Addition is made up of several components. The most obvious being numbers, symbols and words.
(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, +, =)
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Others include the specific concepts of combining quantities and items as well as the actual sum or total. All of the above are abstractions. Abstracting is the process of narrowing down a topic or idea to a single, simple, important element.
I will be taking a focused look at the concept of adding, or +. Now the symbol alone is an abstraction for the idea of addition. However, I'd like to further abstract the thought. A new baby in the family is often thought of as a "new addition." A family grows larger and changes with new life.
Abstractions:
Abstractions are representations that hold the same meaning. The abstraction of a human could be a stick figure. Both are humans, but range in representation.
I chose to represent the concept of adding through the use of "new additions." Both images above represent growth and change. When you add together two numbers like 2 + 3, you will observe a larger number that is different than both parts...5! The addition of a baby into a family is just that. A family may start with two people and grow to three. This particular abstraction can be further represented with the number sentence, 2 + 1 = 3. Relating the concept of addition to growing and changing families will support student understanding. Furthermore, number models can be represented to capture student families in multiple ways. For example, mom and dad (1+1) or my parents and I (2+1) as well as the people who live with me, my grandparents, and my cousins (3 + 2 + 5).
The second representation is another type of "addition." This form of addition takes shape with the adding on of train cars to make a long extension that passes, one after the other. The adding on of train cars can be related to the classroom with the adding on of manipulatives. Boys and girls can use unifix cubes to build number representations and create a concrete visual that supports addition. For example, 5 red cubes and 7 blue cubes equals 12 cubes altogether. It appears that a "cube train" has been built with the connecting of colored cubes. The manipulatives demonstrate the same growth and change as the new addition to a family.
These ideas impact my topic of addition while both simplifying and clarifying the overall concept. Whether you are adding numbers, objects, money or thoughts the process will result in a larger total that is different from its parts.
Below is a link to a company with its own play on abstract addition...
http://identitydesigned.com/addition/
Furthermore, addition can be seen with a different take on "addition." A train can grow and change by the adding on of cars. This can be realized while waiting for a long train to pass at a train stop.
Abstractions:
Abstractions are representations that hold the same meaning. The abstraction of a human could be a stick figure. Both are humans, but range in representation.
I chose to represent the concept of adding through the use of "new additions." Both images above represent growth and change. When you add together two numbers like 2 + 3, you will observe a larger number that is different than both parts...5! The addition of a baby into a family is just that. A family may start with two people and grow to three. This particular abstraction can be further represented with the number sentence, 2 + 1 = 3. Relating the concept of addition to growing and changing families will support student understanding. Furthermore, number models can be represented to capture student families in multiple ways. For example, mom and dad (1+1) or my parents and I (2+1) as well as the people who live with me, my grandparents, and my cousins (3 + 2 + 5).
The second representation is another type of "addition." This form of addition takes shape with the adding on of train cars to make a long extension that passes, one after the other. The adding on of train cars can be related to the classroom with the adding on of manipulatives. Boys and girls can use unifix cubes to build number representations and create a concrete visual that supports addition. For example, 5 red cubes and 7 blue cubes equals 12 cubes altogether. It appears that a "cube train" has been built with the connecting of colored cubes. The manipulatives demonstrate the same growth and change as the new addition to a family.
These ideas impact my topic of addition while both simplifying and clarifying the overall concept. Whether you are adding numbers, objects, money or thoughts the process will result in a larger total that is different from its parts.
Below is a link to a company with its own play on abstract addition...
http://identitydesigned.com/addition/
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