Multiplication tables

When I give tutoring classes, I realize that parents find difficulty in helping children who do not attend Montessori schools find a mnemonic way to facilitate the learning of multiplication tables.

I have therefore decided to help by teaching you how things are done in a Montessori class, so that you can do the same at home.

Board with beads 3 x 1

You can start out with a board which gives the most concrete concept and allows manipulation, therefore permitting a sensory absorption of what a multiplication really is.

The board with the multiplication 3 x 2

The material consists in a board with little holes and red beads (about one hundred). The child must learn that doing a multiplication consists in putting the same number of beads a certain number of times (or any other identical object).

Board with beads 7 x 3

So to calculate 3 times 4, you can ask him to place 4 times 3 beads. He must count « 1, 2, 3 », then « 1, 2, 3 », then again « 1, 2, 3 » and one last time « 1, 2, 3 ». He can then absorb the fact that he repeated « 1, 2, 3 » 4 times and he applied the little beads vertically to the board four times. This is essential for the child to integrate the concept.

The board with beads 3 x 5

Then, you can ask him « to count the beads on the board » and you can begin to count «1, 2 and you insist on 3 », then « 4, 5 and you insist on 6 » and so on insisting on the multiple of 3. When you reach 12, you conclude that 3 times 4 equals 12.

Repeat this exercice several times. You can prepare a booklet for each table and ask him to write down the results as he goes along the exercices.

Colored beads’ bars 5 x 5

Another piece of material consists in colored beads’ bars (which we have already used with the addition). In the same way, it will help your child understand that when he is doing a multiplication, he must put together the same colored beads’ bar a certain number of times.

Colored beads’ bars 4 x 7

This way, he will visually integrate the concept of the multiplication table. Repeat the exercices several times. For example, for 5×3, he can take the beads’ bar corresponding to 5 three times or he can put together three bars of 5. Have him count insisting on multiples of 5 : 5, 10 and 15.

Colored beads’ bars 9 x 8

The child will integrate little by little, in a sensitive way, the fact that when he is doing multiplication tables, he is counting multiple by multiple. For example for 6×6, he is counting from 6 to 6 four times : 6, 12, 18, 24. He will then fill out more table booklets and, without learning by heart, he will learn the tables and the nmemotic way to find the result.

Double entry board + tokens

The child will learn by heart thanks to the repetition of the manipulations.

It is of course a good thing that a child learns multiplication tables by heart but it is even better when he understands the reasoning that will allow him to always get back to the result. Indeed, in case of stress or other constraints, the child can easily forget them. He must then always have a way to succeed.

The self correction board

I often met children (especially the gifted ones) who refused to learn multiplication tables by heart. These children must be able to use a simple way to get back to the results. The use of concrete material which allows a sensory teaching is very important and very useful.

This concrete material is also of great help for children who have problems with calculus. They need to manipulate with their hands, to « see » things to learn them.

Questions for games

Another piece of material can be used to deepen these notions and that is the multiplication table with tokens. This table consists in a double entry board with tokens from 1 to 100. The child must place the tokens in the place which corresponds to the result of the number written horizontally multiplied by the number written vertically. It is important to give him the same board with the written results. He can then proceed to self correction. This also helps him with the learning. These boards are very easy to make at home.

Never forget that the playful aspect is very important to a child. In my class, I would play games with children using « material with questions » (for example : 3×4= or 6×7=, etc…). Children would pick ten card games in a box, would recopy them and write down the results. They can also play games together, by writing the result or by finding the token which corresponds to the right answer and self correct themselves with the board on which they find the right answers.

Results of the multiplication tables

The teaching of multiplication tables is essential to prepare children to notions that they will have to face in the resolution of divisions, fractions, etc… I often noticed that a child who does not know his multiplication tables is very penalized.

During car trips, another easy way to learn for the auditive types is to learn multiplication tables through
singing.

It is therefore important to make this learning process fun and solid with a concrete comprehension and a sensory concept begun at the earliest age (a long time before primary classes).

Sylvie Rousseau-d’Esclaibes