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. | |
Then we model the second number with 4 blocks. | |
Count the total number of blocks. |
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. | |
Model the second number with [latex]6[/latex] blocks. | |
Count the total number of blocks | There are [latex]8[/latex] blocks in all, so [latex]2+6=8[/latex]. |
try it
Model: [latex]3+6[/latex].Answer:
Model: [latex]5+1[/latex].Answer:
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. | |
Model the second number with [latex]8[/latex] blocks. | |
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. | |
Now we have [latex]1[/latex] ten and [latex]3[/latex] ones, which is [latex]13[/latex]. | [latex]5+8=13[/latex] |
try it
Model the addition: [latex]5+7[/latex].Answer:
Model the addition: [latex]6+8[/latex].Answer:
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 | |
Model the [latex]26[/latex]. | [latex]2[/latex] tens and [latex]6[/latex] ones | |
Combine. | [latex]3[/latex] tens and [latex]13[/latex] ones | |
Exchange [latex]10[/latex] ones for[latex]1[/latex] ten. | [latex]4[/latex] tens and [latex]3[/latex] ones [latex]40+3=43[/latex] | |
We have shown that [latex]17+26=43[/latex] |
try it
Model each addition: [latex]15+27[/latex].Answer:
Model each addition: [latex]16+29[/latex].Answer:
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
- Prealgebra. Provided by: OpenStax License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].