Abacus Monochrome
Abacus
This is a virtual abacus. An abacus is a physical calculating device made out of wood, wires, and sliding beads. It was first developed in ancient China. It gives a physical representation of a number in base 10. Before the advent of electronic calculators, an abacus was used effectively to help quickly perform many arithmetical computations. Today an abacus can help develop number sense.
Each vertical wire has two sections of beads. Each bead in the top section represents 5 of the beads in the bottom section. A bead is considered part of the represented number if it is slid to the middle bar, (i.e. the beads in the top section must slid down to count and the beads in the bottom section must be slid up to count). One only really needs one bead in the top section and four beads in the bottom section to represent all natural numbers. Like many physical abacus this one has one extra bead in each top section and one extra bead in each bottom section. This allows one to use the abacus making intermediate steps with more beads than necessary.
For example, one can add 24 + 78. Start by first setting up the abacus for 24 by sliding 4 beads on the bottom section of the rightmost wire up to the middle and 2 beads from the next section up to the middle bar. Next we want to add 78. 8 = 5 + 3. We start by sliding an additional 3 beads up on the units place. However, there is only 1 bead left to slid up we slide it up making 5 beads up. We then slide all 5 of these beads down and replace it by sliding the other 5 bead down. We then slid up the additional 2 beads up. We slide up the two 5 beads and replace it by sliding a 1 bead up for the next place value. Next we slide one 5 bead back down. At this point we should see that 24 + 8 = 32. Now we need to add the 7 = 5 + 2 to the ten's place. Adding the 2 beads to the lower section ends up with all 5 beads up. Slide them down and replace by sliding down a 5 valued bead in the top. Add the other 5 tens to see that both 5 beads are down. Slide them back up and replace with sliding 1 bead up in the lower section of the 100's place. Ultimately, we see that 24 + 78 = 102.
Notice how 5 beads in the lower section can be replaced by 1 bead in the upper section when adding, or one bead in the upper section can be replaced by 5 beads in the lower section when subtracting. Similarly, 2 beads in the upper section can be exchanged with 1 bead in the lower section of the next higher place value.
In the applet above, use the move tool to select a bead and slide it up or down as needed. In some cases, this will move other beads. Just click on them and move them back as needed.
Clicking on the checkbox will introduce a decimal point that can be placed where you want it along the abacus. In this way we can use the abacus to perform and illustrate decimal arithmetic as well.