Addition and Subtraction
Introduction to Addition and Subtraction
A Foundational Pillar of Mathematics
As we grow older and travel further in our mathematical journey, we begin to become more and more comfortable with basic operations. However, the reason we find them so challenging initially is all down to the way in which it is introduced to us in schools. The conventional approach ignores number sense and throws children head first into the world of operations, making things unnecessarily complicated.
The Big Idea: What are Addition and Subtraction?
The core, fundamental principle behind addition and subtraction is simply grouping! Yeah, it’s that simple. Being foundational concepts, kids start to inherently perceive basic addition and subtraction from when they are as young as a few months old! The key difference between addition and subtraction is while one is piling on more to a group, while the other is counting while taking things away.
The Foundational Nature of Addition and Subtraction
Addition and subtraction literally from one of the cornerstones of mathematics. These operations find their applications in all branches of math no matter the complexity or grade. Be it abstraction, calculus, statistics, data handling, you name it, addition and subtraction will pay a crucial role. That is what makes them such essential concepts to understand and apply properly.
This is how we at Cuemath position addition and subtraction:
How do I understand or visualise addition and subtraction?
Considering addition and subtraction are foundational topics of mathematics, visualisation at the early stage is quite straightforward, and frankly that’s when it’s the most important as well. Allowing children to internalise the concepts by being able to picture them is key towards them being able to handle more and more complex problems mentally.
While it’s easy to understand the basic principle of addition and subtraction, it’s a whole different ball game when it comes to the advanced applications. Therefore, it becomes essential that kids build a strong number sense alongside building their concepts of the operations. This is best enabled by the usage of the number line.
Why addition and subtraction? How are addition and subtraction important?
Well, as you can see from the lattice above, addition and subtraction form one of the key building blocks of your child’s math knowledge. Hence, it’s of paramount importance that these topics are understood to their fullest.
A lot of concepts can be arrived at while understanding how to add and subtract. Place and Face Values for example are concepts that get fortified over time as you add and subtract numbers. Here, have a look for yourself:
This is but one basic example of addition and subtraction leading to a broader understanding of math. These operations lead to multiplication and division which then lead to topics like statistics, calculus, abstraction, so on and so forth. Essentially mastering the basic operations gets you through the doors of the palace of mathematics.
Here are a few links that will take you through the journey that every Cuemath students undertakes in the pursuit of understanding Addition and Subtraction along with practice worksheets:
How do you teach Addition and Subtraction?
Schools often fall short in providing the individual attention that your child needs in order to fully understand a topic. This is primarily due to the absurdly high student to teacher ratios. Well, the thing is, here are a few things that you can do to ensure that your child understands a topic to its completion and realizes that they have nothing to fear from math.
Break it down:
Remember that the big idea behind addition and subtraction is Grouping. When you take a look at the lattice above, you see that topics like number sense and recognition of numbers form a stepping stone to addition and subtraction. Ensure that your child is comfortable performing those operations and with those concepts beforehand. This practice is called Chunking.
Chunking is a time tested method that ensures that learning happens at an optimal level. It builds from previously laid down concepts and helps your child connect the dots with newer concepts more easily. To get the most out of your child’s learning ability with chunking, feel free to incorporate a few problems from natural and whole numbers and place and face value here and there in between the addition and subtraction problems.
Flash Cards are your friends:
Prepare flash cards for your child for fractions. Make sure that the flash cards cover all the salient concepts of the topics of addition and subtraction that your child is currently tackling. Frequent and regular usage of flash cards is an excellent way of cementing and internalizing concepts.
Show them the concepts visually:
Concepts gained and reinforced through visual means stick. So, when your child is starting off with operations, allow them to mix “Play time” with “Study time”. Hand them their favorite toys, be it legos, claydough, hot wheels cars or what have you and ask them to perform rudimentary addition and subtraction problems. If you wish to turn up the level a bit, refer to the interactive widgets above to help you in allowing your child to visualise the math.
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 the common doubts:
Children don’t always speak up in class when they don’t completely understand a concept. Moreover, thanks to the absurd student teacher ratios, teachers themselves assume all is well and move on. However, that doesn’t mean that your child will automatically fill the lacunae in their understanding through practice. In fact, quite the opposite happens. The problems persist and get compounded. Here are a list of common mistakes and doubts that we have observed in children, and should be addressed by you post haste:
- When adding or subtracting Three digit and Two digit numbers a lot of children have trouble with Place value. Instead of right aligning the digits, kids sometimes will left align them, causing the 2-digit number to become a 3-digit number and hence leading to errors in calculation.
- Children quite often struggle with the concepts of carrying over and borrowing when it comes to addition and subtraction. It is a very commonly observed mistake that kids will forget to add the carried over value in a sum or get stumped when borrowing needs to be done over two place values. The best way to get your child used to carrying over and borrowing is to have them write it out explicitly in the beginning and then slowly getting them in the habit of doing it mentally.