We are going to spend this time looking at numbers from the Greek perspective. This means that we’re going to think of numbers as being sticks of specific lengths. With this in mind, addition of numbers is represented by finding the total length of two sticks put end-to-end.
One of the reasons that the Greeks liked this framework is because it allows us to work with abstract ideas about arithmetic rather than actually having to measure out physical lengths. We can simply replace the numbers with variables and the picture remains meaningful.
Draw a diagram to represent the calculation \(b + a\) and compare your diagram to the diagram of \(a + b\text{.}\) Explain why the two end results are the same length. Which property of addition is being demonstrated by this?
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Using this framework, the meaning and validity of the associative property of addition is made much more apparent as well.
Determine which diagram represents \((a + b) + c\) and which one represents \(a + (b + c)\text{.}\) Explain how you reached your conclusion.
