Two years ago you could not have convinced me that a little six-year-old girl could easily and enjoyably add a column of nine addends with four digits each.
Now I know I was wrong.
This is a very simple material, and today I’m going to show you exactly how it is used. I’m also going to share this printable version that I made, so that you can make your own board. And this isn’t just for those who follow the Montessori method; any teacher can use this.
In the sequence of Montessori materials, this one comes after working on addition with the golden beads and the stamp game. Once a child feels comfortable with sums with the stamp game, this material can be introduced. You can see Miss Adventuress working with the stamp game in this post.
You can purchase this material from a company like Kid Advance. If you buy it, it looks like this:
You’ll notice one difference between this board and the one I use, which I made myself (and I’m sharing with you at the end of this post!): On the board, there is a blank column to the right where the equation is written. I added a column with squares, like graph paper, to help my daughter keep the numbers aligned. You can choose to use it if you wish. If the child has done extensive work with the stamp game first, they will probably not need the graph paper column.
Now, let’s get to work!
First, the child writes nine addends in a column. Each addend should have four digits. The child invents his or her own addends. Do not give them a problem you made that they must solve! They will be more engaged with their own equation. And there is one thing you must know about this material from the beginning: the purpose of this material is NOT to get the correct answer. It is to better understand the process of carrying, and how it will work in the algorithm. Being sure to always have the correct answer comes later.
The child begins with the first addend in the column; 1372 in this case. She puts one dot for each unit in the units column. As you can see, there are two dots in the units column, for the two units (or ones) in 1372.
She adds a dot for each ten of 1372, or 7 dots, to the tens column. We always start at the top-left square in each column, working left to right, and then top to bottom.
Ahora ha añadido manchitas para las 3 centenas y 1 unidad de millares a las columnas adecuadas.
Now she’s added dots for 3 hundreds and 1 units of thousands to the corresponding columns.
Here’s how it looks after adding the dots for the second addend, 2648.
Ahora se han añadido las manchitas del tercer sumando, 1903.
And this is how the column of addends looks at this point. After putting all of the dots for one addend on the board, we put a checkmark to the right of the number to keep our place.
This is how it looks after putting all of the dots for six addends on the board…
And now we have all of our dots for all nine addends! And we can appreciate why we don’t focus on having an exact answer with this material; if the child misses one little dot, it will turn out incorrect…and no one is going to want to repeat all of that work for the same problem over again! So we work on understanding the process of addition and carrying with this material, and for that purpose, it works wonderfully. Let’s add already!
We begin with units, as always when we are adding. We count ten dots, and cross them out with one line. Don’t tell the child, so she can discover it on her own, that in each row fit ten dots. She will discover it on her own very soon!
Right after crossing out ten dots (with the black marker), we put a red dot in the same column, at the bottom, in the top left of that box.
We continue crossing out groups of ten, and putting a red dot for each group.
Now we can’t cross out another group of ten; we only have four dots left. We write a 4 in the last box in the units column.
We look at the red dots. We recognize that each one represents ten black dots…in other words, a ten. So those dots actually belong in the tens column! We count the red dots and see that we have three. We write three in the tens column, just to the left of the line that separates the columns.
And we add three red dots to the tens column dots.
And we repeat the process with the tens: cross out groups of ten dots and put red dots below, and write the number of black dots that are left (7 in this case)…
Then counting the red dots and writing that number(4) to the left of the line, in the hundreds column; adding that number of red dots to the hundreds dots; counting the hundreds dots and crossing out groups of ten, putting a red dot below for each group…
Counting the hundreds dots that are left (2) and writing that number at the bottom of the column…
Contando las manchitas rojas de la columna de centenas que hay que mover a la columna de unidades de millares (4), escribiendo el número, añadiendo las manchitas…
Counting the red dots in the hundreds column that need to be moved to the units of millions column (4), writing the number, adding the dots…
Crossing through groups of ten, putting a red dot for each one below, counting the units of thousands dots that are left, and writing that number at the bottom of the column (|)…
And finally counting the red dots and moving them to the ten thousands column. The child will see that she cannot make any groups of ten, and will put the number of remaining dots (4) at the bottom of the column.
We’ve finished our addition!
Now we write the sum in the column. With the red marker we add the period (Latin American style) or the comma (American style).
And we’ve finished our work! Well, with Montessori we haven’t finished our work until we’ve put the material away, ready for the next student to use it. But the addition is complete. Sometimes the child will want to write the equation in her notebook, but this is not required. Doing the addition and absorbing the process is enough for now. We prefer that she use her energy in adding, instead of on writing the work down, with this material.
Ready to try it yourself? You can download your own copy of these sheets! I’m sharing them below. Just click on the images. Enjoy!
And if you want the full Montessori presentation, or if you’re interested in following the AMI Montessori method completely, you’re going to need the albums, which describe how to use each material, and how and when to present them to the child. I recommend Jessica’s albums, from Keys of the Universe, both for Primary (age 3-6) and Elementary (ages 6-12). They follow AMI Montessori, and she is always available to answer questions.
Esta entrada también está disponible en: Spanish