Tag Archives: look-up

Operators, Functions, and Properties – part 40

In this series, we’ve spent considerable space playing with operators, which we’ve pictured as black boxes with inputs and outputs, often as part of a machine with state.  In more recent posts, e.g. this one , we’ve looked at operators … Continue reading

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Operators, Functions, and Properties – part 39

In this series, we’ve been looking at operators in various settings, and looked for ways to use them to shine a different colored light on some aspects school math.  In the last four posts, we’ve explored the notions of equivalence  … Continue reading

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Operators, Functions, and Properties – part 36

In the previous post in this series, we broached the subject of equivalence classes.  We did so in the context of looking at an addition table and noticing how each value in the table occurred multiple times.  We drew a … Continue reading

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Operators, Functions, and Properties – part 15

In this series, we’ve been playing with the mathematical notion of an operator, seeing if we could make it useful for making a bridge between arithmetic and algebra.  In the previous post, we started to investigate the notion of a … Continue reading

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Groupings, Shopping Lists, Vectors: part 7

In part 6 of this series, I introduced an operation called inner product between two vectors, as a way to find the total price of an order using a price list.  In this post, I want to give a bunch … Continue reading

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Groupings, Shopping Lists, Vectors: part 6

In this series on vectors we showed vector addition in this post, and then took a small excursion to show a surprising connection between some vector additions and the distributive property. In  this post, I will combine vectors with look-up … Continue reading

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Notes on Lookup – Another Sieve for the Collatz Problem

This post is a follow-up on an earlier post in which I introduced the Collatz Problem and designed a sieve that systematically builds solutions and is very efficient in the work it does.  In this post, I’ll give a version … Continue reading

Notes on Lookup – Histograms as Sieves

I think I overlooked one interesting example of something like a sieve being used in the typical K-12 math curriculum, and this post is intended to remedy that.  It is possible and instructive to look at a histogram as a … Continue reading