# Monthly Archives: July 2010

## Operators, Functions, and Properties – part 13

In this series, we have been looking at little machines that do things like “add 2”, and we’ve been chaining such machines together by connecting the output of one to the input of the next.  We’ve been exploring the behavior … Continue reading

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## Operators, Functions, and Properties – part 12

In this series, we’ve been looking at operators as something that takes an input and turns it into an output, and we’ve been looking at chains of such operators, which we’ve called trains.  In the last post, we posed the … Continue reading

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## Operators, Functions, and Properties – part 11

In the prior post of this series, we looked at pairs of operators in which one of the pair cancels out the effect of the other.  We call one of these the inverse operator of the other one.  For example, … Continue reading

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## Operators, Functions, and Properties – part 10

In the prior post in this series, we looked at chains of operators for which the net effect was to do nothing.  We started by comparing the picture on the left with the picture on the right, below, and noticing … Continue reading

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## Operators, Functions, and Properties – part 9

In the last few sessions in this series we’ve looked at operators that do things like “add 2” or “multiply by 3” or “divide by 10”.  Each of these operators takes a number as its input and produces a number … Continue reading

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## Operators, Functions, and Properties: The Series

This series of posts introduces the notion of an operator as something that changes the state of some machine or device.  Often, an operator is invoked at the press of a button.  A special case of an operator is one … Continue reading

## Operators, Functions, and Properties – part 8

In the prior post, I played with putting together little boxes that perform actions on numbers coming in – simple actions like adding two – and reported on an experiment with seventh graders to find equivalent boxes.  I’m going to … Continue reading

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## Operators, Functions, and Properties – part 7

Continuing on from the last post, where we introduced some simple operators that operate on a number, like “add 2”, I want to show more examples of composition of these operators. The figure above shows five pairs, each pair consisting … Continue reading

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## Operators, Functions, and Properties – part 6

In this series, we’ve been playing with the idea of operators as some kind of action that alters the state of some device or some system, perhaps invoked at the press of a key or a button.  We’ve emphasized that … Continue reading

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