Counting is the process of finding the number of things in a group of things. We use the method of counting to find the total amount of money in our piggy bank. We use counting to get an idea of the number of books we read in a month. And we use counting also to find the number of chocolates we have without our parents noticing it. Counting is used almost everywhere. While learning to count, we can count with the help of our fingers. Once we are more comfortable with the process of counting, we can count with numbers in our minds.
We count things to get an idea of their quantity. Humans learned to count for survival. Tens of thousands of years ago, human beings mostly hunted and gathered their food. So, people started counting the number of animals they hunted or the number of fruits and vegetables they collected in order to determine whether they could feed their families. As people settled down and built empires and countries, we found many new applications for counting.
There are too many numbers in the number system. We can keep counting as long as we want. Let’s start taking baby steps by learning to count up to 120. First, let’s start with the basic idea of numbers. We need to learn about digits before we start counting.
Observe the number 120. The number is made up of 1, 2, and 0. These numerals, which are part of a number, are known as digits. All numbers are made up of one or more digits. The number of digits in a number increases as the number gets bigger. (counting of numbers using place values)
First, let’s start by counting numbers that have only one digit. These numbers are known as single-digit numbers.
The two-digit numbers are:
The three-digit numbers up to 120 are:
We can count up to 120 in multiple ways. We can count by including all the numbers, or we can count by skipping numbers, following a specific pattern.
When we count using the “count by ones” method, we include all the numbers and count in increasing order.
Counting by tens is similar to counting by ones, except that you only count every tenth number. We can start from 1 and count up to 10. Encircle 10, and count ten more. Circle the number, count ten more, and circle that number. Repeat these steps until you reach 120. You will get the following result.
These numbers are also known as decade numbers. We get decade numbers when we count by tens starting from 1. We can also count by tens, starting from any other number. Suppose you count by tens starting from 6. You will get the following result.
Example 1: Count by ones and find the missing numbers.
Solution: If we are counting by ones, we need to count every number after the starting number. Here we are starting with 43. So the numbers should be:
Example 2: Count up and count down by ones from the following number to get the missing numbers.
Solution: First, let’s count up by one from 81 to find the three missing numbers on the right-hand side.
Now, let’s count down by one from 81 to find the missing numbers on the left-hand side.
Example 3: You have 25 chocolates and you want to share them equally with 20 classmates. How many extra chocolates will you have after distributing them among your classmates?
There are 20 students in your class, and you have 25 chocolates with you. Since there are only 20 students, you can only distribute 20 chocolates equally among your classmates. To find the number of chocolates you have remaining at the end, you can count by one, starting from 20 until you reach 25.
Since we counted up to 5 to reach 25, there are 5 extra chocolates.
Example 4: Count by tens to find the missing numbers.
Solution: To count by ten starting from 31, we need to write down every tenth number from 31.
As you can see from the table, we get 41, 51, 61, 71, and 81 after 31, when counting by tens. So, the missing numbers are:
Example 5: Tony is participating in a quiz competition and his current score is 23 points. Three questions are remaining in the ongoing round, and he will get 10 points for getting the right answer to each of the three questions. If he gets all three questions right, he will get a bonus question, which will give him 5 more points. What will be his score if he gets all four questions right?
Solution: Tony’s current score is 23 points. If he gets the next three questions right, he will get 10 points for each question. We can count by tens 3 times to find Tony’s score after answering the four questions.
After the first question, Tony’s score will be 33 points. After the second question, his score will be 43 points. And after the third question, his score will be 53 points. Finally, if he answers the bonus question, it will give him five more points. To find the final score, we can use the “count by ones” method to count up by 5 starting from 53. So, Tony’s final score will be 58 points.
Example 6: You are asked to count up to 70 without using more than 7 numbers. Would you count by ones or tens?
Solution: In order to get to 70 by counting just 7 numbers, we need to count by tens. If we count by ones, we will only reach 7.
When you count by ones, you are counting every number. But when you count by tens, you are only counting every tenth number.
We count coins using the “count by ones” method. We use the same method to count the number of animals on a farm.
We often use the “count by tens” method while counting $10 bills. The same method is also used when counting scores while playing games.