

How I Taught Third Graders Binary Numbers - sown
http://www.exploringbinary.com/how-i-taught-third-graders-binary-numbers/

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tokenadult
There are some interesting ideas in this post. I teach binary numeral
notation, and then arithmetic with that notation, to third graders each year
as part of the math classes I teach in my town. One of my favorite resources
is the book Algebra by Gelfand and Shen,

<http://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773>

which includes problems in representing numbers in binary notation and doing
arithmetic with binary notation that are very approachable to young learners.
(The problems are also very good review for undergraduate math majors

<http://www.ocf.berkeley.edu/~abhishek/chicmath.htm>

and help adults think more deeply about mathematics, which is why I like
teaching with this book as a source of lesson topics.)

Edit after seeing other comment: I also mention to the children in my classes
the Babylonian numerals,

[http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Babyl...](http://www-
groups.dcs.st-and.ac.uk/~history/HistTopics/Babylonian_numerals.html)

in which the implicit base is base sixty. The link shown here mentions
speculation from ancient Greece that that base was chosen because it has many
different prime factors. That Babylonian system of numerals, whatever its
origin, appears to be related to historical relics such as counting sixty
minutes in an hour or 360 degrees of arc in a circle.

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win_ini
A slight variation that I read years ago using only the socratic method (the
teacher only asked probing questions) to teach third graders binary
arithmetic. Interesting how he weaved aliens into it.

<http://www.garlikov.com/Soc_Meth.html>

Edit: If I'd read to the bottom - I would have seen the author also references
the above post.

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geekzgalore
The socratic method seems to be more effective and intuitive. I was about to
paste the same reference.

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corin_
Maybe overly pedantic, but I don't like [http://www.exploringbinary.com/wp-
content/uploads/27.decimal...](http://www.exploringbinary.com/wp-
content/uploads/27.decimal.png)

For the tens you're counting lines of blocks, and for the ones you're counting
blocks, so it doesn't match up. Maybe if the ones were lined horizontally so
you're still counting vertical lines, they just happen to be 1 block tall
instead of 10 blocks tall.

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andrewcooke
yes. this confused the heck out of me. the units need to be horizontal, or
(when using physical objects) the multiples could be piled on top of each
other. as it is, it's just misleading.

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cormullion
There was a cool computer game called the Zoombinis that we used to play at
home. One of the puzzles taught binary arithmetic using strange characters
that had two expressions. There's a picture here:

<http://www.computingwithkids.com/column/20011026.asp>

The addition went up to 15 I think. You had to aim the pinballs at the group
that would 'overflow' and jump in the river.

There were some very challenging puzzles in the Zoombinis titles - but they
were teaching the conceptual foundations and encouraging intuition, not
focussing on the terminology and modern applications.

Edit: a more useful link, with educational context and a larger picture, is
this, although it's in French:

[http://la-rochelle-ecole-barthelemy-profit.pagesperso-orange...](http://la-
rochelle-ecole-barthelemy-profit.pagesperso-orange.fr/Zoombinis2/page3.htm)

~~~
brokentone
Man, Zoombinis, those were the days. A few friends and I all "played" it in
our elementary days; however I am convinced that the lessons I learned there
about binary numbers, problem solving, and spacial and mathematical efficiency
stick with me to this day.

As was written in this article, many students apart from CS never fully
understand number bases, which is unfortunate. I applaud this attempt and
others (Zoombinis, etc) to teach some of these basic concepts at an early age.

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anncaryn
I love how you showed them three different ways. Brilliant. Research shows
that kind of patterning repetition in learning is key.

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hrasm
I think such engaging and visual teaching methods are far more etching on the
mind. Great post.

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ralfd
He could have also mentioned the old babylonians and their base 12 system. We
still have an extra word for 12 (a dozen) and it explains our strange counting
of time (2 _12 hours in a day, 5_ 12 in an hour or minute).

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sixtofour
Great idea for a site, so simple and yet so deep.

