## High School Math Classes – Tips for remembering Popular formulas

One of the most difficult issues for many math students is the fact that high school math classes are recipe dependent. Some students have difficulty memorizing formulas. Other students can memorize formulas without difficulty, but do not understand how to use the formula, or do not understand what the result of the formula does. If you get into any of these categories, then success in math class will be difficult to achieve. There are, fortunately, some tips and techniques that can help

formulas fall into two main categories :.

1) Computational Skills. This is the type of formula that typically arise in Algebra and is particularly difficult to understand because the symbols often have no meaning. Memorize that a ^ 2 – b ^ 2 = (a + b) (a – b) may be easy, but it may have absolutely no meaning for you and will therefore have little value to you. The technology that we will discuss is especially important for this type of formula.

2) Obvious Real-Life Application. This is a more in geometry and trigonometry. They are easier to understand, but the techniques can help with this as well

Tips to remember formulas :.

1. Understand the importance of the most important formulas that they state relationships always exist – are always true. This means they can always help you! However, for formulas to help you, they must have meaning for you. Computational formulas take considerably more effort to create the meaning. We will discuss this well # 3

2. Memorize the formulas as you encounter them. You may be able to do your homework just by looking at the formula, and not wait until the night before the test to try to memorize many formulas. Working with formulas you encounter them and get them into long-term memory immediately will ensure that this information is learned forever and not just for testing.

3. Memory formulas in symbols and words. The formula d = RT will not have as much meaning or kept as long as the word version: distance is equal to the speed / velocity multiplied by the time the rate

This can be more difficult. computational formulas, but it is worth the extra effort. For example: the formula a ^ 2 – b ^ 2 = (a + b) (a – b) how to factor the difference of two perfect squares. “To element” means to “re-write the multiplication.” Thus, the recipe should be read as: “. The difference of the squares of the two numbers, written as multiplication, is equal to the product of the sum and difference of the two numbers”

4. Always read the formulas as complete thoughts or sentences. Formulas must always have the same sign. Thus, the formula for the distance is not rt. The formula for the distance d = RT.

5. Always confirm that the formulas are true. For example: The difference of two perfect squares might look like 25 – 4. Obviously, the value is 21, but if we get this value using the formula we will have established formula. Is described by formula, 25 – 4 could be written as 5 ^ 2 – 2 ^ 2 and would like element (5 + 2) (5-2). = 7 (3) = 21. Thus, the formula is confirmed

6. Know how to mark answers recipe and what the answers mean. Be specific reading formulas. Since all the area formulas start with A =, it is better to add more information. The A = (PI) r ^ 2, it is best to read what “. The area of ​​a circle equals pi times the square of the radius of the circle” Be sure to remember this area is always measured in square units.

Probably the best way to learn formulas to make flash cards and you encounter new formulas. Do 2 sets of maps. The first set should have the formula name on one side – Triangle Area – and the full recipe on the other side -. A = 1/2 b H

The two sets of cards should have a recipe on one side – A = 1/2 bh – a worded version of the formula on the other side – the area of ​​a triangle is equal to half of the base product times the height of the triangle

When working with flash cards :.

a. Have someone working with you,

b. Only work for about 10 minutes at a time, but

c. Make several sets a day until all the memory and meaningful

Final thought:.! Do not just learn the popular recipe – master them all

## Tips, tricks and techniques – Help Solving Word Problems

If you need help solving word problems you’ve come to the right place. Mathematics has always been a fascinating subject to me because of the logical and accurate it is. It is similar to learning a second language in the case of solving word problems, very much like solving a puzzle. If you are going to be good at solving word problems, you have to be a good investigator and be able to pick up on the clues that will help you solve the mystery. Working with a problem requires reading comprehension as well as the ability to solve mathematical equations. With that said, the purpose of this article is to offer help solve word problems and provide aspiring mathematicians with a strategy to solve these problems

The length of the NBA basketball court is 44 feet more than it is wide. The length of the court in terms of its width.

The first step in working with word problems is simple, but important. Read all problems … then read it again! As basic as this may sound, this is where reading comprehension skills come in to play. It is at this critical time, you must do the following things:

1. Identify the information you need :.

The court is 44 feet longer than it is wide

2. Identify the information you need not (and still have) :.

length of the court

3. Determine what a problem is to ask

equation expressing the length of breadth

The next step is to start planning indicators Your .. Start by first assigning variable names to pieces of information that you have and have not. Name (s) should be clear and meaningful. So we will allocate length basketball court parameter name “L” and width variable name “W”.

One thing that has always helped me to understand the terminology is drawing them on paper. Usually, if you can visualize a concept, he or she can better understand it, whether it’s math or something else. So after you know the information you have and assign unknown parameters, draw a picture. Be sure to mark it with known data and unknown parameters.

last step is to look for a problem for keywords. Some words will tell you what mathematical operation is needed or at work to find a solution. In the table below are some of these terms:

Addition: Total sum, increased by more than, wholly / together, combined, in all or in addition to

Deduction .: difference, less / fewer than dropped by, minus or less

Multiplication: .. Multiplied by, times, or the product of

Division: for, to, of, rate of, quotient of, or percent

Equals: .. Is, are, was, were, give or yield

Using basketball court our example, we are told that the length of the court is 44 feet more than it is wide . There are two keywords / indicators that we can recognize in this statement; “more than” indicating that the addition (+) will be the mathematical operation that will be at work here, and “is” which can be translated as “peer” or “=”.

Here’s where we make our translation from English terms mathematical concepts to come up with an equation. We are asked to express the length of the court in terms of its width. We need to come up with an algebraic equation shows the length “L” written in terms of width “W”

Here is a translation :.

L = 44 + W

The nation “is” 44 feet “more than” width.

So is the answer to our problem words expression L = W + 44

Now just kicks and laughs, let’s look at a few more simple examples of translating from English to math equations by defining keywords.

Example # 1 Write the sum of y and 16, Tory.

This can be written as “y + 16”

Example # 2 Write the difference between 2x and y that stood

This can be expressed as “2x – y”.

Example # 3 Write the rate of 6 more than 2 times y X that expression.

This can be written as “(2y + 6) / x”

key to help solve a problem is to develop the ability to search for keywords and phrases translated phrases and mathematical equations. As with everything else in mathematics, this skill can only be sharpened by making lots and lots of these problems. After that, when you come across the word problems you will be confident in your ability to deal with it instead of looking at it and thinking to yourself …. “Word Problems … Ughh !!!”

happy to solve the problem !!! Now, go to practice!

## Mathematician Jobs – Are you interested in becoming applied or theoretical mathematician

?

Math is a very old science that has been practiced for thousands of years, and mathematical functions can be divided into two major categories that include theoretical and applied mathematics. These experts will solve various engineering and business problems, often with algorithms and computer technology to achieve solutions.

Theoretical mathematicians are responsible for the treatment of various laws of physics and engineering with the principles of mathematics, and they will use abstract knowledge in order to further scientific progress. These professionals are generally hired university and they will usually have the dual role of teaching and research.

Applied mathematicians will take mathematical theory work and use computational methods to solve everyday problems in the social sciences, such as developing new drugs or designing smaller silicon chips. These professionals will usually take complex issues and boil it down to its simplest elements, using computers to analyze variables, in order to solve problems.

Most mathematicians work in a fairly cushy jobs and have a 40 hour work week, usually a combination of teaching and research. Most people will be required to have a PhD in order to get employment, even if they work for the Federal government may be able to get employment with only a master’s degree in mathematics.

Other appropriate that these individuals should have a capacity to analyze complex problems and to apply mathematical principles of complex situations. Mathematician jobs are expected to grow at an average rate of population growth in America, and the job itself is fairly immune to the downturn.

In 2006, these individuals had about 3,000 jobs in America, with most of the work for the state and federal governments, with the Department of Defense to be the most common Federal employer. Most private employers are scientific organizations and technical advice. Other mathematicians may work for software design companies and insurance agencies, as well as pharmaceutical manufacturers and aerospace companies.

In 2006, the middle 50th percentile of these individuals between \$ 63,000 to \$ 106,250. In 2007, a theoretical mathematician working for the Federal government had average salary of \$ 93,539.

## Music and Mathematics – there are many Connections

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

For those with a rudimentary knowledge of music, 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 points pattern wave physics and frequencies. The sine wave is one of the basic pattern surge in mathematics and is displayed well alternately Crest-lowest extent. Many physical phenomena and real-world can be explained by this basic wave pattern, including many of the fundamental tonic properties of music. Certain musical notes sound good together (musically this is called reconciliation or consonance ) due dots pattern waves strengthen each other at select intervals.

If you play the piano, then how each of the different notes sound to you depends on how your instrument is configured. There are different ways to tune instruments and these methods depend on mathematical principles. These artefacts are based on the whole frequency applied to a particular mind, and as such, this product whether groups of notes sound well together, but we say such comments are in harmony, or incompatible, but we say such remarks are out of harmony or dissonant.

When this product coming from the launch of criteria instruments manufacturer and today there are certain criteria that these fabricators follow. Still criteria Despite a multiple nature of mathematics. For example, in more advanced mathematics, students learn some numbers. A series is simply the pattern numbers are determined by some rule. One famous series is harmonic series . This includes the reciprocals of integers, it is 1/1, 1/2, 1/3, 1/4 … The harmonic series serves as one set of criteria for certain tunings, one in particular called Pythagorean intonation .

In Pythagorean intonation, comments are set according to “ rule that perfect fifth .” A perfect fifth consists of “ musical distance ” between the two tones, such as C and G. Again without trying to turn this article into a thesis on musical theory, are notes between C and GC #, D, D #, E, F, F #, and G. The “ from ” between each of these notes is called a half-step. Thus, the perfect fifth 7 half-step, CC #, C #, D, DD #, D # -E, EF, FF # and F # -G. When we consider the notes in a musical harmonic series, a number considered a C note and attributed to G mind will always be in the ratio of 2: 3 So the frequency of these notes will be adjusted to their ratios in accordance with the 2: 3 There is C- note the frequency will be 2/3 G-note frequency, or vice versa, G note frequency will be 3/2 C note frequency, the frequency is measured in cycles per second or Hertz.

Now, continue to adjust according to the perfect fifth, fifth above G is D. Use perfect fifth rate , D note will be tuned to the frequency of 3: 2 G frequency or watched from below, G note is 2/3 frequency D note. We can continue the same way until we complete what is called Ring of the fifth , bringing us back to the C note by applying a series of ratios 3/2 in the previous note in the cycle. This includes the Twelve Steps and when complete, the frequency of the second C or higher octave C note should be exactly twice frequency lower C note. This is a requirement of all octaves. But this does not happen by applying this ratio to 3/2.

Musicians have corrected this problem by resorting to none other than the field irrational number . Recall that the numbers are such that they can not give up the offense, that is, a decimal representation of them, like the number pi or the square root of two, providing not and do not repeat. Thus failure of a Pythagorean tuning method for producing perfect octaves, tuning methods have been developed to prevent this situation. Is called “ equal temperament ” Tuning, and this is standard procedure for most practical applications. Believe it or not, this tuning method involves the rational powers of the number two. That’s right: folded chose number two . So if you thought you were studying rational exponents for nothing in algebra class, here is one example of where such a debate is used in real life

Route equal temperament tuning works as follows :. Each note through its octave has a frequency multiplier repeated twelfth root of two to get to the next higher note. That is, if we start with the traditional note, which vibrates at 440 Hertz, let’s say, getting to # 440 multiplied this by 2 ^ (1/12). Because the twelfth root of two is equal to 1.05946 to five decimal places, A # was tuned to 440 * 1.05946 or 464.18 Hertz. And so continues tuning with the next Note B by taking 2 ^ (2/12) * 440. Note that with the increase of twelfth power 2 by 1 every time the power 2 of 1 / 12, 2/12, 3/12, etc.

What is nice about this process is exactness, unlike inexactness of Pythagorean intonation method discussed earlier. Thus when we arrived at the octave note, almost on top of the standard A, which should vibrate twice the original frequency of 440 Hertz A, we get A octave = 440 * 2 ^ (12/12) 440 * 2 = 880 Hertz, as it should be — exactly. As we noted earlier, when the set of the Pythagorean method, this does not happen because of repeated use rate 3/2, and the accommodation must be made to bring into line the inexactness of this approach. These great cause noticeable dissonance between certain notes in certain keys.

This tuning exercise shows that math and music are closely intertwined, and indeed it can be said that these two disciplines are inseparable. Music truly is mathematics and mathematics is well, yes music. Since many people think of musical talent coming from “ creative” species and math capabilities come from “ nerdy ” or non-creative types, this article is in some part help disabuse these same people of this idea. Yet the question is: If two ostensibly different fields like music and mathematics are happily married, how many other areas out there that at first seem to have nothing to do with mathematics, are just as intricately linked to this most fascinating material. Consider that for a while.

## How to win the lottery mathematics

If you really want to increase your odds of winning the lottery then you need to do two things. First, you can increase your chances of winning by working with law probability. To do this is relatively easy. You can also play more lottery numbers than you would normally. Using a mathematical system that you can take more numbers than usual and make sure they all end up together on the target.

Let’s look at how you can play more lottery number combinations in the lottery without having to spend a fortune to do it. Play more numbers than normal on the lottery and mix them so that you have all the possible combinations is called “wheeling.

Lottery Wheeling is a method you can choose more numbers than you normally would with a standard ticket. For example, 6 of 49 tie (like the UK lottery) you do not pick 6 numbers than a 7, 8, 9, or any amount you can afford to play.

You create the combination of these numbers so that every possible combination is on target. You’re there with a better chance of winning the prize. If you select the 6 winning numbers in the combination of numbers then you will definitely win the jackpot prize. Therefore, you have a better chance to select 6 winners because you’re picking more figures. However, it also means you win more prizes when you do the math winning numbers because they tend to fit in some of the target.

When the wheel numbers that you will be ready to buy more tickets. While you will be required to buy more tickets it is well worth the investment especially if you play the part of the coalition. For a measly £ 28 you can increase the number of bikes on the UK National Lottery and bring your odds of winning the jackpot prize down from 14 million to 1 only half a million to 1! The odds of winning smaller prizes are incredibly high.

Even though you greatly increases the chances of winning the top prize by using WHEELING system this is not their primary purpose. When using Wheeling with lottery numbers to ensure you win many smaller prizes when you select just a few of the winning lottery balls.

When you add Wheeling system to other systems designed to work with the laws of probability you increase your chances to win even more – sometimes amazing

Although there are very sophisticated methods to manipulating the law likely the easiest one for you to use now is to choose the lottery hot number. Hot numbers are the numbers that appear in the lottery more than usual. These numbers come up in the lottery draws much more to the rest and they can usually be found under the “hot numbers” on the lottery Web site or by searching the internet.

There are better lottery systems that have been designed to give you amazing chances to win, but now you can use Wheeling and likely to increase your chances.

## ASVAB Math Tricks – Multiply the numbers that end in zero

If you are studying for the math part of the incoming Armed Services website vocational Aptitude Battery, or ASVAB test, you will probably face many calculations at first glance seem to require either a calculator (which is not allowed) or long handwritten form calculations to get the answer. My goal is to show you not only how to simplify the mathematical process, but also to show you some mathematical tricks. In particular, this article will focus on multiplying numbers that end in zero

If you are facing the ASVAB style question asks you to multiply two medium or large numbers, such as 22 times 37, you can find yourself spending too much time with a pen and paper. If instead you simplify the numbers to the point where your calculations are significantly shorter, you will find that you have more time to complete both Mathematics Knowledge (MK) and numbers reasoning (MR) parts

Check out the latest problem sample exam practice you and answer choices. Look at the answer choices given. The figures provided is not so close to each other to perfectly accurate calculation is required. Instead, the numbers will be far apart that even with some rounding and evaluation answer will still be close enough to just one of the answer choices.

With the above example, instead of calculating 22 times 37 the long way we can round each number to the nearest unit 10. Since 22 is very close to 20 to round it down. And 37 is very close to 40, so we round it up.

Now we have a new example reads 20 times 40. Once again you have a chance to figure out this long way, which will still be more or you can take this one step further and actually do the math the head

How?

is not the number 20 actually just 2 times 10? And is not the number 40 really only 4 times 10? If we think of two digit numbers that end in zero as the number times 10, we can simply get these problems requires a calculator, that does not even have a pen and paper

instead of 20 times 40 we have now trouble les 2 times 10 times 10 4 times multiplication allows us to rearrange the order of the numbers, so let’s look at this example 2 times 4 times 10 times 10

Is not everything one look so much simpler? 2 times 4 is 8, and 10 times 10 is 100 That leaves 8 times 100 is 800

Actual answer for 22 times 37 is very near 814th Since the ASVAB will not give you a choice of close to real In response, 800 will still be the closest value. Was it worth doing all that extra math for differences 14?

## Cancer remission: What is it exactly

Many people seem to have a distorted and incorrect definition of the word “ remission ,” as it is used in conjunction with cancer patients. Most people seem to believe that going to remission means that the patient is treated and safe.

However, according to the American Cancer Society, remission of cancer is a “period when the cancer is responding to treatment or is under control. The most cancer remission , all signs and symptoms of the disease disappear … complete remission of cancer may continue for several years and considered cured. “

So, someone who goes cancer remission does not show signs of cancer. It does not matter how many cancer cells are still going strong and growing in the body of the patient, for the time it does not cause “symptoms” patient is said to be in remission.

Oddly enough, there is not much covered in advertisements for traditional cancer treatments for an extension of the length of life for the patient. And there are not many discussions about the quality of life of the patient.

These two concepts are not a factor in when talking about “ remission of cancer ” in patient.Typically speaking, cancer remission direction shrinkage in tumor size or altering some of the tumor markers. Tumor markers are substances, usually proteins, which are produced by the body in response to cancerous growth or tissues. However, much of the markers also found in non-cancerous conditions so they are not really a good diagnostic tool for cancer.

Traditional cancer therapies are successful in shrinking tumors and reducing tumor markers. For this reason, after the administration of cancer is used as an indicator of “successful” cancer.

Cancer remission does not necessarily mean the patient does not die. For example, a patient is said to have been treated for cancer if the therapies put them into remission, even if they die from pneumonia. Despite the fact that the pneumonia was only fatal cancer treatments, because cancer remission hand, it was successful treatment.

most people, no treatment that still results in death should be considered successful. But when it comes to cancer remission , that’s exactly what can happen when they pursue only traditional cancer treatment options.

## Mathematics, Numbers and symmetry of God

The essence of mathematics is not to make simple things complicated, but to make complicated things simple. ~ S. Gudder

Actually, math State of brains get rankled and hearts seem to lose their grip on reality. Even in this seemingly senseless world, simplicity Metamorphoses from the complex; natural unfolding of irrationality and floral order from chaos. If you doubt these proposals, then observe the bizarre environment by following numerical calculations, and then see if you are still skeptical that God does in fact indwell numbers and math.

1 x 8 + 1 = 9

12 x 8 + 2 = 98

123 x 8 + 3 = 987

1234 x 8 + 4 = 9876

12345 x 8 + 5 = 987 65

123456 x 8 + 6 = 987 654

1234567 x 8 + 7 = 9876543

12345678 x 8 + 8 = 98765432

123456789 x 8 + 9 = 987654321

And now with the number 9:

1 x 9 + 2 = 11

12 x 9 + 3 = 111

123 x 9 + 4 = 1111

1234 x 9 + 5 = 11111

12345 x 9 + 6 = 111 111

123456 x 9 + 7 = 1111111

1234567 x 9 + 8 = 11111111

12345678 x 9 + 9 = 111111111

123456789 x 9 + 10 = 1111111111

But the number 9 still has a magic to it. To wit:

9 x 9 + 7 = 88

98 x 9 + 6 = 888

987 x 9 + 5 = 8888

9876 x 9 + 4 = 88888

98765 x 9 + 3 = 888 888

987654 x 9 + 2 = 8888888

9876543 x 9 + 1 = 88888888

98765432 x 9 + 0 = 888 888 888

number 1 is one of the five most important numbers in mathematics. Not only is 1 of Multiplicative identity , number 1 dazzles us with some amazing multiplicative properties contained in this repunits (a repunit number consists of all 1 ‘s)

1 x 1 = 1

11 x 11 = 121

111 x 111 = 12,321

1111 x 1111 = 1234321

11111 x 11111 = 123454321

111111 x 111111 = 12345654321

1111111 x 1111111 = 1234567654321

11111111 11111111 x = 123456787654321

111111111 x 111111111 = 12345678987654321

After witnessing this array of numbers of juveniles, it is difficult to imagine that the supreme deity was not able to control such magic. Maybe if the teachers implemented bit symmetric razzmatazz like to start a class, students could perk up and listen for a change. Then true study would have a shot at the beginning and all kinds of positive results could be achieved. After all, when God is in charge, everything else goes well. Try it out and have fun.

## How to access the Math word problems Pharmacy Tech Test

The Big Secret: Do not think about the problem until you write down all of the elements

Sounds too easy, right.? But that’s where all the sticks. Start by carefully reading the entire question from the beginning to the end and read important. Then go back and you can read it again, to write down only the necessary elements. Components are not just numbers, but also things like days, percent sign, pm or what will help keep it straight to you. . Also neat writing numbers below or above numbers will be added to or subtracted from the set up any part of

Write equate where it belongs

This is important; logo is like switch in our brains that we have been taught since third grade. Now the problem is what written with an equal sign instead, the light will generally go on and you will start working on the problem. From here, the only hang-ups you may encounter are things like did not trade or have to change all such factors. Even if you write down the elements wrong the first time, you’ll likely see how to re-arrange them and start

Sloppy writing is not allowed in mathematics :.

success in mathematics is subject to write all the factors neat and organized. When you come across a math word problem, the first thought that should come in the head is to take a piece of paper to write it out. As you jot it down, write neatly and leave you some space between lines.Beware: Exam writers prey on bad habits

When I create practice math word problem for free practice exams, I have to think up. three dummy answers. How do I do it? It may sound sadistic, but I try to consider what answers would come up if someone was sloppy. I think about things like if the element was left out, or if someone did equation in a hurry, or their heads. Exam writers who write for public exams do the same. After all, the test used to weed out unqualified applicants. If you want to pass the exam, actually get to write it down completely, neat and organized.

When you get a question of math word problems.

First, relax and know that all the facts are available to you to resolve it. Then take a deep breath and follow these steps: Do not try to speed up or used to shorten

writing down only the necessary elements

math

Need more Pharmacy Tech math practice?

For FREE help with pharmacy technician math, visit http://www.pharmacy-tech-study.com . You’ll find a complete review of the mathematical calculations including violations strength ratio, algebra, and much more.

## 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 differentially 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 not make compelling class. I have to Teach math!” It’s an assumption worth exploring.

Take Ron Berger’s middle-school math project to study radon levels 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 superintended? What would happen to real estate values ​​in That area? What he found is that students were highly Engaged in mapping, Taking aver ages, looking at standard deviations- students That heretofore did not care one bit about radon or the other concepts.

So what’s the trick? The trick is that there is not one. You can not trick students Into finding something compelling if it is not. Take a little bit of time to developping 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-CD.

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 do not 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 support administrator, look Into the school reform movement of Expeditionary Learning Schools WHO have an excellent Thematic approach to teaching.

2. Do not use extraneous rewards Such as candy, purchase points, stickers, etc.

There is nothing more certainties than seeing the culture of a math class decline over a period of years When a teacher briber theme. The intent of the teacher, of course, is good. A teacher cares about his or military students and wants the very best for themself. “I do not care how They Learn math,” one teacher said to me. “I just want Them to Learn it so thatthey are prepared.” 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 is not worth doing on its own.” The research is clear on the matter too, and shows us That extrinsic, non-Related rewards hurt learning.

Even if the effects are not immediate, over time so called “positive reinforcements” Like These mentioned above Erode Otherwise an high-quality math program. As a teacher, you are much better off Trying to createTextNode inherently compelling curriculum than buying candy.

3. Build a culture where students Teach eachother.

For Many teachers, one student helping another is called cheating. But I found That Actually the better middle-school math programs all Encouraged students to team together at times certainties 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. But before you give up and Decide it does not work, determiner if you are Following tips # 1 and # 2 first.

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. Do not. It ACHIEVE little learning.

Choose the most Important pieces Before the beginning of the year, and keep it simple. Teach the concepts you do Teach with depth.

The national advisory Counsel is 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 themself 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 Oftel depth 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. Oftel this is a very large text or an entireties series.

In the classroom, teachers and students become overwhelmed and seems 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 anything That 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.

Do not show a student how to Solve something. Instead, “Think Aloud”. For example, you might have a whiteboard with a problem up, and start by saying, “ok, I notice That the 4 numbers I am to some are all in the thousands category, and That the first is near 3,000, the second near 5,000 , and the third … 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 mathematician think . One piece of research That is helpful to know is that mathematician 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, Related to the task, non-comparative, and leads the way to next steps.

Many teachers believe That grading is a form of feedback. It is not. Grading, When done well, Can Be a form of assessment of learning, but the distinction shouldnt be clear. Grades are not an Effective tool as assessment for learning. Grades are the end of the road, When You assessable what has been learned, but They should not be superintended to inform a student where to go next.

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 Level Gins Strategies of assessment for learning. That way, When you are conducting an assessment of learning (ie grading), you’ll notice That you are momentarily stepping out of the role of Improving a student’s learning and will not have the conflict of Trying to do two things at once.

7. Change mimeographed sheets to problems you and your students Personally developable.

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 determiner 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 themself fun. Celebrate Them by posting themself in class. Give Them 5 home-made story problems They createTextNode for homework Instead of a mimeographed sheet with 30 problems, and really Dive Into Improving themself 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 they began Sorcery. Write about spice trading ships on the deep seas. Write a story That Last 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 powerfulness effect of enhanced engagement.

9. Get math tutor volunteers once a week for two-months beforehand 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 testing beforehand) to have volunteers come in to Teach math in small groups. But what’s nice is that if Developed correctly, These volunteers do not need to have special training in Any math.

Start with a simple plan. 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 the every week for two months beforehand 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 periodic ally to gain a better sense of where They are. And, just let themself feel how They feel. If They like math, They like it. If They are bored, empathize. If your students can not stand math, Will you 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 are not 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. That’s o.k. Sometimes it Will. And then slowly, over a period of years, build Those compelling pieces Into your classes so That you punctuate boring times with excitement and joy.

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 developping a Coherent math program at my middle-school and Even then, we occasionally slipped in to old Patterns. Good luck!