Explain that each column on the abacus represents a column of place value. The beads in the upper section are worth five times those in the lower section. Therefore, the right-most column on the lower section expresses ones and the upper section expresses fives. Move over one column to the left. Observe 10s on the bottom and 50s on the top. The next column has 100s and 500s; the numbers progress accordingly. Beads are counted when they are moved toward the center bar and canceled when moved toward the outer frame. Move all lower beads down and upper beads up to start.
Demonstrate how to represent a number with the beads. For instance, move one five bead down and three one beads up to make eight. Show a two-digit number like 23 by moving two 10s and three ones up. Try a number over 50, such as 73, by moving one 50 bead down and two 10s and three ones up. Make a few mystery numbers and ask students to read the number. Put the students in pairs. Let them take turns making mystery numbers and having their partner read them.
Give students several numbers and let them practice representing numbers on the abacus. Pass out a blank abacus worksheet and have students draw the bead configuration for each number.
Write an addition problem on the board and ask students to make the first number on their abaci. Demonstrate how to move additional beads up or down to add the second number. Point out that when both fives are down, they should be traded for a ten by raising the five beads to the upper frame and the one ten bead to the middle frame. The same rule applies to trade fifties for hundreds, or five hundreds for thousands and so on. Give students a practice problem and let them try to solve it while you circulate to check for understanding. Pass out an addition worksheet to give them more practice.
Write a subtraction problem on the board and ask students to represent the first number on their abaci. Demonstrate how to borrow by trading one 10 bead for two five beads or a 100 bead for two 50s. Give students a practice problem. Let them try to solve it while you circulate to check for understanding. Pass out a subtraction worksheet for more practice.