Did you read the blog on addition and subtraction facts? Let’s continue this thought with 4-digit addition, using the Cotter Abacus. This approach and process helps child understand how and why the traditional addition algorithm works.
Start by writing the equation of 4817 + 2639 in a vertical format.
Turn the abacus to side 2, with 1000, 100, 10, 1 on the top. Clear the abacus by having all the beads at the bottom as shown. Each bead now represents the denomination of the column it is in. In other words, 4 beads in the hundreds column represents 400 and 7 beads in the tens column represents 70.
Enter the first quantity, 4817, on side 2 of the abacus. It is important to keep the beads on the two wires as even as possible to make trading easier.
We will start adding with the ones. Add 9 ones on the abacus.
Do we need to trade? Yes, there are more than 9 beads in the ones column. Trade 10 beads in the ones column for 1 bead in the tens column.
After the trade, we have 6 in the ones column. Write a 6 in the ones place. Did anything else change? Yes, we added another bead in the tens column. Show that change by writing a little 1 right above the other tens in the equation.
Because we want to align the abacus to the paper and pencil format, it is vitally important to record the sum and any carry after each step.
Next, we will add the 3 tens.
How many tens do we have now? We have 5 beads, or 5 tens. Do we need to trade? No, as there are less than 9 in the tens column. Write the 5 tens as shown above.
Continue by adding the 6 hundreds.
Do we need to trade? Yes, we do. Trade 10 hundreds for 1 thousand.
Once the trade is made, what do we have now? We have 4 in the hundreds column. Write a 4 in the hundreds place. Did anything else change? Yes, we added another thousand. Record it with the other thousands.
Add the 2 thousands and record.
The final sum of 4817 + 2639 is 7456.
Advanced Bead Trading Game
This game will help the child practice the process of adding on the Cotter Abacus and on paper. For this game, use place value cards less than 4000: 1000 through 3000, 100 through 900, 10 through 90, and 1 through 9. Here is a download with the place value cards. Using these listed place-value cards, the player creates 3-digit and 4-digit numbers and lays them out.
Choose two of the numbers and write them in a vertical format. The player then enters the first number on the abacus and proceeds to add the second number, recording each step as it happens.
Once the sum is found and recorded, choose a third number from the place-value cards, write it below the sum, then add it to the amount on the abacus. Remember to record each step.
Continue until all the place-value numbers have been added. The final sum will be 10,995.
Play the game a second time, creating different numbers with the place-value cards. People are often amazed that the final sum will be 10,995 again.