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Represent addition as "add to/put together" and subtraction as "take from/take apart" with objects, fingers, mental images, drawings, sounds, or verbal explanations (limited to five). M.AAS.K.8

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The primary media type of this source is visual. The content illustrates how a student can add using their own fingers. This could be very useful in a classroom because it shows that addition can be done with anything, including the students' own fingers. This directly addresses the ALCOS Standard as it states that students should represent addition with their fingers. I decided to select this image because it very concisely shows how to add on fingers and there is no confusing pictures or information.

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The primary media type of this source is audio. The content of this audio explain to students the basic concepts of subtraction. It describes how when you subtract you get the difference and to get that difference, you much take away one number from another. The song gives examples of subtraction problems, such as eagles flying and landing.This supports the ALCOS Standard because it teaches subtraction as taking from or away a certain number and how much do you have left. I decided to select this song because it is a different way to teach and you could make it fun by making a dance with it.

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Subtraction Song for kids | Subtraction Facts | Subtraction Action | Jack Hartmann

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The primary media type for this source is an information website. The content of this website very simply explains the basic concept of subtraction. The website also uses a picture of candy to show taking away as the main factor of subtraction. This source also includes fun facts and songs that would be fun for the students to learn. This website supports the ALCOS Standard because it teaches that subtraction is the act of taking a certain number away from another number. This could be very helpful in a classroom because this website can be used by the student themselves. They can read and learn this information all on their own and interpret it by themselves before the teachers explains it.

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Let's learn!

In math, to subtract means to take away from a group or a number of things.

When we subtract, the number of things in the group reduce or become less.

The minuend, subtrahend and difference are parts of a subtraction problem.

Here's another example of a subtraction problem.

Fun Facts

Subtraction is just the opposite of addition.

Also, every addition problem can be rewritten as a subtraction problem.

Let's sing!
Eight little blue birds sitting on a tree, Five flew away, and then there were three.
Let's do it!

Instead of handing out math subtraction worksheets to your children, play the number plate game with them while driving them to school or for classes. Ask them to subtract the first, second or third digit in the number plate of the car ahead from the biggest digit in it. Ask them to be quick in answering.

Related math vocabulary

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SplashLearn - Fun Math Practice Games for Kindergarten to 5th Grade

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In math, to subtract means to take away from a group or a number of things. When we subtract, the number of things in the group reduce or become less. The minuend, subtrahend and difference are parts of a subtraction problem. Here's another example of a subtraction problem.

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The primary media type of this source is a video. In this video, subtract is explained in a really fun way. The narrator takes students through a situation while making it exciting and subtracting cowboy hats. Subtraction is very well explained and students will enjoy how fun the narrator makes it. This video supports the ALCOS Standard because it teaches students that the main principle of subtract is taking away. That exactly how it is stated in the video the same way it is stated in the Standard. This could be so much fun in the classroom that is full of students. It is funny and very interactive because it constantly asks the students question throughout. I would for sure use this as a teaching tool.

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The primary media type for this source is an information website. The content of this website very simply explains the basic concept of addition. The website also provides pictures, but they are well explained and easy for young students to understand. This supports the ALCOS Standard because it shows that addition is simply combining two amounts of strawberries or putting the two together. This will be extremely useful in the classroom because this website is meant for the students' use. This means that they get to read and interpret the information on their own, which can later be explained by the teacher.

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What Is Addition?

Addition is a way of combining things and counting them together as one large group.

The first mathematical operation that students are introduced to in elementary mathematics is addition. To add means to bring together or combine two objects. Students then build over this understanding to learn how to add more than two numbers. In higher grades, addition is the basic element to understand more complex operations like multiplication and division.

Definition of Addition

Addition in math is a process of combining two or more numbers. Addends are the numbers being added, and the result or the final answer we get after the process is called the . It is one of the essential mathematical functions we use in our everyday activities. There are many situations in which we add numbers. One of the most common everyday uses for adding numbers is when we work with time or money-for example, adding up bills and receipts.

The addition has an infinite number of applications in our day-to-day life. We use addition while cooking food, while calculating bills at supermarkets, while calculating distances, and much more.

Addition Symbol

The addition symbol used to indicate addition of numbers is $"+"$ (also called the plus symbol). For example, we read $5 + 3$ as $"5$ plus $3"$.

An addition sentence is a mathematical expression that shows two or more values added together and their sum. The two or more values that are added are called addends. The parts of addition sentence are two or more addends, plus symbol(s), equal sign, and the sum.

Let's look at this with the help of another example.

Let's say we have two yellow stars,

and three purple stars.

In order to find the total number of stars we have, we count all the stars together. That is, together we have 5 stars.

Mathematically, we write this as

$2 + 3 = 5$

Here, "+" denotes addition. The total that we get on adding two or more numbers is also called the sum. Therefore in this example, 5 is the sum of 2 and 3.

Considering one more example, if we add the numbers 6 and 4, we get the sum 10; and we write this as
$6 + 4 = 10$

Solve Addition Problem

We can add two numbers easily using the various methods discussed below. These methods are more convenient for adding small numbers.

In their quest to master addition, students start by learning how to add one- digit numbers using their fingers or the number line and then move on to adding bigger numbers using place value or column method. Let's learn about the addition of two numbers: using fingers, on a number line, using the number grid, by counting forward.

Using Fingers

Addition of small numbers can be done using your fingers.

Example 1: Let's say we have to add the numbers 5 and 2. Show 5 fingers on one hand and 2 on the other. Count the total number of fingers to find the sum.

Similarly, to add 2 and 2, show 2 fingers on one hand and 2 on the other. The sum is 4 since four fingers are shown in total.

Example 2: Let's add the numbers 5 and 3.

Step 1: Show 5 fingers on one hand and 3 on the other.

Step 2: Start counting the fingers together like this to find the total.

And we have our total

$5 + 3 = 8$.

Using The Number Line

We can use the number line to add. Let us look at the following addition example.

Example 1: To add 5 and 7, we can count forward 7 steps from 5, as shown below.

Example 2: Let's see how we can add the numbers 11 and 3 using a number line.

Step 1: Mark the bigger number on the number line.

Step 2: Jump forward as many times as the second number.

So, we have

$11 + 3 = 14$.

Using The Number Grid

Number chart is another way to add numbers.

Example: Add 57 and 16 using a hundred grid.

Step 1: Locate the bigger number (57). Step 2: If the number to be added (16) is more than 10, break it into tens and ones. $16 = 10 + 6$. Step 3: Jump as many 10s as in the second number.$57 + 10 = 67$ Step 4: Move forward as many ones as in the second number.$67 + 6 = 73$.The number reached is the answer. So, $57 + 16 = 73$

By Counting forward

Let's use another example to see how this strategy works. Let's say we have to add the numbers 5 and 4.

Step 1: Keep the bigger number in mind. In this case, 5.

Step 2: Count forward as many times as the second number i.e., 4 times.

Like this: $→ 6 → 7 → 8 → 9$.

We get 9.

So, 4 added to 5 is 9 or the sum of 5 and 4 is 9.

Vertical Addition or Column Method

While solving the problem, we can add the numbers vertically. Here, we arrange the numbers vertically using their respective place values, like ones, tens, hundreds, thousands, etc. We start adding from the right side (or digit at ones or unit place). While solving such problems, we may come across some cases with regrouping and some without regrouping. Let us understand with the help of examples.

Addition without Regrouping

Example 1: Add 41 and 26.

Step 1: Write the numbers one below the other as per the places of the digits.

Step 2: Start adding from the digits in ones place $(1 + 6 = 7)$. Write the sum under the ones digit.

Step 3: Add the tens digits $(4 + 2 = 6)$.

Example 2: Let's add the numbers 34 and 52.

Step 1: Write the numbers one below the other as per their place value like this:

Step 2: Start from the right and add the digits in the ones column first.

Step 3: Move on to the next column and add the digits in the tens column.

And so we have our answer:
$34 + 52 = 86$

Addition with Regrouping

This is the aspect that comes into play when the sum of the digits in any column exceeds 10.

Example 1: Add 57 and 16

Step 1: Write the numbers below the other as per the places of the digits.

Step 2: Start adding from the digits in ones place $(7 + 6 = 13)$. If the sum of the ones digit is greater than 9, write the ones digit of the sum under the ones and carry forward its tens digit to the tens column.

Step 3: Add the tens digits. If there was a carry-forward digit, add it along. $5 + 1 + 1$ (carry-over) $= 7$

Example 2: Let's try adding the numbers 29 and 46 using this method.

Step 1: Write the numbers one below the other as per their place value like this:

Step 2: As done previously, start from the right and add the digits in the ones column first. Here the sum of 9 and 6 will be 15. We think of 15 as $10 + 5$; keep the 5 in the ones column, and give the 10 as 1 ten to the tens column as a carryover.

Step 3: Move on to the tens column and add the digits in this column along with the carryover digit to find the answer.

And so we have our sum: $29 + 46 = 75$

Properties of Addition

We can swap the numbers in an addition equation and the sum will remain the same.

$19 + 14 = 33$

$14 + 19 = 33$

When zero is added to a number or a number is added to zero, the sum is the number itself.

$15 + 0 = 15$

$0 + 15 = 15$

While adding three or more numbers, the sum of the numbers does not depend on the order in which the numbers are added. For example, we could add the numbers 5, 8 and 6 in different ways like this:

$(5 + 8) + 6 = 13 + 6 = 19$

$5 + (8 + 6) = 5 + 14 = 19$

$8 + (5 + 6) = 8 + 11 = 19$

If the sum of two numbers is multiplied by a third number, then the product is equal to the sum of the products obtained when each number is individually multiplied by the third number.

Consider the example: $(2 + 3) 5$

$(2 + 3) 5 = 5 5 = 25$

$(2 + 3) 5 = (2 5) + (3 5) = 10 + 15 = 25$
Fun Fact

Adding zero to a number gives the number itself.

Adding 1 to a number gives the successor of that number.

Changing the order of the addends does not change the sum.

For example, $5 + 3 + 2 = 5 + 2 + 3 = 10$

Conclusion

Adding numbers is a fundamental mathematical process that combines two or more numerical values. We use this operation in our daily lives; some easy examples are calculating money, calculating time, counting students in a class, etc. The symbol of this operation is a '+' (plus sign). Visit SplashLearn to learn more math facts.

Solved Examples on Addition
Question 1: What is the sum of the first 10 odd numbers? Solution:
The first ten odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19.

The sum of the first ten odd numbers

$= 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19$

$= 100$
Question 2: If a bag has 5 balls and 4 more balls are added to it, how many balls are there in the bag?
Solution:

Originally, there were 5 balls in the bag. Now 4 more balls have been added.

The number of balls in this bag is now $5 + 4 = 9$.

Therefore, the bag has 9 balls.
Question 3: The present age of Manny is 7 years. What will be his age after 10 years?
Solution:

Current age of Manny is 7 years.

To find Manny's age after 10 years, add 10 to his current age.

After 10 years, his age would be $7 + 10$ or 17 years old.

Question 4: Samantha bought a bag for $214 and some books for $\$149$. How much did she spend on both?

Solution:

To find the total cost, add 214 and 149.

Thus, Samantha spent $\$363$ in all.
Question 5: Add 56 and 11 using the column method.

Solution: Question 6: Add 4 and 6 on the number line.

Solution:
$4 + 6 = 10$

Question 7: Find the missing number in $7 + \underline{} = 9$

Solution: $7 + 2 = 9$.
Question 8: Add and write the total number of fingers.

Solution: $2 + 5 = 7$.

Question 9: An overhead tank A has 345 gallons and another tank B has 248 gallons of water. What is the total amount of water in both the tanks?

Solution:

Amount of water in overhead tank A $= 345$ gallons

Amount of water in overhead tank B $= 248$ gallons

The total amount of water in both the tanks can be calculated by adding 345 and 248.

$345 + 248 = 593$ gallons
Question 10: There are 596 men, 632 women, and 407 children in a town. Find the total population of the town.
Solution:

Number of men $= 596$

Number of women $= 632$

Number of children $= 407$

Total population of the town is 596, 632, and 407.

We get $596 + 632 + 407 = 1635$

Practice Problems on Addition

Frequently Asked Questions on Addition

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What is Addition? Definition, Formula, Properties & Examples

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Addition is a mathematical operation in which two or more numbers or quantities are added together to form a sum. Learn more through illustrated examples.

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The primary media type of this source is a text-based website. This document contains valuable information for teachers such as addition vocabulary and different ways to teach addition. This source supports the ALCOS because it equips the teacher with the appropriate knowledge to teach their students effectively in addition and subtraction. It gives the teacher unique ways to represent addition and subtraction. This can be extremely useful especially to newer teachers. This document provides many good ideas of activities for the teacher to adopt as well as vocabulary to help explain the concepts better.

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Understanding Addition as putting together and adding to

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Identify the reasons for the Civil War [SS.AAS.4.8]

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The primary media type of this source is an informational website. This website is honestly amazing for teachers. It goes into different sections of the Civil War and tells teachers new ways to teach the information. This supports the ALCOS Standard because it explains to teachers an efficient way to teach the causes of the Civil War pretty gently. This would be extremely helpful in the classroom for the teacher. It brings new ideas and provides guidance into teaching such serious topics.

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The Civil War is a supremely ironic moment in our common heritage. For several decades, the country had just barely held itself together, struggling to tolerate its disagreements, divisions, and disunion. Finally, to become a real country, a real union, it had to, in four short years, literally tear itself together.
- Ken Burns

The Civil War film tells the story of the bloodiest war in American history. It interweaves thousands of photographs and paintings with the words of those who lived through a war that shattered a union and shaped a nation. History's famous and forgotten figures from the war-politicians, generals, soldiers, slaves, free African Americans, and civilians from the North and South-are featured throughout the series and the classroom materials.

Educational Resources

The classroom section provides teachers and students with a myriad of educational resources. These tools include episode descriptions, discussion questions, and standards-based, multidisciplinary classroom lessons and activities created by award-winning educators. The site also provides a comprehensive Civil War timeline and biographies of the men and women involved in shaping the impact of the war on our historical and national narrative.

The lessons and activities for The Civil War series have been updated to accommodate new educational standards and commemorate the 25th anniversary of the film. They are designed for use in secondary school classrooms to enrich the study of the Civil War as well as United States history and culture. The classroom activities integrate carefully selected video segments from the series into lessons to underscore content themes and enhance student understanding. They can be used as stand-alone resources, in conjunction with curriculum scope, sequence, and textbooks, or even modified as homework. The activities are closely aligned to content-based national standards and Common Core.

In the Classroom with THE CIVIL WAR
Educator Eden McCauslin explains how she uses THE CIVIL WAR series with her students.

Discussion and Activity Lessons

The Civil War series is rich in educational themes and content, and provides opportunities to explore a range of topics in depth. Because class time is limited, addressing all the lessons and themes can prove challenging. As such, the following activities provide student and teacher handouts, video clips from the film, additional resources, and discussion questions that can be covered in a class period or less, used as an introduction for a larger unit or as the basis for a term paper or project.

This activity works well as an introduction to learning about the Civil War. It sets the stage for student understanding of why the war was fought, the objectives and strategies of both sides, and the sectional differences that augmented the debate over the direction of the country. Students view three video clips from The Civil War that depict the dissolution of the Union after the election of Abraham Lincoln and the entrenched ideologies of both the North and the South. Students also analyze a map of the Union's "Grand Strategy" to defeat the Confederacy.

When the Civil War broke out, free African Americans and runaway slaves found themselves waiting on the sidelines of a conflict in which they played a central role. Until the issuance of the Emancipation Proclamation, the war was said to be fought to preserve the Union, despite the central role that the dispute over slavery played in breaking it apart. Once admitted to the military, African-American soldiers faced the same prejudice and racism as before. This activity explores how the Emancipation Proclamation was implemented in the military, with discussion questions on how it changed the nature of the war. Students also examine a final letter from Colonel Robert Gould Shaw, commander of the Massachusetts 54th Regiment Volunteer Infantry, to his wife, Annie, on the eve of the battle at Battery Wagner, where he attests to the bravery of the men who proudly served with him. Students discuss Shaw's observations and how African-American soldiers faced and overcame many of the same prejudices and racism they faced before the war.

Music played an important role for both the North and the South during the Civil War. Songs such as "Battle Hymn of the Republic," "Dixie," and "Battle Cry of Freedom" defined many of the issues and emotions held by both sides. Both the North and the South adopted the "theme songs" of the other and put their own lyrics to the melodies. Often, the resulting song showcased satire and humor on a level that would rival (and foreshadow) song parodies of the following century. Students listen to "Dixie" and "Battle Cry of Freedom," performed by both sides, and analyze the symbolism of the lyrics and the impact the songs had on both northern and southern societies. This activity is a great integration of history and music.

The Civil War still holds the distinction of being America's bloodiest war. More than 3 million Americans fought in it and over 600,000 men-2 percent of the population-died in it. For many Americans, it was difficult to even conceive how the war might end, and, even if it did, even more challenging to envision how the two sides could ever find a way to share the same nation once again. But the two sides did reconcile, beginning with the terms of surrender bestowed by President Abraham Lincoln through General Ulysses S. Grant to Robert E. Lee and the Army of Virginia. Students watch a detailed account of the surrender ceremony from The Civil War series and examine the surrender agreement as well as a passage from Grant's memoirs to gain a deeper understanding of his compassion and character. The activity provides an in-depth study of compassion toward former enemies after a conflict is resolved.

"War is all hell," declared General William Tecumseh Sherman. Believing that the only way to ensure surrender from the South was to bring the full force of war to the civilian population, Sherman devised a tactic to march from Atlanta, Georgia, on a 60-mile-wide swath across the Deep South. This was known as total war, the likes of which most Americans had not previously experienced. Students assess this controversial move from different angles. First, to grasp the circumstances surrounding the event, students view a segment from the series on Sherman's March to the Sea. They then analyze two primary sources: a letter written by Sherman to Grant as Sherman's army approached Savannah, and the lyrics to the popular song of that period, "Marching Through Georgia." The discussion examines the details and controversy of the march.

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The Civil War is a supremely ironic moment in our common heritage. For several decades, the country had just barely held itself together, struggling to tolerate its disagreements, divisions, and disunion. Finally, to become a real country, a real union, it had to, in four short years, literally tear itself together.

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This primary media type of this source is visual. In this video, the narrator explains the causes of the Civil War with the aid of great visual. Not only are the students hearing the information, but they are able to see it with their own eyes. This very blatantly supports the ALCOS Standard because the whole video is dedicated to teaching the causes of the Civil War. This video would be useful in the classroom because, like said earlier, students are able to visibly watch something. This aids so many students in the processing of information, especially serious information like this. This video also gives students a chance to process this information for themselves before the teacher and class start discussing.

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Causes of the American Civil War - Educational Social Studies Video for Elementary Students & Kids

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The primary media type of this source is audio. This song is absolutely amazing. It breathes a new life into the telling of the Civil War to the tune of a popular song. I can just picture students dancing around to this song while learning about the Civil War. This supports the ALCOS Standard because it is basically a song about the causes of the Civil War. It very simply explains how the Civil War started in an exciting way. This will be so helpful in a classroom because it will get kids excited to learn about the Civil War, which rarely happens. It is a very light hearted way to introduce some very heavy information.

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North vs South: Lincoln vs Lee (Sia's "Cheap Thrills" Parody) - @MrBettsClass

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The primary media type of this source is visual. This picture very briefly describes each of the main reasons of the Civil War in a clear and concise manner. Each cause is represented with a little image, so students can easily recall the causes by remembering the symbols. This image directly supports the ALCOS Standard in the fact that it states the reasons for the Civil War. This pictures helpful in the classroom because it is a good spring board for the teacher to intrude the topics and then explain them on a deeper level.

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The primary media type of this source is an information website. This website is so much fun. It gives such fun and interesting ideas of activities students can perform to investigating the causes of the Civil War. This was actually created by another teacher, so I definitely trust that it is effective. This supports the ALCOS Standard because it provides different ways for students to explore the causes of the Civil War. Not only are they just learning the causes, but they are exploring them at a deeper level. This would throw something new and exciting into the classroom that students would love. This source is incredibly helpful to provide teachers with some ideas on how to make learning about the Civil War fun.

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Ask students what types of things cause wars. Start discussion by asking what students know about the Civil War, and then if they know what caused it. Guide students to use the regional geographic terms "North" and "South".

Let students know they will be watching a video about causes of the Civil War. They need to write answers to these questions:

1. How did each side feel about slavery?

2. How did each side view states' rights?

3. Which side did the import tariff enacted at the time benefit?

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Investigating Causes of The Civil War - Teacher-Created Lesson Plan | Common Sense Education

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Ask students what types of things cause wars. Start discussion by asking what students know about the Civil War, and then if they know what caused it. Guide students to use the regional geographic terms "North" and "South". Let students know they will be watching a video about causes of the Civil War.