Long Division with Test Tubes

Math, 5+

Impressive material huh? The Montessori Long Division material has always fascinated me. If you are not familiar with the process, let me show you how it makes long division accessible, for children as young as 5.

The Long Division beads, a.k.a. Test Tubes, are an excellent material to reinforce the process of division, and understand exchanges. There are 10 tenths in one hundred, 10 hundreds in one thousand, etc… And it’s ok to exchange beads to break the numbers down, and continue distributing them equally until the very end, at the unit level.

To start, the child is given an equation. 4 digit dividend (9,764) divided by a one digit divisor (4). We start with a one digit divisor, which will only require one green board. This work can usually be performed in a group of 2 or 3 children when using a greater divisor with 3 or 4 digits, such as 463 or 8532.

The child will build the dividend by putting beads in their respective cups. The color coding is very important. Green for units, blue for tenths, red for hundreds, and green again, for “units” of thousands. Montessori-educated children are more than familiar with that.

Once the beads distributed, the skittles are placed on the top of the board. They represent the divisor, 4.

Now we are ready to distribute beads, starting from the thousands cup. Why? Because it will show the child to exchange 1 thousands for 10 hundreds, and keep having more beads to keep distributing equally among the skittles.

For this equation, we had one extra thousand bead (9,000 to distribute to 4 skittles, each gets 2, you have 1 green bead left). So we exchange that 1 thousand for 10 hundreds. We marked our result for the quotient by writing “2,” above the line, then we distributed the 10 hundreds, and the 7 hundreds located in the cup. That’s 17 hundreds to distribute. We could already tell that only 16 beads could be distributed equally among 4 skittles. Therefore, one extra hundred bead would have to be broken down to 10 tenths, and distributed with the 6 tenths in the cup. You get the idea?

We keep on going from left to right, from thousands to units, until we have almost none less. Whatever is left at the unit level is called the remainder, which we can mark on paper.

In Montessori, we care about the process more than the product. Of course, we will encourage and expect that the child challenges himself to more accuracy in the future, but we always celebrate the process.

This was my son’s first long division. His joy at the end was priceless. I didn’t check if it was accurate, because I was by his side, and he followed the process well. I realized he understood in advance if there was going to be extra beads to exchange. During this process, I know he used all processes. When pouring beads in cups, he’d keep 3 and pour 7 knowing that each tube contains 10 beads. He subtracted when writing down what was used and what was left. He unconsciously used multiplication when he saw the arrays (I have 4 skittles and only 16 beads will fit). This is also why it’s wonderful to use different materials to use all 4 processes, on long multiplications and divisions.

I hope you enjoyed this post, as it always looks more complicated than it is. 🙂 It is a lot of fun, and helps children build self-esteem and confidence.

Ready for a lesson?