### Learning Outcomes

- Use symbols and words to describe addition of single and double digit numbers
- Model addition of single and double digit numbers using base-10 blocks, or shapes

## Use Addition Notation

A college student has a part-time job. Last week he worked [latex]3[/latex] hours on Monday and [latex]4[/latex] hours on Friday. To find the total number of hours he worked last week, he added [latex]3[/latex] and [latex]4[/latex].

The operation of addition combines numbers to get a sum. The notation we use to find the sum of [latex]3[/latex] and [latex]4[/latex] is:

[latex]3+4[/latex]

We read this as *three plus four* and the result is the sum of three and four. The numbers [latex]3[/latex] and [latex]4[/latex] are called the addends. A math statement that includes numbers and operations is called an expression.

### Addition Notation

To describe addition, we can use symbols and words.

Operation | Notation | Expression | Read as | Result |
---|---|---|---|---|

Addition | [latex]+[/latex] | [latex]3+4[/latex] | three plus four | the sum of [latex]3[/latex] and [latex]4[/latex] |

### example

After talking to her counselor, Esmeralda needs to determine how many classes she has taken so far at Blue Sky College. Last year she took [latex]6[/latex] classes, and this year will complete [latex]8[/latex] classes. She needs to determine the sum of [latex]6[/latex] and [latex]8[/latex]. First translate the sentence into math notation and then calculate the results.

Translate from words to math: [latex]6+8[/latex]

*The operation of addition combines numbers to get a sum*

We read this as *six plus eight* and the result is the sum of six and eight.

[latex]6+8=14[/latex]

### try it

## Model Addition of Whole Numbers

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

Each addend is less than [latex]10[/latex], 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 [latex]7[/latex] blocks in all. We use an equal sign [latex]\text{(=)}[/latex] to show the sum. A math sentence that shows that two expressions are equal is called an equation. We have shown that. [latex]3+4=7[/latex].

### example

Model the addition [latex]2+6[/latex].

### try it

Model: [latex]3+6[/latex].

Model: [latex]5+1[/latex].

When the result is [latex]10[/latex] or more ones blocks, we will exchange the [latex]10[/latex] blocks for one rod.

### example

Model the addition [latex]5+8[/latex].

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.

### try it

Model the addition: [latex]5+7[/latex].

Model the addition: [latex]6+8[/latex].

Next we will model adding two digit numbers.

### example

Model the addition: [latex]17+26[/latex].

### try it

Model each addition: [latex]15+27[/latex].

Model each addition: [latex]16+29[/latex].

Watch the video below for another example of how to use base [latex]10[/latex] blocks to model the sum of two whole numbers.