SIMPLE MATH ON THE ABACUS COUNTING MULTIPLICATION ADDITION
SIMPLE MATH ON THE ABACUS COUNTING MULTIPLICATION ADDITION SUBTRACTION
COUNTING ON THE PYTHAGOREAN ABACUS It is always helpful to use a story or image sequences to direct solution processes when teaching math. For the process of counting, the work of gnomes mining and stacking stones from a mountain may be used.
In the top figure one gnome sits on a resting stone. Push the leftmost bead against the left post.
Now the gnome, hard at work, brought out a stone and placed it on the ground. The next white bead has one brown bead above it.
Then two gnomes followed and one placed his stone on the ground beside the first, and the other placed his stone above and between the two on the ground. And so the hard working gnomes continued from 1 to 9.
SIMPLE ADDITION A little gnome wanted to be king, So he built a rocky tower thing. ? =2+4
He climbed part-way up doing his best. ? =2+4
Then the next day he climbed the rest. ? =2+4
NOTE SYMBOL IN GRAPH 6=2+4
SIMPLE SUBTRACTION The little gnome started down, But could not reach the ground. ? =6 -?
(count from right 4 beads) He had climbed to the topmost stone, ? =6 -4
But now from the bottom some were gone. NOTE SYMBOL IN GRAPH 2=6 -4
6=1+5 6=2+4 To explore the addition and 6 = 3 + 3 subtraction facts, students 6=4+2 can solve problems by 6=5+1 drawing pictures of the solutions. These solution can 6 = 6 + 0 be derived from the images 6 = 7 -1 that motivated exploration 6=8 -2 on the abacus. 6=9 -3 6 = 10 - 4
A hardworking little gnome Everyday went mining stones. MULTIPLICATION The image sequence of a gnome putting stones from tunnels into a cart may be used for multiplication. The gnome takes three stones from each tunnel and puts them in columns in his cart.
First he dug deep, deep holes Down to where the crystals grow 4 × ? The abacus shows a triangle with a three-beads base, pushed to the right. × 3 = ?
Then carefully from each He gathered all the stones He could reach. 4 × 3 The gnome fills his cart with four columns. On the abacus an adjacent triangle with four beads in it’s base is pushed to the right, displacing a rectangle above it. × 3 = ?
NOTE SYMBOL CART MAKES 4 × 3 = 12 Pushing this triangle back to the left leaves the rectangle above it in the middle of the two. The rectangle includes a total number of beads equal to the stones the gnome placed in this cart. 4 × 3
1 X 3 To explore the multiplication facts students can solve problems by drawing pictures of the solutions. These solutions are derived from the tunnel mining images that motivated exploration on the abacus. 2 X 3 3 X 3 4 X 3 5 X 3 6 X 3 7 X 3
- Slides: 18