Kids Math

Kids Maths Training

2011-05-31T16:47:00.001-07:00

I am planning on making videos to explain counting in more detail and further stress on building a sequence of videos that kids can understand. Question remains if toddlers can stay focused on watching videos, or some form that is sufficient to gain their attention and have them involved. This is just a thought, I will blog as usual, but something up for grabs as time goes.

Let's take another view on Fraction

2011-05-28T18:53:00.000-07:00

Write down the first 10 simple numbers that come to your mind. Now add them together. Once you get the total divide it by 10. What do you get? Can you divide it first of all. Do you see that if you divide, it comes to a whole number. Ask your mom about whole number and natural number, or I will discuss it in later post. For now consider it anything that is a normal number starting from 0 onwards. You may be lucky if you got a whole number as the answer, if not you have come to a point where number does not divide further. That remaining number is called remainder. For example, if you had the following 10 numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 then the total will be 45 and divide it now by 10. You will notice that 45 in 10 parts will likely be 4 plus something and to get that something you have to divide 5 into 10 parts. Number 5 in this example is called remainder and when you get remainder that is not divisible directly by the divisor(10), then any further division requires us to add a decimal next to 4 as that something is now going to be in fractions following a dot. And now you can add a zero next to 5, coz with decimal in place this number is 10 times at the tenth place. That means now 5 at unit place(before decimal) is 50 at (after immediate location to decimal). Dividing 50 by 10 is now easier, you know it. So you answer will be 4+something(50/10) or 4.5.

Above part was somewhat logical and somewhat mechanical in explanation, however another aspect of fraction is that you can have as many fractional numbers between two whole numbers as infinity(???). For example between 1 and 2, you can have 1.1, 1.2, 1.3, 1.4,.....1.9, 2.0 or 1.11,1.12,1.13,....1.19,1.2,1.21.......1.3,.....1.4,.....1,9,2.0 or 1.111,1.112,1.113....,1.12....1.13...1.2,....2 and on and on. You can fit in any number of fractions between two numbers or in effect infinite numbers, as there is no limit. This part is just for thinking, I will leave it there.... Learn the division where fraction comes, but understand fractions allow us to calculate those numbers that are not easily divisible to a whole number. Like split an apple, if you can not get a single apple in the end.

Understanding Fractions

2011-05-24T18:10:00.000-07:00

or Simply Fractions

I think you are already ready about counting, addition, subtraction, multiplication and division are useful tools to help you count any problem you face. The apples, oranges, hands, legs, whatever countable nouns you know of, but what remains is another problem.

Alright let's focus on this simple thing, let say I have to divide the 100 apples in 10 parts or baskets, I think you know it by now, you will have 10 apples per basket. Now if I have to provide my fellow friends 2 apples out of the 100, then using subtraction, you can find that I have only 98 remaining. Ok, so now if I have to divide the remaining 98 apples to 10 parts or baskets, I will run short of 2 apples, isn't it. Count. 10 apples in each basket will give you 100 apples in total, however 9 apples in each basket will give 90. Therefore it is difficult to divide remaining 8 apples in 10 parts. Can't we simply cut each remaining apple to 10 parts and then the total number of apple parts would be 10 times 8 apples or 80 parts. Then it is easier to divide the 80 parts into 10 baskets, simple place 8 parts each into smaller baskets. Wow, that is easy now. So now you have 9 full apples and 8 parts of an apple in each basket. This division or chunking of a full apple or any big object generates smaller objects of equal size and many of them together form a single object. Each smaller object or apple part is called a fraction as it is only a fraction of the full. This in mathematics provides the basis to count numbers that are not full, but fraction of a large count. In this case, we have 9 full apples and 8 smaller parts. We write fractions next to the full number separated by a decimal. A decimal is a dot. This decimal is used to say that we are dividing the full number by 10 and every number following on the right hand side of the dot is one tenth of a full number times the number of parts. Here total number of apples in a basket were 9 and 8 parts or 9.8. The fraction .8 reflects the fact that it is 8 times 1/10 of an apple at that location. Say you had to divide the smaller part further into 10 more parts say parts-parts then, parts-parts are nothing but 1/10 or 1 tenth of the 1 tenth or 1/10 times 1/10. We will explain this puzzle later, stay tuned...

Math that speaks volume

2011-05-23T17:39:00.000-07:00

Make sure you are working on the counting part and strengthen it. This is the part if not practiced well, can cause one to jumble up when asked to do with large numbers. Counting is your strength and tables allow to do it quickly. Math tables are very valuable help. They create shortcuts and really stronger ones that you will use your entire life. That is the value they have. Make a point that you memorize math tables upto 30, try hard, I know it takes effort and time, but believe me you will enjoy as time passes and some of the calculation will just run through without so much of mind bending. Remember, this world is a show, where every effort counts in making the show beautiful, people are impressed if you show them your skills especially these skills. These are more important than many you will learn in due course.

Respect and Care

2011-05-21T07:57:00.000-07:00

I could not say more about this topic be it any world time zone. While this blog is dedicated in bringing best of mathematics in kids, it is important that it touches a bit of human aspect to learning. These are conditioning of our understanding that it requires greater effort and purpose for a meaningful dedication in acquiring knowledge. It is in that spirit that I am writing this post and making our kids aware of our responsibility and reasons for distilling the beauty of mathematics while working with our friends and teachers with more respect and care. It is often seen that a kid involved deep in mathematical practice tends to spend time alone working on the nuances of the course, it is also observed as in the past that science is not about the individual working on the subject by himself but by community for which and with which it attains that supreme knowledge only essential to make our community more safer and responsible.

The care that comes naturally in our human behavior we often notice and earn respect in eyes of others. Not that the respect is the ultimate objective in our pursuit of knowledge but it is more essential than any other observable mental and physical wealth that we earn in our entire life in the community. With this view in my mind, that I will leave this post and expect every kid to respect and care for others around you and possibly build relationship to understand other's viewpoint and you shall see that life is far more beautiful than otherwise perceived and that respect and care are the ultimate form of art that no human can ignore.

I will come back to this topic again in our later post, so stay tuned, until then enjoy May 21, the judgement day..

Reading A Short Introduction to Mathematics

2011-05-19T17:52:00.000-07:00

I am reading A very short introduction to Mathematics in a wonderful series of books by Oxford University Press. Amazing exposition I should say, everybody should make a point to read this if they think Mathematics could be interesting in their life and it will definitely motivate to explore more.There are many other short introductions on various subjects, I haven't them all, but I will pick some of them sooner. This one is on Mathematics.

Must read.

Digits

2011-05-18T18:23:00.000-07:00

I think you are already familiar now with the apple example and mom has already taught you about the 100 apple basket and how to count it. But did you notice something, that the number can increase one by one to a larger and larger number. That is one + one is two or ten + one is eleven. Ah, let's write it down below:

1+1 = 2

9+1=10

10+1=11

19+1=20

99+1=100

999+1=1000

Now you can see a positive counting does not stop but keep on increasing the value by one or many folds as you add. But somehow we always find a way to write it down a new number. How do we do that. We should thank this to the great invention of the number 0. That could not have made the math more simpler. Imagine you had some other way of writing this number like in roman numerals. The roman numerals are more like english alphabets. Where possibly after a while it requires a lot of thinking to even write it down. The number zero on the other hand, just made it very simple to increase the number by another place. This system was structured in India nearly 2500 years ago and reached to west through Arabs in around 10 century. Imagine how different it was in those times, when we could hardly get to know what is across the ocean. The world was actually a multiverse. Anyway back to the subject. So these numbers actually increase from 0 to 9 and then to 10. So the first time instead of defining a new number with a different shape, we simply write back 9 to as 0 and create a new digit next to it and call it 10th place. It actually creates the first 10. Then you increase it to 11, 12...Notice now only the second digit or unit digit is changing until it again hits the 9 and then 9 becomes 0 and a change to the tenth digit happens again but this time to 2 and the number becomes 20.

Interesting, isn't it. This is what works for carry as well in addition with multiple digits. Now you can imagine, I ask you to write one million, it would be really easy, but if I had asked to write 1 million in roman...imagine...I will it here, so that you can think about this system often called decimal system because of 10 numerals. More to it. I know you are learning fast and finding it interesting.

Some of these stuff is very simple and sometimes naive, but I think it is important to understand how and why things are for what they are...That's the first step towards open and elaborate thinking.

Worksheet

2011-05-18T18:00:00.000-07:00

We should be able to design and upload worksheets sooner.

Teaser with Division

2011-05-15T17:58:00.000-07:00

Counting could not be simpler for kids. Division is yet another tool that solves the problem by dividing it. Like we solved the big basket apple problem. Let's take a look at the problem again. There are 100 apples in a big basket and you have 10 smaller baskets. This time smaller baskets can hold more than 3 apples, we don't know how many. But we know that all 10 smaller baskets together can hold 100 apples. So the question is to find the number of apples that each smaller basket can hold. Lets do some counting again, this time with multiplication. Lets see if have 1 apple in each smaller basket. Then the total will be 1 apple times 10 basket or 10 apples, but that is far from 100 that we wanted to divide. Let's try again, take 2 apples in each smaller basket and see how many you get in total for 10 smaller baskets..hmm...2 times 10 equals 20..I think you are getting the pattern here, a short note, if you remember the math tables then you can quickly find the answer here, we will discuss that later. Let's get back and increase the smaller basket apples to 5 and see, hmm..again the total is 5 times 10 equals 50, half the size we are looking for.Isn't it. It appears if we double the number 5 to 10 and assume every smaller basket can now contain 10 apples, calculate the total apples now..10 times 10 equals 100, exactly what we are looking for here... You can notice here that if you do not remember the math tables, division becomes little trickier, that is why it needs practice and lot of practice to memorize the math tables. If only you could recall 10 times 10 is 100, dividing 100 into 10 parts could have been easier or just 10, simple....No worries, division is tricky but simpler with practice. We will discuss tips in later posts to identify division parts or sometimes known as factors, because we are factoring a large number into smaller parts.

Right now focus on practicing this example with dividing 50 with 5 smaller baskets or 20 with 2 smaller baskets or 30 with 3 smaller baskets or 30 with 10 smaller baskets. I am sure you will see patterns, math is all about patterns. A simple pattern at times brings elegance in answers.

Division

2011-05-15T08:42:00.000-07:00

Maths is simple and counting is even simpler. Kids really enjoy counting, negative counting and also multiplication as tools to solve their day to day problems. Multiplication as explained in our earlier blog is a simple counting method of counting things multiple times in a same count. Like count 5, 10 times will be equal to 50 or counting 3, 7 times will be equal to 21. Interestingly if you notice counting 7, 3 times is also equal to 21 or counting 10, 5 times is also equal to 50. That means if want to remember these short cut counts in a table format, then you will only have to remember one way, the other way is equal anyway, like 4 times 7 is 28 and 7 times 4 is also 28, therefore you can exchange the numbers without changing or affecting the results. Simpler isn't it.

Let's discuss another important tool called division to understand how dividing the problem into several equal sized parts sometimes solves the entire problem. Coming back to the big apple basket problem where you had 100 apples, and 10 smaller baskets that you used to fill apples from the big basket. If you remember the teaser we asked where each smaller basket only could fill 3 apples at a time, therefore 10 baskets would have only filled 10 times 3 apples or 30 apples from the big basket. Now you might have noticed that if you only look at the 10 smaller baskets with 3 apples each, you will see it's actually dividing apples into 10 parts, where each part or each basket is containing 3 apples each. Doesn't it ring a bell? you have already divided 30 apples into 10 parts where each part is 3. Or simply put 30 divided by 10 is 3. Could not be simpler right.. yes that is called division, or dividing a larger number into several smaller parts of equal size. Think about this post for the day, I will elaborate more in the next blog and explain how you could have used it to solve some of the earlier problems posted in the blog.

A sweet teaser in counting

2011-05-14T08:42:00.000-07:00

Now you know counting, you also know how subtraction works or the negative counting. I have deliberately left the addition, as it's only naturally counting forward. With these tools in hand and multiplication it should be easier for you to solve the teaser I am about to present to you. It's simple, ask your mom. So let's get back to the same example you worked on earlier. You have 100 apples in a big basket and 10 smaller baskets. You use smaller baskets to fill apples from the big basket. Each smaller basket can only contain 3 apples.Now here is the teaser, use multiplication to find out how many apples you will remove from the big basket if you fill 10 smaller baskets. And use subtraction or negative counting to see how many apples are left in the big basket. Isn't it a simple teaser. I am sure you can solve this, and you are also learning to use multiple math tools to solve these kind of teasers. I will come back with Division in my next post. That is another very basic math shortcut to counting. We will move along don't worry, nothing too fast and nothing too slow.

Subtraction

2011-05-08T06:04:00.000-07:00

I know this may not be a simpler exposition, kids need to understand subtraction as a negative count. Let's look at this game, you have 10 apples and 2 oranges. A friend of your come and says give me 2 apples and 1 orange. So how many apples and oranges are left with you. A negative count is where we are heading for. Alright lets take the longer way to solve this problem. Count again all the apples you had and all the oranges you had. Ah, now you see counting orange is simple because it's very small number, so you have just 1 orange. But counting apples, you still have to count from beginning and see if they are 1.2.3....8 apples. Took some time isn't it compared to oranges. Yes a smaller count is easier, but a longer one takes a long time, that's why we have shortcuts in counting. This shortcut today we are discussing is called subtraction or a negative count.

Let's start again, so you have 10 apples and 2 oranges, and a friend of yours ask for 2 apples and 1 orange. Now you have to count, how many apples and oranges are left? So, if you take out something from a number, you basically remove that number or subtract that number or your mom would call minus that number. How many apples were taken out, 2, therefore you will take 10 apples and remove 2 or say 10 - 2. Here you are subtracting 2 from 10. you noticed number 2 has a negative sign or minus. That's the negative counting. So instead of counting from the beginning like 1, 2, 3....8, 9, 10, you will count backwards or negative count starting from 10. Lets count 2 starting from 10 backwards and stop whenever you run out of the counting. So one step at a time. Count 1 backwards and you have 9. Count 1 more backwards while at 9, and you are at 8. So in total you have counted 2 backwards starting at 10 and what remains is 8. Therefore 10 -2 is equal to 8. Isn't that simple, now you don't to count from 1 to 8, but just a backward or negative counting from 10 to 8. So now you know you have 8 apples left. For orange, it was simpler anyway, but lets see if you can count, I am sure you can...How many oranges left, if your friend took 1 orange from you....That's your homework for today...

For the starters, read Kids Math Training, that gives introduction to this series for under 5 kids.

Multiplication

2011-05-07T19:31:00.001-07:00

Kids take some time digesting concepts but they are really fast learners. The counting does not stop at addition, or just culling, it moves to form the very interesting idea of repetition. Any repetition for that matter, number of apples say 10 at a time or number of pencils 2 at a time. Let say you have 5 pencil boxes and each have 10 pencils. How do you know what is the total number of pencils...you already noticed the boxes are 10 pencils each. So any single box would mean 10 pencils at a time. Therefore 2 boxes would mean 10 and 10 or a total of 20 pencils. Similarly 3 boxes would mean 3 boxes 10 each or 3 10s are 30 or 5 boxes mean 5 10s are 50. Now you recall teacher in the class is talking about maths table, another beautiful way to memorize counting shortcuts. So 5 boxes were 5 times 10 pencils or 50 pencils or as we said 5 10s are 50. 5x10=50. There you go the technique you noticed already is repetition at it's best. you are repeating 10 pencils in the form of box for 5 times. This is also known as multiplication of an item or a number by several times. This is a very good technique in maths to do quick calculation, as you will see how important and easy it is to remember the number tables that run the multiplication chart for normally 2 through 20 numbers. Make a point and learn one table everyday, and repeat as they repeat those numbers so many times...

That's it for today, I will come back with more counting short cuts, subtraction, I think you have heard already, another good thing...will tell you in the next post...

Still counting

2011-05-07T07:52:00.000-07:00

I am counting and still counting, that's the nature of mathematics..It counts all the time..be it multiplication, be it addition, be it subtraction, it moves back and forth and finds shortcuts to count. No wonder, I am spending more time in explaining what counting is..As it helps in many ways to explain what you see around yourself. Anything I agree sometimes things are uncountable, you might study in your english class.But in mathematics, you still can count, find a way to count those quantities or measure as they say.

Alas, I am also counting how many kids are reading this blog, are they really finding it helpful. My view counts are very low here, I can count it myself, a simple 1.2.3.4..

Counting

2011-05-05T15:26:00.000-07:00

Back at the counting, wasn't that simple to just use a calculator and key in the value and there you go primary math class is over....No, I would mind that and seriously anybody would though calculator allowed to get the answer the entire exercise to evaluate, carry over and finding the solution is what can give you the real pleasure...Show it to somebody how you calculated it, and you can see it really is fun...

Alright so counting is probably the most important step that you have taken in math, rest everything is around it, in making it simpler and simpler..Let's come back to the apple example, there you wanted to calculate a basket of apples, with a smaller basket. Let say you have 5 apples in a smaller basket and 100 apples in big basket, how many of your friends can enjoy one smaller basket each. Before we explain solution for this, you need to understand another important technique called multiplication. Let say you have 2 smaller baskets, then how many total number of apples you have collected....Hmmm....Thats like counting smaller baskets twice, or 1,2,3,4, 5 and again 6,7,8,9,10. So it's called 2 times smaller basket. Or 2 times 5, and you know the result that is 10. Put simply 2x5=10. Similarly if you had 3 baskets, then basically that is 5 more apples as, you have added one more basket. So the total will be 3 times 5 or 3x5=10+5=15. Likewise work out how many total number of apples you will have if you have 20 smaller baskets....

That's it for today, I think solve this and you are ready for a fast paced learning.....

Let's start

2011-05-04T18:31:00.000-07:00

First question, a kids question, why do we count?

Yes, we count all the time. We count every step of ours when we walk. We count every apple that we eat so that we don't eat more or kind of check ourself. Let's no go there. Let's just think...How counting helps us. If you have to draw a line of say length 10 centimeters, you use a scale. What does that read. bunch of numbers isn't it. Yes, that helps us in measuring 10 centi meter. And we measure reading on the scale or counting on the scale until we hit 10. What if the scale is only 6 centimeter. Ah, quite difficult I am already talking mensuration here. But without getting into details, on that scale we count until we hit 6. And then we use a marker at the end of the scale and measure another 4 cm next to it to give a total of 10 cm. Now that's quite simple, isn't it. We wanted to see 10 cm...But that does answer why we needed counting... Well, while we measure the scale, we realized that counting helped us in defining a length. Similarly if we were to count the number of apples in the basket, we could simply counted the apples one by one. Or used a smaller basket to have say 5 apples, and then count the number of baskets...Oops, too fast, we are already getting into maths. or really basic maths.... We will catch up on this again in our next post...We are yet not done on why we count, or why we do addition. It's very fundamental and has existed for thousands of years, possibly explaining why still need this....

For quick questions:

Add 146729 with 234521 and see if you can add and understand how carry works. Have you ever tried Vedic mathematics. Additions are trivial anyway...

Remember, we are not a replacement for a math book, we are crawling and possibly walking...might run at times, but we will post questions..sometime simpler..very subjective...but very important attempt and solve. As we progress we will get serious.. Enjoy until then. Remember, solution lies in books, figure it out.

Kids Math Training

2011-05-04T18:26:00.000-07:00

Under 5 years old normally require more mathematical rigor than we think. It is easy to pass a subject at that level, however to really understand and educate and prepare for next level requires puzzles and questions that leads to many unanswered questions that he or she can only answer in the next level. That's what a kids math training require. Well this is not a New York Times post, that it goes over several detailed math wiz kid's mathematical gymnastic, it tries to make the ground open for learning and yearning.

This is what we strive to do anyway in this society....Oops! come back this is for Kids Maths, let's start that. First with the basic, addition, subtraction, multiplication and division, some of the challenges parents face early on, however it's important to understand that we ask questions and let the kid find the answer. I know it's often the other way.

I will set forth a list of questions for the kids to answer and if they succeed, my subsequent posts will challenge them more...Not everybody is prepared for these questions on the same level, so some may find it very simple but some may find it interesting...I hope it samples more number of kids than ever in every post, that it suffices the need of everyone out there...More importantly my own kid will find it helpful someday, sooner, that's all I can say.