Addition Within 10

What is Addition?

Imagine you have some toys, and then you get more. The total number of toys you have has increased. This process of joining groups together is called addition!
Let's try it. If you have 4 red blocks and your friend gives you 2 blue blocks, how many blocks do you have now?

$\quad$ and $\quad$

Let's count them all together: One, two, three, four, five, six. You have 6 blocks in total!

Definition Addition

Addition is joining groups together to find the total, called sum.
In mathematics, we use symbols to write this down:

The plus sign ($+$) means to add.
The equals sign ($=$) shows that what is on one side is the same amount as what is on the other side.

We can represent "$\textcolor{colordef}{\text{four }}\text{plus}\textcolor{colorprop}{\text{ two}}\text{ equals }\textcolor{olive}{\text{six}}$" in many ways:

With numbers: $$\textcolor{colordef}{4} + \textcolor{colorprop}{2} = \textcolor{olive}{6}$$
With cubes: $+$ $=$
With fingers: $+$ $=$ \

How to Add

Method Counting All

The first strategy to learn addition is called "Counting All." This means we combine our groups and then count every single item from the beginning to find the total.
Let's solve: $3 + 2 = ?$

Step 1: Show the first number. Hold up 3 fingers on one hand.
Step 2: Show the second number. Hold up 2 fingers on your other hand.
Step 3: Count all the fingers that are up. Point to each one as you count: "One, two, three, four, five!"

The total is 5. $3+ 2 = 5$

$+$

$=$

Method Counting On

A faster way to add is called "Counting On." Instead of starting from 1, you start with the bigger number and then "count on" the smaller number.
Let's solve: $4 + 3 = ?$

Step 1: Start with the bigger number. The bigger number is 4. Let's show 4 fingers on one hand and say the number "Four" out loud.
Step 2: Get ready to count on. We need to add 3 more. So, get 3 fingers ready on your other hand. These are the fingers we will count.
Step 3: Count on from 4. Touch each of the 3 fingers one by one as you continue counting: "Five, six, seven!"

The last number you said is the total. The total is 7. $4+ 3 = 7$

$+$

$=$

Adding on the Number Line

Method Using a Number Line to Add

A number line is a great tool for visualizing addition. It's like taking steps on a path.
Let's solve: $3 + 5$

Start at the first number. Find the number 3 on the number line. This is your starting point.
Jump forward. The second number, 5, tells you how many jumps to make. Since we are adding, we move to the right, where the numbers get bigger. Make 5 jumps.
Find your landing spot. The number you land on is the answer.

After 5 jumps, you land on 8. So, $\textcolor{colordef}{3} + \textcolor{colorprop}{5} = \textcolor{olive}{8}$.