Teaching Subtraction

I wanted to make subtraction easier to understand for our nine year old daughter. The commonly used method has too many conditionals (do something different based on this particular case) and so I devised a method of teaching subtraction that uses the same steps for each digit regardless of the values in this column or previous columns. Once your child has mastered the sequence of steps for deducing one digit of the answer he/she can perform subtraction of numbers of any length. I am not the first to think of this method for teaching subtraction (For someone else's explanation see link to "Arabic Numerals - subtraction" at the bottom of this page), but I for one haven't seen it taught to children in any school.

Start at the right column of the two numbers. If the rightmost digit in the minuend (top number) is greater than or equal to the rightmost digit in the subtrahend (number you are subtracting from the top number) then just write the difference in the rightmost digit of the difference (the answer). However, if the minuend digit is less than the subtrahend digit then first add ten to the minuend digit and add one to the subtrahend digit in the column just to the left of the column on which you're currently working. After adding the 10 and the 1, do the subtraction for this column and then move left to the next digit. That's it! Just keep on moving left, applying the same rule until the subtraction is finished.

The reason teaching subtraction using this method makes it easier for young kids to understand is that the commonly taught "borrow" method (borrow "1" from the digit to the left) becomes more complicated if the digit to the left is a "0". Young children don't do well with negative one, and the above described method does away with that problem.

Please visit the latest version of this article on our web-site which includes a diagram comparing the two methods: Teaching Subtraction.

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If you have a young child that is just starting to learn about numbers, the Kidknows TM Outdoor Thermometer for kids is now available on-line and at select Learning Express stores nationwide.

Arabic Numerals subtraction

Children's Math

I was discussing teaching our young daughter how to subtract large numbers and other children's math methods with my brother and he asked, "How does a microprocessor do it?" (We're both engineers; I'm an integrated circuit designer) My response? "They don't [subtract]. They take the two's complement [of the subtrahend] and then add." I thought this idea might help improve my children's math teaching skills.

Microprocessors work in base 2 (each digit of every number is either 0 or 1), but let's do a subtraction example in base 10 (each digit between 0 and 9 inclusive) the way a microprocessor would subtract if it was a human being. It's really easy, easier than the method we humans commonly use.

230895

- 3904

----------------

996095

1

(1)226991

In the figure above, we start by computing the nine's complement of the subtrahend (the number we're subtracting from the top number). The nine's complement of a number is just the number who's individual digits in each column add up to nine with the digits of the original number.

For this example, the nine's complement of 3904 is 996095. To do the "subtraction" you need to extend the nine's complement to be as wide as the minuend (the top number) so insert leading zeros to make 3904 into 003904 and then for each column write down the digit that with the subtrahend (003904) sums to 9 for that column (you write the digit: 9 minus subtrahendDigit). That's how we get 996095.

To get the answer add the minuend (top number), the nine's complement of the subtrahend and "1". There will always be an overflow (a 1 in the column farther left than the leftmost digit of the minuend); remove that 1 from the answer and you're done! Children's math can be child's play!

Please visit the latest version of this article on our web-site which includes graphics illustrating the example: Children's Math.

... or visit our home page: Kidknows TM Outdoor Thermometer.

If you have a young child that is just starting to learn about numbers, the Kidknows TM Outdoor Thermometer for kids is now available on-line and at select Learning Express stores nationwide.

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Memory & Reading Technique for Leaving Cert Students

In the months before sitting your leaving certificate, you are going to read a lot, but that is not going to be of much value if you do not remember it. Memory is the essential ingredient that will tie work, revision and note-taking together, ensuring that you perform to the best of your ability on the exam day.

If you find yourself agreeing with any of the below statements you should read the following article to improve your memory & concentration skills.

I often have to revise a topic I covered from scratch

Sometimes, something distracts me and next thing I know, the bell has gone and class is over

I'll read a chapter of a book, close the book, and I can't tell you really what I just read

If you agree with any of this, then read on!

The RQRR method.

The RQRR method is a way of more actively engaging with texts and has been proven to be much more effective for information retention in young adults.

Review Spend two minutes skimming over what you will read. Pay special attention to headings, subheadings and diagrams. Get a feel for the articles structure.

Questions Based on your review what questions occurred to you? Look at your learning objectives and work out a list of questions you should be able to answer about the topic.

Read Now read the text as you normally would, highlight important information and take your time in complex places (provided these areas are necessary to help you answer your set questions - there is no point wasting time on unnecessary information). Re-read paragraphs if necessary as the goal here is understanding and being able to answer the questions you set earlier.

Review Without referring to the text, go over the main points of what you read. Briefly recount what you have just learned. This early review helps cement the information in your memory.

→ The result will be that you are significantly better at retaining and remembering what you have studied

The CRAM Method

Memory is simply the way that we store experience - when you can't remember something it means that your brain doesn't know where it stored the information - so to improve memory you have to improve the way information is stored. Try our CRAM method.

Cluster People's short term memory tend to hold an average of 7 pieces of information. Group information in clusters such that at any stage you have no more than 7 pieces of information. For example, in geography, divide a topic into 3-7 subtopics and then each of these subtopics into 3-7 sub-subtopics. A country might have physical, social and economic information. Each of these subtopics has a number of smaller topics, e.g. economic geography has exports, employment, etc.

Review Information has to be regularly reviewed - one month after you learn something you will have lost 80% of information is lost if not reviewed. So, review everything the following day and once per week, do a review of everything you have done.

Apply it The information will be better remembered if it is applied. Some ways to do this are having a discussion with friends about the topic, doing extra reading online, or trying to answer questions on the topic.

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Is Homeschooling For Us? Yes Or No

The single hardest decision facing homeschoolers is not what topics to discuss, or even which programs to use in your school. For homeschool moms and dads, the decision on whether or not you will home school your child is by far the most challenging obstacle you will have to face.

Home schooling is not just a classroom - it is a commitment. It is also a parents way of sharing what they know and what they believe with their own children. It also shows that the parents will commit their time and their efforts to teaching their children, even when it is inconvenient or difficult.

There will be ample time for activities, spending time with the kids, limitations of the topic areas which are of concern for the parents; but there will also be times when parents won't want to be around their children, will have to address topics which will be controversial, and ways to find socialization for their children. These topics and events need to be thought about long before a commitment to home school your child is ever made.

The decision and commitment to homeschool a child needs to be made between the parents long before a program of study is picked, if you have children that are already school age you also need to talk about this with your kids. You will have a major fight if you don't. This is one of the major decisions that, if possible, needs to have been made long before your children are old enough start school.

Changes in your childs school status can be made if later if necessary but overall it seems that it is always easier to introduce your kids to public school after being home schooled than it is to introduce them to home school after being in public school. Homeschooled students normally interact differently with their peers than do kids brought up in the public school system.

Lets think about this even more. During the process of deciding whether or not to homeschool your kids, probably the second largest obstacle you come across will be your family. This is a decision that involves everyone in your household and they will also need to be sold on the idea. This isn't the just kids who will be homeschooled we're talking about; it is also the grandparents, the siblings, other family members of the parents and there will also be the nay sayers - the people who have seen the parents fail in the past. These people can easily either be your greatest asset - or your greatest liability.

Research in making this decision is a definite necessity and nothing to be taken lightly. Check with your local school system, teachers in your area, families who have done homeschooling in the past and those that are doing it now. You'll need to know all the requirements to do homeschooling before going any further, and there are many. It isn't just as simple as suddenly deciding to keep the kids home today. There are many legalities to consider as well in making the decision to homeschool.

Talking with others who are homeschooling their own children will help make this decision easier in the long run, but it won't make it a breeze. This is a huge undertaking. Remember, home schooling is more than just a classroom - it is a commitment to your child and their education.

How is Materialism Destroying Society?

When tough economic times hit, there is always the question as to whether greed is the cause of our economic problems. However, this isn't necessarily the root of the problem. It is a bit more complex than that. Railing against the greed in capitalism doesn't take into consideration the other factors that are equally present. Greed can also be for power. Power comes with money, but it isn't always the money people are after. This is why big government is as dangerous as corporate monopolies. The people who have consolidated significant power tend to be corrupted by it. As human beings, we all tend to lean toward materialism in our actions, and find our personal significance and value in things we control and own.

There is a spiritual aspect to the problem of materialism. It is a worldview that fuels greed. Our society has been increasingly embracing the worldview of naturalism, of which materialism is a part. Naturalism holds that knowledge is limited to what we can see and that everything must be thought of in physical terms. Naturalism ignores the spiritual aspects of life, considering them more like superstitions. So we tend to move toward seeking our personal value in the things we possess and the things we control. To make matters worse, we also discount objective truth. The end result is there are no standard set of values we all hold common, and that means there is no foundation for society to build on.

So in America, we have come to equate financial wealth with a higher level of happiness. This is partly what is wrong with the caste system in India. The belief behind it is materialistic. This worldview is illustrated well in the movie Slumdog Millionaire. However, what we really need is a purpose for our life. But we can't find purpose in physical things. Since we have decided that objective truth can only be found in scientific conclusions, we have dismissed the existence of truth beyond what we can see, hear, feel, taste, or touch. Yet there is a non-physical reality where we find our sense of purpose and meaning in life. We are ignoring half of the knowledge we could be gaining by ignoring the knowledge from the non-physical realm. In Hosea 4:6 in the Old Testament, it tells us what happens when we lack knowledge. There are moral shortcomings that lead to a downfall. The ways of the people are characterized by self gratification and greed.

So the real solution to our economic and financial problems doesn't lie in putting our trust in an economic theory about what will restore our economy, but rather it lies in recognizing the thinking that has led us astray. As a nation we are turning away from the Bible as a source of moral authority, which was certainly in the minds of the founders of our country. It is found throughout the federal and state constitutions, as well as our Bill of Rights. It even says on our money "In God We Trust". It was this moral compass that has guided legislation in the early years of our country. But, as we have strayed from those original moral principles, we have caused the problems we have today. We have led our citizens to strange ideas about how the world works, and they have adopted them. We have let the marginalization of faith and the emphases on a materialistic worldview dominate, governed by a postmodern philosophy that denies any objective truth. It confuses our laws and destroys the core of what made this country strong.

Each individual can rise above this problem by returning to the Bible as a moral guide for their own lives and no matter what happens to us as a nation, they will find the strength through their faith in God to do what is good and right. They will find a sense of purpose that will give them the power to overcome adversity and will be the last ones standing in the end. These will be the people who were able to recognize their faith in God and the truth of the Bible heeding the wisdom of Proverbs 3:5 where it tells us to trust the Lord and not lean on our own understanding. We know what God teaches us in the Bible is reliable, and if we place our trust in that most reliable source, we've gone a long way to rising above the problems we have today.