Math question-Did you learn base 10 conversions in school?

[TX Native]

I came across this last night reading ahead in my child's math curriculum. I had no idea what the lesson was talking about. I have since watched several videos and looked at several websites. I finally understand it.

 

However, I don't remember learning this in school. I have a vague memory of being briefly told about binary numbers, possibly in a bare bones high school computer programming class. I was an honors student and took math through trig in high school. I went to a lower performing public school in a mid sized city. My major didn't require math beyond college algebra. My husband did not learn this in small town, USA public school in a different state. His college math was mostly geometry based. He 1st heard about base 10 conversion when I got stumped on it last night.

 

Is this taught in regular public schools? Did my husband and I just sleep through class that day? Did we school in the dark ages? I plan to teach it to my children because I find it fascinating and it is in the lessons, but is it necessary to be taught? If it is taught regularly in school, when is it taught. One video I watched that explained the concept so well was made by a middle school math teacher. Besides computer programming, when is it necessary to convert a number from base 10 to something like base 7 or base 14? There's this whole new concept of hexadecimal numbers I just learned about. I feel cheated out of a full math education! If you know all about this, when did you learn it? When have you used it IRL? When I teach my kids about it, what can I tell them about why they need to know how to do these conversions beyond "because mom thinks it is neat!"?

[vonfirmath]

I remember learning about base conversions in gifted classes in 7th grade (1980s).  I remember because I had been bored for SO long in math and this was FUN!  I really got into it and would not be surprised if I did more excercises than assigned about it.

 

Certainly base 2 and base 16. But they touched on others as well, for proof of understanding.

 

Honestly, the biggest thing for me is lt really cements why a number is the way it is.

Edited August 7, 2016 by vonfirmath

[luuknam]

I *think* it was on some worksheet the remedial teacher gave me in 5th grade (the school didn't have a gifted program, so the remedial teacher saw the gifted kids occasionally to give them some extras). Beyond that, I don't think it was ever mentioned in K-12. And I graduated in 2002. But yes, I would want my kids to learn about binary and hexadecimal (and I guess octal, and just the concept in general). I already mentioned sexagesimal when we dealt with the Sumerians, and talked a little bit about other bases, but we haven't covered it in math yet.

[Tanaqui]

We covered it in either the 7th or 8th grade.

[Jackie]

I remember covering it, would guess 5th or 6th grade?

 

I have never used the information and only find it interesting because I generally find math interesting.

[Arcadia]

We learnt hexadecimal systems on our casio scientific calculator because we were so bored in math class in probably 4th and up in the early 80s.

 

It is similar to what is describe in this article (contains swear words)

https://www.theguardian.com/education/datablog/2014/jan/10/words-you-can-write-on-a-calculator

 

We learned binary, chinese zodiac (base 60), mayan system for enrichment in primary school. We didn't have a national textbook until I was in primary 4 though in 1982. I'm not from US.

Edited August 8, 2016 by Arcadia

[SKL]

I remember base conversions in elementary school.  It seemed a big waste of time to me, but yeah, we "learned" it.

[JenneinCA]

In school? Yes, when I was in college.

 

In elementary, junior high, or high school? No. My math instruction before high school was extremely limited. Think private religious school where the most important trait to get hired was having the correct religious background. Once I got to public high school, I had real math teachers with actual subject knowledge. But I don't remember them covering it there either. It might have happened but I don't know for sure.

[Lecka]

I learned it in middle school. It was not gifted, but I took Algebra I in 8th grade, and was on that track starting in 6th.

[justasque]

Yes, I learned in in a couple of different classes over the years.  I think many people don't really understand what "base ten system" really means until they have learned about other bases.  I do think it is necessary to be caught.  Beyond that, it is useful in computer science.  I've used it quite a bit, including helping my tutoring students really get base ten.  It is such a simple concept, with such potential for deeply increasing conceptual understanding, that I do feel it is an important part of a good math education. 

Beyond that, of course, it's fun!

[Lecka]

I remember that we made up our own symbols and wrote out numbers to compare between bases.

 

I don't think I learned to convert other than writing out numbers and then comparing them, if that makes sense.

 

Like -- if I wrote one system out to "20" in base 10, then I would count how many numbers I wrote to get there. If that makes sense? I think I did that.

 

At least that is what I remember.

 

I remember it being fun to make up the symbols,

I think we all liked it.

 

I don't remember learning any formula for it. I think on the test the teacher would write numbers in the different base and we would write them in Base 10 (or the opposite) but as far as I can remember I was just writing out the numbers to get the answer.

Edited August 8, 2016 by Lecka

[Lecka]

Oh, and making up symbols the way we did it came in for numbers higher than 9.

 

If the base is higher than base 10, you need a single digit to represent the new "number 10." But we could make up our own little symbols for these new digits.

 

We could do it for every number, too, if we wanted, but I think I thought it would get too confusing. Iirc.

 

I remember it as a really fun unit! I remember having the "art" from the coolest-looking papers displayed for a long time, and being able to look at them.

 

I agree on it helping with understanding the base 10.

 

Practically I think it helped me with converting minutes to a decimal (like 15 minutes equals .25). I think it helped in geometry when we did angles.

 

It really helps to understand "why" we have to do this when it is mentioned that this is related to why we don't have a nice round number like 100 minutes in an hour and 100 seconds in a minute, or 100 degrees to make a rotation (instead of 360 degrees).

 

Anyway -- I remember liking it. I think it was one of the more interesting things.

[Lecka]

And practically on my time sheet I have to put time periods in to 15 minutes, and then put in .25, .50, and .75 for 15 minutes, 30 minutes, and 45 minutes.

 

I am afraid I would have forgotten how to do that without having the understanding that way. I think I would want to just put .15 for 15 minutes instead of .25.

[tm919]

Yes - in a pretty fanciful way... it's getting vague but it had something to do with doing business with various imaginary alien races (e.g., one had 4 fingers on each hand). I remember thinking it was neat but there was absolutely no indication that it might be useful information.

Edited August 8, 2016 by tm919

[Lecka]

I have the vaguest memory of rads in geometry, and converting between degrees and rads.

 

I think in rads a rotation was a number besides 360.

 

Then also, in chemistry we used the kind of numbers where they all divide into each other by 10s. And then it works bc it is base 10. So then in a way it made that seem easier. Bc in a way it is weird I think, that they are all by 10s. Then in chemistry we spent a lot of time doing things like getting a number 50 centimeters and converting it to millimeters.

 

And, I think kids are getting introduced to that Kilo- centi- milli- thing earlier. I am pretty sure I had never heard of much besides centimeters until 11th grade and then there was a huge list.

 

I think I was doing pounds and ounces and feet and inches until then, but I think kids are doing grams and liters now even in elementary school.

Edited August 8, 2016 by Lecka

[Garga]

I remember learning about base 16 once a loooooong time ago. In fact, I thought maybe it was something I'd just made up because I never heard about it again until a few years ago when DH mentioned something about it and I thought, "Oh ho! So it *is* a real thing!"

 

I do remember thinking it was just wonderful and loved the lesson, which is probably the only reason I have even that lone dim memory of it.

Edited August 8, 2016 by Garga

[TX Native]

I am so jealous of those of you who were taught alternate number base systems. Trying to explain this clearly is tough, but here's a shot: When 1st researching it, I was confused on why the conversions from base 10 to another number base were seemingly randomly figured by using one higher power of the new base number in the columns from right to left. It took a bit for my brain to catch on that in our base 10 system (from right to left) the one's column is 10 to the 0 power, the 10s column is 10 to the 1st power, the hundreds column is 10 to the 2nd power, and so on. So, duh, in a base 5 numeric system the ones place would be 5 to the 0 power, the tens place would change from 10 to 5 to the 1st power, the hundreds place would change to 5 to the 2nd power, and so on. I made close to 30 on my math ACT eons ago and I have never fully understood place value in this way until today! All As in math my entire life.

 

I showed this to my 10 yo earlier tonight just because I thought he would find it interesting. After demonstrating the concept on paper and showing him a couple videos, he asked to work some problems right then. It was well past his bedtime so I said not now, but it would come up in his math lessons soon. Then he asked if I could please let him do some base conversions for his math assignment tomorrow.

[Arcadia]

This young math book titled Binary Numbers is good even for preschoolers

 

https://www.amazon.com/Binary-Numbers-Young-Math-Books/dp/0690009933

 

Understanding number systems well would help in understanding logarithms' changing of bases.

[Ellie]

I learned it somewhere, but I cannot tell you where or when.

[Dinsfamily]

I remember learning it in school but I have no odea what grade it was...sometime in middle school maybe?

 

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[scoutingmom]

I don't think we learned it in school..... but I learned binary, octadecimal (a bit) and Hexadecimal on my own as a kid.... but, I was into computers. I eventually learned it officially for sure in my technical college as I took Computer Engineering Technology. I can translate from Binary to Hex and back in my sleep. But goibg back to childhood, I remember a friend of the family giving me a book on math tricks/games/puzzles and all keen to show me Binary... but I already knew it.

 

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[mom2att]

I did not learn other base number systems until college, when it was part of a math for elementary teachers sequence I had to take. I found it very confusing, maybe because I was never introduced to it in elementary school which was when the course was suggesting it should be taught. Interestingly, I used a number of different math curricula with my kids through the years but have not encountered this concept in any of them. I do notice that it is listed as one of the last lessons in my younger son's Algebra I book for the upcoming year (Math U See). So I guess I'll be seeing it again!

[Laura Corin]

We had a couple of lessons on different base systems at school (England, 1970s) when I was maybe thirteen?  It was just touched on.

[creekland]

We learned all about it, and like others, did some fun things with it as well as conversions.

 

I don't recall what grade it was - perhaps 7th because we started Algebra in 8th and I think it was before that.  I know I learned enough that I never forgot what it was or how it worked.  I grew up in NY and graduated high school in the mid 80s.

 

I agree that it's a fundamental concept for math, so I wouldn't skip it.  Many kids who are good at math love it.  Many who aren't so good get a better understanding of what the "symbols" are for and how they work.

 

Yes, it is taught in public school sometime before high school.

 

Bases come back into play with logs later on.

[deerforest]

We loved this book from Prufrock about alternative number systems: https://www.amazon.com/Can-You-Count-Greek-Exploring/dp/1593630565/ref=sr_1_1?ie=UTF8&qid=1470656908&sr=8-1&keywords=Count+in+Greek

[UCF612]

I never learned it. I'm 34 and was a public school student.

[Guest]

Base conversions were part of fifth grade rural public school for me, so early 70s. The district had switched to space age math and set theory was in there too. My group had a lot of fun with it, as they didnt shirk on fractions or decimals either.

 

Its not part of the NY core curriculum, so I taught my own children and the other bored kids in their first grade class after they had enough of nim. Imagine you have met an alien, he only has three protrusions on each of what looks like it could be two arms...how would he count? Extend to design your own alien and his counting system.

Edited August 8, 2016 by Heigh Ho

[Guest]

No. Until my son told me, I was not even functionally aware that there are multiple bases.

[Lecka]

Fun fact, there are counting systems based on base 8 where people didn't count their thumbs. There are counting systems for 12 where people count the webbing at the base of their thumb.

 

Did I hear there was a base 20 where people counted fingers and toes? Not sure. Maybe it was just an example.

 

For the thing where there is a row and it shows 10exp0=1, 10exp1=10, and 10exp-1=0.1, I needed that for 11th grade chemistry.

 

We did a ton with that in 11th grade chemistry. There was a lot of converting units and memorizing what word went with each exponent. Like, 10 to the -2 means centi, if that is right (I am not positive). There was a word to memorize like that with every place on the place value chart.

 

That is the highest (and only I guess) chemistry I took, but I think it would be great to be solid on the math part of it ahead of time. I remember the chemistry teacher saying he had talked to the math teacher about covering some of it the year before so we would not be lost in chemistry the next year.

Edited August 8, 2016 by Lecka

[EKS]

We did base 2 in 6th grade.  My impression is that it was just something the teacher added.  I loved it.

 

I loved it so much that my son and I made some base 6 blocks to do Math U See style lessons with.

[Paige]

I remember learning base 5 and base 2 in 5th grade. 

[luuknam]

I have the vaguest memory of rads in geometry, and converting between degrees and rads.

 

I think in rads a rotation was a number besides 360.

 

There are 2pi radians in a circle.

 

I read this book to the kids last year. I thought it was really neat, it mentioned some things I didn't know (more about the history of counting than about different bases, but still):

 

https://www.amazon.com/History-Counting-Denise-Schmandt-Besserat/dp/0688141188/ref=cm_cr_arp_d_product_top?ie=UTF8

 

ETA: to the people who said they made up their own symbols - that's certainly an option, but when e.g. computer programs use base 16, they count 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, 1B, 1C, 1D, 1E, 1F, 20, 21, etc.

Edited August 8, 2016 by luuknam

[daijobu]

Wow, I'm really impressed so many were taught this in school.  I had a pretty decent math education in high school that included lots of competition test prep (AHSME), but was never formally taught different bases.  Except on schoolhouse rock videos which I didn't really get because it went by so fast.  

 

In addition to the pp's reasons, learning base numbering systems is a good idea if you plan to participate in competition math like MathCounts and AMCs as there are a lot of problems that are easy to knock out if you have some familiarity with them.   

[Ravin]

I remember being introduced to the concept while reading a science fiction novel when I was around 10 or 12. I played with the numbers and different bases for a while, because it seemed interesting to me. But I don't think I ever encountered it in school.

[City Mouse]

Yes I remember learning about different number systems while in school I the early 1980's. I don't remember specific years when this was taught.

[Guest]

Ha! I was looking over next week's math lessons and we are set to hit on it this week. I'm like, WTH?!? So, today has been filled with Khan Academy videos and mom doing math on the whiteboard, lol. No, I don't remember ever learning about this, and I never even remember hearing about different base systems until I started hanging out here.

[dirty ethel rackham]

I was a math/computer science major in college and I hadn't heard of it in high school.  I had to learn about it to program in Assembly language my sophomore year.  I had never seen it before until then. At the time, I felt like I was the only one who hadn't seen it, but, then again, I felt like I was the only person who had not built a computer in their basement before I got there.   I could see learning binary conversions as a mental exercise, but no reason for hexadecimal or any other non-utilitarian base conversion unless you were doing some number theory stuff or machine language. 

[daijobu]

I was a math/computer science major in college and I hadn't heard of it in high school.  I had to learn about it to program in Assembly language my sophomore year.  I had never seen it before until then. At the time, I felt like I was the only one who hadn't seen it, but, then again, I felt like I was the only person who had not built a computer in their basement before I got there.   I could see learning binary conversions as a mental exercise, but no reason for hexadecimal or any other non-utilitarian base conversion unless you were doing some number theory stuff or machine language. 

 

 

This is way OT, but I think you bring up a really good point about girls in engineering.  (I'm assuming you're a girl!)  For me, it was wiring up a breadboard.  I felt like I was the only one in my class who hadn't played with a radio shack electronics kit as a kid, like all the men in my class.  I survived that electronics class, barely, but I made sure my own daughters know their way around resistors and jumper wires.  

[Hunter]

I remember being introduced to the concept while reading a science fiction novel when I was around 10 or 12. I played with the numbers and different bases for a while, because it seemed interesting to me. But I don't think I ever encountered it in school.

Me too. A science fiction novel. I was just thinking about that book yesterday. I wish I knew the title.

[calihil]

I didn't know what you were even talking about so I had to look it up. No, I don't remember ever learning about that. I went to public school in the 90s and early 2000s.