## How subtractions with carry on should be taught

In a previous article, I showed you how to teach the subtraction to very young children. We were using the units.

Today, we will learn how to teach your child the subtraction with carry over. In traditional schools, children are never taught in a correct way and it is important that your child properly understands the reasoning.

Let us study the example: 42 – 17 =

At the Lycée International Montessori – Ecole Athéna, we use golden pearls and a rug with 4 columns: one column for the units, one for the tens, one for the hundreds and one for the thousands.

• Take 2 units and place them on the rug at the top of the unit column,
• Take 4 tens and place them in the ten column on the same line of the units.

Exchange a dozen

When doing a subtraction, we know that we are taking away, withdrawing.

We have 2 units and want to take 7 away. How can we do that?

Exchange one dozen for 10 units

The only solution is to take one ten among the 4 tens set on the rug and exchange it for 10 units which you will place in the unit column. We therefore have 12 units and can take away 7. We are left with 5 units.

Take away the units

Then, we have 3 tens and take away 1 ten. We are left with 2 tens.

Take away the dozens

The result of the subtraction, called the difference equals to 25.

Let us study a more complicated example: 3 102 – 1 845 =

We set the operation

Place 2 units, then 1 hundred, and 3 thousands.

We want to take 5 units away but only have 2 on the rug. How can we manage?

Exchange the hundred with ten dozens

Exchange one dozen with ten units

Exchange the hundred for 10 tens, then one ten for 10 units.

We then have 12 units. We can therefore take 5 away and are left with 7.

We are left with 9 tens to which we withdraw 4 and are left with 5.

Take away the units

Take away the dozens

We are left without a hundred to which we want to withdraw 8. How can we do that?

The only solution is to take a thousand and exchange it for 10 hundreds.

We end up with 10 hundreds to which we withdraw 8. We are left with 2.

Take away the hundreds

Take away the thousands

We now have 2 thousands, and withdraw 1. We are left with 1.

The result of the subtraction equals to 1 257.

After the golden pearls, and once that the child has understood that in one ten, there are 10 units, and that in one hundred there are 10 tens, that in one thousand, there are 10 hundreds, you can use the stamp material which is easy to make at home.

To teach the abstract phase, the operation should be written as above.

Sylvie d’Esclaibes