Counting Numbers

Our ancestors knew numbers in the form of more or less, to measure the objects or materials they had. This knowledge had led to the concept of “Counting”. Many other civilizations have come up with their way of representing numbers and methods of counting. Of all, the modern method of numbers or the Hindu-Arabic numerals took its stand globally.

Counting is the process of determining the number of elements in a set of objects. Counting will always result in either zero or a positive number. The traditional way of counting consists of continually increasing a counter by a unit for every element of the set.

Types of Counting

• Finger Counting
• One can use fingers to count. This is often used by children to ease counting.

The chart below depicts the representation of fingers corresponding to the number of objects.

Can you read it out loud for yourself?

• Tally Method
• Tally method can also be used to count. In olden days, this method was used by counting sticks, carving lines on wood, bones or walls of the caves. Draw a mark (or line) for each object and then count all of the marks. When counting things over time, this method is useful.

Is this not matching objects to fingers? But once all the fingers were matched people ran out of fingers to map more objects. Hence, they started using the Barter system.

• Barter System
• It is a process of trading the number of objects one owns in exchange for the same number of objects the other person owns.

Let’s see if we can match the number of objects in column A to the same number in column B.

You’ll notice in the table above that, pears are paired with strawberries, apples are paired with bananas, chikoos are paired with cherries, watermelon is paired with pineapple, and mangoes are paired with oranges. This pairing was carried on between similar quantity objects. There you go, it is matching again!

Yet again the problem with this method was as the quantity of objects increased it became difficult to match them and also the value of the objects was not taken into consideration. You cannot exchange pearls for candies just because they are of the same quantity.

So, man thought of creating numbers with values associated with each number. The whole process can be summed up into a poem below.

What is a Number?

A number is a mathematical object used to count, measure and label. Numbers can be represented in language with number words. More universally, individual numbers can be represented by symbols, called numerals.

The representation of numbers in the form 1, 2, 3, 4, … are called numerals. The representation of numbers in words as One, Two, Three, Four, … are called number names (or number words).

Number names are the form of expressing numbers in the word form. The table below shows the list of number names from 1 to 20.

To enhance your skills in counting let us count the number of objects and match with the given numbers. The activity below shows the matching of the objects with its corresponding numbers.

Various Counting Skills

After learning counting, children will get confused about the order of counting. Where to start from? Do we count in the progress manner or in a reverse manner? These are the common questions children get.

• Forward and Backward Counting
• Forward counting is counting by adding one more, every time. The order in which we count numbers starting from 1, 2, 3, 4, 5,… and so on is called forward counting.

Mr. Monkey is sitting on the mango tree as shown below. He is collecting mangoes in the basket for his baby monkey.

Now, Monkey is eager to know the number of mangoes in his basket.

Let us use the forward counting concept to help the monkey to count the number of mangoes. Remember that you are actually adding one to the previous number as you move one step ahead.

Therefore, from the image above, we can conclude that Mr. Monkey has 8 mangoes in his basket.

Do it yourself! Count the number of cubes.

Backward counting is counting by removing one, every time.

Let us consider the same example of Mr. Monkey. When Mr. Monkey is back home; he and his baby monkey share and eat 5 mangoes. How many mangoes is he left with?

Here, we reverse count while taking out the mangoes from the basket. Remember that in backward counting, you count the numbers in the reverse order; you are actually subtracting one from the number to move backward. Mr. Monkey had collected 8 mangoes in total, so in order to share he must start backward counting from number 8.

Mr. Monkey is finally left with only three mangoes. The order in which we count numbers starting from 8, 7, 6, 5, … and so on is called backward counting.

Remember!

1. As you count forward the value of a number increases.
2. As you count backward the value of a number decreases.
3. While counting, the number words are always said in the same order. One, Two, Three, Four,… Not Four, Two, One, Three, ….

Do it yourself! Count the number of tiles.

• Ten Frame
• A ten frame is a rectangular frame divided into ten individual boxes. The boxes are arranged in 2 rows of 5. Numbers up to ten can be shown by adding an object/dot in each box. For example, number 6 can be shown in a ten frame as shown below:

The dots in a ten frame can occupy any of the ten boxes in any configuration.

Children can easily see more than or less than 5.

Why do we need to use a frame of ten
?

Ten frames are wonderful as they provide a visual representation of a number and show its value. They help children to develop a better understanding of numbers than just memorizing their names and order. Children can see the amount of dots that a number stands for using the frame of ten. They can also investigate patterns and groupings within the dots. This helps in building a number sense.

Ten frames help kids with composing and decomposing numbers. It’s also great for teaching addition and subtraction. For instance, children can describe different ways for 7.

Math Facts

1. Counting numbers stimulates your brain cells!
2. There is only one number which has the same number of letters as its value. It’s 4-four.
3. Bees can count. According to researchers, bees can count up to 4. Also, they can learn basic arithmetic.

Mathemagician

Brahmagupta made a remarkable contribution in the field of mathematics and astronomy. Invention of ‘zero’ and its properties made a vital development in the field of mathematics and science.

His contributions are as follows:

• He defined “zero is the number which is obtained when the number is subtracted with itself”.
• He stated “zero divided by any other number is zero”.
• He also stated “zero divided by zero results zero”, but this was proved wrong by the later mathematicians.
• For working with positive and negative numbers, Brahmagupta devised rules such as:

• Adding two negative integers together will always get a negative number.
• Adding two numbers is the same as removing a negative number from a positive number.
• The result of multiplying two negative numbers is the same as multiplying two positive numbers.
• Dividing a positive number by a negative number, or a negative number by a positive number, you get a negative number.
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Know more about other concepts of Number Sense on Number Line, Ordering Numbers, Odd and Even Numbers, Comparing Numbers and Ordinal Numbers

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