One thing that really helped me learn this lesson is being able to describe the Identity, Associative, Commutative, and Closure Properties for Addition.
As a reminder, I will write down the properties for those of you who want to use this to study from. (I started on page 143 of the text book.)
Additon of Whole Numbers: If set R has r elements and set S has s elements, and R and S are disjoint, then the sum of r plus s, written r + s, is the number of elements in the union of R and S. The numbers r and s are called addends.
- Remember that as a teacher, it children will learn how to add at an early age from adding objects together (and taking away). The same is with how we learn our addition today, just in different bases -- we put sets together and define their union together.
Closure Property: For every pair of numbers in a given set, if an operation is performed, and the result is also a number in the set, the set is said to be closed for the operation. If one example can be found where the operation does not produce an element of the given set, then the set is not closed for the operation.
- Another way to say this, or understand is say that this is the closed for the operation of addition. Here is a great video that simply shows the closure poperty clear and effective.
Identity Property for Addition: For any whole number b,
0 + b = b + 0 = b
and so on.
This is the easiest of them all! For both addition and multiplication, anything that equals itself (0 + x = x) and ( 1 * x = x) this will be the identity property.
Associative Property for Addition: For any whole numbers, a, b, and c,
a + (b + c) = (a + b) + c
It does not matter what order the numbers fall into, arranging numbers will not make a difference. Explination when using real numbers is show in This Video, and this really helped me understand.
Commutative Property of Addition: For any whole numbers, a and b,
a + b = b + a
When there are two whole numbers being added, they maybe changed (communted) without effected the outcome of the sum.
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I've got to disagree on that closure video. The video creator's use of the word "unique" is not really closure. For example, 8*1=8 and 8 is not unique because it was in the problem ...
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