Addition within 100

What is Addition?

Su has a collection of cubes. She has 18 red cubes and 23 blue cubes.

$+$

How can we find out how many cubes Su has in total?

To find the total, we need to add the red cubes and the blue cubes together:$$\textcolor{colordef}{18} + \textcolor{colorprop}{23}$$When we join the groups, we can see the total.

$+$

$=$

In total, there are $\textcolor{colordef}{18} + \textcolor{colorprop}{23} = \textcolor{olive}{41}$ cubes.
Counting every single cube would take a long time. Let's explore faster ways to add!

Definition Addition

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

The plus sign ($+$) means to add.
The equals sign ($=$) indicates that the expressions on both sides have the same value.

We can represent "eighteen plus twenty-three equals forty-one" in many ways:

With numbers: $$\textcolor{colordef}{18} + \textcolor{colorprop}{23} = \textcolor{olive}{41}$$
With cubes:$+$$=$
With a part-whole model:

Adding Ones Then Adding Tens

Method Adding Ones Then Tens Using Cubes

To calculate :$\textcolor{colordef}{12} + \textcolor{colorprop}{23}$

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Step 1: Group the tens and ones
Step 2: Add the ones $$\textcolor{colordef}{2} \text{ ones} + \textcolor{colorprop}{3} \text{ ones} = 5 \text{ ones}$$
Step 3: Add the tens $$\textcolor{colordef}{1} \text{ ten} + \textcolor{colorprop}{2} \text{ tens} = 3 \text{ tens}$$
Result: There are 3 tens and 5 ones. So, $$\textcolor{colordef}{12} + \textcolor{colorprop}{23} = 35$$ $+$ $=$

Now, let's calculate $\textcolor{colordef}{18} + \textcolor{colorprop}{23}$. This time, when we add the ones, we get a number greater than $9$. This means we'll need to regroup the ones into a new ten. Let's see how this works.

Method Adding Ones Then Tens with Regrouping

To calculate:$\textcolor{colordef}{18} + \textcolor{colorprop}{23}$

$+$

Step 1: Group the tens and ones
Step 2: Add the ones $$\textcolor{colordef}{8} \text{ ones} + \textcolor{colorprop}{3} \text{ ones} = 11 \text{ ones} = 1 \text{ ten} + 1 \text{ one}$$
Step 3: Add the tens $$\textcolor{colordef}{1} \text{ ten} + \textcolor{colorprop}{2} \text{ tens} + 1 \text{ ten (regrouped)} = 4 \text{ tens}$$
Result: There are 4 tens and 1 one. So, $$\textcolor{colordef}{18} + \textcolor{colorprop}{23} = 41$$ $+$ $=$

Adding Using Columns

Method Adding in Columns

To calculate:$$\textcolor{colordef}{12} + \textcolor{colorprop}{23}$$

Step 1: Set up the addition
Write the numbers in a vertical column, making sure the digits line up by place value (ones under ones, tens under tens).
Step 2: Add the ones $$\textcolor{colordef}{2} \text{ ones} + \textcolor{colorprop}{3} \text{ ones} = 5 \text{ ones}$$
Step 3: Add the tens $$\textcolor{colordef}{1} \text{ ten} + \textcolor{colorprop}{2} \text{ tens} = 3 \text{ tens}$$
Result: There are 3 tens and 5 ones. So,$$\textcolor{colordef}{12} + \textcolor{colorprop}{23} = 35$$

Let's add $\textcolor{colordef}{18} + \textcolor{colorprop}{23}$ together! This time, when we add the ones, we’ll get a number bigger than 9. We’ll need to regroup the ones into a new ten. We move (or carry) a group of ten to the tens place.

Method Adding in Columns with Carrying

To calculate:$$\textcolor{colordef}{18} + \textcolor{colorprop}{23}$$

Step 1: Set up the addition
Write the numbers in a vertical column, making sure the digits line up by place value (ones under ones, tens under tens).
Step 2: Add the ones $$\textcolor{colordef}{8} \text{ ones} + \textcolor{colorprop}{3} \text{ ones} = 11 \text{ ones} = 1 \text{ ten} + 1 \text{ one}$$ Write the 1 in the ones place and carry the 1 ten to the top of the tens column.
Step 3: Add the tens $$\textcolor{colordef}{1} \text{ ten} + \textcolor{colorprop}{2} \text{ tens} + 1 \text{ ten (regrouped)} = 4 \text{ tens}$$
Result: $$\textcolor{colordef}{18} + \textcolor{colorprop}{23} = 41$$