Have you ever wondered why children find it so difficult to understand mathematical language based on numbers, symbols and definitions?

To answer this question it is necessary to differentiate between two types of thinking:

– **Concrete thinking** , which is based on particular phenomena and allows us to describe tangible facts and objects, that is, they are “real.”

– **Abstract thinking** , which allows us to think about elements that are not in front of us at that moment and reflect on the causes or principles of certain phenomena

Well, during childhood abstract thinking is not yet fully developed and, for this reason, children need to start from a reality that they can see and touch.

For example, it is not the same to tell a child “five” and have him not have any image in his head of what it means, than to say “five” and he can mentally evoke a geometric representation of that quantity that he has previously constructed. the same.

Numbers and arithmetic operations are one of the biggest headaches for children, parents and teachers during Early Childhood and Primary education. But, did you know that there is a very simple material that allows children to visualize and understand numbers and the operations performed with them?

In case you don’t know it yet, I present it to you below.

## Counters and counter trays

As you can see in the image, this material is only made up of two elements: the counters and the counter trays.

### Accountants

They are chips similar to those of *Parcheesi* , but in two colors, one for each side.

In the photograph you can see the ones we have in our online store, which are red and blue.

If you don’t have meters, it is not necessary to buy them. *You can use ludo* tiles , polycubes, or any other small item you have on hand in two colors.

You can even easily make your own counters, with two-color cardboard or with those adhesive felt protectors they sell for furniture legs. You simply have to stick a protector of one color with a protector of another color, joining their adhesive sides.

### Counter Trays

Perhaps you have never heard of **trays for counters** or *ten-frames* (“ten-frames” in English), since it is a material little used in Spain. However, in other European countries its use is widespread.

A counter tray is a rectangular array of 2 x 5 squares.

Optionally, you can have 5-square trays (1 x 5 square matrix) which are especially useful with younger children. Two trays of 5 squares make a tray of 10.

At the end of this article you can download the free templates for the trays for 5 and 10 counters ready to print and start working.

These arrays can be “filled” with counters to create geometric patterns representing different quantities.

In this way, as I said at the beginning of the article, children have an image that they can associate with each quantity. For them it is no longer an abstract concept but a real element.

Furthermore, having two-color counters allows two quantities to be represented simultaneously on the same tray: one quantity will be represented by the blue counters and the other by the red counters.

## Benefits of using patterns with counters

The use of counters and trays is not a new idea.

In many countries they have been used for years and are considered a very useful tool for learning mathematics in Early Childhood and Primary education. There are a large number of books and articles that support its use and that offer teaching guidelines to teachers.

The creation of geometric patterns associated with numerical patterns directly affects two fundamental aspects: **subitization** and **numerical sense** .

### The subitization

A strange word, right?

It refers to the ability to perceive at a glance the number of elements in a set without counting them one by one. You could say that it is the ability to “count without counting.”

I’m going to give you an example so you understand exactly what I mean.

Look at the following image. Can you say, without counting, how many points there are?

Now count them.

How are you? Have you obtained the same result?

Humans, like other animal species (such as crows, laboratory rats or chimpanzees), are able to accurately identify small quantities simply by taking a glance. Maximum 4 or 5 elements. For larger quantities, we need to count them one by one. And, of course, the more elements there are, the more time we need to do it.

Now, what happens if the points in the previous image are arranged in a certain pattern? Like dominoes, for example.

Even if you are not a big fan of this classic board game, it is probably now much easier for you to identify the number of points there are. And, in our minds, we have associated this pattern with a *double **four* , that is, 4 + 4 points.

The same thing happens with counter trays: children associate each visual pattern with a quantity. In addition, on a counter tray there are two reference numbers that make work easier:

– 5, which corresponds to a full row

– 10, which corresponds to the entire tray full

From these two reference numbers, children end up internalizing that:

– a full row minus one counter represents the number 4

– a full row and a counter, the number 6

– a full row and two counters, the number 7

– a full tray minus two counters, the number 8

And so on, without having to count the counters one by one.

### The number sense

You probably already know what number sense is and why it is so important.

With this term we refer to a set of skills that allow us to understand numbers and operations and use them in different contexts to solve specific problems.

These skills are:

– counting and understanding quantities

– numerical relationships

– numerical composition and decomposition

– understanding place value

– introduction to addition, subtraction, multiplication, division and even fractions

– etc.

## What activities can you do with trays and counters

Now that you know about trays and counters, you may be wondering what you can do with this material, beyond representing quantities and creating geometric patterns.

Well, here are some ideas:

– Compare and order quantities

– Build the numerical sequence

– Decompose a number into two addends

– Introduce the concept of ten and the positional value of figures

– Introduce the operations of addition, subtraction, multiplication and division

– Build square numbers and triangular numbers

– Introduce the concepts of fraction, decimal number and percentage

As you can see, it is a material that offers many possibilities. Your children or students will surely love it! Do you dare to work with patterns, counters and trays?

## Numbers and Operations with Patterns Course

If you want to delve deeper into the use of counters and counter trays and learn how the decimal system, operations, fractions, decimal numbers, percentages can help you work with your children or students… here I leave you. information about my online course “Numbers and Pattern Operations”.

In it you will find 38 activities ready to do at home or in your class, with detailed explanations, video tutorials and templates to download