What are Counting Numbers? Why do we count?
So, the first question that pops into the mind is, “what is counting?” Counting is a way of understanding the number of objects available in a given space.
If one was asked to find out the number of pens we have here, how can one figure it out?
It is by counting, of course. We count using numbers.
We stop placing these numbers when all the objects are covered.
Here’s another way counting helps us. We can compare and understand as well.
Now, which of these baskets has more fruits?
The only way to find this out is by counting the total number of fruits in each basket.
There are four apples in basket one and five mangoes in basket two.
Therefore, we can say that there are more mangoes than apples in the baskets shown here.
If we were to add two more apples to the first basket, the number of apples would increase to seven, and the second basket would have five mangoes. Now, there are more apples than mangoes between the two.
Another way we can include more apples in the first basket is by reducing the number of mangoes. So, if we remove 2 mangoes from the second basket, we will be left with 3 mangoes, and keeping the first basket the same, we will have 4 apples. Now the number of apples is greater than the number of mangoes.
To make the number of apples equal to the number of mangoes, all that needs to be done is to either reduce the number of mangoes by one or increase the number of apples by one.
Let’s try it both ways.
Here we remove 1 mango from 5 mangoes and therefore we have 4 mangoes left, which is equal to the number of apples, which is also 4.
Now, here we add an apple, so we have 5 apples and the number of mangoes remains the same, which is 5. Hence, the number of apples is equal to the number of mangoes.
Counting Numbers with the help of a number line
We can understand counting better with the help of a number line. A number line, as the name suggests, is a line with numbers on it. As one counts from the left to the right, the value of the numbers increases. So, as we count, we keep moving to the right. As we move to the left, the value decreases.
We can move up the number line by repeating the addition of certain numbers. In the first one here, we move up by five units. Or, in other words, we count by fives.
If we are to count by tens, we skip ten units. This is what it would look like on the number line:
If we were to skip 100 units, it would look like this:
Questions
1)A handful of balls were thrown by Sam and Lola into a few hoops. The hoop into which Sam threw the ball is worth 10 points, and the hoop into which Lola threw the ball is worth 5 points. What is the least number of throws each of them would have to attempt to get a total of 50 points each?
To solve the answer to this question, we may need to draw two number lines. One of them will have increments of ten till 50, and the other one will have increments of 5 till it reaches 50.
Now, let us count the number of times a jump has to be made to reach 50.
To reach 50 in the first case, one needs to jump 5 times. This denotes the least number of attempts Sam has to make to get to 50. So Sam needs to throw the ball at least 5 times to get 50 points.
In the second case, one needs to count by fives 10 times to reach 50. This denotes that Lola has to make 10 jumps to get 50 points. So, this also means that Lola needs to throw the ball at least 10 times to get 50 points.
2)Jessica buys 5 apples, then she buys 5 pencils, and finally she buys 5 chocolates. Using the number line, find how many objects she has now.
First, we draw a number line. Then we start counting by fives from 0. She buys 5 apples, so we count on by 5 to reach 5, then she buys 5 pencils, so we count on by 5 and reach 10, and finally she buys 5 chocolates, so we count on by 5 to reach 15.
So the total number of objects is 15.
The number line is a representation of a given situation. This means it is only an idea that is being shown in the form of a number line and it is only created for our understanding. The length of the number line does not matter as long as the value it represents is properly placed.
The number line can represent any set of numbers. There are infinite numbers, so there is no limit to how many numbers can be represented on a number line. The numbers should be selected according to the question or the situation at hand.
Counting on a number line means adding numbers, which implies that we move to the right of the number line. Counting back, on the other hand, involves subtracting numbers, which means moving to the left side of the number line.