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Math for Kids

Comparing fractions (II)
Using a single multinumber-line segment comparison of two fractions is easier. However, for comparing more than two fractions it is better to use more than one number-line segments.
Comparing fractions (I)
We will see how to compare fractions with the same numerator using a fractions wall and fractions chart.
Equivalent Fractions (IV)
There is always one and only one equivalent fraction with lowest terms for all the equivalent fractions with higher terms. We can always get it using same division operation on both the numerator and the denominator of the given fraction. We repeat this process of division until further division of the numerator and the denominator with a number higher than one is not possible.
Equivalent Fractions (III)
Diagrams and number lines are also useful in finding out equivalent fractions.
Equivalent Fractions (II)
Identifying equivalent fractions using paper expands understanding of fractions drastically.
Equivalent Fractions (I)
Identifying equivalent fractions using fraction kits is fun.
Making Fraction Kits (II)
A fraction chart is another useful tool for understanding operations on fractions.
Making Fraction Kits (I)
Fraction wall is a useful visual tool when working with fractions.
Introducing Fractional Numbers (VII)
If children are familiar with ways of representing fractions pictorially, they usually make no mistakes in comparing, adding, subtracting, multiplying, and dividing fractions.
Introducing Fractional Numbers (VI)
Emphasizing different meanings of fractional numbers by handling actual objects is discussed in this article.
A New mathematical Device - Numeroscope
Numeroscope is a device developed by me for teaching mathematics. This device has been awarded a commendation for the year 2004 by "Commonwealth Association of Sc, Tech, and Math Educators".
Introducing Fractional Numbers (V)
Different meanings of fractional numbers taught so far need to be repeated many times, so that children try to make sense of fractions in different ways.
Introducing Fractional Numbers (IV)
Linking fractional number with one of the methods we use to represent division, makes understanding of fractional numbers easy.
Introducing Fractional Numbers (III)
Introducing fractions using discrete sets of objects is discussed. Writing fractional numbers and their word names can then be introduced using paper folding work by children.
Introducing Fractional Numbers (II)
In this article some more types of experiences, which need to be given are discussed. Also some misconceptions related to fractions are presented.
Introducing Fractional Numbers (I)
Fractions should be introduced by conveying the concept of congruence. Some ideas to do it are discussed here.
Adding Sequential Numbers (III)
Short cut methods for adding sequences of even numbers and odd numbers are discussed.
Adding Sequential Numbers (II)
Application of adding sequential numbers and some more examples of arithmetic sequences.
Adding sequential numbers (I)
Adding sequential numbers can be managed quickly if you apply addition, multiplication and division together.
Quick Eight Times (III)
In three simple steps you can find quickly eight times of any number.
Quick Eight Times (II)
Finding eight times of any number quickly can be accomplished by using complementary method of subtraction.
Quick Eight Times (I)
Finding eight times of any number quickly is not easy, as it requires subtraction.
Quick Seven Times (II)
Finding out seven times of an odd number quickly is easy but needs little more care.
Quick Seven Times (I)
Learn to find seven times of a number quickly.
Quick Six Times (II)
Learn the modifications required to find out six times quickly of a number having odd digits.
Quick Six Times (I)
Learn how simply linking the known facts we can have a method to find out six times quickly.
Quick five times
Know how to use the quick division by 2, is useful in multiplying any number by five.
Quick division by two
Enjoy dividing any number by two quickly and efficiently
Speedy division
Learn how to manage division in one step.
Checking division
Find out ways to check the divisions.
Complex divisions (IV)
Learn how it is easy to divide beginning from the lowest place value digit in the dividend.
Complex divisions (III)
Learn about the types of mistakes children generally make in complex divisions.
Complex divisions (II)
Learn about the graded practice to prepare children for complex divisions.
Complex divisions (I)
Learn how I prepare children for complex divisions.
Role of Zero in division
Read tips for teaching division with zero as a dividend or a divisor.
Properties of division
Know the important properties of division
Introducing Division (IX)
Know how the play money works as a powerful aid for teaching division of larger numbers.
Introducing Division (VIII)
Know the ways of expressing divisions with remainders and how to help visualizing division.
Introducing Division (VII)
Know the method of introducing division with remainder.
Introducing Division (VI)
Know the method of introducing more aspects of division in stepwise fashion.
Introducing Division (V)
Know the method of recording division when repeated subtraction is used.
Introducing Division (IV)
Know the number line model for teaching division and four different notations of division.
Introducing Division (III)
Some activities are suggested which are very useful in introducing the concept of division.
Introducing Division (II)
Here are some interesting activities to introduce division.
Introducing Division (I)
Know the two meanings of division, we should to teach our children.
Quick Twelve Times
A year has 12 months and watch dial shows 12 hrs. What other sets of 12 you can think of…can you multiply by 12 quickly? See for yourself.
Quick Eleven Times (III)
Multiply quickly by 11 extend the skill to complex multiplication too.
Quick Eleven Times (II)
Get eleven times of any number in a jiffy!
Quick Eleven Times (I)
See how quickly we can get eleven times of any number.
Cross-product
One more definition of multiplication is of cross-product. You can find it very useful in solving many problems in real life.
Quick Two Times
See for yourself how quickly you can double a given number.
Introducing Multiplication
In this article ideas for teaching multiplication to elementary school children are discussed.
Painless Nine Times (IV)
Method of finding out nine times of larger numbers in one line by complementary method of subtraction is discussed in this article.
Painless Nine Times (III)
Method of finding out nine times by subtraction is discussed in this article.
Painless Nine Times (II)
In this article patterns in the nine’s multiplication are discussed further. How can one remember nine times of larger numbers with the help of fingers is also shown.
Painless Nine Times(I)
In this article pattern in the nine’s multiplication is discussed. How can one remember nine times with the help of fingers is also shown.
Relating Addition and Subtraction
How we can help children understand the relationship between the addition and subtraction facts is discussed in this article.
Checking Subtraction (IV)
Estimating subtraction by front-end estimation and complementary or inverse addition method is discussed here. Useful links are provided for getting practice in subtraction.
Checking Subtraction (III)
In this article we continue with the method of checking subtractions by estimation.
Checking Subtraction (II)
In this article we continue with the methods for checking subtractions.
Checking Subtraction (I)
In this article methods for checking subtractions are discussed.
Dealing with Subtraction (III)
This article discusses some methods of subtracting mentally.
Dealing with Subtraction(II)
In this article examples of decomposition method of subtraction are given and the method of equal additions is discussed.
Dealing with Subtraction(I)
In this article ways of simplifying teaching of arithmetic subtraction are discussed.
Checking multiplication
In this article methods for checking multiplication are discussed.
Applying multiplication rules (Part II)
In this article some more multiplication problems are considered to understand how multiplication rules simplify them.
Applying multiplication rules (Part I)
In this article we will see the application of multiplication rules.
Three rules simplify multiplication
Three rules explained here are very easy to follow. These make the task of handling complicated multiplication simple.
Speedy and accurate addition (Part V)
In this article a method to add horizontally and checking addition by estimation is shown with examples.
Speedy and accurate addition (Part IV)
In this article methods of adding real lyquickly are discussed.
Speedy and accurate addition (Part III)
The logic of casting out nine, i.e., finding out the remainder of nine, is discussed here in detail. The method of checking addition by casting out nine is shown through examples.
Speedy and accurate addition (Part II)
Comparison of the lattice method of addition with the conventional method is presented. Several methods for checking additions are also shown.
Speedy and accurate Addition (Part I)
It is unsound to introduce a child to the difficulties of ‘carrying’ in addition before s/he has attained a high degree of efficiency in the basic addition facts involving numbers less than 10.
Visualizing the Numbers (Part VII)
It is necessary to offer the experience related to larger numbers as well. By using pattern cards we can give children the idea of larger numbers as well. I have observed that most of the children experiencing difficulty in learning mathematics, whatever their age, lack this experience.
Visualizing the Numbers (Part VI)
This article is continuation of the previous article. The ideas here help children to know the general outcomes of the division.
Visualizing the Numbers (Part V)
In this article I have discussed the difficulties children face in dealing with the operation of division and the way we can help children understand the related general rules.
Visualizing the Numbers (Part IV)
While teaching subtraction, I use cards having numbers’ patterns. I encourage children to observe the results of all possible combinations of subtractions. It then becomes easy for them to realize that division is only a shortcut for repeated subtraction.
Visualizing the Numbers (Part III)
The focus here is on constructive learning of the multiplication table. Using patterns children could be provided with concrete experience of building up his/her own multiplication table. This way children not only enjoy arithmetic, but develop a meaningful understanding of the multiplication table. Details of some web sites offering practice in memorization of multiplication tables are provided.
Visualizing the Numbers (Part II)
In this article I have shown how I use the number patterns discussed in the previous article to develop the sense of numbers while teaching additions and multiplications.
Visualizing the Numbers (Part I)
Success of the multiplication method described in the previous article depends on two things: Child’s command over the multiplication table for numbers from 1 to 10 and Child’s ability to carry out the required additions accurately. The process of rejecting the various numbers as possible answers is actually our ability to visualize numbers. Let us see how we can help children to visualize the numbers.
Trouble with Multiplication?
As a teacher-educator of Mathematics in elementary, secondary and high school, I have always enjoyed teaching computations to children. To provide proper guidance to the children in computation, I have studied a large number of children’s homework and class-work in detail. This revelation has inspired me to share my experiences, ideas related to children’s difficulties in learning computation, with teachers as well as parents.

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