Negative and Positive Number Line
A number line is a line with arrows on each end, and is divided in the middle by zero. There are tick marks on the line representing numbers on either end of zero; anything to the right of zero is a positive number, and anything to the left is negative. Using a reference point, such as 3, you can determine what is greater than 3 and less than three by seeing which numbers fall to the right of 3 on the number line and which numbers fall to the left. Fractions of numbers are included in a number line, but not usually notated.
Using a number line can be useful when you are adding and subtracting numbers.
Let’s take a look at a problem:
Lacy has 9 pieces of gum. She gave two pieces to her friend Martha in first period. In second period, she gave 1 piece each to Jonathan, and Casey. In her last period she gave a piece to each of her three lab partners. When Lacy’s mom picked her up from school she gave her a new pack of gum with 10 pieces in it. How many pieces of gum does Lacy now have total?
So, let’s start by first drawing our number line.
Now, let’s read back through the problem and follow what happens with the gum on our number line.
So, we start at 9, because Lacy has 9 pieces of gum.
She gave two pieces of gum to her friend Martha. That means she has two less pieces than what she started with. So, we move to the left of our number line two places. Which, puts us at seven.
Now, what happens next? Well, she gives 1 pieces away, each, to Jonathan and Casey. So, now she has two less pieces than 7. So, we move to the left of our number line two places. Which means we are now at 5 pieces of gum.
What’s next? Well this girl Lacy has now given away a piece of gum to each of her three lab partners. That is three less pieces of gum that she now has. So, we move to the left on our number line a total of three numbers. Which puts us at two.
But wait! What happens? Mom comes in to save the day with ten more pieces of gum! That means we are adding 10 pieces to our existing 2. So, we move to the right of our number line 10 numbers. Which means Lacy ends up with 12 pieces of gum!
Number lines can be really useful to help you visualize changes taking place, and to help you keep track of where you are at in your word problem.
I hope this was helpful.
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See you next time!