MACKINDER BOX: WHAT IT IS FOR, HOW TO MAKE IT AND USES - MATHS - 2024

The Mackinder box is a methodological element with various applications in mathematics. Helps teach basic operations: addition, subtraction, multiplication, and division. It is also used to separate subsets of sets and to subtract cardinals; It is used to decompose and recompose additive structures of numbers.

Basically it is about placing a central large container and 10 smaller containers around it. Within the smaller containers unit quantities are represented, which will later be deposited in a larger container, to represent that a quantity is added, referring to progressive addition or multiplication.

On the contrary, it can also represent that an amount is withdrawn from the larger box, referring to the division.

What is it for?

The Mackinder box is a method that was developed in 1918 in Chelsea, England, by Jessie Mackinder, who was an educator in that city.

This method aims to promote the individualization of education in subjects such as mathematics, reading and writing, using simple but interesting materials such as containers, cards and bags, which are used freely.

This instrument consists of ten containers surrounding a larger central container, all placed on a flat base. These elements are used to do basic mathematical operations, such as adding, subtracting, multiplying, and dividing. It can also be used to separate sets and subsets.

The Mackinder box is used in the early years of education. It facilitates the understanding of mathematics because its methodology is based on the use of didactic materials, giving the freedom for each participant to manipulate or interact directly with the material.

How to do it?

The Mackinder box is made up of very basic elements. To form it, you can even use recycling material or any type of container that serves to place small objects that represent the units that will be counted. Among the most common ways to do it are the following:

With cardboard boxes

The following materials will be needed:

- A rectangular base, which can be made of cardboard (shoe box) or cardboard.

- 10 small cardboard boxes. They can be boxes of matches.

- 1 larger box.

- Glue.

- Tokens, matchsticks, seeds or paper balls that can be used to count.

With plastic containers

The materials to be used are the following:

- A rectangular base, made of cardboard (shoe box) or cardboard.

- 10 plastic containers, make them small.

- A large plastic container; for example, a CD case.

- Glue.

- Tokens, matchsticks, seeds or paper balls, which can be used to count.

Process

- Cut the base in a rectangular shape.

- The largest container (the cardboard box or plastic container) is glued in the center.

- The smaller containers are glued around the large container and allowed to dry.

- The containers can be painted in different colors and left to dry.

- The chips, matchsticks, seeds, paper balls or any item used for counting can remain stored in another container or inside the central container.

Usage examples

With the Mackinder box, basic mathematical operations can be carried out, taking into account that the containers represent groups or sets, while the elements of each of these will be tokens, seeds, paper balls, among others.

Addition or addition

Two small boxes are used to make a sum. In one of these the tiles representing the first addend are placed, and in the other box the tiles of the second addend are placed.

The tiles in the box with the least amount of these are counted and they are placed in the central box; at the end of the chips from the first box, continue with the second.

For example, if in one box you have 5 tiles and in the other 7, you start counting from the one with 5 tiles, placing them in the central box until you reach 5. Then you continue with the tiles from the other box and so on. until reaching 12.

Subtraction or subtraction

To subtract, all the tiles representing the minuend are placed in the central box; that is to say, from the total amount to which another quantity will be subtracted (subtracting).

From that big box, the amount of chips that you want to subtract is taken out, they are counted and placed in one of the small boxes. To find out the result of the subtraction, the number of tiles that were left in the big box is counted.

For example, you have 10 tiles in the central box and you want to subtract 6 tiles. These are removed and placed in one of the small boxes; Then, when counting the pieces that were left in the big box, there are 4 pieces in total that represent the result of the subtraction.

Multiplication

Multiplication consists of adding the same number several times. With the Mackinder box, the first number of the multiplication represents the groups that will be formed; that is, the number of small boxes to be occupied.

Instead, the second number indicates the number of items each group will have, or the tokens that are to be placed in each small box. Then all the tiles in each small box are counted and placed in the central box, to obtain the result of the multiplication.

For example, to multiply 4 x 3, 3 tiles are placed in 4 small boxes; then they begin to count the chips in the first box, placing them in the big box; this is repeated with the 3 boxes. In the central box you will have: 3 + 3 + 3 + 3 = 12 chips.

Division

Division is about dividing a number of elements equally. For example, to divide 16 chips into 4 small boxes, they are placed in the central box, and they are distributed into small boxes in such a way that the same amount of chips remains in each box.

At the end, the number of chips in each box is counted to determine the result; in this case, each one will have 4 tiles.

References

1. Alicia Cofré, LT (1995). How to Develop Mathematical Logical Reasoning.
2. Carolina Espinosa, CC (2012). Resources in learning operations.
3. (1977). General didactics. Tupac.
4. Mackinder, JM (1922). Individual work in infants' schools.
5. María E. Calla, MC (2011). Learning logical math skills in girls and boys. Lima: Educa.