Math is EDUCATIONAL!!

Fractions of amounts questions.

1) Work out 1/5 of .

2) Work out 4/7 of 42 g.

3) Work out 5/6 of 24 ml.

4) Work out 2/9 of 45 kg

5) Work out 2/3 of 24 m.

6) In a jar there are 30 sweets. 4/5 of the sweets are toffees. Work out the amount of toffees in the jar.

7) Andy receives pocket money per week. He spends 2/3 of his pocket money on buying books. How much money does he spend on buying books?

At a school play there is an audience of 420 people. 2/7 of the people in the audience are over the age of 60. How many people are over the age of 60 in the house?

9) On a coach there are 24 people. 5/8 of the people on the coach are women and the rest are men. Work out the amount of men on the coach.

10) Gavin is a semi-professional pool player. Last year he played 720 pool games. Out of these games Gavin won 5/8 of the games. Work out the amount of games Gavin won last year.

Answers.

Score 1 mark for each correct answer.  Award ½ of a mark for the correct working out but the wrong answer.

1) 35 ÷ 5 =

2) (42 ÷ 7) × 4 = 24 g

3) (24 ÷ 6) × 5 = 20 ml

4) (45 ÷ 9) × 2 = 10 g

5) (24 ÷ 3) × 2 = 16 m

6) (30 ÷ 5) × 4 = 24 sweets

7) (12 ÷ 3) × 2 =

(420 ÷ 7) × 2 = 120 people

9) (24 ÷ × 3 = 9 people

10) (720 ÷ × 5 = 450 games

If you score 9 or 10 marks award a grade A.

7 or 8 marks award a grade B.

 5 or 6 marks award a grade C.

Less than 5 marks award a grade D.

For extra help try these:

Fractions of amounts 1.

Fractions of amounts 2.

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Mathematics is deemed as the most fundamental subject for those who want to build their career in science and commerce fields. It gives opportunity to students to score good marks only if they know how to apply knowledge in an acceptable manner. However, if you are not that good in maths and want to improve your basics and make fundamentals more clear then consider the guidance of a knowledgeable and educated maths tutor.

Maths tutors make the entire maths learning process extremely beneficial and fruitful for your child. They have acquired impressive knowledge and skills in teaching maths and own the adaptability to teach maths to learners of various groups and levels. A Math tutor is accustomed with various practices of teaching and making intricate equations easy to do without hassle for students. They distinguish between curriculums and student abilities, adapting to the learning style of the students and syllabus.

With their proper approach, students find themselves more comfortable, confident and progressively more sure of concepts. As a result, they start solving teacher’s questions in the classroom more assertively. There are lots of Maths tutoring companies available on the internet that provides private tutoring for all grades in mathematics.

They are individually qualified to deal with distinct types of teaching techniques that suit each child’s potential. A Math tutoring company is an excellent resource where you can find suitable math tutor professionals that can guide your child to get ahead in math class and recoup the confidence, success, and self-esteem in a successful manner. It takes expertise to work with students in a kindly and gentle way. Good tutors know what types of methods and algorithms really help students in scoring high math marks.

Will you be as confused as Archie?
Video Rating: 4 / 5

Step 1

The key thing to remember is the phrase “Reverse-reverse”. Think of the Cha-cha Slide, if it helps. “Reverse-reverse” is the rule for dividing fractions, which you will soon understand more deeply.

Step 2

Let’s use the problem 1/2 / 1/8 (one half divided by one eighth). Wait! Unlike in multiplication, you can’t do this straight across. A few adjustments, so to say, must be made, but later on, you will be able to  So how do you do it? By reversing the operation and the numerator and denominator of the second fraction. Division becomes multiplication. The denominator, 8, is now the numerator, and the numerator, 1, is now the denominator, for a fraction of 8/1 (eight over one). If you would like, you can also simply think of it as “opposite reciprocal”. Look below to see the example, and watch as the operation switches from division to multiplication and 1/8 (one eighth) becomes 8/1, or eight.

1                 1                1            8

-         /        -       =        -      *     -

2                 8                2            1

Step 3

And now that you have the problem set up correctly, you can multiply straight across! 1 x 8 = 8, and 2 x 1 = 2, so you get 8/2 or 4. Congratulations! You are now able to divide fractions! Soon, you can move past this building block onto more complicated math; fun!

1            8            8            4

-      *      -      =     -      =    -      =      4

2            1            2            1

Tips and Warnings

Don’t rule out the power of making kinetic connections; aka getting up and moving! If you’re a teacher, especially, use this in a lesson plan: get up and start dancing to the Cha-cha Slide! Pay special attention to the “reverse reverse” part; the “reverse reverse” in the song is similar to the “reverse reverse” when you switch the operation (division to multiplication) and flip the second fraction (use its reciprocal).

Have you ever tried teaching a first grader in school? Aside from the teachers, Usually students who takes up Education as a course could have possibly experienced. You would know what makes them bored, what makes them sleepy and irritated or uneasy. In subjects some loves mathematics as a subject but most of them does not enjoy learning math. That is why First Grade Math games were created.

Click Here For making math more fun Instant Access Now!

This is for them to be able to learn while having fun, they would not feel the boredom of counting numbers, memorizing and analyzing. They would be enjoying learning math if Math Games would be applied in teacher’s daily lesson plan. It would be really effective if it will be included in a period of class.

For first graders, they themselves seeks on having fun while on class, it could be reason why we’ll really find them very noisy and always in a comotion.

So we have to look on the brighter side of it, let us give them what they want and at the same time registering lessons needed to be learned.

So that would be First Grade Math Games that should be included on the lesson plans. We have to make sure that the level of learning that we would be giving them would just be enough, not that difficult of course, for them to enjoy what they are doing and could easily adjust on the type of learning we would be sharing them.

Aside from these First Grade Math games, we should also consider that they are on their first level, so we have to be patient and we have to support them thoroughly until they can learn the right things being taught.



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In math, basically surds are square roots. To simplify a surd, all you need to do is split the surd into a pair of factors, with one of the factors being a square number. Then use the rule:

√(a×b) = √a × √b

You should then be able to take the square root of the square number, so the surd can be simplified.

Also make sure that you have learnt your square numbers. The first 12 square numbers are:

1,4,9,16,25,36,49,64,81,100,121 and 144.

Example 1

Simplify √50.

First we need to look for a pair of factors, that 50 can be split into. The factors pairs of 50 are as follows:

1 × 50

2 × 25

5 × 10

Now the pair which we are going to choose is 2 × 25 as 25 is a square number.

So √50 may be written as √(25 × 2)

Now use your surd rule which is written above.

√(25 × 2) = √25 × √2

Now the square root of 25 is 5.

So √25 × √2 = 5 × √2 = 5√2

Example 2

Simplify √108.

Again we need to look for a pair of factors that 108 can be split into. The pair of factors that we need this time is 36 × 3 as 36 is also a square number.

So √108 may be written as √(36 × 3)

Again use the surd rule √(a×b) = √a × √b.

√(36 × 3) = √36 × √3

Next take the square root of 36 to get:

6 × √3 = 6 × √3 = 6√2

Let’s do one last example.

Example 3

Simplify √20

Well √20 = √(4×5) = √4 × √5 = 2√5

Extra Tips

Sometimes instead of asking you to simplify the surd, an exam question might ask you to write the surd in the form a√b. So in the last example the question could ask you to write √20 in the form a√b. If this is the case just do exactly the same thing as shown above.

For some more questions on simplifying surds or radicals click here.

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Thermoscope, invented by Galileo Galilei

Image via Wikipedia

Galileo (his full name is “Galileo di Vincenzo Bonaiuti de’ Galilei”) was the Italian inventor whom created this device in the 1600s, a liquid filled vertical glass tube that contains precision weighted spheres (today, of either colored water or alcohol and mostly for decoration purposes,) each calibrated to a specific density. The liquid filled tube is sensitive to the ambient air on the outside, and since temperature and density of liquids are uniquely intertwined, this device can measure this change.

As the floatation liquid’s density changes in relation to changes in temperature, the weighted bulbs will move up and down seeking an quilibrium state. –A tool for indicating temperature. Galileo more or less stated that the laws of the natural world are mathematical, and this accurate device shows a relationship keeping with this statement.

Metal Counterweight Tags Attached

Each sphere is adored with a small ringlet and labeled tab, indicating a temperature. The tags serve as counterweights for the floating sphere because the hand-blown glass spheres cannot possible be made the same thickness, mass, size, etc.

What happens is that each sphere is hand-adjusted to attain neutral buoyancy at the target ambient air temperature. Subject to two natural forces, gravity and buoyancy, this sealed liquid-filled glass tube seeks to maintain the same temperature as the air. This in turn is relayed to the spheres and if a sphere is denser than the specific gravity dictated by the water’s temperature, it sinks.

Image Source

Image Source

And if any sphere is less-dense than the current specific gravity of the water at temperature, it will rise. The sphere that is closest to the ambient temperature of the liquid in the sealed tube (which strives to be the same temperature as the ambient air surrounding it) is ‘neutral’; it sinks as much as it rises. The forces of gravity and buoyancy are in a state of homeostasis thus; the specific sphere  is stationed at the middle of the glass tube and reveals the actual temperature.

Image Source

Broken Tip on a Modern Galilean Thermometer

Image Source

Sadly, these modern version will exceedingly beautiful, are prone to breakage as seen here in this image. But these devices are common and replaceable, many scientific and even ‘big box stores’ often have them.

The Galileo Six

Image Source

Too bad only six glass bulbs are shown here, for if there were seven glass bulbs we could call this “The Galileo Seven” which to us Star Trek fans out there, means something.

Image via Wikipedia

This was the name of a classic Star Trek episode and the name of a doomed U.S.S. Enterprise shuttlecraft. I wanted to mention all of this as the author of this image cites that this thermometer was a gift from his sister and, as such, it seems fitting to remember it here again.

After the breakage and the fluid runs out, the  device is effectively destroyed. There is no fixing it. But at least you can be left with some very interesting object trouvé for a display in vase or bowl.

www.MarkFiore.com Take a look at the latest “cuts” in defense spending, brought to you by . . . just about everybody. Obama, Congress, defense contractors, they all get in the act and somehow manage to make an increase sound like cuts. After wading into the budget wilderness, it becomes a little more clear. And, yes, it is worse than this cartoon depicts. A Mark Fiore political animation.

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Our first multiplication trick applies to multiplying two digit numbers close to base ten. while this quick multiplication trick works for any two digit number, only 11-19 calculate easily in your head.

This trick is as follows:

our problem: 12 x 14 =

we solve this question first by  taking our first two digit number: 12 and add the last digit of the second two digit number: 4. 12 + 4 = 16.

The first 2 digits of our sum will be the product of this answer: 16

now we will take the last digit of both numbers and multiply them: 2 x 4 = 8

This product will be the final digit of our number: 168

12 x 14 = 168

Now, what if our final digit gives us a product greater than 9.

Consider this example.

13 x 19

as with the first example, we add 13 and 9 to get the sum of 22. These will be the first two digits of our number: 22

our second step is to now multiply the last digit of both numbers with each other: 3 x 9 = 27

we need to, in this case carry our numbers. so, 22 and 27 now turns out to be 247, this is because we can not have anything greater than a three digit numbers unless we are multiplying numbers in excess of 30.

The final product of this equation is 247.

While this trick works easily in your head, it is best to just keep it to numbers multiplied close to ten.

In order to multiply two digit numbers by two digit numbers in your head that are more than 20 there is a far easier way than that of our last example.

please follow.

Our example: 23 x 42

first to get our first digits we multiply the first two digits of each of our two digit numbers: 2 x 4 = 8

This number will be the first digit of the product. 8

for the final digits we will multiply the last two digits of each number by each other: 3 x 2 =6

This number will be the final digit in the product.

Our product should look like this so far: 8X6

For our final digit which will be between the first two we placed all we do is multiply the digits furthest from eachother and the digits closest to the middle seperately and then add both products together. This should look like 2 x 2 = 4 and 3 x 4 = 12. now we need to add these products together. 4 + 12 = 16.

So the middle digit will be 6 and we need to carry the one over to our first number. Our product for the equation will be 966.

23 x 42 = 966

We’ll try one more example now so that you can firmly plant in your mind the process of mentally finding the answer to this equation of multiplying two digit numbers by two digit numbers.

Our final example problem.

56 x 63

First we multiply the first digits of these two numbers: 5 x 6 = 30

Then we multiply the final digits of these two numbers: 6 x 3 = 18

our product will look like this so far 3018

we then will multiply the digits furthest from the middle and then the digits closest to the middle seperately: 5 x 3 = 15 and 6 x 6 = 36 we now take the product of these two equation and add them together: 15 + 36 = 51.

Now plug this number into the middle of our product and carry the first digit over. The product will now look like this 3528. To clarify, we added the two digits in the third place to eachother essentially carrying over our final digit in the equation.

While this second trick may seem complicated at first, with a little practice you should be able to calculate most two digit numbers in your head in abut 6-8 seconds. What will help immensely, that is if you have not already done so, is memorizing your multiplication table.

feel free to check out my other articles in this series of Mental Math Tricks!

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The two numbers that this mental math trick has in common are 25 and 50 consecutively. To begin all we do is simply take our number, so for this example we will use 47.

For example:

Our number:     47.

We first subtract it by 25.        47 – 25 = 22

The product will be the first two number of our answer.     22XX

We then take our number: 47

We now subtract it from 50.         50 – 47 = 3

We take our product and now square it:     3 x 3 = 9

This will be our final number. So the answer should look like this so far:     22X9

Then we place a zero in front of our final number:     2203

Let’s examine another problem.

Our number:     42.

We take 42 and subtract it by 25.     42 – 25 = 17

This will be the first 2 digits of our number.     17XX

Now we will subtract from 50 our number 42.     50 – 42 = 8

We take our product 8 and square it.     8 x 8 = 64.

This product will be the final 2 digits of our number.     1764.

Simple enough?

What may help you significantly is to memorize your square roots between 2 and 9.

A small table of this will be provided at the end of the article for practice along with other questions for excersize.

Before we move onto the excersizes lets consider one more example in dealing with our numbers over fifty so as to get a full sense of how this trick works.

For example:

Our number 53.

We first subtract this number by 25.     53 – 25 = 28.

So the first 2 digits of our number will be 28.     28XX

Since our number is over 50 instead of subtracting our number from 50 we will subtract 50 from our number.

53 – 50 = 3

We now will square our result.     3 x 3 = 9

The product will be the last digit of our number.     28X9.

Like our first example, if the square of our last number is not greater than 1 digit we simply place a zero in front of it for our result.     2809.

The series of numbers is short for this trick, a little practice and soon calculating in your head will be fun and easy.

Try these excersizes:

58 x 58 =          43 x 43 =          49 x 49 =          56 x 56 =          48 x 48 =          53 x 53 =          59 x 59 =          46 x 46 =

Quick reference for numbers between 2 and 9 squared.

2 = 4     3 = 9     4 = 12     5 = 25     6 = 36     7 = 49     8 = 64     9 = 81

Answer to excersizes in reverse order:

8)2116     7)3481     6)2809     5)2304     4)3136     3)2401     2)1849     1)3364

Be sure to check other articles in the “Mental Math Tricks” series and also excersize sheets.

Homeschooling with a homeschool math curriculum can solve the major problem afflicting mainstream schools: failing children in math. Rather than children failing math, it is the schools that are failing our children. Returning to basics in education is a likely formula for success.

Schools often tout “New Math” in many guises and forms, but often, it isn’t sustainable. Fads come and go as math scores drop precipitously, along with U.S. rankings among countries that excel in math and science. (Search and find the dismal worldwide stats online.) The good news is that math curriculum in a homeschool setting, that’s tailored to your child(ren)’s needs and abilities can insure success with a sensible, solid, back to basics math approach.

The domino effect seems to prevail when these basic math skills are not learned (and indeed, sometimes not taught) in the lower grades. A poor grasp of the four processes can hamper any student’s progress. Lack of times tables’ fluency is a major drawback that negatively affects math performance as early as second or third grade, severely constrains success with the fourth grade math curriculum (fractions and decimals), and virtually obliterates higher math skills.

Concrete approaches like Waldorf Education and the Montessori method enjoy a measure of success. As some experts in education (like Maria Montessori, Rudolf Steiner, and Jean Piaget, among others) have noted, a child’s thinking is very different from an adult’s. There’s a need, from age seven through eleven, for the child to be taught concretely rather than abstractly. A basic and concrete math curriculum then, is indeed the likely recipe for success!

Children should also be taught holistically, with all the pieces of information fitting together, so their world makes sense. When the beautiful underpinnings of math and science are taught early and in an understandable way (for example, images of math in nature like the spiral found in a sunflower, the hexagon in a honeycomb or snowflake, or the star pattern in an apple), your math curriculum will lose its foreignness and thus its fearsomeness.

Bringing math and all the other subjects home by joining the growing homeschool community may be the best solution for your family and child(ren), since homeschooling is such a wonderful venue for bridging the gaps and focusing on an optimal, quality education for all of our children. Waldorf, Montessori, and other innovative methods fit beautifully into the homeschooling mix.

One such innovative method is the Sacramento Homeschool Math By Hand curriculum. Like the Waldorf system, it’s hands-on, experiential, concrete, child-friendly, and arts-integrated. The 4 processes are introduced together and early in the first grade curriculum, cloaked in stories and taught with concrete manipulatives. The second and third grade curriculums then focus on place value and times tables’ mastery, as they pave the way for fourth grade fractions and decimals.

The Math By Hand curriculum recommends a block-scheduling format because it enables a “steeping” in each subject for deeper and more effective learning. A binder is included, with the full year’s lesson plans, instructions for projects and activities (all materials are supplied), along with detailed tie-ins with state and national math standards. Visit our website and see how color, manipulatives, interactive learning, and integrating art, language arts, movement, and crafts will make a big, positive difference in your child(ren)’s math curriculum.

Marin holds a Masters Degree in Waldorf Education, and a California teaching credential in art. She’s had years of experience as a Waldorf class teacher in the early grades, has taught hands-on science and math to homeschoolers in grades 1-6.

Defining “pip”
Pip stands for “Price Interest Point”. A pip is the smallest increment of price change possible for an exchange rate and is almost always quoted to four decimal places (1/ 0.0001). The only exception to this rule is the Japanese Yen which is quoted to two decimal places (1/0.01). One pip in a currency pair can be calculated by multiplying one pip in decimal form by the notional amount of the trade. ( Notional amount is the size of the base currency). For example:

Using EUR/USD, calculate 100000 EUR (1 Unit) x .0001 = per pip For GBP/USD, calculate 100000 GBP (1 Unit) x .0001 = per pip

Determining the value of a pip

The value of a pip is different for each currency pair because of differences in the exchange rates for each currency. The formula for calculating the value of a pip is as follows: (One pip/currency exchange rate) x (Notional Amount). For Example:

Using USDJPY the formula gives us
(.01/139.46) x USD 10,000 = .77
Or 77 Cents per pip

Using EURUSD the formula gives us
(.0001/.8942) x EUR 10,000 = EUR 1.1183

To convert the pip value to USD we multiply EUR 1.2283 X (EURUSD exchange rate)
EUR 1.1183 x .8942 = .00

For any currency where the currency is quoted first the pip value is always .00 per 10,000 currency units (mini lot) or per 100,000 currency units (standard lot).

The effect of leverage on pip valuation

Leverage is the amount of money you are able to spend as a result of borrowing investment capital. Basically, the more leveraged you are, the riskier your position. As shown above, pip value is the effect that a one-pip change has on a dollar amount. It is important to note that pip value does not vary based on the amount of leverage used, but rather that the amount of leverage you have affects the pip value. Increasing your leverage increases the volatility of your position because small changes in pip value will result in larger fluctuations in your account value. For example: if you trade one standard lot of USDEUR a one pip move will result in a .00 change. But if you trade five standard lots of USDEUR a one pip move will result in a .00 change. Using leverage can increase the effects of a price movement tremendously, which means your account can be wiped out very quickly, but also you can make huge gains quickly. You need to use extreme caution when making leveraged trades. Do not enter a highly leveraged trade unless you are certain you know what you are doing or you will almost certainly lose all your money very quickly.

Calculating Profit or Loss on a trade

Calculating profit and loss is very easy. There are only two formulas to remember.

When USD is the quote currency (the second currency in a pair), the formula is:

Profit = Price Change in Pips x Units Traded

When USD is the base currency (the first currency in a pair), the formula is:

Profit = Price Change in Pips x Units Traded / Exit Price

Let’s say you buy EURUSD and the trade goes your way. There is an increase of 17 pips. If you traded a standard lot 17 pips would be .0017 X 100,000 =$ 170.00.

When the USD is the quoted currency (second currency in the pair) a pip is always worth .00 when a standard 100,000 unit lot is traded. When a mini lot is traded (10,000 units) a pip is always worth .00.

Now, let’s look at an example where USD is the base currency. We’ll execute a buy of 100,000 units of USD/JPY at 117.22. The price rises and we sell at 117.35.
We just made 13 pips.

To calculate our profit we use the second formula:

Profit = Price Change in Pips X Units Traded / Exit Price

Or
Profit = .13 X 100,000 / 117.35 = 0.78.

The math behind forex trading is simple, the hard part is determining which way the market will move for the currencies you are trading. Making this determination requires continuous research, analysis and learning.

Music video by Manchester Orchestra performing Simple Math. (c) 2011 Sony Music Entertainment

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