What is addition?

Addition is a mathematical operation. It is a method or activity that has to do with numbers.

It can be explained as the combination of two or more quantities, or simply put, finding the total value of two or more numbers. It is one of the four primary arithmetic operations along with subtraction, multiplication, and division. All school curriculums introduce this mathematical skill early on.

The foundation for many other math skills is built on addition, so it is crucial that children become confident with it at an early age. After early learners build their grasp of basic number concepts, addition is the next big step. As with all first steps, it can be difficult. It need not be that way, though. With easy lesson plans developed by the teachers, students can get a better understanding of the concept.

To start with an example, 7 + 4 means combining the numbers 7 and 4 to derive a solution. The result as we know is 11.  A sum can be broken down into addends and the sum. Addends are the numbers being added, and the answer to the addition is the sum. To solve a sum, the addends must be combined together.

So the expression 7 + 4 = 11, can be written as:

Reference: https://cutewallpaper.org/download.php?file=/21/additoin/What-is-addition-Definition-Facts-and-Examples.png

Here are some quick facts that can help you understand this concept better

  • Addition is symbolized by the plus (+) sign.
  • The (+) can be used multiple times as required. Eg. 1+2+3=6.
  • Usually, when there are a lot of numbers, it is easier to write them one after the other and carry out the calculations at the end.
  • The answer to the problem is always the same irrespective of the order the numbers are added. Eg. 1 + 2 + 3 + 4 gives the same answer as 4 + 2 + 1 + 3 which is 10.
  • Adding 0 to any number makes no difference to the total. Eg. 6 + 0 = 6.
  • In advanced stages, addition can also be denoted by ‘sum’ or the symbol ∑.

After learning to count to ten, learners can usually perform additions up to ten easily. For example, if a learner is given three piles of cards, one pile containing 4 cards, the second containing 3, and the final pile containing 2 cards, they can count all the cards and come up with the answer 9. The use of fingers is quite common when learning how to add or count. Adding dots drawn on a piece of paper, or using a number line are also some of the common procedures for learning addition.

When digits are recognized, it is easy to perform the same sum by simply viewing the problem. Adding the same number to itself (doubling) becomes quite straightforward upon gaining a basic understanding, such as 2 + 2 = 4. When adding a number to itself, it is the same as multiplying it by two so 2 + 2 can be written as 2 x 2 (verbally 2 into 2).

There are four properties commonly used when performing addition:

Closure Property: The resultant sum from adding two or more numbers is always a whole number. For example, 5 + 3 = 8

Commutative Property: The sum of two or more addends will be the same regardless of the order in which they are added. For example, 8 + 7 = 7 + 8 = 15

Associative Property: An addition of three or more addends will always have the same sum irrespective of the grouping or the order in which they are added. For example, (5 + 7) + 3 = (5 + 3) + 7

Additive Identity Property: The sum remains the same if we add a zero to the actual number. A sum does not change in value when the whole number zero is added to it. For example, 0 + 7 = 7.

How can you explain addition to children?

Helping a child grasp the concept of addition can help lay a solid foundation for their academic future. Different teaching tools can make addition a more fun and interactive experience for the children, whether they are in a classroom or tutored at home. By using a variety of methods or tools, a child learns how to think independently of what is being counted.

  • As mentioned earlier, counting on fingers is the most intuitive place to start before a child can transition into using dice, cards, or paper cutouts.
  • Children also respond well to visual tools that help them understand addition concepts. Starting with a small number of items you can demonstrate number relationships easily.
  • Using play tools such as modeling clay to create objects, combining your addition lesson with an art lesson.
  • Often movement is incorporated. Teachers place students in small groups, place them together, counting out the total once more are added.
  • Employing game pieces, like dice or play cards in new ways to create simple and fun teaching sessions. Providing extra challenges for quick learners by instructing them to add the results of three or more items can speed up the learning process.
  • Using Abacus. It is a simple counting tool with rods and beads that can slide. An abacus with large and brightly colored beads will be ideal for children, as it will be visually stimulating while being easy to manipulate.

It is always advised to familiarize students with the basic symbols. Teach them the meaning of plus “+” and equal to “=.” Assist them with simple horizontal  “number sentences”, like “1 + 2 = 3”. Already young children learn that they should write words and sentences “across” paper. Following the same process with number sentences will be less confusing. Once children have mastered this concept, then vertical sums can be introduced.

It is also important to teach children the words that signify addition. You should use terms such as “together,” “in total,” “sum,” and “total” that commonly indicate that one needs to add two or more numbers. Also, you can utilize word problems to help them better understand the concept. A simple example is if A has two toys and after opening all his birthday presents he now has 5 toys, how many toys did he receive for her birthday. Despite the fact that some students may find story problems difficult, others will gain a better understanding of the relevance of addition when they understand its real-world implications.

Some other common methodologies are:

  • Transition to visuals: By using illustrated sums, or having students draw objects they can count, you can improve their understanding capability.
Reference: https://www.smartick.es/blog/matematicas/algebra/propiedad-asociativa-suma-multiplicacion/
  • Using a number line: A number line helps ease the calculation process. If the sum is 2 + 3, for example, a child can put their finger on the two to start with, and then count up three places to reach 5. They will not be required to count out the 2 first to reach the solution.
Reference: https://www.liveworksheets.com/worksheets/en/Math/Counting/Number_line_Addition_lv855312of
  • Counting Up: Once a child is familiar with the number line, you will want them to use the same strategy in their heads. Having them count their fingers aloud will help them gain confidence.

Let us stick with 2 + 3 as an example: The child can start with a closed fist and say “2” and then count up “3, 4, 5”, extending three fingers one at a time. Once three fingers are extended, remind them that the answer is not 3. They started with a 2 in their fist and then counted up, so the answer is 5.

Reference: https://english-grammar.biz/dictionary/img/wlibrary/a/5fdc96b3468824.77644204.jpg
  • Mental Maths: Finding the ten is a common mental math trick used to develop procedural fluency in students. When students add two numbers, instead of adding them together as they are, have them add them up to 10 and then add the remainder.

For example, the process for 6 + 7 is 6 + 4 = 10. We still need to add an extra 3, to make it 13. 10 + 3 = 13. You can also use manipulatives to help the child master mental maths. Using a sheet of paper, draw two rows of 10 boxes, one underneath the other, and then let students fill them in with manipulatives to represent the sum.

  • Word problems: These types of problems encourage your child to identify addition even when not clearly specified. You can introduce them to the language of addition by saying:
    • A plus B
    • A extra
    • A added to
    • the total amount
    • Sum total

As they become familiar with the language, you can move on to reasoning and problem-solving activities.

Reference: https://www.liveworksheets.com/worksheets/en/Math/Addition/Addition_word_problem_kc1180163zu
  • Number charts: These charts are another way to add numbers. To share an example, let us add 57 and 16 using a hundred-grid.
    • Step 1: Mark the bigger number. Since 57 is the larger number here, mark it.
    • Step 2: If the number you want to add is more than 10 then break it into tens and ones. So, 16 = 10 + 6
    • Step 3: Jump tens as many times as the second number. So, 57 + 10 = 67
    • Step 4: Move forward as many ones as in the second number. Here, 67 + 6 = 73
    • Finally, you have the answer. The total is, 57 + 16 = 73
Reference: https://cdn-skill.splashmath.com/panel-uploads/GlossaryTerm/4b606e025c1241b595b48d5e743c845c/1564661046_addition-table.png
  • Memorize the math facts: Ultimately, you want the child to be able to add quickly and accurately without using any means. In order for them to progress to more complex problems, they must memorize every single digit addition fact.
  • Here are a few strategies that can help:
    • Breaking it down: It might be overwhelming to look at the entire table of addition facts at one time, so just focus on specific sections at a time. For instance, you might begin by focusing on 1 + 2 + 3 one week, then move on to 2 + 2 + 3 + 4, etc.
    • Gamifying the process: By integrating quizzes, group challenges, and rewards, rote learning will become more engaging. Just be careful not to make it too competitive so that students who are having difficulty will be scared away. Learn simple ways of gamifying your classroom.
    • Using EdTech tools: Using EdTech tools can help learners learn addition in an engaging and interactive way. Choosing a fun program that students can access independently means they will be practicing at home too.

Examples of addition

Here are some examples of addition that can assist your child to understand the concepts better

3 + 4 = ?

3 + 2 + 1 = ?

4 + 3 + 2 + 1= ?

6 + 5 + 2 + 3 + 1=?

  • The first problem consists of three terms. The missing number is the sum of the numbers on the left-hand side. 3 + 4 = 7
  • The second one has four terms. The sum total is 3 + 2 + 1 = 6
  • The third problem has five terms. The total is 4 + 3 + 2 + 1 = 10
  • The final problem has six terms. The total is 6 + 1 + 2 + 1 + 1 = 17

Word problem examples

  • At a ball, 3 women wear their hair up and 2 wear their hair down. How many women are at the ball? So 3 + 2 = 5
  • There are 5 books on a shelf. 5 more books are added. Now, how many books are there? The answer is 5 + 5 = 10
  • Mrs. Jones’s class raised three groups of silkworms. In one group, 5 silkworms turned into moths. In the second group, 4 silkworms turned into moths, and in the third, 6 silkworms turned into moths. In total, how many silkworms turned into moths? The sum is 5 + 6 + 4 = 15

Types of addition

The types of addition can also be termed as various methods used in addition. For example, vertical addition, addition using number charts, the addition of small numbers using your fingers, addition using the number line, etc, as already explained above.

Also, basic addition problems can be broken down into the following types:

  • Add To: Three balls are in a basket. Four more balls are added by the coach. How many balls are there now? It is 3 + 4 = 7
  • Put Together: There are four red balloons and three white balloons in a park. How many balloons are there? Sum total is 4 + 3 = 7
  • Compare: Dean has won four more games than Sam. Sam has won three games. How many games has Jack won? Here the total is 4 + 3 = 7

How to use it?

The concept of addition comes in handy in everyday life. You can calculate the overall mileage of a route by adding the miles (or kilometres) you will travel at each step of the journey. Planning fuel stops could be made easier with this information.

Addition can also be used to calculate how long something will take. As an example, if you get on a bus at 11:00 and it takes 25 minutes to get there, what time will you arrive? In the same way, you can add up days, weeks, months, or years. It is important to remember that there are 60 seconds in a minute, and 60 minutes in an hour when adding minutes or seconds. This means 100 minutes is actually 1 hour 40 minutes and not 100 minutes.

Addition is most commonly used when dealing with money. You can, for example, add up bills and receipts. To find the total for the visit, add up all the individual prices.

The tips and tricks that follow addition can be used to identify a problem and find a solution in quick simple steps.

Importance

Many different types of problems can be represented and solved using addition. Learners should actively seek to recognize and represent these situations symbolically, building on counting with whole numbers. A child’s understanding of addition helps him/her learn basic facts quickly. Students solve arithmetic problems by using an understanding of addition (using sets or number lines to combine or separate sets), relationships and properties of numbers (such as place value), and properties of addition. They develop, discuss, and use efficient, accurate, and generalized methods to add multidigit whole numbers. Depending on the context and numbers involved, they select and apply appropriate methods for estimating sums. The addition of numbers, including standard algorithms, can be learned through fluency, understanding of how the procedures work, and their application in solving problems.

Conclusion

Once the basics are in place, and the child has a basic understanding of the concepts they can progress to further study of arithmetic operations in mathematics. A strong number sense is an invaluable advantage when moving to advanced mathematical study such as algebra. Hence, learning the basics of addition is an essential part of early education. Clearly, mathematical understanding begins with arithmetic operations which include addition. For a child to master the techniques and apply the learnings, It is important to have daily experiences with strategies and activities. The tutor should utilize the many opportunities that are available throughout the day to teach strategies of addition. Although, learning should not only be limited to school or a classroom. We can take advantage of available opportunities as they arise in our daily lives, adapting to the child’s needs and making learning a fun interactive process.

References:

  1. https://www.splashlearn.com/math-vocabulary/addition/addition
  2. https://www.cuemath.com/numbers/addition/
  3. https://www.twinkl.co.in/teaching-wiki/addition
  4. https://www.storyofmathematics.com/addition
  5. http://www.homeofbob.com/math/numVluOp/wholeNum/addSub/adSubTypsChrt.html
  6. https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-factors-and-multiples/properties-of-numbers/a/properties-of-addition