Base 2 numbers in sixth grade math

[zimom]

Is there a reason I need to teach my DD (6th grade math) Base 2 numbers???  I am really confused as to why this is being introduced.  Not to mention somewhat confused by the subject myself  :lol:

 

I even asked my adult son who obviously has had advanced math much more recently then I have, and he can see no reason why it is being taught.  This is Horizons 6 btw.

 

I know I'm old but I don't ever remember learning, using or anything about Base 2 and I have a pretty extensive math background.  

[maize]

It can help kids gain a better understanding of the base ten system and how it affects the ways we work with numbers.

[EKS]

Learning about other bases can help reinforce kids' understanding of place value and if done right, can be a lot of fun.

 

How about making some base 2 blocks?

[forty-two]

It can help kids gain a better understanding of the base ten system and how it affects the ways we work with numbers.

This.

 

And also so you can appreciate awesome geeky jokes like:

There are 10 kinds of people in the world:

Those who can count in binary,

And those who cannot.

:tongue_smilie:

 

But really, working through the process of counting in another base, maybe making the equivalent of a hundred table to get the hang of how place value works in general, and then making an addition table and multiplication table and using them to add/sub and mult/div with the standard algorithms - basically repeating the steps of learning to do base 10 arithmetic but in another base - seeing how the algorithms work with fresh eyes - that sounds like an awesome use of an afternoon. (I'm geeking out at the thought - arithmetic in base 5 might be in my future today ;).)

[wapiti]

I *love* the Young Math book on binary (looks like it's getting more expensive)

[kiana]

It can help kids gain a better understanding of the base ten system and how it affects the ways we work with numbers.

 

That's the biggest reason.

 

What does it mean to have a number be "in the tens place", really?

 

Although I think that for a first exposure binary is less transparent than computing in something like base 6 or base 8 ... where not everything gets carried immediately.

[zimom]

ok :)  I'll take the time to understand it.  

 

My adult son asked one of his other geeky friends why she might need to know it, his friend's answer was so that she would understand the Matrix better.  

 

See, I'm so old it wasn't taught when I was a kid  :confused1:

[freesia]

It surprised me when we hit it in Horizons 6, too. But dd and I found it fun. Kinda like a code. If your child understands base 10, it won't be very difficult.

[forty-two]

Although I think that for a first exposure binary is less transparent than computing in something like base 6 or base 8 ... where not everything gets carried immediately.

I agree.

 

  

ok :)  I'll take the time to understand it.

My adult son asked one of his other geeky friends why she might need to know it, his friend's answer was so that she would understand the Matrix better.

 

Understanding different bases is extremely helpful in working with computers - my major was computer engineering and I got comfortable in base 2, base 8 and base 16 (and actually I'd already had experience in base 16 just from learning the codes for colors in paint programs - it comes in handy even if you don't program).

 

In my experience, learning to work in another base is like learning another language - the second base is the hardest, as you are wrapping your brain around new ways to refer to the same concept, and things start to really come together when learning the third base, and adding additional bases after that is child's play, because you really *get* how it works and it's easy peasy to apply it to any base you want. And unlike languages, you can learn a new base in an afternoon ;).

[Jane in NC]

ok :)  I'll take the time to understand it.  

 

My adult son asked one of his other geeky friends why she might need to know it, his friend's answer was so that she would understand the Matrix better.  

 

See, I'm so old it wasn't taught when I was a kid  :confused1:

 

Actually, learning about bases other than ten was introduced in elementary math books in the post-Sputnik days ('60's) when math and science education in the US was beefed up.  I thought it was fun then although this was one of the things that parents grumbled about when their kids were introduced to the "new math".

[wendyroo]

Peter and I were just talking about this.  He wanted to know how Buddy the Tyrannosaurus would count on his fingers, so we spent a while doing t-rex math (aka Base 4).  

 

We drew t-rex decimal street (from MUS).  First a house that held up to 3 t-rexes. then a house that held up to 12 t-rexes, then a house that held up to 48 t-rexes.  Peter got pretty good at number conversions.  If a person counted 62 acorns they would express that with the number 62, but if a t-rex counted the same pile of acorns they would use the number 332 to describe the quantity.

 

Next he wants to try counting with an octopus.

 

Wendy

[kiana]

Peter and I were just talking about this.  He wanted to know how Buddy the Tyrannosaurus would count on his fingers, so we spent a while doing t-rex math (aka Base 4).  

 

We drew t-rex decimal street (from MUS).  First a house that held up to 3 t-rexes. then a house that held up to 12 t-rexes, then a house that held up to 48 t-rexes.  Peter got pretty good at number conversions.  If a person counted 62 acorns they would express that with the number 62, but if a t-rex counted the same pile of acorns they would use the number 332 to describe the quantity.

 

Next he wants to try counting with an octopus.

 

Wendy

 

This is a great way to do it.

 

For examples in more adult series -- in Larry Niven's known-space series, the Kzinti (alien pseudocats who have 4 digits) count in base 8 -- and it's pretty cool how consistent they have been, with them talking about things like 'eights of eights of eights of warriors'

[FairProspects]

Would this be the same thing as modular arithmetic? As in using a 6 hour clock to do various counting calculations?

[raptor_dad]

 (I'm geeking out at the thought - arithmetic in base 5 might be in my future today ;).)

 

Base 5 is a really fun and easy to introduce since you can us pennies, nickels, and quarters... This lets you build your hundred chart using concrete manipulatives.

 

 

[Arcadia]

Would this be the same thing as modular arithmetic? As in using a 6 hour clock to do various counting calculations?

Yes. Modular arithmetic is in AoPS intro to number theory, iMACS foundations Operational Systems (http://www.elementsofmathematics.com).

[Tanaqui]

I remember learning how to convert into base 2 in the 6th grade, and that was some 20 years ago. I thought it was an awful lot of fun, and spent many hours being bored in class doing conversions into different bases to keep myself awake as the years went by.

 

Really, if you can do decimal math, binary is simple. You have your 1s place, just like in decimal. That's 2^0. Then you have your10s place, just like in decimal, but in decimal that's ten times 1, and in binary it's two times 1. Then you have your 100s place, except instead of being ten squared it's two squared. The 1000s place is two cubed, and so on.

 

Re: the earlier joke:

 

There are 10 types of people in this world.

There are those who understand ternary, those who don't... and those who thought this was gonna be some kind of binary joke.

[FairProspects]

Yes. Modular arithmetic is in AoPS intro to number theory, iMACS foundations Operational Systems (http://www.elementsofmathematics.com).

 

And just when I decide AoPS might be too difficult for us, I realize we might be ok after all.

[zimom]

all these years I've called myself a math person.  I'm beginning to think I lied.  Or I guess it is just more proof of how bad my schooling was  :banghead:

[Tanaqui]

all these years I've called myself a math person.  I'm beginning to think I lied.  Or I guess it is just more proof of how bad my schooling was  :banghead:

 

http://xkcd.com/1053/

 

Don't forget to read the mouseover text!

 

[1053]

.

[eternalsummer]

We learned it in 2nd grade in public school (20+ years ago, alas).  It was very cool then, I thought.  

 

The only thing it teaches, conceptually, as far as I understand it, is an important thing - what do place values *mean*?  How do numbers actually work, what do they actually represent?  It's kind of like learning a second language (only much easier); it teaches you something about how language itself works, what it's for, what it means.

 

Base 2 instead of anything else because it's the easiest, and the point is not the base itself but the concept that there are different ways to count/organize groups of things.

[Bootsie]

Not only does it help with understanding of place value, you can count to 512 on your fingers using a base 2 system.

[Tanaqui]

Not only does it help with understanding of place value, you can count to 512 on your fingers using a base 2 system.

 

Or you can count up to 6561 using a base3 system, where touching the top part of your finger with your thumb is a 0, the middle part is a 1, and the bottom part is a 2.