higher octave C note should be exactly twice the frequency of the lower C note. This is a requirement of all octaves. However this does not happen by applying this ratio of 3/2.

Musicians have rectified this problem by resorting to none other than the field of irrational numbers. Recall that those numbers are such that they cannot be expressed as fractions, that is, their decimal representations, like the number pi or the square root of two, do not end and do not repeat. Thus as a result of the failure of the Pythagorean tuning method to produce perfect octaves, tuning methods have been developed to obviate this situation. One is called "equal temperament" tuning, and this is the standard method for most practical applications. Believe it or not, this tuning method incorporates rational powers of the number two. That is correct: fractional powers of the number two. So if you thought you were learning rational exponents for nothing in algebra class, here is one example of where such a topic is used in real life.

The way equal temperament tuning works is as follows: each note throughout its octave has its frequency multiplied by successive twelfth roots of two to get to the next higher note. That is, if we start with the standard A note, which vibrates at 440 Hertz, let us say, to get to A#, we multiply this 440 by 2^(1/12). Since the twelfth root of two is equal to 1.05946 to five decimal places, A# would be tuned to 440*1.05946 or 464.18 Hertz. And thus the tuning continues with the next note B obtained by taking 2^(2/12)*440. Note that we increment the twelfth power of 2 by 1 each time, obtaining powers of 2 which are 1/12, 2/12, 3/12, etc.

What is nice about this method is its exactness, unlike the inexactness of the Pythagorean intonation method discussed earlier. Thus when we arrive at the octave note, the next A above the standard A, which should vibrate at twice the frequency of the original 440 Hertz A, we get A octave = 440*2^(12/12) which is 440*2 = 880 Hertz, as it should be---exactly. As we stated earlier, when tuning by the Pythagorean method, this does not happen because of the repetitive use of the ratio 3/2, and therefore accommodations must be made to bring in line the inexactness of this approach. These accommodations result in perceptible dissonances between certain notes and in certain keys.

This tuning exercise demonstrates that mathematics and music are well intertwined, and indeed one could say that these two disciplines are inseparable. Music is truly mathematical and mathematics is, well, yes musical. Since many people think of musical talent coming from the "creative" types and mathematics ability coming from the "nerdy" or non-creative types, this article in some part helps disabuse these same people of this notion. Yet the question remains: If two ostensibly different fields as music and mathematics are happily married, how many other fields out there, which at first seem to have nothing to do with mathematics, are just as intricately linked to this most fascinating subject. Meditate on that for awhile.

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