As a follow up to my article on the Montessori board , used to teach mathematic notions, I will now show you how to do additions and subtractions.
The simple addition:
Let us study the example: 6 523 + 3 1 34
On the top right hand side of the board (see photo), set the first numbers of this addition vertically: write 6 523 starting off by the units, the tens and so on…
Under the first number, leaving a few empty holes between the two, place the number 3 134 (starting off with the units).
Remember that when doing an addition, you are “putting things together” and calculating a sum.
Now, take the nails from the first number (6 523) making sure you follow the sequence units-tens-hundreds-thousands and place them vertically with the digits of 3 134.
Count the result: 7 units, 5 tens, 6 hundreds and 9 thousands.
Now place the nails corresponding to the result in a horizontal line and read out the number: nine thousand five hundred and fifty seven. So the sum of six thousand five hundred twenty three and three thousand one hundred thirty four gives a total of nine thousand five hundred and fifty seven.
Addition with “carry over”: :
Let us study the example: 4 654 + 4 578 =
Like the example above, place the first number 4 654 on the top left hand side of the board starting off by the units.
Then, just under the first number, place the second number of the addition: 4 578.
Then: “adding means putting everything together”, so round up the units, the tens, the hundreds and the thousands.
Then count the units and get to 12. Ask the child “can 12 units be replaced by something else?”. He should answer: “12 can be replaced by 1 ten and 2 units“. Exchange the 12 units for 1 ten and 2 units (one blue nail and two green nails). Place the nail corresponding to the tens with the other tens and leave the two units in their place.
Then count the tens and get to 13 that you will exchange for one hundred (red nail) and three tens (3 blue nails). Place the tens under the other tens and leave the three blue nails in their place.
Then count the hundreds. You will find 12 hundreds (red nails)that you will replace by one thousand (one green nail) and 2 hundreds (2 red nails).
Place the green nail of the thousands with the other thousands and leave the 2 hundreds in their place.
Then put all the units together and count them. You will find 9.
Then place the result in a horizontal line at the bottom of the board starting off by the units: 2 units, 3 tens, 2 hundreds, and 9 thousands.
Conclude by saying: the sum of four thousand six hundred fifty four and four thousand five hundred seventy eight is nine thousand two hundred thirty two.
To solve additions, your child must know that 10 units can be changed into 1 ten, that 10 tens can be changed into 1 hundred, and that 10 hundreds can be changed into one thousand. If your child does not remember this notion, have him play games. Give him 14 green nails and ask him with what he can exchange them (one blue nail and four green nails for example).
The simple subtraction:
Let us study the example: 7 825 – 2 513 =
Place the first number of the subtraction vertically at the top left hand side of the board starting off by the units.
Then withdraw 1 ten, 5 hundreds, and then 2 thousands.
The result is what is left: 2 units, 2 tens, 3 hundreds, and 5 thousands.
Place the nails corresponding to the result horizontally at the bottom of the board and say: “the difference between seven thousand eight hundred thirty five and two thousand five hundred thirteen is five hundred three thousand twenty two”.
Subtraction with carry over:
Let us study: 7 732 – 4 365 =
Place the first number as for the example above. Then, start withdrawing the units, which means taking away 2 units and not having any more at disposition. “Then what?”, “you can change one ten into 10 units”, which means “one blue nail with 10 green nails”.
You therefore withdraw one blue nail and add ten green nails to the units.
Then take away the three remaining units.
You are left with seven units.
Then go on to the tens: withdraw 6 tens. Take away one, two, three, and you are left with no more. “What now?” “you can change one hundred with 10 tens so one red nail for 10 blue nails”.
Make the exchange, take away one red nail and take out 10 blue nals that you place with the tens.
Take away four, five, six.
Then, go on to the hundreds, and take away three hundreds, or three red nails which is now possible.
And on to the thousands: take away 4 thousand or four green nails.
The result of the subtraction is now on the board: 7 units, 6 tens, 3 hundreds, 3 thousand. Place these nails horizontally at the bottom of the board and read out the result: “the difference between seven thousand seven hundred thirty two and four thousand three hundred sixty five is three thousand three hundred sixty seven”.
To complete this last subtraction, your child must be familiar with the possible exchanges between the units, the tens, the hundreds and the thousands.
In my next article, we will study the multiplication, with one or more numbers with the help of the Montessori board.