One of the worst things that can happen to a student is using plagiarized content. Plagiarism is considered academic dishonesty so it may lead to very serious consequences. To avoid plagiarism in your papers, you should properly cite all the sources according to the necessary citation format. In addition, various styles require you to format the entire paper in a certain way.

In this article, we are going to consider the APA (American Psychological Association) format, which is commonly used in education, psychology, and other social sciences. 

General Features

When formatting your paper according to APA style, you should use double spaces, one-inch margins on all sides, and a simple font, such as 12 pt. Times New Roman. You should also include a running head at the top of each page. The running head must contain a shortened title of your paper written in all caps and a page number.

Title Page

The title page must include the running head, the title of your work, your name, and affiliation. Use both upper- and lower-case letters, and provide this information at the top half of the title page. According to the APA guidelines, your title shouldn’t be longer than 12 words. Don’t use unnecessary words that don’t add any meaning to your title, such as “a study of…” or “an investigation on…” You should also avoid using degrees or titles (Ph.D., Dr.) before and after your name.

Reference Page

The reference page must include all the sources that you’ve cited in your paper. This is the last section of APA papers. It must begin on a new page and be titled “References,” with no quotation marks. The References title shouldn’t be italicized or underlined.

When listing authors, sort them in alphabetical order, starting with their last names. The first line of a reference must be flush left, while the following lines should be indented. When citing articles, you should only capitalize the first letter and a letter that follows a colon. However, when writing the title of a journal, you need to capitalize all the major words. Titles of journals should also be italicized, along with the volume number. If there are several sources written by the same author, sort them chronologically, starting from the oldest one.

Begin each entry in the Reference page with the author’s last name, followed by their initials and the year of publication in parentheses. After this, provide the title of the source. When citing articles, the title of an article must be followed by the title of the journal. After this, provide the volume number and page number, as well as a DOI, if it’s available. When citing books, an italicized title of a book must be followed by the city where the book was published and the publisher.

Wrapping Up

APA is one of the most common academic formats, which is used in numerous disciplines. It may seem a little bit tricky, especially if you’re writing your very first paper in APA format. But no need to worry! It’s actually easier than it might seem.

To learn more about the rules of APA format, please check out the official APA website. If it doesn’t help, you can always find a professional writer or editor to help you with it. Review websites like LegitWritingServices can help you find an essay writing service to format your essay according to the required format or write it from scratch. A professional editor will give you a sample of what you need and explain all the peculiarities of the APA format.

Many institutions of higher learning try to recruit students into challenging STEM fields. If you’re the parent of a young child, how can you ensure they have the requisite skills to succeed in the area if they choose? If you’re a teacher, how can you prepare your students? 

The earlier you begin preparing children for STEM careers, the higher their chances of future success. Early math education provides the building blocks for future knowledge in engineering and coding. When students experience success in the subject during their formative years, they develop confidence in their abilities. 

STEM Careers Remain in High Demand 

Today’s generation faces a highly competitive job market. The rise of the gig economy has gutted traditional benefit programs, and wages haven’t kept pace with inflation in many sectors. STEM careers offer a path to financial prosperity, but only if students have the requisite background to succeed in them.  

Fortunately, a natural window of opportunity exists between the ages of 5-7, when children begin forming abstract concepts and create a picture of the world in their heads. As parents and educators, you have the solemn responsibility to seize this chance to foster a love of math in young learners. The attitudes they form toward the subject now will influence their future success. 

That accomplishment extends beyond the classroom. Already, STEM careers make up some of the hottest job fields for millennial workers. As technology continues to advance, these paths will expand. Students who embrace the attitude that math is fun will have the best chances of entering these challenging but lucrative fields. 

Early Math Education Provides Critical Cognitive Building Blocks

Many educators and parents alike consider STEM classes something children enter in their teenage years, and in some ways, they are correct. However, before teenagers can decipher complicated engineering formulas, they need to know how to perform necessary computations. If the mathematics demanded aren’t appropriate for the grade level or aren’t explained conceptually, students will struggle with how everything fits together. A solid foundation in mathematics is key to success in engineering or programming. 

This need for a solid mathematical foundation doesn’t mean teachers should treat the subject as a vacuum. It does mean they need to recognize the importance of mastering concepts like addition and subtraction. The best way to prevent future frustration in students is to ensure they understand basic principles before moving on to more advanced topics. 

Early Math Achievement Inspires Confidence in Future Success

Why do some students choose to pursue a STEM education later in life while others claim they’re “too bad at math?” Early exposure — when tied to achievement in some cases — proves key. One recent study found that among white and Asian students, early exposure to math and science influenced their later decisions to enroll in higher education. However, among underrepresented minority students, math achievement at a young age had a more significant influence on their belief they could succeed in the subject. 

To encourage greater participation in STEM, especially among underrepresented groups, parents and educators can praise children for math achievement. They can promote activities such as the following:

  • Math Bingo: In this activity, you begin by creating 25 math problems and writing the answers on a Bingo card. Use 5×5 cards and quiz little learners. 
  • Pizza fractions: In this activity, students create a pizza out of paper or a discarded pizza box. Then, they add toppings to their pie to represent different fractions. For example, they might make one that is one-half pepperoni and one-quarter mushrooms. 
  • Survey and graph: Children love learning about themselves through surveys, and you can use that motivation to inspire a love of math. Have children survey their classmates or family members on a subject,  and then create a visual representation of their responses. 

To Pique Student Interest in STEM, Start With Early Math Practice

Early math practice provides the cognitive and emotional framework for success in STEM. If you want your children and students to embrace this challenging field, start inspiring them when they’re young. 

About the Author

Alyssa Abel is an experiential education writer who focuses on developmental learning, college and career prep and unconventional education. Follow her work on her blog, Syllabusy.

I was giving the amazing opportunity to take a look at the IPEVO IS-01 whiteboard system and see how well it worked in the classroom. I always love the “out of the box” experience and this product did not disappoint. The system comes in a very well presented and fairly small package with all the components easy to unpack and setup.

The initial setup was very straightforward and the “easy setup guide” helped to get the system up and running very easily. However, I am pretty “tech savvy” so that may have helped the process! The most difficult part of the setup was the calibration, but if you have used an interactive board system in the past, then this eventually becomes self explanatory.

I initially set up the system at home and then done the same in a classroom environment. I found setting up the product for the second time even easier and found that the interactive board worked better in a classroom environment where there was a lot more space and I could manage light coming into the room. After the calibration using the system and pen is a little tricky but after a bit of trial and error it becomes easier to use. It is worth noting that the product requires a projector of your own to work, I say this as a colleague of mine thought that my projector came with the product and we had a little laugh about the fact that the HD projector was actually mine.

I would suggest making sure that you practice using the system for a while before you use it in a lesson. I was highly confident and used it in a lesson and ended up embarrassing myself a couple of times. Although I was very impressed with the technology I decided to get some colleagues to test the product too. We were all in agreement that the product is useful in terms of a device that is mobile but writing on the board was not as free flowing as other interactive board systems. This may improve the more we use the product and become familiar with it.

One member of my team actually wanted to purchase the product for his home tutoring business and another was intrigued about the next version of the product. We all felt that for the price you pay for the system, it is definitely good value for your money. I found the pen a little too long for me, and it did not feel as good as other pen devices that I have used in the past. Also, standing in front of the projector meant that the device was in a state that you could write on the wall until the projected image was visible. This although, a little frustrating took a bit of time getting used to.

If your school has a limited budget and you need an affordable and easy to use whiteboard system then this product may be a solution to look into. The fact that it is mobile and will allow you to take the system wherever you go is a great advantage.

For more information on the product and how it works you can visit the IPEVO website or visit their youtube channel for some great videos on the product. Please feel free to leave comments and questions below and I will be more than happy to respond to them.

You’re busy and the to-do list is only getting longer.

It’s hard to find the time to think about your classroom environment. But just a few simple considerations can help maximise learning and even improve your results.

Here are 5 simple ways you can make your classroom work effectively for everyone:

  • Get the basics right
  • Make your room flexible
  • Sort your displays
  • Decide your seating arrangements
  • Organise your resources

1: Get the Basics Right

It’s hard to learn if the physical environment isn’t right. Make sure the ‘big four’ fundamentals are perfect for your learners.


On a freezing day, it’s tempting to keep the windows and doors firmly shut. But stuffy rooms can stop your class from performing at their best. To avoid moans from the children when the weather is cold, open the windows at the start of the day and break times.


Often classrooms alternate between stark strip-lighting and semi-darkness. Try to let as much natural light into your room as possible by fully drawing the blinds. Don’t be tempted to stick posters onto your windows as this can reduce light levels.

Indirect sources of light work best for learning. Make sure sunlight doesn’t stream down onto your whiteboard or shine in students’ eyes.


Are you working in a loud echoey room or do you have a noisy neighbouring class? It can make listening hard for your students.


  • Using fire-proof fabric instead of backing paper on your display board to absorb noise
  • Adding large rugs or sections of carpet on the flooring
  • Keeping the internal doors between classrooms shut
  • Discussing noise levels in staff meetings and agreeing on procedures to reduce corridor noise


Your class won’t get much work done if they’re feeling too hot or cold. Talk to your caretaker if the heating in your room isn’t working effectively to see if adjustments can be made.

If your classroom gets too hot, keep windows open, even a small amount, to allow fresh air in. Portable fans can circulate air but make sure they are safety checked before use.

Typically, it is in wintertime that heating systems decide to break down! If your classroom is too cold, consider letting students keep their coats on whilst working. Add in physical activities to warm them up before, during and after lessons.

2: Make Your Room Flexible

The best classrooms allow you to make changes to suit the learning that is happening. If you have space, consider creating zones to allow different activities to take place at the same time.

If you have limited space, think about how you could rearrange your equipment to change the layout. Train your class to move furniture into different positions with minimum disruption.

3: Think about Wall Displays

Too many visual distractions on walls can have a negative effect on learning. Often classrooms can become cluttered and overwhelming with the number of resources on display.  Make sure you have plenty of empty plain spaces to break up the busy displays.

Avoid using lots of bright colours in the same space. This can make your classroom feel cluttered and overwhelming. Instead, use muted neutral colours on most of the walls. Bright colours aren’t banned but limit them to one bold display or feature wall for a positive impact.

Only display resources that are currently being used so your class notice and use them. Keeping displays current can have a big impact on learning.

Give your children a sense of classroom ownership by presenting their work on display boards. They will love seeing their best work and feel like a valued member of the class.

4: Consider Seating Arrangements

Every teacher has a favourite way of arranging the tables. The jury is out on which layout is best, but there are simple ways to make most work effectively.

Think about:

  • Can all the children see the board?
  • Can you see the class?
  • Is everyone able to move safely around the classroom?

Think about if you prefer your students to work alone, with a partner, in a small group or as a whole class in most lessons. This will help you decide whether to arrange your tables in rows, a horseshoe shape or clustered into groups.

5: Organise your Space

Classrooms can be busy places. It’s easy for them to become messy with resources piled up in every corner. Your class will show more respect if everything has a place it always gets returned to. Label storage containers and encourage the class to help themselves to any equipment they need.

Think about where you store resources to make them easily accessible for everyone. In smaller classrooms, you may need to use table monitors or helpers to set out and return items.

Organise resources into three separate categories:

  • Rarely used topic specific

Keep these in a central location outside of your classroom. Most schools will have a resource area for these types of items.

  • Often used

Find a sensible place in your room for storing these items. You will need to access them, but they shouldn’t be in the way of daily teaching.

  • Everyday items

Consider keeping these out on display for children to use independently. Labelled drawers, tabletop boxes, and bookcase units are tidy and effective.

Classrooms easily become cluttered with outdated resources that will never be used. Resist the temptation to keep things just in case they come in handy in the future.

The Perfect Classroom Environment

Unless you’ve been given a budget to use, don’t spend your hard-earned wages on items for your classroom. Think creatively and look to repurpose things to meet your needs. Use local selling markets online and ask friends and colleagues for resources. It’s amazing what you can source for free.

The perfect classroom environment will always be a compromise. It is unlikely that your room has the space for lots of zoned areas or perfect light and heating all year round. Instead, make simple changes where possible to make it work for you.

NOTE: I’m from the U.S., and will use the many-centuries-old abbreviation “math.” You Brits are welcome to continue using your newfangled, one-century-old alternative “maths.”

Every math lover hears it: “Oh, I’m bad at math.”

I get why people say it. Math can put people ill at ease. It can make them feel stupid. By disavowing your own mathematical ability, you cut the conversation short. You avoid the painful encounter with the thing you feel inept at.

That’s why, when I write about math, I put my worst foot forward. I always include my inept, stick-figure illustrations.

The drawings help explain the concepts, too. But a big part of their purpose is to put the reader at ease. Anyone who draws this bad can’t be a threat!

When the drawings are bad – and the artist is so obviously out of his comfort zone – you can forget about who’s good at what, and just enjoy exploring new ideas.

I continued the approach with my second book, Change is the Only Constant: The Wisdom of Calculus in a Madcap World.

In this book, the math got heavier, but the approach stayed light. The U.S. sees calculus as the culmination of secondary math education. The subject has an intimidating reputation. But I hope that my silly pictures can put the reader at ease.

I think there’s a lesson here for every teacher of any intimidating subject: don’t be afraid to show a little humanity. We’re all learners, and the road to expertise is paved with a million mistakes. (In my case, those mistakes are silly-looking, long-necked stick figures.) There’s no better way to invite folks into the project of learning than to model it ourselves.

Getting kids into maths can be challenging, especially if you’re not into it yourself! So, if you’ve ever wondered how you can get your children to enjoy maths, then keep reading to discover three of the best ways to get them excited about one of the most critical subjects on the planet.

1. Be passionate about maths

Research shows that maths is one of the most universally hated school subjects. As a result, many parents unknowingly pass on their hatred of maths to their children. So, if you’re one of the many that disliked maths at school, try not to let your feelings influence your kids! This is easier said than done, but with perseverance, you will no longer have to scowl when your son or daughter asks for help with their maths homework!

Leading by example will mean that your children won’t go into school with preconceived notions about how tricky or tedious maths is, and they will be able to formulate their opinions about the subject based on their own experiences. Remember, just because Mrs Smith made your high-school maths lessons memorable for all the wrong reasons, doesn’t mean your kids will have the same experience!

2. Consistency is key

During holidays, especially the long summer break, children forget things that they have learned during term-time. In fact, an estimated 11 weeks worth of maths skills are lost over the summer! According to MyTutor, summer learning loss means that a whopping 6 weeks of the autumn term are used to simply relearn everything from the previous year, meaning that the real learning doesn’t begin until October.

You can help combat this problem by making sure your kids are actively learning throughout their school holidays. Active learning encourages student interaction and participation in the learning process, as opposed to passive learning, which involves merely reading or listening. You could always do this yourself, but if you really hate maths or struggle with doing long division, then the best option is to hire someone who is not only good at maths but is also genuinely passionate about everything maths-related. Enthusiasm is catching, so exposing children to people who love maths is an excellent choice if you want to get them excited about it too.

3. Make it fun

Making maths fun is the number one means of getting children excited about maths. Many people don’t like maths because they find it dry, dull and overly abstract at school. They can’t see the point of doing trigonometry or learning about the Pythagorean Theorem. So, try to make your child’s experience more positive by showing them the relevance of mathematical theories and the potential fun that can be had with them.

When teaching kids about the importance of trigonometry, you could walk around your town and work out how high the buildings are. Or if you are super creative, you could create your own rocket out of a plastic bottle, baking soda and vinegar, and then get kids to work out the projectile angle. There are so many ways of making maths fun and interesting for kids, but also remember to have fun yourself!

Is your child is preparing for the 11 plus exam in the UK? Maths skills need to be strong, as it’s one of the main topics that will be assessed.

In the 11 plus, the maths section tests your child’s numerical skills, as well as other core maths concepts.


What is the format of the test?

In, short – it depends.

The maths test varies based on the area and also the school.

For example, some schools set out multiple-choice style maths tests, while some others set a single paper that is a combination of both maths and English types of questions.

The test varies a lot from school to school, therefore it’s important to consult with the school to understand what assessment they do.

Some schools do the GL or CEM Assessment, while others will do a combination and write part of the test themselves.

Some schools will exclusively write their own 11+ assessment.

It’s important to know what test your child is doing, so you can prepare them in the best possible way.

How long do the tests take?

The time varies from school to school, ranging from 30 minutes to an hour. Some schools also set numerical reasoning tests as a way of making the exam harder to revise for.

The reason for this is that assessment boards want to remove bias from learning, to give everyone an equal chance.

What can you do to help your child prepare?

  • Incorporate gamification into learning: Really, this is a biggie. Most children lose focus on learning, due to the many distractions that exist nowadays. Phones, tablets, games are all distractions for everyone and attention spans have never been shorter. As a result, we need to find fun ways to keep our children’s attention. Through the use of games, your child will learn and enjoy themselves simultaneously! Maths based learning games are particularly useful and help prepare for the 11+.
  • Use Past Papers. While hitting the 11+ books too early is a bad idea, it’s never too early for your children to start practicing and preparing for a test environment. There are many e-resources for past papers available online. You can set your child a past paper a week, well in advance and measure their progress. Overall this is useful as it flags areas they need to improve, as well as areas that they are strong.
  • Timed Work. Exams are usually under strict timed pressure, so you have to be on your game todo well. Having knowledge is one thing but being able to do the work in a structured manner is equally as important and something that children should prepare for. When exam day comes around, your child will be comfortable working under times pressure which will benefit them.
  • Don’t put too much pressure on your child. You might be lucky and find your son or daughter sails through the 11+ preparation and exam without any hiccups along the way, but I’ve yet to speak to a parent who hasn’t had to deal with at least the odd issue along the way. Don’t worry about it; it’s natural. It’s best to keep offering encouragement and support.
  • Make lots of time for enjoyment and try to keep life as normal as possible. At the end of the day, it’s important to not put too much pressure on your child, everyone learns in different ways and it’s important to not put pressure on your child and to not overwhelm them.
  • Developing their Critical Thinking Skills: Regular practice and workbooks are a good way to help children understand what to expect. This can be done through puzzles, games, and activities to help keep your child stimulated.

What types of Questions are involved?

Problem-solving and critical thinking is key for the 11 plus exams, the

test is focused on key mathematical concepts and the basic

principles of maths.

As mentioned above the test differs from school to school, but are focused

around fractions and decimals, numbers, shapes, problem-solving, data

handling and measurements.


The foundation of 11 plus learning should start from a young age is

important to get your child familiar with a test environment.

Knowledge is accumulated over time and is built on a strong

foundation, so children should prepare well in advance to have the

best chance of success.

“Mathematics is not about equations, numbers, algorithms, and computations. It is about understanding.”

Mastering math technique not only helps the students to do math quickly, but it also develops greater confidence within them, sharpens their math skills, and deepens their understanding in math.

“Its math test time. Goodbye, calculators!”

9 easy techniques to solve any math problem quickly!!

If you are not allowed to carry calculators in the math tests, then you have to rely on some math techniques to solve complicated math problems with speed and ease. It can make the calculation less daunting. Instead of depending upon the calculators, students adopt some interesting strategies which can improve their estimation skills and concentration.

When you are attending a quiz session, you must submit all the answers quickly. Here, we will discuss nine techniques to assist the students in solving math problems faster.

#Technique 1:   How to add large numbers?

You can add the large numbers in your head. But this is difficult as well as time-taking. Here, you will show you how to simplify the addition by turning the numbers a multiple of 10.

Some numbers are hard to deal with. If you can round them up, the numbers will be more manageable.

For example,

Q) 746+ 187


Suppose you have only a few seconds of time to solve this! What will you do? Rather than solving it in a conventional way (from right to left), learn this trick.

Here we go-


Round up both the numbers by making them multiple of 10.

So, 746 turns into 750 and 187 become 190


Add 750 and 190 together. The total would be 940.


This is not the answer to the original equation. Hence, determine how much you have added to the numbers for rounding them up.

750-746= 4 and 190-187=3


Add two remaining results together 4 and 3. The total is 7


This is the final step. Subtract 7 from 940 to detect the answer of the original addition.


Hence, the answer is 746+187=937

#Technique 2:  How to Subtract 3 digit numbers from 1,000 quickly?

This is one of the simplest techniques you can apply while doing a quick calculation.

When you are subtracting a three-digit number from 1000, the basic rule is to subtract the final number (the extreme right) from 10 & subtract the rest numbers from 9 individually.

For example,

1,000- 737

Step 1: Subtract 7 from 9=2

Step 2: Subtract 3 from 9=6

Step 3: Subtract 7 from 10= 3

Hence, the answer is 263.

#Technique 3:  How to multiply any number with 5 without knowing the table?

What will happen if you forget the table? Or Do not sure about the answer while multiplying in a hurry?

If you multiply any number with 5, then the scenario is quite different. It is even not necessary to know the multiplication table of 5 if you follow this technique.

  • Multiplying 5 by an even number

As an example,

Q) 5 X 6

Step 1:

Consider the number which is multiplied by 5 and make it half. Here, 6 digits are being multiplied by 5, and it becomes 3.

Step 2:

Put a zero to the number to find out the answer. In this instance, the answer is 30.

So, the answer is 5 x 6 = 30

  • Multiplying 5 by an odd number

For instance,

Q) 5 X 7

Step 1: Subtract one from the digit being multiplied by 5. Here, 7 turns into 6.
Step 2: Now, you have to cut it half. Here, this 6 becomes 3.

Step 3: Place 3 in the first place and make 5 the last one.

Then, the answer is 5 x 7 = 35

#Technique 4:  Squaring any two-digit numbers ending with 5

A square is an outcome of multiplying any number by itself. Squaring two digit numbers is quite difficult. Every student invests a little more time on this kind of problem in the math tests. However, the time slot for most of the online math tests is very low.

So, you must master a unique technique to find out the answer quickly. Squaring the two-digit numbers that end with 5 is easier if you only follow two or three math tricks.

1st Step:

You can always place 25 at the end of the product.

2nd Step:

You must multiply the first digit with itself after adding 1 with it.

For instance, if you are given 85 squared, you must solve it like the following method:

85 squared = [8 x (8 + 1)] & 25

8 x 9 & 25

72 & 25


Hence, 85 squared= 7225

This is how; a time-consuming multiplication can turn out to be an easy one with this magical math trick.

#Technique 5:  How to calculate the squaring of a two-digit number ending with 1 easily?

Working out on the multiplication of the squared two-digit numbers is an arduous process. Only an effective short cut can save your time. You have to make sure the last digit is 1. The students need to follow four vital steps to find out the short cut.

As an example,

Q) 612

  • Step 1: Subtract 1 from the two-digit number, which is given to you for calculation. Here, 61 – 1 = 60
  • Step 2: Square the number which has become comparatively easier: 60 x 60 = 3600
  • Step 3: Now, add 60 with the resulting square two times: 3600 + 60 + 60 = 3720
  • Step 4: As in the 1st step, you have subtracted 1, so now in the final step you also have to add 1 with the remaining result. : 3720 + 1 = 3721

This shortcut abolishes the complications surrounding the second digit. It allows the students to calculate the squaring easily as the number turns into a multiple of 10.

#Technique 6:  What tricks to follow for multiplying any number by 9 quickly?

The math students, however, brilliant they are, get tensed when they solve maths question papers. Besides, they tend to misplace numbers and forget some formula while solving the problems.

Suppose you cannot recall the 9 times table in the exam hall, an easy method will help you to solve it correctly.

How does it work? Scroll down!

This method can be applied for the one-digit number, which is multiplied by 9.

Let’s take an example of 9 x 8

  • First, cut off 1 from the number which is being multiplied by 9

Here: 8 – 1 = 7

Number 7 would be the first number to place in answer to the equation.

  • Secondly,

Cut off that number from 9. In this instance, 9 – 7 = 2

Put the result in the second place. It is the second number in the equation.

So, the final answer would be 9 x 8 = 72

#Technique 7:  How do doubling and halving help to multiply two integers?

When you have to multiply two integers, you need not spend much time on the calculation. If you follow a unique technique, you will take lesser time to solve the problem.

You can speed up the multiplication if one number is an even number.

You have to halve the even number and double up the other number.

You can continue the process until the equation becomes manageable or you cannot halve the even integer,

Check out this example to adopt the whole process:

Example: Q) 53 x 32

  • 53 x 32
  • 106 x 16
  • 212 x 8
  • 424 x 4
  • 848 x 2
  • 1696 x 1
  • 1696

The answer would be 53 x 32 = 1696

The only requirement to successfully solve the equation by following this technique is the 2 times table.

#Technique 8:  Can one calculate percentage easily with any trick?

You must develop cross multiplication skills to solve these types of problems. If you can master this math skill, then there is an easier way to find out percentages.

Let’s go through the following example,

If the students want to find out what 45 % of 225 is, they will have to multiply the two numbers together by following cross multiplication. Then, they must move the decimal place and put it two digits to the left.

In this case, 225 x 45 = 10125

After placing the decimal at the right place, the answer would be 101.25, which is the accurate answer.

This shortcut is indeed a time-saver at the math quiz sessions and online math tests.

#Technique 9:  Division tricks to solve some math problems easily!

These division tricks will surely help you in the math tests to find a route of the problem solution. It is a quick way to know when you can divide a number evenly by certain numbers:

  • A number that ends with 0, then it can always be divided by 10
  • How will you know a number is divisible by 9 or not? You have to add all the digits and need to detect whether the total is evenly divisible by 9
  • If the last digits are 000 or evenly divisible by 8, then the number can also be divided by 8.
  • You can divide a number by 6 if it meets two parameters. Firstly. It has to be an even number. Secondly, the total of all the digits is divisible by 3.
  • You can divide any number by 5 ending with a 0 or 5.
  • A number that ends with 00 is divisible by 4. If the last two digits of the number can be divisible by 4, then also we can divide the number by 4 as a whole.
  • One can divide a number by 3, when the result of the all added digits is evenly divisible by 3
  • If the numbers end with 0, 2, 4, 6, 8, then we can divide the numbers by 2.

Hope these 9 techniques can guide the students to tackle tricky math questions. Practicing these techniques helps one to construct logical and critical thinking. These can also be stated as ‘mental math exercise.’

However, you can grasp all the math tricks at a time. You may face many hurdles to solve the math problem correctly. Besides, some students also have no time to invest their thinking about learning these tricks. They can acquire MyMathLab answers from the online math experts to submit 100% error-less answers within minutes. This is a more relaxing process and probably the best one to get excellent marks without giving much time and hard work!

School is starting very soon and you find yourself struggling with your Math work.  Math. Whether you have fallen behind because you have mismanaged your time or your workload is too heavy, one thing is pretty clear: you need help with Math. Giving up is not an option. Try to catch up. It is not too late. Math is indeed a demanding subject, but it is a subject that can be learned. As long as you put in the necessary work, you will be just fine. Forget about past experiences and focus on your learning. Please continue reading to learn how to catch up on your Math studies if you have fallen behind. It is not complicated, as you will see.

Slay Your Summer Classes

To catch up fast with Mathematics, go to a Cambridge summer program. Educational institutions do not close their doors during the summertime, so they can tend to your needs. Summer schools in Cambridge, for instance, offer programs to students between the ages of 11 and 18. They offer youngsters the chance to learn from top academics and professionals. Not only do summer schools have practitioners with years of experience, but also they leverage innovative technologies such as artificial intelligence, augmented reality, and cloud computing. The point is that you should consider joining a Cambridge summer program. It will offer you the chance of a lifetime.

Take summer school classes if you want to get ahead or catch up.. Educators will teach you how to approach Mathematical problems and how to apply theories and formulas. Summer schools are not equal with some more academically rigorous than other. However, summer schools provide the optimum learning environment for you to further your education and instill confidence for your mathematical future. 

Read A Chapter in A Day and Get A Passing Grade

The importance of reading in the Mathematics classroom cannot be overstated enough. It builds important knowledge. Undoubtedly, the theory needs to be combined with minds-on activities. Even if you do not like reading about abstract theory, you have to do it. It makes the subject more comprehensible and ensures your success. Once you start reading, you will see that Math is not that scary. Some good books explain the theory behind the equations and which cover more than what happens in the classroom.

Read one chapter a day, take notes, and, most importantly, do some exercises. Find a quiet place in the house where you can study. Hand-writing the most important formulas will definitely boost your memory. Use a pen and paper, as it will be easier to revisit your ideas and notes and frees you from digital distraction. s. By the time you have finished the chapter, the content you have read will be present in your mind. Make sure you read sections you find hardest very carefully and take regular breaks when you are done. Learning isn’t a one-time process, make sure to revisit your work again and again!

Do Not Waste Time on Details and Commit to The Fundamentals

The main reason why many students fall behind studying is that they do not have a good understanding of the fundamentals. They are not capable of handling complex equations because they do not even master the basics. Get started on mastering the fundamentals of Math. This is the best way to prepare for success. What you need right now is a comprehensive grounding in arithmetic. As you progress, you will develop your ability to think mathematically, learn about various concepts and relationships, not to mention apply the knowledge you have just gained.

Foundational Mathematics is an important building block – addition, subtraction, and multiplication – are one of the most important steps. You can continually practice this through daily mental arithmetic and even new maths apps on your smartphones! You will eventually master adding and multiplying large amounts of digits. Math fundamentals are easy and there is no reason to be scared. If you’re struggling we recommend purchasing some fundamental maths books to help guide you through the process – you’ll be there in no time! They will help you understand and solve your problems. It does not matter if you are in higher Math at school. It is imperative to brush up and consolidate on the basics.

Find A Study Buddy to Help You Stay on Track

If you want to stay on track with your goals, get a study partner right away. There is nothing better than studying with a buddy. You can grade each other before school starts and get to the bottom of unsolved problems. If you do not know the answer, you can lean on the knowledge of your study buddy. You may discover that studying with a fellow friend keeps you more engaged and learning Math for longer! It forces you to do the necessary work and meet deadlines. If you do not have a good understanding of calculus or you are not very good when it comes down to geometry, it helps you to lean on not only your teachers advice but a fellow student who understands the topic.

The best study partner is the one with whom you can work well with. You do not need someone that distracts you from your learning by talking about video games, playing on their phones or simply talking to you. However, if you can’t find a suitable buddy, it is recommended then to go to a library look online. Libraries are great places to meet like-minded students who are in a similar position to you – wanting to learn! Take advantage of this and socialise at appropriate times to meet people who can become your study buddy!

Research is an annoying part of academia regardless of which subject it is in, but researching mathematics is a difficult beast to manage because it’s hard to do. What do you look for? How do you research math in the first place? It’s just extremely difficult to do, especially when you’re young and don’t have the experience in the field you need to make it a little more bearable. But if you are interested in conducting honest math research, here’s the way to go about it.

Your Research Doesn’t Necessarily Have to Answer a Question

Original math research generally requires you to tackle a problem that no one has solved yet. However, if you are still in high school, you likely don’t even know all of the aspects of math you would need to make a breakthrough on these extremely difficult problems that even experienced mathematicians haven’t solved. But your math teacher usually knows this, and they hardly expect you to make the next huge math breakthrough in your research. You almost definitely won’t be penalized if your research doesn’t amount to a valid answer. Of course, it’s frustrating for all of your effort to come to naught, but it isn’t something that will affect your grade.

Along that same line, don’t be disappointed by the fact that you aren’t really making any progress on the problem you’re tackling. You’re a high school student; it would be ridiculous for you to solve some math problems that mathematicians haven’t solved yet after all the decades the problems have existed. The research isn’t trying to facilitate actual success, but learning through the research.

Know Who to Ask for Insight

Believe it or not, but math research isn’t very common. It isn’t a normal pastime for your average person. That being the case, it is very difficult to get good advice on it, in person or otherwise. Your best bet is to actually get aid from, well, math people. Math teachers, math professors, mathematicians, whoever; the best way to learn how to conduct math research is to ask people who have, in fact, conducted math research of their own. After all, no one is going to be able to explain the very difficult and technical process than they.

Of course, most of us don’t have a mathematician on speed dial, so other than your actual math teacher, you might not have anyone to turn to in person. It’s a bit harder to find the kind of information you need with a Google search, but the info is out there. This, for example, is an extremely detailed, thorough explanation of mathematical research and how to go about it. Finding such examples and lessons from experienced mathematicians is a great way for you, a high schooler, to get a firm grasp on how this complex and frustrating process works.

It’s Easier to Pick Open Questions

As a high schooler, it’s very difficult to try and answer a problem no one has solved before. It’s even more difficult to try and come up with a problem that no one has ever even asked before. That said, don’t try to. You don’t need to come up with some extremely elusive question that has never been asked by anyone in the history of math. That’s more trouble than you want, and it’s more than your teacher is expecting of you. You won’t have to do something like that to get a good grade.

It’s much easier to pick open questions; problems that have been asked before, even if no answer has been found. The benefit of this approach is that you don’t have to come up with a whole research topic from scratch. You won’t have to brainstorm for a brand new problem to solve, and there will already be some research for you to look into and base your own research off of. For a high schooler who absolutely does not have the math knowledge to be conducting their own original research into their own original problem, this is the safest bet for you in conducting a well-graded math research project.

A More Expensive, Less Troublesome Option

Despite how difficult math research is, it is, like most things, something you can pay someone else to write a research paper for you. Even something as frustrating and technical as math research can be bought from a willing individual online. There are many essay writing services online that tackle just about any problem, including math research of any length or difficulty. A legitimate essay writing site will conduct research and write a research paper even for mathematics. 

Of course, this is definitely one of the subject types that costs a lot of money. Since math research is quite difficult, you’d have to pay an essay writing service a pretty penny for them to carry out all the hard work for you. But that said, if you have money to spare instead of time or motivation, it is probably a good deal. 

Ultimately, math research is not easy, and it’s more about your application prowess and not your overall knowledge of mathematics, which is clearly not as complete as it needs to be to truly do real math research. Know where to set your sights and what is expected of you, and things will go much smoother.

Today the future is all about technology and STEM-centric schools enjoy more popularity than ever. They top prestige rankings and have their pick among the best applicants from across the United States and the entire world. That makes them highly selective, with MIT, for example, accepting only about 8% of their applicants. How can you impress the admission officers of a school that is as demanding as that?

I am not going to lie, it isn’t easy. Even if you get a perfect My Admission Essay review on your personal statement and your GPA is sky-high, no one can guarantee the acceptance letter will land into your mailbox. Often it’s up to a chance. Yet you do want to improve your chances, right? Here are the tips to do it.

Use your strongest side

I guess, that aiming for a stellar STEM college you must be a technical-oriented person. Otherwise, why would you want to be there in the first place? If your strongest side is left hemisphere, you may think that you are not that good at writing and other things that are considered “creative”. Not to worry! You can do it, only you will have to change your approach a little. Don’t try to be someone you are not. Be a confident STEM person and use STEM strategies for your writing:

  • Compare yourself to other potential applicants. What is the variable that makes you unique? Is that your unrivaled talent with numbers? Is that your great vision? Is that your passion and being driven?
  • Everyone has a creative side. It can be expressed in finding elegant solutions to problems and innovating. Show your unique way of expressing creativity.
  • Construct your essay as an engineer. Make a blueprint (aka the outline). Look at the proportions and ratios of the main parts and supporting paragraphs. Harmony can be verified with math, you know.
  • Make a list of things that must be in your essay and check them out one by one. Satisfying, right?

Make it about something important to you

You don’t have to write an essay exclusively about yourself, but you must write it in a way that will show who you are. Your unique voice is what admission officers want to hear. That is why the admission essay is nothing like the essays you used to write at school.

Did you hate to analyze someone else’s work and stock up on quotes to prove your point? Great, because you must NOT do this for your personal statement. It is called “personal” for a reason. It is much more like a short story than your average writing assignment. You write about places, experiences, feelings, people that are important in your life. It’s a narrative from your point of view and there is no “correct” stance on it. The objective is not to write what the admission officers want to read, but to make your story unique, personal, and more importantly – memorable.

Be clear about your goal

One of the reasons why colleges want an essay from you is to have an insight into why you apply. Your motivation is very important. That is why they ask about your favorite subjects or the ways you contributed to improving the life of your community. They want to see you already making the steps in the direction of your dream. Ideally, they want to see how their school can help you on your way to changing the world for the better. Simply wanting a degree and a nice job isn’t enough.

Ask yourself honestly, why this school? Is it because it’s prestigious and selective? Or is it because they have the best research lab facilities the country that will allow you to conduct the experiments you envisioned? Show you are a doer. Schools are quite okay with being for their students only a means to an end, as long as the end in question is laudable.

Polish up your writing

However honest and inspired your writing is, you must make sure it’s free from mistakes, typos, pleonasms, and other writing faux pas. One of the reasons why you are required to submit a piece of writing is, of course, to show off your writing skills.

Your sufficient grammar and spelling proficiency kind of can be deduced from your high GPA score, so this might not be a number one reason when you apply to a selective college. Still, it’s worth considering. If you are not sure that your writing is impeccable, use online editors or hire a proofreader to make sure that you had your best shot.

When you are looking for ways to improve essay writing skills, ordering a cheap essay writing service might seem the least feasible option for you. Though, if you believe so, you are mistaken. We will explain to you how to improve essay writing skills if you have already a ready paper of the best quality. So, here we go.

Order Your Essay from a Reliable Provider

If you decided to buy your writing assignment, then select the most reliable company or just place your “help me improve my writing skills” request with us. why should you select us? Well, we can describe to you why we are among the best writing services providers, but you are interested in a different thing now. So, you just need to get a proper paper, whatever type of it you need:

  • A usual essay
  • A dissertation or a thesis
  • A research paper
  • A term paper

Or whatever else. Our experts are able to write any of them, in any field and of any level. And their papers can serve you as a sample from which you can learn.

Learn about the Paper Structure

Each paper consists of standard elements. Learn which elements your work has. Are there any elements typical for this kind of papers only or all of them are standard? Pay attention to transitions between these structural elements and paragraphs. Are they fluent enough? All these things you can analyze based on the paper submitted by our specialist.

What Words and Expressions Did a Professional Writer Use?

Words, phrases are important to create that unique fascination of a paper that catches the reader and keeps him/her reading until the paper is over. Are there any catchy expressions that attracted your attention? Are they taken from some sources or the writer invented them? Which of them would be useful for your future papers? By the way, it is always a good idea to write down all the interesting details that could be used by you for your future writing assignments.

Make Sure You Format the Paper Properly

Some people don’t pay attention to formatting, but it is important indeed. You would not experiment with fonts and colors in a dissertation, would you? By the way, formatting is what makes your paper look professional. Check the work that our writer delivered and make sure you understand all details connected with formatting.

What about Taking an Unusual Route?

As long as we provide a cheap essay writing service indeed, you can experiment with your paper. What about making all in a different way? If you have time and know how to write essays but want to improve your writing skills, to master them, write your own paper. Yes, you understand all correctly: you place your order online with us but you do not wait till our writer delivers your paper. You write your own paper meanwhile.

After you have two papers, one done by you and the other one – by our writer, you compare them. Do they have the same structural elements? Do they follow in the same order? What about the formatting? Did you consider all those details that your teacher wants from you?

Finally, you might even ignore our cheap essays writing service. You might want to use our cheap editing services instead. This is the simplest and the most logical way. You write your paper on your own and order editing services from us. 

Well, the advantages are evident: you spend significantly less and you are proud that you handled it on your own? Are there any disadvantages? There are, and the main disadvantage is actually the most important. You do not have a sample to compare with. You will be able to see two versions of your paper: the initial version and the edited version. But you will not have your paper written by a professional writer. Hence, the improvement of your skills will be very limited.

You know that theory alone doesn’t bring a wished effect if you don’t practice. We offer you a unique opportunity to improve your writing skills by analyzing a high-quality sample and by practicing. And if you have any doubt or questions, our friendly customer support is always available to clarify all the details.

Mathematics. How charming this word is. For thousands of years, people study it, research, make investigations, put forward theories, and solve problems in such a brilliant way that other mathematicians believe that this is art. Unfortunately, for most people, math is just a subject at school, which they prefer to pass and forget. For those who are in love with math, there is another problem, how to enter the world of science and express yourself as a professional. Unluckily, the times of correspondence between scientists are gone. It is impossible to write the problem on the margins of the letter like Fermat did and became one of the most significant problems for a few centuries. Before you are able to have your own voice in science, you need to pass all steps, and writing research papers is among them.

There are 5 tips to make it easier, but anyway you should remember that the main part of every mathematics research is research itself but not a form.

  1. Make a timetable. People who are fond of math are almost addicted persons. They never forget to research, but always forget to give a form to this research. You should understand that research paper is not your huge amount of drafts, where you used a red marker to highlight the main thought and perfect solution. A research paper is a structured and logical text with rules. Therefore, the schedule will help you with planning your time not to forget every step of writing.
  2. Try to use as more modern resources as possible. There is a proverb, says that great minds think alike. There are many known facts that in different countries at the same time scientists make the same discoveries. They worked separately and used different approaches to solving the problem, but the result was the same. Unlike us, they had an explanation. They didn’t have internet or emails. But we have all of this. Therefore, if you will present your titanic job, which you are proud of and someone will say that saw the same research in another scientific magazine, it will be a disaster. So, first, discover the current situation of the topic you choose.
  3. Use as much help as possible. Remember, that your mentor spent much more time studying mathematics. Maybe in some intermediate result, he will see more impressive next step. Don’t be afraid to talk about your research with your colleagues or college friends. It is possible that some of them are working with a similar problem, and together, you will have a synergistic effect. If you need immediate help with your assignment, and your professor is not available, you can always address a high-quality academic paper writing service which will write your research paper on time.
  4. Use Mathematics or the Wolfram Language for equations, figures, and forms. Your paper will have a more professional look than without using them. In MS Word there is inside instrument called MS Equation. You can also use it. Remember, that only specialist will read your paper, so you don’t need to make footnotes to explain known theorems or lemmas. To be sure that you didn’t skip some necessary explanation, give your paper to read to your mathematician friend.
  5. Use common structure instructions for research paper. There should be a title, an abstract, an introduction, a body, a conclusion and a list of sources. It works to every paper, but mathematician research paper has one big difference that sounds ‘Fewer words, more symbols.’

Try your best in writing! Use the tips above, and we believe that your paper will be stellar. But there is one more remark. If you are a scientist but not a writer, use the proofreading and spend this vacant time for more research because Mathematics is a Queen of Science and every new study is a step of development of our society.

When having an exam, you don’t want to mess up with the marks that come with PSLE ratio word problems. These marks are a chunk of the total marks for the exam, and it’s only safe to earn as much as you can.

Various methods are involved in solving PSLE math’s, and any one of those methods can be used by the math’s tutor to trick you. However, irrespective of how the questions might be twisted, there are 4 basic PSLE ratio that will be tested during an exam, and these are;

Example: John and Peter both have shares in a particular sum of money, in the ratio 5:6. After a couple of days, Peter spent $16, this caused the ratio to become 3:2. At the end, how much does Peter have?

  • The “Constant part”: This simply means that in a Mathematics question, one of the various parts didn’t change, while others did. This is a basic mathematical word problem with a simple approach to solving it. In solving this forms of math problem, all that needs to be done is to make the part that refused to change, equal to each other. If you see a question in the format below from your math tutor, this is the simple approach needed to solve it.

In solving this, you should know that the amount owned by John would remain the same in both cases, as he did not spend any amount of his share.

  • The “Constant Total”: This refers to a case in which the total of a word problem remained the same. Most times, this concept is used when dealing with ‘internal transfer’. Taking a look at this scenario: If X transfers some cash to Y, the amount of cash on X would reduce, while that of Y would get to increase, and by the same amount. However, the total amount of cash on both persons would remain the same, before and after the transfer.

Example: John and Peter both have shares in a particular sum of money, in the ratio 5:4. After a couple of days, John gave Peter about $20, this caused them to have the same amount of money. At the end, how much money does Peter have in the end?

In solving this, you should know that the total amount of money owned by the two persons would remain the same.

  • The “Constant difference”: This refers to the case in which the difference remained the same. In most cases and examinations, you would find out that this concept is used with respect to” Age”.

Irrespective of the number of years that goes by, the difference in the ages of two individuals will always remain the same. This is simply because both individuals grow older, together.

Example: John and Peter both have ages that are in the ratio 4:7. However, in 3 years’ time, they would be at ages with the ratio 3:5. What is the current age of Peter?

In solving this, you should put into consideration that the both John and Peter grow older, together. Hence, the difference in their ages would always remain the same.

  • The “Everything Changed”: This is just as the name implies, in questions like this, every variable is bound to change. The difference changed and so also did the total. None of the variables remained the same.

In most exams, questions that run on this principle would most likely carry the last 5 marks. This is a very important type of question, and you should ensure that you maximize it. However, there are a number of methods that can be used to solve these types of problems. The breakdown of a method goes thus,

Example: The ratio of John’s money to Peter’s was 2:1. Soon, John saved another $60, while Peter spent $150. This caused the ratio to change to 4:1. What was the amount of money John had in the first place?

In solving this, these steps are applicable:

  • Pen down the starting ratio, then effect the changes
  • Have a comparison between the final units and the final ratio
  • Have a cross multiplication of the final units and the final ratio
  • Finally, solve for just one unit.

These four concepts are the very basics and can be used in examining you, once you understand them, you are good to go. A

revision student

How Can You Write an Essay on Technical Research In 5 Steps?

Do you feel you are bogged down by your dissertation?  Never let it frighten you.  Continue reading for some dissertation writing tactics that will certainly turn your dissertation from a beast into something a lot more workable.

1.  Respect your essay

Before everything else, admit that writing your dissertation is a complicated and difficult project and treat it appropriately.  Your long term career will depend on you carrying out good work with it, and, most significantly, finishing it with the help of any dissertation writing service London.

To be able to give yourself the most beneficial chance of completing the dissertation, help it become your top priority of life for the time it takes to complete it.  Put as many other things in your life as you possibly can on hold, or at best try to limit your involvement in them till you have completed the dissertation. 

2.  Manage yourself

On the flip side, take care of yourself.  Get frequent exercise and enough sleep. Your dissertation doesn’t get any better when it’s written by a person who is sick and tired or sleep-deprived.

3.  Do not forget that you’re the expert

Keep in mind that you’re the expert.  You’re the one who did the studies or the analysis that you’re going to write about in the dissertation. So, there’s no need to be consumed with stress.  Just make-believe you are going to explain everything to your friend or coworker in a very lengthy letter. 

4.  Comprehend the basic framework of your dissertation

The majority of dissertations, complex or otherwise, adhere to a comparable structure if they’re according to first-hand analysis, which technical dissertations are typical:


In this particular part, you give a summary of your whole dissertation and its objective.

Theoretical information

In this particular part, you provide a summary of the main study on the subject matter of the dissertation and clarify the way the dissertation analysis relates to everyone else’s analysis.  This is the place to spell out everything you expect to find in the research, i.e., your speculation.

Your studies or some other exploration

In this particular part, you explain your research you did and the way you did it — in specific detail.

The results

At this point, you explain exactly what your outcome was, and provide tables and graphics as required.

What it all means

At this point, you explain the way your final results relate to the speculation as well as some other people’s analysis and focus on the implications of exactly what you found.


This is actually where you present a synopsis of the entire dissertation and make recommendations for further analysis if you have not already done so in your previous section.

5.  Write everything down

Once you know the fundamental framework of the dissertation, the precise writing of it will always be less daunting.  Given that you have done all your groundwork, which was truly the most difficult part, your job is now “simply” to write everything down.

Begin by explaining your research, i.e., by writing sections a, b, and c, in that order. Most of these should write on their own, and once you’ve done them, you will have the bulk of the dissertation written.

Find a subject matter that you like and worry about. Opt for a subject matter that you’ll be in a position to deal with, think about continuously, and even dream of for a couple of years. Once you complete your dissertation, you ought to be, for a short time at least, the world’s leading professional on your subject matter.