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Study Guides > Prealgebra

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 [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-display]6+8=14[/latex-display]
   

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. CNX_BMath_Figure_01_02_019_img-02.png
Then we model the second number with 4 blocks. CNX_BMath_Figure_01_02_019_img-03.png
Count the total number of blocks. CNX_BMath_Figure_01_02_019_img-04.png
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]. 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 [latex]2+6[/latex].

Answer: Solution [latex-display]2+6[/latex] means the sum of [latex]2[/latex] and [latex]6[/latex-display] Each addend is less than [latex]10[/latex], so we can use ones blocks.

Model the first number with [latex]2[/latex] blocks. CNX_BMath_Figure_01_02_016_img-02.png
Model the second number with [latex]6[/latex] blocks. CNX_BMath_Figure_01_02_016_img-03.png
Count the total number of blocks CNX_BMath_Figure_01_02_016_img-04.png There are [latex]8[/latex] blocks in all, so [latex]2+6=8[/latex].

 

try it

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

Answer: No Alt Text

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

Answer: No Alt Text

  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].

Answer: Solution [latex]5+8[/latex] means the sum of [latex]5[/latex] and [latex]8[/latex].

Each addend is less than [latex]10[/latex], se we can use ones blocks.
Model the first number with [latex]5[/latex] blocks. CNX_BMath_Figure_01_02_017_img-02.png
Model the second number with [latex]8[/latex] blocks. CNX_BMath_Figure_01_02_017_img-03.png
Count the result. There are more than [latex]10[/latex] blocks so we exchange [latex]10[/latex] ones blocks for [latex]1[/latex] tens rod. CNX_BMath_Figure_01_02_017_img-04.png
Now we have [latex]1[/latex] ten and [latex]3[/latex] ones, which is [latex]13[/latex]. [latex]5+8=13[/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].

Answer: No Alt Text

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

Answer: No Alt Text

  Next we will model adding two digit numbers.

example

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

Answer: Solution [latex]17+26[/latex] means the sum of 17 and 26.

Model the [latex]17[/latex]. [latex]1[/latex] ten and[latex]7[/latex] ones CNX_BMath_Figure_01_02_018_img-02.png
Model the [latex]26[/latex]. [latex]2[/latex] tens and [latex]6[/latex] ones CNX_BMath_Figure_01_02_018_img-03.png
Combine. [latex]3[/latex] tens and [latex]13[/latex] ones CNX_BMath_Figure_01_02_018_img-04.png
Exchange [latex]10[/latex] ones for[latex]1[/latex] ten. [latex]4[/latex] tens and [latex]3[/latex] ones [latex]40+3=43[/latex] CNX_BMath_Figure_01_02_018_img-05.png
We have shown that [latex]17+26=43[/latex]

 

try it

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

Answer: No Alt Text

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

Answer: No Alt Text

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

Licenses & Attributions

CC licensed content, Shared previously

  • Model Addition of Two Digit Whole Numbers Using Base Ten Blocks. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
  • Question ID: 143045, 143046. Authored by: Alyson Day. License: CC BY: Attribution. License terms: IMathAS Community License CC-BY + GPL.

CC licensed content, Specific attribution