Introduction to Addition

Let’s say you go to the supermarket and see two individual groups of tomatoes. One group has 4 and the other has just one. Now, you go ahead and bunch both groups of tomatoes together, to get 5, well, that’s basically what addition is at the core of it. To help your child visualize the operation, addition is putting two or more groups together to end up with a larger group in the end.

Adding Tomatoes

 

When you get on your school bus, there are 6 children when you get up on the bus. So now there are 6 + 1 = 7 children in the bus. At the next stop, 5 more children get on the bus, and later two more children get on the bus. So, when the bus finally reaches your school, the number of children in the bus = 6 + 1 + 5 + 2 = 14.

These are just a few examples which tell us that the addition of things is something that is so basic that you get introduced to addition at a very young age!

The Big Idea: Addition

A simple idea: What is addition?

If you look at the example of the tomatoes with you above, it will give you the basic understanding of how to approach addition. So if you need to add 5 and 7, then assume that you have two bunches of tomatoes, with one bunch having 5 tomatoes and the other having 7. Then the addition of these two groups can be written in this way:

Addition Idea

When the numbers grow larger, the sets of tomatoes also become bigger, like in the addition of 37 and 51. 
Another simple idea used for addition of two numbers is the concept of place value. As the numbers become bigger, they gain place values. The key concept to remember is that ONLY like places can be added at a time. So, if you have a four digit number 1423, being added to a three digit number, 176, the addition would look like

So, in order to add 1423 and 176, you write both the numbers one below the other in such a way that the place values are all aligned. So, it would look like this:

\(\begin{align}  {\rm{1}}\;\;{\rm{4}}\;\;{\rm{2}}\;\;{\rm{3}}\\    {\rm{ + }}\;\,{\rm{1}}\;\;{\rm{7}}\;\;{\rm{6}}\\    \overline {\underline {1\;\;5\;\;9\;\;9} }    \end{align}\)

In ancient times, simple additions were done with the help of a simple, yet powerful instrument called the abacus.

How is it important?

The concept of carrying over

In the above example all the addition results are less than 10 in each of the place values. But before we see what happens if the sum of a particular place value exceeds 10, we need to understand why we are considering the number 10. Well, the answer comes from the fact that each higher place value is a higher multiple of of 10 multiplied by itself compared to the one just above it.

So, the tens place = 10 x 1 = 10.
Similarly, thousands place = 10 x 10 x 10 = 1000, and next place value ten thousands place = 10 x 10 x 10 x 10 = 10000

Carry Over

Every time the sum of a particular place value exceeds ten, we keep only the units place number, and ‘carry over’ the tens place number to the next line. We do this every time the sum of numbers in any place value is greater than 10. This will be clear with a simple example.

Instead of 1423 and 176 which we saw earlier, let us see how to add 1476 and 246. We will first write the numbers with place values aligned.

\(\begin{align}  {\rm{1}}\;\;{\rm{4}}\;\;{\rm{7}}\;\;{\rm{6}}\\    {\rm{ + }}\;\,{\rm{2}}\;\;{\rm{4}}\;\;{\rm{6}}\\    \overline {\underline {\qquad\quad\;\;\,\\} }    \end{align}\)

Now that you have the operations set up porpely, it’s simply a question of adding up the digits occupying similar places one at a time starting from the units place. Doing that, we get:

\(\begin{align}     &\;\;\;\,{\;^1}\;\,{\;^1}\;\;\;\;\\     &{\rm{1}}\;\;{\rm{4}}\;\;{\rm{7}}\;\;{\rm{6}}\\     &{\rm{ + }}\;{\rm{2}}\;\;{\rm{4}}\;\;{\rm{6}}\\     &\overline {\underline {1\;\;7\;\;2\;\;2} }     \end{align}\)

Common mistakes or misconceptions

  • In addition, when carrying over a number from one place value to the other, children make mistakes.
    Generally this happens because they have memorised the steps to add and if thy forget the rules, mistakes happen. Instead of using the Base-10 blocks help children visualise the addition procedure. This way they’ll internalise the steps better.
  • When adding a three-digit number to a two-digit number, students may place the numbers one below the other incorrectly.

This generally happens once again due to an incomplete understanding of place values and the idea of addition. Rather than telling students to simply align numbers from the right, it is better to ask them to model this addition problem using Base-10 blocks so they understand why the numbers are aligned from the right.

Tips and Tricks

  • Help children associate addition with common words used in everyday language like “put together”, “in all”, “altogether”, “total”, etc. This association will help them with comprehending word problems.
  • Break numbers by place values to make addition easier. 32 + 46 can be split as 30 + 2 + 40 + 6. While this looks like it is more work, it makes mental addition easier. Help children add the tens first and then the ones.
  • Start with the larger number and add the smaller number to it. Adding 11 to 37 is a lot easier than adding 37 to 11.

 

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