Addition within 1000
What is Addition?
Louis has two boxes of cubes. One contains 218 cubes, and the other contains 123 cubes.
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To find the total, we need to add the two amounts together:$$\textcolor{colordef}{218} + \textcolor{colorprop}{123}$$If we combine all the blocks, we can see the total sum.
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Counting all those blocks would take a long time. A faster and more organized way to add bigger numbers is to use column addition. 
\(+\)\(=\)Counting all those blocks would take a long time. A faster and more organized way to add bigger numbers is to use column addition.
Definition Addition
Addition is joining groups together to find the total, or sum. The plus sign (\(+\)) tells us to add.
We can show "\(\textcolor{colordef}{\text{two hundred eighteen}}\) plus \(\text{\textcolor{colorprop}{one hundred twenty-three}}\) equals \(\text{\textcolor{olive}{three hundred forty-one}}\)" in many ways:
We can show "\(\textcolor{colordef}{\text{two hundred eighteen}}\) plus \(\text{\textcolor{colorprop}{one hundred twenty-three}}\) equals \(\text{\textcolor{olive}{three hundred forty-one}}\)" in many ways:
- With numbers: $$\textcolor{colordef}{218} + \textcolor{colorprop}{123} = \textcolor{olive}{341}$$
- With cubes:\(+\)\(=\)
- With a column addition:
- With a part-whole model:
Adding in Columns
Method Column Addition with Regrouping
Let's calculate: $$\textcolor{colordef}{288} + \textcolor{colorprop}{545}$$ 
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- Step 1: Line up the numbers by place value.
Write the numbers one on top of the other. Make sure the ones, tens, and hundreds are in straight columns.
- Step 2: Add the ones. $$\textcolor{colordef}{8} \text{ ones} + \textcolor{colorprop}{5} \text{ ones} = 13 \text{ ones}$$ 13 ones is the same as 1 ten and 3 ones. We write the \(\textcolor{olive}{3}\) in the ones place and carry the 1 ten over to the tens column.
- Step 3: Add the tens. $$1 \text{ ten (carried)} + \textcolor{colordef}{8} \text{ tens} + \textcolor{colorprop}{4} \text{ tens} = 13 \text{ tens}$$ 13 tens is the same as 1 hundred and 3 tens. We write the \textcolor{olive}{3} in the tens place and carry the 1 hundred over.
- Step 4: Add the hundreds. $$1 \text{ hundred (carried)} + \textcolor{colordef}{2} \text{ hundreds} + \textcolor{colorprop}{5} \text{ hundreds} = \textcolor{olive}{8} \text{ hundreds}$$ Write the \(\textcolor{olive}{8}\) in the hundreds place.
- The Result: $$\textcolor{colordef}{288} + \textcolor{colorprop}{545} = \textcolor{olive}{833}$$
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