Notation and Modeling Additions of Whole Numbers

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

3

hours on Monday and

4

hours on Friday. To find the total number of hours he worked last week, he added

3

and

4

. The operation of addition combines numbers to get a sum. The notation we use to find the sum of

3

and

4

is:

$3+4$

We read this as three plus four and the result is the sum of three and four. The numbers

3

and

4

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	$+$	$3+4$	three plus four	the sum of $3$ and $4$

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

6

classes, and this year will complete

8

classes. She needs to determine the sum of

6

and

8

. First translate the sentence into math notation and then calculate the results. Translate from words to math:

6+8

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.

6+8=14

Model 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

\text{(=)}

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

. Doing the Manipulative Mathematics activity "Model Addition of Whole Numbers" will help you develop a better understanding of adding whole numbers.

example

Model the addition

2+6

Answer: Solution $2+6[/latex] means the sum of [latex]2[/latex] and [latex]6$ 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 $2+6=8$ .

try it

Model:

3+6

Answer: No Alt Text

Model:

5+1

Answer: No Alt Text

When the result is

10

or more ones blocks, we will exchange the

10

blocks for one rod.

example

Model the addition

5+8

Answer: 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.

try it

Model the addition:

5+7

Answer: No Alt Text

Model the addition:

6+8

Answer: No Alt Text

Next we will model adding two digit numbers.

example

Model the addition:

17+26

Answer: 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 $17+26=43$

try it

Model each addition:

15+27

Answer: No Alt Text

Model each addition:

16+29

Answer: No Alt Text

Watch the video below for another example of how to use base

10

blocks to model the sum of two whole numbers. https://youtu.be/_smXQAPbygQ

Notation and Modeling Additions of Whole Numbers

Learning Outcomes

Use Addition Notation

Addition Notation

example

Model Addition of Whole Numbers

example

try it

example

try it

example

try it

Licenses & Attributions

CC licensed content, Shared previously

CC licensed content, Specific attribution

Study Guides > Prealgebra

Notation and Modeling Additions of Whole Numbers

Learning Outcomes

Use Addition Notation

Addition Notation

example

Model Addition of Whole Numbers

example

try it

example

try it

example

try it

Licenses & Attributions

CC licensed content, Shared previously

CC licensed content, Specific attribution