Multiplication and Division
Introduction to Multiplication and Division
A Foundational Pillar of Mathematics
Foundational topics may seem easy to us, but think back to when you were children, they felt difficult, even things that seem trivial today felt like the Millennium problems. The difficulty with these topics mainly arise due to the formulaic approach of the conventional system. This is why we feel kids find the basic operations a challenge to the point that the fear of math sets in early.
The Big Idea: What are Multiplication and Division?
At its very core, Multiplication is repeated addition and Division can be looked at as breaking down a large group into several smaller, equal groups. That’s actually all there is to it. Simple right?
The Foundational Nature of Multiplication and Division
Just like addition and subtraction, multiplication and division form one of the cornerstones of mathematical tools, upon which your child’s entire mathematical prowess is built. Here’s a handy little ladder that showcases what all your child can achieve by attaining a mastery of multiplication and division.
How do I understand or visualise multiplication and division?
Visualisation and application of concepts are key when it comes to understanding any fundamental topic. Multiplication at its core is simply repeated addition. The question that arises as a fallout of that is what does that mean?
As you can see it’s just making groups and adding them repeatedly.
There are two broad ways to picture division. The first being repeated subtraction and the second equal division. However, they both have the same result and are just two different ways of looking at the same picture.
Why multiplication and division? How are multiplication and division important?
First and foremost, a mastery of multiplication and division is crucial to your child’s mathematical future. Almost all branches of math, and even the rest of science hinge on these operations. As you can see from the lattice above, the operations play a central role in the understanding and practice of math.
This is the mathematical journey your child will be taking over the years with Cuemath. Each grade seeks to address one or more key aspects of the function, and by the end of it, you child will be a master.
Here are a few links that will take you through the journey that every Cuemath students undertakes in the pursuit of understanding Multiplication and Division along with practice worksheets:
How do you teach Multiplication and Division?
The primary issue with schools is that teachers just can’t give the personal attention that your child needs to clear any doubts that may arise when such crucial topics are introduced. That’s where you come in! Here are a few essential tools that will help you aid in your child’s learning and help them reach their full potential.
Break it down:
The thing to remember when starting off with multiplication and division is to never lose sight of the big idea. Help your child remember that both multiplication and division are simply repeated addition and subtraction at the end of the day.
To aid in your child constantly reinforcing these concepts, throw in a few practice problems of both addition and subtraction in to their practice routine. The cementing of foundational concepts that lead to more advanced topics is called chunking. It is an age old technique used to solidify the foundations upon which advanced knowledge rests and is very important to build a sound understanding.
Flash Cards are your friends:
The one thing that helps cement new concepts in place is frequent practice in short bursts. For this, prepare some flash cards for your child so as to be able to get them drilling at a moment’s notice.
Practice makes perfect:
Ensure that whenever you are done showing the concepts to your children, they put it into practice. Nothing helps children learn faster than applying the concepts that they are taught. Research has shown that it allows them to cement their concepts and it leads to longer retention.
Address common doubts:
While to us adults these operations may seem second nature, think back to when we were first being introduced to them. It was daunting and confusing, and if only we had someone to guide us and show us that it’s not that difficult right at the beginning, this irrational fear of math would never have set in. Som don’t let your child fall to the same fears that plagued your early math years. These are a few common doubts that arise and it’s best that they be cleared out as early as possible:
- Guide your child through the concept of place value. One of the most common mistakes that arise while multiplying two numbers of 2-digit or greater is that students forget to transfer the place value when they move to the second number. That zero is there for a reason, it’s because you have moved one place higher. From the ones place to the tens place, which necessitates the addition of the zero. In essence you are just decomposing the lower number and adding the sub-parts. The concept is clearly shown in the example below:
- A similar doubt occasionally arises when it comes to division. We’re talking about the situation when you are dividing two numbers and the divisor is greater than the part of the dividend being considered for that part of the operation. This usually leads to the appearance of a 0 in the quotient, and students, in their early stages with division struggle with this. The core concept at play here is that the Dividend = (Divisor x Quotient) + Remainder. So, if a zero arises in the quotient, it’s completely okay, and it’s not a mistake on the part of your child and urge them to carry on.