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WHY DO WE MULTIPLY FROM RIGHT?

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Why do we multiply from right to left?

Multiplication is one of the arithmetic operations that we all use to study in our early classes. It makes our calculations easy and fast and helps us in finding patterns hidden in the number system. With the help of multiplication, we are able to perform our daily calculations very conveniently.

Going into the method of multiplication and as the title of says: -“Why do we multiply from right to left”? Is this the only way of doing multiplication? Is it predefined in the rulebooks of mathematics? Ahh! a lot of confusions.

Let us first try to figure out the meaning of multiplication. Multiplication as we know it, is repeated addition of the same number into one another. In order to get rid of adding, again and again, the same number or to make the calculations easy, we devised one more arithmetic operation known as multiplication. Through this operation, we can find the sum when a number is added to itself tens of thousands or even millions of times, in a very small unit of time and doing very fewer calculations. (Again the mathematics is fulfilling its need of making calculations easy. Here mathematics is making mathematics easy).

The approach that we follow to carry out multiplication of numbers, is what we have learned from our childhood. Let us understand by an example:

Say we want to multiply the number 32 by 4 :
We first use to write this down in the form like:
Then first multiply 4 by 2  to get 8 and then multiply 4 by 30 to get 120 . And write the answer as .

Now in doing this calculation, what we are performing is multiplying the unit numbers first and then the tens number and then add them together.

On the hidden part, we are using the distributive law.
i.e.,

4×(2+30)=4(2) + 4(30) .

\ \ \ \ \ \ \ \ \ \ =8+120 .

\ \ \ \ \ \ \ \ =128 .

This method now seems natural to us, as it’s been inculcated into deep our minds and understanding.

But we never argued, why do we always use this method of multiplication? Is there any other method also by which we can multiply any two numbers?

Let’s now take the title of the article seriously and raise the question “Why do we multiply from right? Why not from left? Why not from the middle or why not from anywhere?

When we multiply from right we used to decompose the multiplier into units, tens, hundreds, thousands and so on and so forth in increasing order, and then use to the multiply the multiplicand by all of the decomposed numbers and add the results to get the final result.

Multiplication from the left would be the same as multiplication from right, just the difference will be in the order of multiplication from the decomposed numbers and the addition.

For example, for the same question done above, the multiplication from the left would be like this:
Say we want to multiply the number 32 by 4:

In this we first multiply 4 by 30 to get 120 and then multiply 4 by 2 to get 8. And write the answer after addition them together as: 128. .

Now in doing this calculation, what we are performing is multiplying the tens number first and then the unit number and then add them together.

On the hidden part, we are using the distributive law. .

i.e.,

4×(30+2)=4(30)+4(2) .

\ \ \ \ \ \ \ \ \ \ =120+8 .

\ \ \ \ \ \ \ \ =128 .

The approach would be the same, just the order has been changed in this approach. We are using here a property that addition holds, which is a commutative property of addition.

According to this property the order doesn’t matter for doing addition:

i.e., for any given numbers a or b: .

a+b=b+a .

For example: .

2+30=30+2 .

32=32 .

So, there is no difference in performing the multiplication from the left or from the right.

Same kind of approach would be followed in performing multiplication from anywhere in between in the number, and there will be no difference in the solution.

Let’s understand by an example:

Say we want to multiply the number 425 by 3:

In order to perform multiplication from anywhere, we first decompose the number 425 into its units, tens, and hundreds:

i.e.,

425=400+20+5 .

First we can multiply the number 20 by 3 to get: 60 .

Then multiply the number 400 by 3 to get: 1200 .

Then multiply the number 5 by 3 to get: 15 .

Now, adding the results of all we get: .

425 \times 3 =1200+60+15 .

425 \times 3=1275 .

And, in this way, we can perform the multiplication from anywhere in the number.

Gaps in Learning Mathematics

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[dropcap]A[/dropcap]s we become conscious about the teaching and learning of mathematics from the children’s point of view; it proves to be more challenging to make children love or learn mathematics. When we consciously plan something for children, we think of lot of methods and strategies by which they will understand and relate to mathematics. .

We are designing a mathematics workshop for school children of middle grades. We are at the stage of content development. It is easy to say that planning something for children is a simple task; we just need to take books of different authors and pick out certain activities and question from them and articulate it to children. Unfortunately this is a slippery path and a small mistake can lead to failure of the whole content development process. Is the planner actually aware of the needs and level of children? Or there is no need to think about the children for whom we are actually planning. .

The whole process came out to be a learning process for ourselves where the healer is healed. While going through the process of planning for workshop we actually struggle with our own thoughts and concepts; that how can we be helpful to them and make them go through different experience of mathematics? Are they actually able to understand, what we are aiming for? It becomes more important when our primary aim is to make children love and enjoy mathematics at a level when it starts becoming more abstract, boring and a rigid subject. .

The society perceives becoming a teacher is the easiest thing to do, anyone can do that. At the other end, it is difficult for students to relate and develop connections with the most of the subjects. The case with mathematics is even worse. We can easily figure out that teaching mathematics is very easy till that point of time when it sticks to textbooks or solving questions. But what when children deal with real life problems? Children fail in dealing with the shopkeeper or are less fluent in finding an average in the cricket match; still after doing all the math in their notebook. It becomes more challenging to equip children experience mathematics in their day to day life. .

This situation somewhere reflects that mathematics is not what we perceive and do in our textbooks. It is far beyond that. When we think about planning from the perspective of children than we realize the essence or nature of the subject matter; whether it is mathematics, language or history. Schools somewhere fail to provide experiences of different nature of the subject to children and limit them to their notebooks, memorization, tests and marks. .

These practices somewhere develop a gap between children’s real experiences and their knowledge. It is important to align children knowledge and experience and bridge the gap between the two for they will never meet without conscious effort and planing. We need to improve planning, pedagogy, textbook, teacher training courses and many more. There is a need of conscious effort in these directions to become an educators and facilitators for children education. .

Grouping Learners in Math Workshop

Teaching Maths in a workshop model offers great opportunities and constraints for both the facilitator and the participants. Identifying learner behavior is one such challenge and catering to their specific needs is even more challenging. One of the strategies that can be taken by the facilitator is to group learner without them identifying the criteria of grouping. This should be so much embedded into the design of the workshop that it either becomes part of some game or an activity. If such an activity cannot be designed, a pre-assessment can go a long way in grouping students according to their potential. Few Points that needs to be taken care for are:

  • It is possible only in a multi-facilitator workshops.
  • The grouping must change from session to session based on the different types of grouping done. For example, type I grouping can be based on previous knowledge while the other type of grouping can be based on their social behavior.
  • Each group must be mentored in a specific way as per the grouping strategy.