Number Line

• A number line is a line on which numbers are placed.
• The line is divided into equal intervals or segments, and each interval is the distance between two equal numbers.
• The intervals are identical in size.
• On the line there are small lines called marks.
• The line is infinite - it has no beginning and no end. We can always extend it as much as we want and add more and more numbers to it.
• As we move to the right - the numbers get larger
  As we move to the left - the numbers get smaller

Imagine a toad named Bethany.
Bethany lives on a house in the swamp and wants to visit her friend Ruth who is not far from her.

In order to reach Ruth, Bethany needs to jump on leaves arranged in a straight line up to Ruth's house.
The gap between each leaf is equal, just like on a number line.

Bethany the toad can hop over several leaves at once. When she succeeds in doing so, she marks where she landed.
Bethany managed to jump to a point that is exactly between her house and Ruth's house.
Note - Bethany's house is marked as $0$ and Ruth's house is marked as $1000$.
So she marked the leaf number as $500$ - the number that is exactly between $0$ and $1000$.
Ruth divided the number $1000$ by $2$ and understood that it's $500$.
$1000:2=500$

What would happen if Bethany managed to jump $4$ times on her way to Ruth?
How would she complete the numbers?

Let's understand how many intervals Ruth has - the answer is $4$
The number of arcs we drew.
Divide the final number $1000$ by the number of arcs.
We get $1000:4=250$
We understand that each interval is an addition of $250$.
Start adding the intervals step by step.
$0+250=250$
$250+250=500$
$500+250=750$
Until we reach $1000$.

In order to complete the numbers we will follow the steps below:

1. Determine the number of arcs between the marks – in order to understand how many jumps there are.
2. Divide the "final" number on the number line by the number of arcs.
3. Add the interval we found from point $0$ each time in order to determine all the numbers on the line.

Pay attention! An interval is the space between each mark. Even if the number is on a mark, the jump to it is called an interval.

And now let's practice!
Complete the numbers on the line:

Solution:

Let's follow these steps:

1. Identify the number of intervals between one mark and another.
   We count $5$ arcs.
2. Divide the final number by the number of arcs:
   $1000:5=200$
   Now we know that the interval between one mark and another is $250$ and therefore we can calculate the missing numbers as follows:
   $0+200=200$
   $400+200=600$
   $600+200=800$

Additional Practice:

Solution:

Let's follow these steps:

1. Let's find the number of intervals between one mark and another.
   We count $10$ arcs.
2. Divide the final number by the number of arcs:
   $1000:12=200$
   Now we know that the interval between one mark and another is $250$ and therefore we can calculate the missing numbers as follows:
   $0+200=200$
   $400+200=600$
   $600+200=800$

Exercise for advanced students!
Complete the missing numbers:

Solution:
Note that we have $2$ types of marks - some long and some small.
First, let's find the number at the large mark -
There are two intervals between the large marks, therefore
$1000:2=500$
Now let's proceed to the small marks:
Count how many intervals are between them and we should obtain the following - $5$
Now we need to understand the difference between $1000$ the final number and $500$
We obtain:
$1000-500=500$
Identify the interval between the small marks:
$500:5=100$
Now we know that the interval between each mark is $100$ hence we can calculate the missing numbers as follows:
$800+100=900$