Interactive Number Line
Fortunately, the number line is easy to understand.
What is the number line?
A line that has evenly spaced marks. Each mark represents a unit.
Numbers to the right are greater than those on the left.
Fox example, a ruler is a number line.
The Number Line Is Counting
We can tell how big a number is by counting how many marks it is away from 0.
If it's 2 marks to the right of 0, then it is +2.
If it's 2 marks to the left of 0, then it is -2.
If it's 80 marks to the right of 0, then it is +80.
A number line problem is a counting problem.
The Number Line and Addition
We can visualise addition with the number line.
Lets take an example
6 + 4
Figure A
First, we move down the number line +6 marks,
then, from where we left off,
we move down +4 marks, where we end is our answer.
We can count the ticks to find that our answer is 10.
We move to the right both times because both of our numbers are positive.
Numbers Must Be Evenly Spaced
A ruler with unevenly spaced numbers is worthless.
A number line with unevenly spaced numbers doesn't make sense.
Each unit (number) should represent a common distance.
When we sketch number lines, we can't draw them perfectly; imperfections in our sketch do not imply imperfect steps along our number line.
The Number Line and Subtraction
Similar to addition, subtraction can be visualized nicely with the number line.
In fact, it is the same as addition except that we change direction.
6 - 4 = 6 + (-4)
Let's look at the problem
6 - 4
Figure B
First, we move down the number line +6 marks,
then, from where we left off,
we move back -4 marks and where we end is our answer.
We can count the ticks to find that our answer is 2.
The Number Line Helps Us Visualize Numbers
We need to be able to visualize numbers, to turn them into something physical.
The number line helps us do that by arranging numbers in an ordered list.
We can draw a number line;
we can measure a number line.
Sketching a quick number line can enlighten us and help us to see things in a different light .
Later in our mathematic careers, visualizing numbers becomes more important.
The Number Line and Direction
A number to the right of 0 is positive.
A number to the left of 0 is negative.
As the number line goes to the right the numbers get larger.
As the number line goes to the left the numbers get smaller.
Any number to the left of another is less than that number.
Any number to the right of another is greater than that number.
Figure C
Finding the Distance Between Two Numbers Is Subtraction
Because the number line is one dimensional, measuring the distance between two numbers is simple;
We subtract one number from the other and take the absolute value of our result.
When we deal with measuring distance between two points, we have to use the distance formula.
The Number Line is Fundamental
The number line and the core ideas behind it will continue to appear in more advanced subjects such as:
We can think of the number line as measuring, therefore it is present in almost all mathematics, even if we don't recognize it at first.
Conclusion
The number line is a useful tool for all stages of our mathematic careers.
We should invest the time to learn it well.
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