Model Addition

Modeling Addition of Whole Numbers

Addition is really just counting. We will model addition with \(\text{base}\)-\(10\) blocks. Remember, a block represents \(1\) and a rod represents \(10.\) Let’s start by modeling the addition expression we just considered, \(3 + 4.\)

Each addend is less than \(10,\) so we can use ones blocks.

We start by modeling the first number with 3 blocks.
Then we model the second number with 4 blocks.
Count the total number of blocks.

There are \(7\) blocks in all. We use an equal sign \((=)\) to show the sum. A math sentence that shows that two expressions are equal is called an equation. We have shown that \(3 + 4 = 7.\)

Example

Model the addition \(2 + 6.\)

Solution

\(2 + 6\) means the sum of \(2\) and \(6\)

Each addend is less than 10, so we can use ones blocks.

Model the first number with 2 blocks.
Model the second number with 6 blocks.
Count the total number of blocks	There are \(8\) blocks in all, so \(2 + 6 = 8.\)

When the result is \(10\)or more ones blocks, we will exchange the \(10\) blocks for one rod.

Example

Model the addition \(5 + 8.\)

Solution

\(5 + 8\) means the sum of \(5\) and \(8.\)

Each addend is less than 10, se we can use ones blocks.
Model the first number with 5 blocks.
Model the second number with 8 blocks.
Count the result. There are more than 10 blocks so we exchange 10 ones blocks for 1 tens rod.
Now we have 1 ten and 3 ones, which is 13.	5 + 8 = 13

Notice that we can describe the models as ones blocks and tens rods, or we can simply say ones and tens. From now on, we will use the shorter version but keep in mind that they mean the same thing.

Next we will model adding two digit numbers.

Example

Model the addition: \(17 + 26.\)

Solution

\(17 + 26\)means the sum of 17 and 26.

Model the 17.	1 ten and 7 ones
Model the 26.	2 tens and 6 ones
Combine.	3 tens and 13 ones
Exchange 10 ones for 1 ten.	4 tens and 3 ones \(40 + 3 = 43\)
We have shown that \(17 + 26 = 43\)

Optional Video: Adding Three-Digit Numbers With Base-10

This video below by Mathispower4u explains addition of three digit whole numbers by using base ten blocks.