Tag: Easy Math

Math Trick – Your Birthday

I found a cute video that shows you a trick with math and a calculator on how to get your birthday.

Try following along with the steps and see if it works for you. It worked for me!

Easy Math Magic Tricks – Birthday Date Calculations
http://www.WorstJokeEver.Com Here comes a math trick to play upon calcualting your birthday date. Suprise your friends and family with this magic calculation…

So did it work?

Have a great day!

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How To Make Learning Math Easy

Most of the time when you ask a child about learning math, they’ll usually respond that it’s hard. Some respond that they’re just not good at math. But did you know that with you’re help, you can make it a little easier for them to learn math? Yes, you can! Check out this article that James Tomas wrote.

Making Math Easy

 Math can be a difficult subject for many children, and often, children struggle in school simply because they do not understand the basic concepts of mathematics. If your child is struggling with this subject, and you want some suggestions for help on math, then you have come to the right place. If you take a proactive approach to your child’s learning needs, you can make math much easier for them. Just consider the following suggestions.

First, remember that school subjects are often considered not fun or even boring. Your child may be struggling with math simply because he or she feels like being in math class is torment. To get your child more interested in the subjects, look for ways to make it fun. Create math based games that will be exciting learning experiences. This is a good way to keep a child’s attention and help them learn without them feeling the normally drudgery of study.

Second, math can easily be taught in everyday situations. You do not have to sit down with a child at a kitchen table to study the subject. When your child needs help on math, look for real life scenarios to help them learn. For example, take them along to the grocery store and let them use a notepad to add up the cost of different grocery items that you are buying. When you purchase something at a convenience store, have the child try to determine how much change you got back from your cash payment. There are many real life scenarios that can easily implement help on math for your child.

Third, remember that illustrating something or making it hands on is a much easier way for children to learn. If you put a math problem on paper, the child may struggle. However, if you make it come to life, they may find it easier to learn. For instance, on a basic level, have the child add or subtract actual items like fruit in the kitchen, books or videos in the living room, or pebbles in the back yard. Bringing math to life gives a better illustration for a child to learn.

Many children struggle with math. If your child needs help on math, remember that you can give them that help. Just keep in mind that you need to make the subject more fun and interesting. You also need to use real life scenarios and illustrations to teach them the subject.

By: James Tomas

Article Directory: http://www.articledashboard.com

Making Math Easy is one of the subjects from the “Education and Reference” category of eCapsulate.com.

 

So you now know what to do to take some of the difficulty out of learning math for your children!

Hope you have a great day!

 

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Math Really Can Be Easy

So many children as well as adults seem to believe that math is a hard subject to master. But as this article explains, it doesn’t have to be that way! Check it out and try some of the suggestions. I’m sure you’ll find it’s not so hard for your child to learn math!

Making Math Easy

Math can be a difficult subject for many children, and often, children struggle in school simply because they do not understand the basic concepts of mathematics. If your child is struggling with this subject, and you want some suggestions for help on math, then you have come to the right place. If you take a proactive approach to your child’s learning needs, you can make math much easier for them. Just consider the following suggestions.

First, remember that school subjects are often considered not fun or even boring. Your child may be struggling with math simply because he or she feels like being in math class is torment. To get your child more interested in the subjects, look for ways to make it fun. Create math based games that will be exciting learning experiences. This is a good way to keep a child’s attention and help them learn without them feeling the normally drudgery of study.

Second, math can easily be taught in everyday situations. You do not have to sit down with a child at a kitchen table to study the subject. When your child needs help on math, look for real life scenarios to help them learn. For example, take them along to the grocery store and let them use a notepad to add up the cost of different grocery items that you are buying. When you purchase something at a convenience store, have the child try to determine how much change you got back from your cash payment. There are many real life scenarios that can easily implement help on math for your child.

Third, remember that illustrating something or making it hands on is a much easier way for children to learn. If you put a math problem on paper, the child may struggle. However, if you make it come to life, they may find it easier to learn. For instance, on a basic level, have the child add or subtract actual items like fruit in the kitchen, books or videos in the living room, or pebbles in the back yard. Bringing math to life gives a better illustration for a child to learn.

Many children struggle with math. If your child needs help on math, remember that you can give them that help. Just keep in mind that you need to make the subject more fun and interesting. You also need to use real life scenarios and illustrations to teach them the subject.

By: James Tomas

Article Directory: http://www.articledashboard.com

Making Math Easy is one of the subjects from the “Education and Reference” category of eCapsulate.com.

There you have it. Give some of these a try and let me know what you think?

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Complex Math and Mental Math

Is mental math necessarily complex math? I don’t think so!

I found a short article which helps to teach students how to deal with complex and mental math (as well as easy math)!

Check it out:

Mental Maths Activities That Are Beneficial

Considered a complex subject, most students find it intimidating and for most of them, as they age, it becomes more complicated. Though this is the case, it is an important part of life as it equips them with the necessary skills to face real life.

Easy Answers
Mental maths should be introduced from kindergarten grades to students who have a lower capacity of understanding maths. This should be done with easy to answer questions. If it is in a class setting, then the students should be presented with simplified math equations and the first one to get the right answer should shout it out. As this progress, it will eventually reach a point where the entire class shouts out the right answer as a team. As they age and get more equations correctly, then more complex math should be introduced. In this instance, students can use time tables, basic algebra and division facts. For instance this could be something that Y plus four equals 10 and the students should answer what Y is.

Complex Math
A large percentage of maths used in day to day life is mental math tricks. For instance, someone working at a store should figure out what 60% of $20 is, a driver is supposed to figure out how many hours he will drive to cover a 230 mile trip among others. This proves that math is an important part of life and as such, it is ideal to ensure that students solve mental maths equation every day. However, when carrying this out, it is important to ensure that it is age appropriate. For seventh graders 60% of $ 230 is ideal while for fourth graders 10% of 100 is appropriate. Students should be given the time to read the equation and work it out before providing the answers.

Story Problems
This is another important mental maths activity to indulge in. It should be on situational stories and students should be encouraged to work them out mentally. Also known as multi-mental math they are the best. This is attributed to the fact that they require more thought for the answer to be processed as well as mimicking the manner in which maths is used in real life situations. However, it is important to outline the equation in a manner that is easy to understand. Though challenging, these simple mannerisms when employed in the right manner, help students develop an instinctive accuracy handling mental maths.

By: Borat Noviak

Article Directory: http://www.articledashboard.com

To learn much more about the mental math tricks, maths tips can be found at mentalmathtricks.com/.

So  has this changed your mind? Do you believe that these tricks and exercises can helpyour child to learn complex math?

Let me know?

Have a super Memorial Day Holiday.

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How To Help Your Child Learn Math

If you’re not real sure of how to go about helping your child learn elementary math, here’s a good article I found that I’d like to share with you!
 

Three Easy Ways To Help With Elementary Math

 
Are you worried about giving adequate help with elementary math to your child? Has your child ever brought home math homework and you have no idea how to assist them? Students no longer learn math the way you and I learned math. They are now exploring, drawing, and developing their own strategies to solve a problem. This leaves many parents in the dark about how to help their child in math. In addition, some people just are not “math people” and therefore feel like they don’t know how to help their child. I am going to give you three easy ways to help with elementary math from home.

Help with Elementary Math Tip #1- One of the easiest ways for a child to learn math concepts is to use manipulatives. Manipulatives are items that your child can move around, group, take away from, add to, etc. These can be anything you have in your house (beans, skittles, grapes, etc.).Manipulatives help children who are struggling in math because they help to bring the problem to life. Your child will now be able to “act out” the story problem, which helps them better understand what they are supposed to do in order to work out the problem or equation.

When children use manipulatives they show the word problem using the manipulatives. For instance, if a child was dividing 72 by 9, he or she would count out 72 beans and then group them into groups of 9. He or she would then count how many groups they have to find their answer. To extend this activity, students can label what they are doing so they can connect the manipulatives with drawings or numbers.

Help with Elementary Math Tip #2- If you don’t have manipulatives at home or if they are completing their work in the car, before baseball practice, or anywhere that manipulatives are not available your child can draw pictures. It might seem too simple to be true, but I have had many experiences where a child was stuck on a problem until they drew a picture and visually saw the problem instead of simply reading it. Drawing pictures of the word problem or equation helps a child see exactly what they are going to do in the problem. They are also able to manipulate the items they are working with, which makes it more fun and meaningful to them.

Drawings work a lot like manipulatives, but students are now strictly using paper and pencil and drawings instead of physically manipulating items. To make this activity more meaningful, your child should label their drawing with numbers, skip counting, or however they are counting the objects in their picture. I always tell my students that anyone should be able to fully understand what they are doing just by looking at their work.

Help with Elementary Math Tip #3- When your child is stuck on a problem try making the numbers smaller. In many cases, children are overwhelmed with big numbers. They see large numbers and automatically think the problem is going to be difficult. Making the numbers smaller doesn’t change the concept, it just makes it easier for them to work through the problem and it gives them confidence that they can complete the problem. Once they can successfully answer the problem with smaller numbers have them try using the bigger numbers. Just remind them to do the same thing with the bigger numbers that they did with the smaller numbers.

Math is a difficult subject for many children. A lot of times they come home and you just don’t know how to help them. Some of the best ways you can help your child succeed in math is to let them use manipulatives, have them draw pictures, and to change the numbers in the problem. They can use one or all of these strategies on the same problem. Utilizing these three easy tips with your child will help with elementary math skills and get them started on the path towards excellence in math.

 

By: Bethann Baker

Article Directory: http://www.articledashboard.com

 

Hope this helps you. Remember that your children learn from watching you! So be positive and show them that learning math is something to enjoy!

Have a great day.
 

 

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Simplify To Make Math Easy

Here’s an article on one of my favorite subjects – making math easy.

Making Math Easy

Math can be a difficult subject for many children, and often, children struggle in school simply because they do not understand the basic concepts of mathematics. If your child is struggling with this subject, and you want some suggestions for help on math, then you have come to the right place. If you take a proactive approach to your child’s learning needs, you can make math much easier for them. Just consider the following suggestions.

First, remember that school subjects are often considered not fun or even boring. Your child may be struggling with math simply because he or she feels like being in math class is torment. To get your child more interested in the subjects, look for ways to make it fun. Create math based games that will be exciting learning experiences. This is a good way to keep a child’s attention and help them learn without them feeling the normally drudgery of study.

Second, math can easily be taught in everyday situations. You do not have to sit down with a child at a kitchen table to study the subject. When your child needs help on math, look for real life scenarios to help them learn. For example, take them along to the grocery store and let them use a notepad to add up the cost of different grocery items that you are buying. When you purchase something at a convenience store, have the child try to determine how much change you got back from your cash payment. There are many real life scenarios that can easily implement help on math for your child.

Third, remember that illustrating something or making it hands on is a much easier way for children to learn. If you put a math problem on paper, the child may struggle. However, if you make it come to life, they may find it easier to learn. For instance, on a basic level, have the child add or subtract actual items like fruit in the kitchen, books or videos in the living room, or pebbles in the back yard. Bringing math to life gives a better illustration for a child to learn.

Many children struggle with math. If your child needs help on math, remember that you can give them that help. Just keep in mind that you need to make the subject more fun and interesting. You also need to use real life scenarios and illustrations to teach them the subject.

By: James Tomas

Article Directory: http://www.articledashboard.com

Making Math Easy is one of the subjects from the “Education and Reference” category of eCapsulate.com.

eCapsulate.com – Save Time

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Remember that Cherry Hill Mathnasium is here to make math easy for your children!

Have a great day.

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Quick Tips To Help Your Children With Math Homework

Here’s an article to help you learn how to help your children get their math homework done!
It comes coutesy of ArticleDirectory.com

Three Easy Ways To Help With Elementary Math by Clarence Bailey

Have your children ever brought home math homework and you have no idea how to assist them? Students no longer learn math the way you and I learned math. They are now exploring, drawing, and developing their own strategies to solve a problem. This leaves many parents in the dark about how to help their child in math. In addition, some people just are not “math people” and therefore feel like they don’t know how to help their child. I am going to give you three easy ways to help with elementary math from home.

Help with Elementary Math Tip #1- One of the easiest ways for a child to learn math concepts is to use manipulatives. Manipulatives are items that your child can move around, group, take away from, add to, etc. These can be anything you have in your house (beans, skittles, grapes, etc.).Manipulatives help children who are struggling in math because they help to bring the problem to life. Your child will now be able to “act out” the story problem, which helps them better understand what they are supposed to do in order to work out the problem or equation.

When children use manipulatives they show the word problem using the manipulatives. For instance, if a child was dividing 72 by 9, he or she would count out 72 beans and then group them into groups of 9. He or she would then count how many groups they have to find their answer. To extend this activity, students can label what they are doing so they can connect the manipulatives with drawings or numbers.

Help with Elementary Math Tip #2- If you don’t have manipulatives at home or if they are completing their work in the car, before baseball practice, or anywhere that manipulatives are not available your child can draw pictures. It might seem too simple to be true, but I have had many experiences where a child was stuck on a problem until they drew a picture and visually saw the problem instead of simply reading it. Drawing pictures of the word problem or equation helps a child see exactly what they are going to do in the problem. They are also able to manipulate the items they are working with, which makes it more fun and meaningful to them.

Drawings work a lot like manipulatives, but students are now strictly using paper and pencil and drawings instead of physically manipulating items. To make this activity more meaningful, your child should label their drawing with numbers, skip counting, or however they are counting the objects in their picture. I always tell my students that anyone should be able to fully understand what they are doing just by looking at their work.

Help with Elementary Math Tip #3- When your child is stuck on a problem try making the numbers smaller. In many cases, children are overwhelmed with big numbers. They see large numbers and automatically think the problem is going to be difficult. Making the numbers smaller doesn’t change the concept, it just makes it easier for them to work through the problem and it gives them confidence that they can complete the problem. Once they can successfully answer the problem with smaller numbers have them try using the bigger numbers. Just remind them to do the same thing with the bigger numbers that they did with the smaller numbers.

Math is a difficult subject for many children. A lot of times they come home and you just don’t know how to help them. Some of the best ways you can help your child succeed in math is to let them use manipulatives, have them draw pictures, and to change the numbers in the problem. They can use one or all of these strategies on the same problem. Utilizing these three easy tips with your child will help with elementary math skills and get them started on the path towards excellence in math.

Do you think these will help you? Drop a comment below and let me know what you think?

Have a great day!

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Easy Steps To Help Learn Elementary Math

If you have a young child who is trying to learn math – here is a good article that will give you some pointers to help make learning math much easier for your child.

Three Easy Ways To Help With Elementary Math

By: Clarence Bailey
ever brought home math homework and you have no idea how to assist them? Students no longer learn math the way you and I learned math. They are now exploring, drawing, and developing their own strategies to solve a problem. This leaves many parents in the dark about how to help their child in math. In addition, some people just are not “math people” and therefore feel like they don’t know how to help their child. I am going to give you three easy ways to help with elementary math from home.

Help with Elementary Math Tip #1- One of the easiest ways for a child to learn math concepts is to use manipulatives. Manipulatives are items that your child can move around, group, take away from, add to, etc. These can be anything you have in your house (beans, skittles, grapes, etc.).Manipulatives help children who are struggling in math because they help to bring the problem to life. Your child will now be able to “act out” the story problem, which helps them better understand what they are supposed to do in order to work out the problem or equation.

 

When children use manipulatives they show the word problem using the manipulatives. For instance, if a child was dividing 72 by 9, he or she would count out 72 beans and then group them into groups of 9. He or she would then count how many groups they have to find their answer. To extend this activity, students can label what they are doing so they can connect the manipulatives with drawings or numbers.

Help with Elementary Math Tip #2- If you don’t have manipulatives at home or if they are completing their work in the car, before baseball practice, or anywhere that manipulatives are not available your child can draw pictures. It might seem too simple to be true, but I have had many experiences where a child was stuck on a problem until they drew a picture and visually saw the problem instead of simply reading it. Drawing pictures of the word problem or equation helps a child see exactly what they are going to do in the problem. They are also able to manipulate the items they are working with, which makes it more fun and meaningful to them.

Drawings work a lot like manipulatives, but students are now strictly using paper and pencil and drawings instead of physically manipulating items. To make this activity more meaningful, your child should label their drawing with numbers, skip counting, or however they are counting the objects in their picture. I always tell my students that anyone should be able to fully understand what they are doing just by looking at their work.

Help with Elementary Math Tip #3- When your child is stuck on a problem try making the numbers smaller. In many cases, children are overwhelmed with big numbers. They see large numbers and automatically think the problem is going to be difficult. Making the numbers smaller doesn’t change the concept, it just makes it easier for them to work through the problem and it gives them confidence that they can complete the problem. Once they can successfully answer the problem with smaller numbers have them try using the bigger numbers. Just remind them to do the same thing with the bigger numbers that they did with the smaller numbers.

Math is a difficult subject for many children. A lot of times they come home and you just don’t know how to help them. Some of the best ways you can help your child succeed in math is to let them use manipulatives, have them draw pictures, and to change the numbers in the problem. They can use one or all of these strategies on the same problem. Utilizing these three easy tips with your child will help with elementary math skills and get them started on the path towards excellence in math.

Author Resource:->  write my essay

Article Directory : http://ArticleDirectory.com

So there you have it! If you use these tips I believe that you’ll find teaching math to your young student is (as Sherlock Holmes would say) elementary my dear Watson!

🙂
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Learn Math The Right Way – Crawl Walk Run

Lots of folks complain that it isn’t easy to learn math, but I found this article that may just help explain why some folks think it’s hard!

Learning Math is Difficult For Many People – Knowing Why Can Make Mathematics Easy and a Lot of Fun
by Isabel Ambrocio

Mathematics is a language, but it can not be learned the same way most languages are learned. Mathematical principles and concepts must be learned in a specific order. Much like the way we learned to walk. When we were learning to walk we found that we had to crawl first, if we went too fast and tried to stand or walk before we were ready we fell and got a boo boo. The same is true for math, except if we jump ahead of our selves or miss something along the way, we don’t fall and get a boo boo, we begin to believe that we are just no good at it.

To prove my point about the need to learn mathematical concepts and principles in a particular order, most City Colleges around America have elementary to high school level math classes that are offered to students that don’t have the required college level skills in mathematics needed to enter the college system. So the problem is real and recognized by Authoritative Institutions. Mathematical concepts need to be learned in a particular order no matter how intelligent you are. Trying to become proficient in mathematics by learning random bits and pieces will be very difficult if not impossible. Each level in mathematics requires a working knowledge of all the prior levels.

Because Mathematics is a language, you also need to immerse yourself in solving math problems to become proficient. Doing this is a lot easier these days with the aid of the Internet and calculators that do symbolic manipulation. Spending at least one to four hours a day working math problems, everyday, will develop and reinforce the skills needed to become proficient in math. Why so much time? To build, what I like to call, brain circuits.

Solving a problem requires a number of steps to be taken by the brain. Simply put, to solve “1+1=2” the brain needs to look at each character and then calculate what actions to take. If this is the first time attempting to solve this type of equation the brain has not connected up the wires or developed the circuits yet, it resorts back to circuits it has used in the past when attempting to do new things. Try writing with your other hand. Most will find it very difficult. That’s because the brain has not developed the circuits yet to perform the task. As the brain creates and hard-wires the correct circuits used to solve the mathematical problems your working on your mathematical abilities will grow, and as a side benefit, those same circuits will aid in other brain functions. But like everything in nature, the brain is very conservative.

The brain is not going to create and hook up circuits unless there is a real need for them. You need to let the brain know you mean business. The way you do this is by forcing the brain to work on math problems. The brain does not like change, so it will produce chemicals that will make this uncomfortable for you. You must fight back and continue. Soon the brain’s own need to be conservative will require it to build the circuits needed to more efficiently solve these problems. Result, you get better. And if you do things right and stick with it, the brain will become proud of these new circuits it has built and begin to produce chemicals that will make you feel real good. In the beginning it will be hard, but after a bit you’ll enjoy the brains reward. Video game developers have learned how to trigger these chemicals in the brain via their software. That’s why kids will spend hours, even days, in front of a monitor pushing buttons on a game pad.

Building circuits in the brain takes a lot of hard work and time. It took all of us years to learn to walk, talk, write, and perform many other abilities we take for granted. We learned most of these abilities when we were very young. It was called play time. It was fun, exiting and we couldn’t wait to get started. We also had many examples to draw from, people were walking, talking and doing things that helped us see how others performed these tasks we were trying to do. Not true with math. There’s the math book from school, well people with the IQ of a thousand don’t seem to have a problem with it so who am I to complain?

We learn best by example. Here’s the dilemma, there are not too many TV shows dedicated to mathematical problem solving. There are not even too many math courses dedicated to mathematical problem solving. There’s a teacher going at the speed of light spewing out concepts and principles while you try to listen and write at the same time. That’s not the best learning environment for mathematics. Thank God math is so easy or we’d be in trouble. Maybe it’s not you, you may have the makings of a brilliant mathematician, but have never been in a suitable situation to learn.

Solution, look at the answers to as many problem as possible and see how those answers were found. Use the Internet to study ahead of your class, so you’ll know whats being talked about when your instructor buzzes by at the speed of light with new concepts and principles. Remember, one missed item, principle or concept and you won’t be prepared for the next level. It’s very possible that your very good at math, it may be that the tools and road map to learn are missing.

Most problems encountered in learning upper level math come from not fully understanding elementary math. Algebra requires proficiency in elementary math, calculus requires proficiency in both elementary math and algebra. Most kids in elementary school can’t see the importance of math, so they lack the effort. Kid in high school don’t have time for math, so they do the minimum to get by. Then these young men and women, now ready to enter college, feel they are just no good at math, so they opt for other majors. Has a future Einstein been lost to this chain of events.

Take all this into account when learning math and you will find that mathematics is easy and fun. You may have to start at the beginning to find those concepts or principles you missed but you’ll find it pays off as you develop those mathematical skills with easy. But be careful, once you start discovering new things in the universe with your newly developed mathematical skills the brain chemical awards you will receive can become very addictive.

We have set up a website for inventors and people interested in how things work. At http://www.6pie.com you’ll find videos, tutorials, and information about physics, chemistry, biology, mathematics, and alternative energy. Also commonly used formulas and data. Ohm’s Law, Faraday’s Law, Maxwell’s equations and more. Knowledge is power.

So there you have it! Now you know that t’s not really hard to learn math! So go get ’em!

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Teaching Tips For Helping Children To Learn Math

The perception that some children are gifted, born with “math know how” and learn math easily is not a truism!

If you are a teacher and want to effectively help your young students learn math, Jennifer Dobson has written a good article (which GoArticles.com published), and titled it:

How to Effectively Teach Young Children Math 

Here is her article.

For a great number of students, mathematics creates an overload of anxiety. And many children dismiss math as a subject that they will have no use for in the “real world”. As an educator, you know that it is important for your students to develop strong math skills, but you likely find it difficult to motivate your students to learn math. The tips that follow will lighten the load for teachers as they help their students tackle the math monster and overcome their apprehension of math in general.

Stay Positive

Are you anxious about your own math skills? Are you worried that you cannot present math lessons properly? Many people are, and a lot of professionals were poor students in math themselves. Now that you are teaching math, you must keep a positive outlook on the subject as children can pick up on your emotions and learn your secret. Remember that is your students give up on their ability to do math now, they may miss some of the rudimentary basic skills that they need to do more advanced math later on in life.

Ensure Understanding

Understanding math is challenging, and this is especially true for young children. If a student is struggling with a homework assignment or worksheet, ask the student to explain the assignment to you, or to explain how to complete a particular problem; this helps you to gauge their understanding on particular concepts so that you will know how to better help them.

Exploring Math in Daily Life

It is easy for you to incorporate math into your daily life, and helping children understand how math affects their daily routines also helps to make them understand why math is necessary. For instance, create a math problem for subtraction by having the students to count the minutes left on your classroom clock before lunch, or ask them to multiply the number of boys in the class by the number of girls. This can help to reinforce the necessity of math and how it can apply to the real life.

Make Math Fun

Kids learn more effectively when they are enjoying themselves, so making math fun is important. Create worksheets and games that will add a fun element to each math unit. Games can be played with flash cards that allow kids to use math skills they are currently learning, or you can create a “Jeopardy” type game where students compete against one another to solve problems. Computer games also provide effective means for teaching math skills.

Get Parents Involved

You will find that involving parents in the learning process and maintaining communication with parents about each student’s progress in math will help motivate the student to achieve. Identifying any math problems and working with them to make sure homework is completed will go a long way towards helping the student meet the goals that are set for their grade level. Don’t be surprised to find out that many parents are insecure in their own abilities to do math as well. These students may need extra classroom help to make up for the help they cannot receive at home.

About the Author

Jennifer Dobson invites you to take a look at one of her favorite online preschool teaching supplies store, MPM School Supplies. The website has over 20,000 products including a great selection of classroom decoration supplies, art materials, furniture, and more! Visit today and save 10% on your first purchase!

 

 

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