How to Study Math and Physics Effectively

At school I was useless at math. So was Albert Einstein I believe. Many years after leaving school I enrolled in a distance learning course at a university for a diploma in datametrics. I did well in all the computer courses, but I had to do a module in physics as well. I went to write the exam and managed to get a magnificent 38%.
The University allowed me to rewrite a supplementary exam, and I had two months to get myself sorted out. I had already learnt the work with all my heart. Two months later I rewrote the exam, and passed with a mark of 88% ! This enabled me to pass the Diploma cum laude, with distinction.

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Well, I discovered a secret to learning subjects that involve figures, numerical problems and the like. The secret is simple: practice.
The text book I was working out of had the answers to all the problems at the back of the book. So I tried to do the sums without looking at the answer. Then I would check. If the answer was wrong, I would try again, using a different approach. If that didn't work out, then I would start with the answer and work backwards to the start. Then I would do the next question. I solved every question that I could find. I practiced and practiced.
I worked in pencil, with an eraser handy, so that if the sum got messy I could clean it up. I used lots of scrap paper. It was hard work, but after awhile the elation of solving more and more questions first time round started making it a breeze to do.
So to summarize:
1. Get a book with lots of problems to solve in it. Make sure it has the answers in the book.
2. Only look at the answers to check if you got it right. Try to solve it first before looking at the answer at all.
3. If you can't get it right, try again.
4. If you still can't get it right, start with the answer and work backwards.
5. Do every problem you can find. Do them again if you are not yet confident.
6. Be prepared to work hard, and it will pay off big time.
Just the other day I gave this advice to a granny who was looking after her 14 year old granddaughter. This young girl was failing math and Granny couldn't help her much. Three weeks later she saw me again, and couldn't wait to thank me. Like that guy Hunter said in the TV series of the same name -- It works for me!

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Using Printable Math Worksheets

printable math worksheets, an old-style teaching tool!
The Cause
Printable math worksheets can be used by both parents and teachers to help kids overcome some of their most common problems in leaning math.
You see, I'm a professional educator. I teach high school. I'm also a parent. (I wear both hats!) Year after year, I see kids come into my classes completely unprepared to learn math.

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When I diagnose what the problem is, it's virtually always either they don't know their multiplication tables or, more often, they don't know how to work with fractions.
I teach the upper grades in my school, yet I continue to see kids who do not even have basic algebra skills in place.
As a parent, I'm very aware of what my own children are learning in school. For the most part, I've been happy with their progress, but as they rise in grade level, I'm starting to see more emphasis on a loose understanding of the concepts and less emphasis on skills--particularly skills with arithmetic of fractions.
The main problem with what I see with my students and my own children is that kids are taught "concepts" and are not taught skills--unless they're lucky enough to have a teacher who knows better.
Most particularly, children are not taught mastery of arithmetic with fractions. Unfortunately, virtually all of their future math education depends on being able to do fractional arithmetic.
Most of even beginning algebra depends on being able to do two things--one, doing multiplication quickly and accurately in your head, two, knowing how to add, subtract, multiply, and divide fractions.
You might remember a concept in algebra called "factoring." Factoring means breaking up into parts that are multiplied together to give you the whole. You can factor numbers. For instance, 6 factors into 2 and 3--2x3 =6. In elementary algebra we learn to factor expressions such as x^2+4x+4. This particular expression is easily factorable into (x+2)^2.
Just trust me, if you don't know your multiplication tables, you can't factor. If you can't factor, you won't do well at all in algebra, geometry, or trigonometry.
The same is true for mastery of working with fractions.
So, in general, kids who don't learn their multiplication tables and arithmetic with fractions usually don't do well in math. It's been proven that success in science depends to a great extent on success in math. So, these same kids usually don't do well with science, either.
If you want your child to have access to the major portion of jobs in the future, your child must master math. The Solution...or at least part of it
Teachers are actually doing their best to educate children. The problems with education aren't so much on the level of teachers as with the institution as a whole. It's kind of like the state of communications in our country before the deregulation of the telephone companies. Before deregulation, one and only one advancement--the touch tone phone. After deregulation, well you have cell phones, the Internet, instant messaging, you name it!
What dedicated teachers and parents need to do is to supplement public school instruction with strategies that work, that have always worked, to get kids to really master the fundamental skills of elementary math.
One of the most effective ways I've found to help kids in a focused area of weakness are printable math worksheets. The big problem with concept-based instruction is lack of practice. Printable math worksheets solve this problem nicely.
As a teacher, I supplement my lessons with appropriate worksheets. I can then check a student's progress. For parents, printable math worksheets are a great tool for drilling their own kids in those same skills.
Make no mistake, printable math worksheets are not a relic from the past that needs to stay buried. They are useful, focused tools for the classroom or at home.
You can find resources all over the web for worksheets. Finding answers for worksheets, however, is not that easy.
For that you often have to use paid subscription services.

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Easy Mathematics

Many students consider mathematics to be a difficult and scary subject. Difficulties can be overcome when you replace your fear with curiosity. If you give proper attention to this subject you will surely begin to like it. Math becomes very easy once you stop hating it.
What is the importance of math in real life? In fact, its scope is far beyond daily calculations and planning your monthly expenditure. It is said that all biology is ultimately chemistry; all chemistry is ultimately physics and all physics is ultimately mathematics. Today economics is one of the most popular subjects. Every curriculum pertaining to economics also has math as its integral part. At an advanced level its applications are incredible. For instance, the Nash Equilibrium (in Economics/Statistics) can be used to predict stock market trends and even in resolving war between countries. Learning math improves your mental skills. If you are good at math you will be able to solve day to day problems easily. This is because your thinking becomes logical when you properly study it.

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Very few students have an aptitude for this subject. Nevertheless, everyone has the basic capabilities that are needed to study the subject at the school level.
Yet all the theorems, axioms and formulae sound like double-dutch to most of us. First of all, your knowledge of the subject's basics is not sound. Secondly, it could be because of your faulty approach to the subject.
Dealing with the first problem is more difficult. You will not be able to understand anything about Conditional Probability if your concepts of Permutations and Combinations are not clear. Speak to your teacher about any such problem and seek their guidance. If possible, try to consult books from the previous term. You should deal with this problem as soon as possible. The longer it persists the harder it gets.
As far as your approach is concerned, you should never attempt to learn math. The only way to learn mathematics is by understanding it. Try to make it a pleasant experience. Reward yourself with, say, a candy every time you make even a small success. Our brain learns new things by observing and repeating. There is no alternative to persistent practice.
It will become a lot easier if you try to understand it in practical terms, as opposed to theory. For instance, let us speak in terms in LPP (Linear Programming Problems.) There you have to express practical situations, such as rate of production of a certain machine, as a mathematical expression. A proper understanding of both practical and algebraic form of the problem is required in such cases.
Math is easy if you let it be so. Remember that if you do well in mathematics, you will have many exiting and promising career opportunities. People with goods mathematical skills are always wanted in computer related fields. Even animation can't be done without programing that involves a high level mathematics.

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Mathematics in Computer Programming

Mathematics is applicable in various traditional fields of engineering: mechanical and electrical engineering are among them. Mathematics is used in computer engineering too.
As Venn diagrams are helpful in understanding the concepts of logic, they are also helpful in the programming. For instance, De Morgan's laws are used in writing statements involving decisions and Venn diagrams are helpful in understanding these laws.

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Calculations are also important in the science of computers. The text you read on the computer screen is presented in a particular format. Geometry is used in the development of graphics. Actually a graphics screen resembles the co-ordinate plane. Just as we have points in the co-ordinate plane, we have pixels on the graphics screen. Though there are endlessly many points in any bounded part of the plane, while the number of pixels on the graphics screen is limited, yet the techniques of coordinate geometry can be used in drawing various figures on the graphics screen.
Various transformations play a part in the development of software. Two such transformations are famous as 'pop and push transformations'. As the graphs are useful in understanding different kinds of transformations, these help understand, in particular the Pop and Push transformations too.
The classical computer programming language namely 'the C language' makes a lot of use of mathematics. Different graphics commands of this language are based on the mathematical logic.

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Why Advanced Mathematics is Hard

If you are wondering why you have trouble understanding the likes of advanced mathematics, you might consider that the writing and teaching quality in this field is abysmal at best. As someone who has studied mathematics at the graduate level and beyond, I can say without reservation that there are very few books, and indeed, even fewer teachers, who can convey an understanding of this subject at the higher reaches. Mathematics is a wonderful tool which permits us to understand our world; however, the latent complexities of the subject start to manifest as we try to use this tool to understand the likes of black holes, antimatter, and genomic transcription. Yet understand mathematics we must, as we progress and problem solve in direct proportion to our decoding of this wonderful discipline.

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For many algebra and pre-calculus set the limits of their mathematical understanding. Moreover, to understand the nature of the universe and the myriad mysteries of life, we need much more advanced tools: topological spaces, advanced number theory, chaos theory, and partial differential calculus. The lower branches of mathematics provide the raw tools to unravel the mysteries of these higher branches, yet these higher realms once entered, mystification rules and most quit before they even have the chance to start unraveling the fascinating mysteries of mathematics.
As I see it, the main problem in understanding more advanced mathematics boils down to patience on both the teachers and writers who try to promulgate this material. Many professors and teachers will argue that there is not enough room in a text to break down the subject matter too much, that there would be too many breaks in continuity to proceed in this manner. Yet by not providing adequate exposition, these very same "promoters" of the subject are actually losing their audience to obfuscation.
Personally, I enjoy shedding light on the mysteries of mathematics. Granted I am human and subject to the same limitation of comprehension that everyone else is. Thus I find it daunting when I cannot make heads or tails out of the more advanced reaches of this subject. People interested in mathematics want to be able to understand the likes of partial differential equations, abstract algebra, and their underlying theories. Many individuals (talented at that and potential mathematicians) could understand advanced mathematics if we had better writers and educators. Alas, it seems that many who have finally understood the more advanced reaches of the subject insist on keeping such arcana "secret" and only allow certain chosen ones to enter the circle of understanding. Only then can we propagate mathematical education efficiently and thus create more scientists and mathematicians who will at least give us a chance eventually to help solve the many problems confronting us in the world today.

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Music and Mathematics

If you thought music was not a mathematical language, then think again. 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.

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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. The "distance" between each of these notes is called a half-step. 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. 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. 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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10 Tips For Teaching Middle School Math

As a teacher for 11 years and middle-school math teaching consultant, I've seen a wide array of different math programs and classes. I'm sharing here the 10 best teaching tips I've compiled over the years.


1. Provide compelling content to study.

Years ago, a colleague I was working with said, "Maybe class can be fun, but I can't make class compelling. I have to teach math!" It's an assumption worth exploring.
Take Ron Berger's middle-school math project to study levels radon in their own homes. Studying radon is boring. But Berger's class project has got to be one of the most compelling projects in math class history. What if his students discovered dangerous levels of radon in the homes of one geographic area and published the results as they had intended? So what's the trick? You can't trick students into finding something compelling if it isn't. Take a little bit of time to develop a few topics of study throughout the year that you find compelling- the Economy, the Presidential Campaigns, the Human Body, etc. Find an authentic way to present your result- the paper, the web, a magazine. Keep the project small, authentic and do-able.
Students of teachers that do take this kind of time have better outcomes on state tests than students of teachers who only stick to the text. Almost any social studies context provides a backdrop for learning that adds depth.
Even teachers who hold a math "topics" class only once a month see real benefits, so you don't have to abandon your regular class. And, you'll find that students are more engaged when regular class is held.
If you want to go really deep and have solid administrator support, look into the school reform movement of Expeditionary Learning Schools who have an excellent approach to thematic teaching.

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2. Don't use extraneous rewards such as candy, purchase points, stickers, etc.

There is nothing more certain than seeing the culture of a math class decline over a period of years when a teacher bribes them. A teacher cares about his or her students and wants the very best for them. "I don't care how they learn math," one teacher said to me. The teacher cared enough to purchase candy out of her own pocket, but the real message to students is this: the "positive reinforcement" of candy means "math isn't worth doing on its own." The research is clear on the matter too, and shows us that extrinsic, non-relevant rewards hurt learning.
Even if the effects aren't immediate, over time so called "positive reinforcements" like these mentioned above erode an otherwise high-quality math program. As a teacher, you are much better off trying to create inherently compelling curriculum than buying candy.

3. Build a culture where students teach each other.

For many teachers, one student helping another is called cheating. But I actually found that the better middle-school math programs all encouraged students to team together at certain times throughout the week. The activities were usually graded as complete or not-complete, and when tied to meaningful tasks, such as building a survey together and collecting original data, student comprehension was greater than on individual tasks.
Building the kind of culture that works for student pairs or groups takes years and lots of practice.

4. Give less, but more meaningful work, including homework.

The Trends in International Mathematics and Science Study labels the curriculum in the United States as "a mile wide and an inch deep." Their review of math texts in middle-school found that some were almost 700 pages long. With heavy pressure to teach to the standards, as a teacher you might be tempted to skip and jump to many topics throughout the text. It achieves little learning.
Teach the concepts you do teach with depth.
The national advisory counsel formed from the study recommended "put first things first" and suggested that indeed, less is more. Take the time to cull the curriculum to a manageable size for your students, and present them with only that. If you have to "cover" standards, find out what standards and document when you indeed teach them in class. You'll find that teaching with depth often reaches to a broad array of standards.
It's helpful to know what's driving the breadth. As the national study panel concurs, publishers are trying to meet demands of hundreds of different districts by including everything that any school might want. And while publishers have been attempting custom publishing, it is just as difficult to create a math curriculum for a small district as a large one. Thus, the challenges of book publishing lead to a single, uniformly created overarching textbook. Often this is a very large text or an entire series.
In the classroom, teachers and students become overwhelmed and unable to handle the scope or breadth of learning in this form. As teachers, we have to recognize that predominantly negative emotions surround math in middle-school, and that anything we can reduce those emotions will go a long way toward gains in learning learning. Placing a 500 page text in front of a 7th grade student is unlikely to help, so use it sparingly and build little, home-made notebooks for daily use.

5. Model thinking, not solutions or answers.

Don't show a student how to solve something. Instead "think aloud". I am confused about..." Model exactly what you thinking including confusion, emotions, skills, strategies and more.
When you do this, also let your students know how mathematicians think. One piece of research that is helpful to know is that mathematicians spend a long time thinking about how to set up a problem, a little bit of time doing the problem, and a long time "looking back" by asking the question, "Does this make sense?' Model that for your students, by putting up a complex problem on the board and spending time not just jumping into a solution, but just talking about what strategies you might use to solve the problem.

6. Provide feedback that is immediate, relevant to the task, non-comparative, and leads the way to next steps.

Many teachers believe that grading is a form of feedback. Grading, when done well, can be a form of assessment of learning, but the distinction should be clear. Grades are not an effective tool as assessment for learning. Grades are the end of the road, when you assess what has been learned, but they should not be intended to inform a student where to go next.
Take, for example, three groups of students who received different kinds of "feedback" on math papers they had "turned in." The first group received only narrative feedback (no score) informing them where and how they made mistakes. The second group received a grade (or score) and narrative feedback. The third group received just a grade. Not surprisingly, the students who received narrative feedback improved when re-tested. There was no difference between "grade-only" group and the group that received the grade and narrative feedback. Why? The students who received both a grade and narrative feedback completely ignored the written suggestions and only looked at the score. "I got a blah, blah, blah... what did you get?"
Because we live in a world where grades and formalized assessments are so important, work with the system by differentiating assessment for learning and assessment of learning.
When you are grading, one guide is to reference Rick Stiggins strategies of assessment for learning. That way, when you are conducting an assessment of learning (i.e. grading), you'll notice that you are momentarily stepping out of the role of improving a student's learning and won't have the conflict of trying to do two things at once.

7. Change mimeographed sheets to problems you and your students personally develop.

A pervasive aspect of our culture is to give out page after page of information. In faculty meetings, business meetings and conferences, hundreds of pages of documents are handed out. It makes us look organized and prepared. It's also a way to "cover" content. But for a middle-school math student, it also makes it hard to determine what is important. Was it the fractions part? Was it the decimals section? Was it the number line? Was it the triangle puzzle problem? Was it the cartoon?
Instead of another mimeographed page, have your student write their own story problems. Tell them to add artwork for comprehension. Give them the latitude to make them fun. Celebrate them by posting them in class. Give them 5 home-made story problems they create for homework instead of a mimeographed sheet with 30 problems, and really dive into improving them through revision.

8. Use story to teach math.

Write a story, a real story with characters and plot, and add the math problem set. Write about wizards that need to use angles for their sorcery. Write about spice trading ships on the deep seas. Write a story that lasts a whole page before even getting to the math portion. You've engaged the right-side, or less analytical, part of the brain and you'll see a powerful effect of enhanced engagement.

9. Get math tutor volunteers once a week for two-months before state testing.

As a teacher or administrator, spend time during the fall months by planning for and scheduling a single day each week during the months of February and March (right before testing) to have volunteers come in to teach math in small groups. But what's nice is that if developed correctly, these volunteers don't need to have any special training in math.

Each student has 10 skills they have chosen to work on during the whole class tutoring session and have written down their practice problems in class. The phone calls are made, the specific planning with an administrator is done, and volunteers come in and help the students answer the 10 questions during class with support. Schedule tutoring once every week for two months before testing and see your scores greatly improve.

10. Work with the emotions your students have for math.

10a. Ask your students how they feel about math. Use a bit of class time periodically to gain a better sense of where they are. If your students can't stand math, you will gain far more ground by seeing their perspective than trying to prove they are wrong. As a teacher this is hard because we are so accustomed to trying to "fix" the situation, and of course, our ego is tied to student emotion. If our students are bored, we feel like we aren't doing the right thing. But the larger truth is that there is an ebb and flow in all of us for the topics we are learning. When the boredom, frustration and negativity does emerge, try understanding it. Perhaps class does feel a little boring. 10b. Go slowly. Changing the direction of your math class is like trying to change the direction of a large ship, especially when dealing with emotions. Even once everything is place for the changes to occur, you will notice the "ship's" momentum going in the same old direction before you sense any real shifts. This is part of the process. It took me three years to develop a coherent math program at my middle-school and even then, we occasionally slipped in to old patterns. Good luck!

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Tips To Get Ready For College Math

The skill level needed for college level math is quite high. To get yourself ready for any of the higher level math available in college courses you need to follow some of the techniques outlined in this article. If you're already in college trying to catch up may be too late. The time to get ready is now before you have to actually do the work. It's better to be over qualified than under qualified. Take high school math at its highest level to get the most out of your early training. Graduating from high school may not require you to take advanced classes, but the extra effort you put in now will really help you to succeed in college.

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One of the best ways to gauge if you're ready is to attempt to solve some of the math problems you would see in college. It will tell you if you need to study more or take some extra math training to get your skill level up to where you need to be.
Doing a quick search online for college math lessons is a great way to gain extra skills. Many places have video lessons you can learn from. These videos can teach you a lot and will start to give you an idea of what will be required of you when you get to college. One of the great things about sites like YouTube is the simple fact that if you have a problem with what you're watching you can review it again until it comes to you.

There are also e-books you can download that have lessons in them for those trying to get a grasp on college level math. Many of the equations in the e-books have the answers in the back so you can review your work and see if you are doing it correctly.

In some cases if you are struggling hiring a tutor may be an option for you. It is a great way to get some one on one training that you would otherwise not receive. Tutors can become quite expensive so you would need to go over your finances and see if that is an option for you. If you can't afford it you can always see if there are others that would like to split the cost of a tutor with you so you can learn as a small group.

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Magical Strategies for Increasing Math Confidence

As an adult, student, or parent, it is common to experience a lack of confidence in dealing with numbers. This common problem many times gets blown out of proportion and can sometimes be a roadblock to success in school, work, or helping your children become more confident in their abilities. In this article, I outline five skill areas to improve in order to increase your own skill, speed of calculations, and self-confidence when thinking mathematically.
In school, beware of things being taught but with inadequate time given to practice. Think of these ideas as homework assignments for you or your children. If given enough time, these building blocks can tremendously help a student get through mathematical situations in school or life with ease!

Download Links Exam Drill for SNMPTN - Basic Math

Math Skill Building Block #1: Basic Math Facts

This step is very common sense, but extremely important, and is sometimes not practiced enough in elementary school before students are allowed to move on. Everybody MUST know addition and subtraction facts of at least two-digit numbers. Push the calculator away; practice adding or subtracting two-digit numbers comfortably until you can do this quickly without your fingers.

When you really know these, you should be able to list the multiples of 12 easily, or count backwards from 100 by 7's, etc. If you are working with your child, try these multiple lists or counting backwards subtract exercises.

TIP: Break numbers apart in order to add or subtract. Math Skill Building Block #2: Working with Percents

We know how important this is when we work with money, finance, buying & selling, investment, and other parts of our lives.
Students must be able to work with percent concepts. To practice, find 10% of any number.
Likewise, people need to find 1% of a number (move the decimal 2 places to the left), 5% (half of the 10% amount), 20% (one-fifth of something), 50% (half of something), 75% (half of the number, then add half of that). The understanding of percents and their fractional equivalents is HUGE! And, it takes a lot of practice and repetition.

TIP: A magical way of finding the percent of a number is to take advantage of the fact that, mathematically, 15% of 50 is the same thing as 50% of 15 (7.5).

Just switch the percent number with the other number to find an easier calculation. Math Skill Building Block #3: Using Estimation and Rounding.

The ability to estimate how much something will cost, how much paint needs to be purchased, how much space is required, etc., is a critical skill for students to master. With repetitive practice, all of us need to be able to improve our speed of rounding numbers before a calculation, or rounding the result of our calculations. Most of the time, we don't need the exact answer. Knowing how much to round and estimate our numbers is tested all of the time in our math and science classes at school.

Look for opportunities to find estimates: cost of a home improvement project, money earned over time, time it takes to accomplish a task, or increase and decrease of temperature over time. After estimating, challenge yourself or your children to use a calculator or paper to test out how close you are to the actual answer. If students can quickly estimate an answer, even for a complicated calculation or problem solving exercise, their confidence will skyrocket!

TIP: Practice estimation skills when grocery shopping. You or your children can call out the price of an object before putting it in the cart, and keep track of the estimated total. Whoever is closest to the actual total is the winner!

Math Skill Building Block #4: Creating Your Own Word Problems

This skill is the reverse of the dreaded task of reading a word problem from your math textbook and solving it. In this case, parents or students should think of a situation in terms of how it could be written in a math textbook. I encourage my students to put a problem in their own words (aloud), then write it out on paper (they can be really creative at this point), then do the next critical step: look for mathematical operations clues. These "clue words" force the solver to think about how the quantities are related or how they interact in the problem. If students can't put the situation into mathematical language, then they don't really understand what is being asked.

TIP: Mathematical "clue word" to look for, after you write out the problem on paper ---
Addition: sum, total, together, combined, given to, put in the pile, money earned
Subtraction: take away, withdrawn, money paid, amounts lost, less
Multiplication: multiple groups, piles with the same amount, repeated addition, "of"
Division: split into groups, how many in each group, part of, "part"
Math Skill Building Block #5: Understanding Basic Geometric Concepts
The geometric concepts of area, perimeter, and volume are ideas that can be directly relevant to students as they study them in school. A simple connection could be the task of building a house or constructing anything. Other ideas to include are properties of squares, rectangles, and the sides of special right triangles.

Building block #3 (Estimating) ties in to this idea, also.

Have yourself (or your children/students) estimate the volume of water that a certain container will hold. Use simple block shapes at first to reinforce the volume formula of three-dimensional objects (area of base X height, OR length X width X height). Then pour water into the container that has measurements on the side to check the estimate.

Another idea is to measure the two legs of an object that is in a right triangle shape. Then estimate the hypotenuse (diagonal distance). An example would be to find out how high a set of stairs is, how far out horizontally they reach, then measure the distance along the top of each stair down to the lower level. For older students studying the Pythagorean Theorem (for right triangles) this is a great application of the idea. For younger students, ask them how far it looks from one corner to the other of a rectangle or square on a piece of paper. Then measure to see who is closest.

TIP: Geometric ideas relate directly to objects found in our everyday lives. Take advantage of this and practice applying what you know about squares, rectangles, and diagonals to estimate square roots without the calculator. Then check your calculations. You will feel or see increased confidence after several successful tries.

These building blocks are taught in the early days of everyone's education, but sometimes are not practiced enough to be effective tools in your mental toolbox. Whether you are a student, parent, or someone who feels a lack of math confidence, keep these tips in mind. It doesn't have to be dull; just increase your speed with basic math facts and estimation, then learn to work with percent concepts. Look for "clue words" in problem solving situations, and check things out later with a calculator. With these tips, anyone can again rediscover their "math brain!"

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