- 6 popsicle sticks
- 2 pipecleaners (each cut into thirds)
- 42 pony beads
- hot glue
Make the abacus as per the sample:
- Glue a popsicle stick on either side of the 6 pieces of pipecleaner at one end (i.e. yellow popsicle sticks) - sandwiching the pipecleners between the sticks.
- Slide 5 beads onto each pipecleaner.
- Glue two more popsicles sticks onto the pipecleaners.
- Slide 2 beads onto each pipecleaner.
- Glue remaining two popsicle sticks onto the other end of the pipecleaners.
About the abacus:
- there are two beads in the upper deck (these are “heaven beads”), then the “beam”, then 5 beads in the lower deck (these are “earth beads”).
- Common abaci have nine rods for a compact abacus, but we only have six for ours.
- When the abacus is set at 0, none of the beads touch the beam. The beads touching the beam are the ones that are counted for the calculations.
- Starting on the right, the first set of beads is the “ones”, the next is the “tens”, then the “hundreds”, then the “thousands”, then “tens of thousands”, and finally “hundreds of thousands”.
- Registering is when you move a bead so that it is part of the calculation. When a bead touches the beam, it is “registered”.
- Some examples:
- one lower bead on the far right rod touches the beam = 1
- one upper bead on the far right rode touches the beam = 5
- both one upper and one lower bead touch the beam on the far right = 5+1 = 6
- one lower bead on the second rod from the right and one upper bead on the right rod = 10+5=15
- Try to make your abacus show these numbers: 4, 16, 123, 8724, 64283, 713952
- Have the Guider make something on the abacus, and have the girls guess what it is.
- Now we are going to try some addition.
- We are going to try 231+213: first register 231. You will have a 2 in column 3, a 3 in column 2 and a 1 in column 1. Now add 2 more beads to column 3, 1 more bead to column 2, and 3 more beads to column 1. What does the abacus register now? (444)
- When numbers need to be carried, it gets more complicated – If you start with 9 (1 upper bead + 4 lower beads) now add 1, this gives us 5 lower beads and 1 upper bead on the beam… but we aren’t supposed to move the bottom bead at all… so, we move all of these beads away from the beam, and move 1 lower bead up on rod 2. This gives us 10. 9+1=10
- If we are adding any number that is going to have to be carried, we actually have to use some subtraction… so, if we are adding, for example, 4+8. We start with 4 beads on the far right. Now we know that we don’t have 8 more beads on that far right column. So we look at the difference between 8 and 10. 8 is 2 less than 10. So we take 2 beads off of the far right, and add 1 bead on to the second column. What we are, in effect, doing is adding 10 and subtracting 2, which is just like adding 8.