Woohoo!! abacuses! Or abaci. I'll go with abacuses although in real life I just avoid referring to them in the plural... which is difficult when you have such a collection....
This one is just a counting frame, ten beads per rod. I made it out of foamcore board (check the art supply store and make sure your xacto knife is good and sharp!) and if I could find the picture of it half-made, you could see that the wires serving as rods are wound around popsicle sticks inside two layers of foamcore. The sticks are jammed into carved-out hollows in the foamcore and then all taped together. It's definitely of the "jerry-rigged" school of arts and crafts, but at the time I had a little one who was this close to grasping place value and why a one in the tens place was different from a one in the ones place and I used what I had.This abacus is perfect for that one lesson (and fine for several others I'm sure, but just exactly right for this one!) Start with a number, say seven, and slide over seven beads on one rod. Then count up... eight, nine, ten as you slide over each bead to match. When you get to ten, you have one rod full, and no spare beads. That's 10 -- the one and the zero. You can count up to fifty and point it out all the way up, and then you can work with adding and subtracting across a full ten -- like 8 plus 6, 11 minus 3, 5 plus 6, etc. Try counting up if it's confusing for the kid, but then try asking "how many beads do you need to make a full ten? and how many more than that are you adding? (or subtracting?) So 8 plus 6 can be thought of as 8 plus 2, plus 4. And 11 minus 3 is 11 minus 1, minus 2. Play with it, give each other problems to solve, and try thinking in terms of getting to ten, backwards and forwards.
Next! This one was just for fun...
We were studying Ancient Egypt and their counting system, and just couldn't resist. This one we had a little more time on, and help, since the aforementioned child was not in desperate need of any mathematical illustrations and was old enough to be a bit handy. We used a cheap picture frame from the craft store, flexible beading wire from the bead store (everyone has a bead store, don't they? Well try the internet - the type of wire is really not terribly important, but I like the flexible stuff, and with crimping beads it holds up to use rather well.) The beads are made of Sculpey clay. This part was my job -- he may have been handy, but sixty identical blocks of clay was still a bit over his head, not to mention the risk to little fingers trying to make bamboo-skewer holes. I made the blocks, we baked them as directed on the Sculpey package, and then drew the various hieroglyphic symbols for the numbers -- 1, 10, 100, 1000, 10000 and 100000. When you get to a million the number symbol is a scribe throwing his hands in the air. I'm not making this up! We accidentally strung the beads upside down, so you read it from the bottom, so in this picture it's showing 103,264. If I were to do it again, I'd only make nine beads per rod, since you never really need the tenth.
This one is my favorite, and the one we actually use on a regular basis. It's our grocery store abacus. This abacus is modeled on the Japanese soroban, which is different from the counting frame in that the beads don't all have the same values. Below the reckoning bar (in this case a pipe cleaner...) the beads are 1s in whatever place they are (1s, 10s, 100s, etc.) Above the reckoning bar they're 5s (5s, 50s, 500s, etc.) For the grocery store, we use the darker bead rods (those two on the right) for "cents" -- that is, ten cents and one cents. Then the lighter bead rods (three rods on the left) are dollars (100s, 10s and 1s, reading from left to right) So if you were to write an amount, say $142.68, it would read exactly the same way on the abacus. This is true of the regular soroban too, but the type of soroban one usually buys is not made with pipe cleaners. Of coures the type of soroban one usually buys is made with a nice flat non-moving desk in mind. Not a grocery cart. The pipe cleaners keep the beads from clearing every time you turn a corner, and are therefore much less frustrating if you're a kid in a grocery cart, assigned to add up the bill for your mom. Why the hundreds place? Well we used to have a membership at Costco...One thing you figure out with a soroban-type abacus (by the way, if you want to make one for the grocery store, the frame in this case is a piece of mat board. If you don't have a mat cutter, you can get them done at a framing shop, or maybe even pick one up cheap from their mistakes bin) is that now you've moved up from "how do you get to ten" when you add and subtract, to "how do you get to five?" Subtle difference, but one of the things I really adore about this type of abacus. It's efficient in its use of beads, matches rather well with our own monetary system (pennies and nickels, $1 bills and $5 bills, dimes and... okay we don't use a fifty cent piece much anymore but the idea is still good!), matches even better with the Roman numerals that you learned in elementary school and still don't know why they matter... but wait! there's more! Look at your hands! Four fingers and a thumb? Ringing any bells here?
Your fingers are the ones and your thumbs are the fives. So each hand is like a rod of an abacus, and you can count up to 99 before you run out of fingers to count on. Check out Fingermath by Edwin Lieberthal for details, or google "Chisenbop" which is apparently a Korean word meaning "finger counting."
Got a couple more here....
This one isn't an abacus in the traditional sense, but it bears some similarity. It's actually a string of 1000 beads. What's it for? Counting to 1000. Is this a trick question? Okay we made it when DS was just catching on to the whole pattern of numbers, where 20-29 is followed by 30-39 and 40-49... and where after 100 you just start back with (a hundred and) 1 and go back through the whole sequence again... Once you've figured that out you can pretty much count to anything! So he did. It takes a long time to count to 1000, so we had those cards -- they're actually someone's discarded business cards -- on which he wrote the number he left off at, so he could pick up again later and finish. You'll note that it took five sittings to finish... The string is elastic bead cord and the beads are cheap plastic faceted things (if you need 1000 of something you're not likely to be going for the $5-each art glass... or at least I'm not.) I bought two boxes of multicolored beads and one box of red, and I only used reds for every 10th bead, so it was easy to keep track. I figured there couldn't be anything more depressing than counting to 999 and realizing that one had been off by one bead somewhere back there. This was what, five years ago? I still find extra red beads around the house. You've been warned.
Oh look! It's the rest of the red beads! You know they come in a box of like 700, and if I got two boxes of multicolored and one of red, I could only really have used 100 red beads in that whole 1000-bead project, which means 600 beads left over! So this was just a little thing we did. It's really as far from "abacus" as I can get without making a new post... but here's the deal: these are base ten rods. Each wire holds ten beads (to show the very-important "set of ten") and then there are some spare ones to use for the ones place. This is great for a couple things... first off, place value (which we used the first abacus all the way up there for) -- same general idea. Second, adding with carrying and subtracting with borrowing.. you can set up a number -- like what's shown in the picture is 38 (3 rods, 8 units) and add 24 (2 rods, 4 units) and show that now you have more than 10 units for your ones place -- you have something like "fifty-twelve". Ten unit beads from that twelve can be traded in for a nice neat rod, to make your fifty-twelve into sixty-two. And for subtracting, take your 62 and subtract 8. How do you get eight units out? trade the nice neat rod for ten individual unit beads (fifty-twelve again!) and then take out the eight.If you're beyond the adding and subtracting stage, the other thing I absolutely couldn't have taught without these is long division. But that's more complicated... so I'll give it its own post instead of hijacking my own abacus soapbox for the purpose.
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