Introducing terms such as the commutative property of arithmetic to kids in basic mathematics is in general the time we start to completely lose and confuse them! This is because we start to use language that they are not familiar with.
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If we break these terms down to language they are familiar with understanding comes soon after. HOWEVER, once understanding is there, the proper terms must be used at the right times, as this is how mathematics is communicated!
When we discuss this in basic arithmetic, or further on in Basic Algebra, we are simply referring to the order in which numbers appear and are operated upon.
If we operate on the numbers in one order, then change the order and operate again - if we get the same answer the operation is said to be commutative. And that is simply it!
Steps to be taken |
Action |
Result |
Addition problem Change Order Are the answers the same? Addition IS Commutative ie - the order in which you add numbers does not change the result. |
3 + 5 5 + 3 8 = 8 |
8 8 Yes |
Steps to be taken |
Action |
Result |
Subtraction problem Change Order Are the answers the same? Subtraction is NOT Commutative ie - the order in which you add numbers does not change the result. |
9 - 3 3 - 9 6 is not equal to -6 |
6 -6 NO |
Steps to be taken |
Action |
Result |
Multiplication problem Change Order Are the answers the same? Multiplication IS Commutative ie - the order in which you add numbers does not change the result. |
3 x 5 5 x 3 15 = 15 |
15 15 YES |
Steps to be taken |
Action |
Result |
Division problem Change Order Are the answers the same? Division Is NOT Commutative ie - the order in which you add numbers does not change the result. |
9/3 3/9 3 is not equal to 1/3 |
3 1/3 NO |
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