Integers
Negative and Positive Numbers - And What They Mean
Integers are either "whole" positive numbers or "whole" negative numbers.
Examples: -2, 7, 5, 476 and -19,672.
Non-Examples: -2.4, 3/8, 121.5 or
Integers are either "whole" positive numbers or "whole" negative numbers.
Examples: -2, 7, 5, 476 and -19,672.
Non-Examples: -2.4, 3/8, 121.5 or
What are the "parts" of a number line?
- Your starting point is 0. It is where you always start on a any number line. It is the first place you put your pencil when you get a problem that requires you to add and subtract numbers.
- Negative numbers are to the left of zero.
- Positive numbers are to the right of zero.
- Zero is special - it's neither negative nor positive.
How To Add Any Two Numbers
If I was given the problem 0 + 3, here is what I would do:
I would "start" by putting my pencil at 0, and move 3 spaces to the right. Positive numbers tell us to "Go Right!"
EVEN if I was given a problem like 4 + 3, I would "start" at 0. In math, a lot of things are "invisible." One of those things is plus signs in front of negative numbers. 4 + 3 is the same as (+4) + 3 OR (+4) + (+3).
Since my first number is positive, I know I must start at 0, then move 4 spaces to the right since a positive number tells me to "Go Right." Once I reach + 4, I would move another 3 spaces to the right.
If I was given the problem 0 + 3, here is what I would do:
I would "start" by putting my pencil at 0, and move 3 spaces to the right. Positive numbers tell us to "Go Right!"
EVEN if I was given a problem like 4 + 3, I would "start" at 0. In math, a lot of things are "invisible." One of those things is plus signs in front of negative numbers. 4 + 3 is the same as (+4) + 3 OR (+4) + (+3).
Since my first number is positive, I know I must start at 0, then move 4 spaces to the right since a positive number tells me to "Go Right." Once I reach + 4, I would move another 3 spaces to the right.
So, what would a negative number tell us to do?
Bingo! A negative number tells me the number of spaces I need to go to the left.
Take the number -6. Just so you remember, I can also write it like (-6).
Step 1: Become a cartoon man with a soda.
Step 2: Start at zero.
Step 3: Walk 6 spaces to the left.
Bingo! A negative number tells me the number of spaces I need to go to the left.
Take the number -6. Just so you remember, I can also write it like (-6).
Step 1: Become a cartoon man with a soda.
Step 2: Start at zero.
Step 3: Walk 6 spaces to the left.
Integers: Level 2
Power up, people! We are going to the next level.
On a number line, our starting point is...? Right!
1. Can you figure out the starting point on this map of the world?
2. How is this map different than a number line? How is it like a number line?
On a number line, our starting point is...? Right!
1. Can you figure out the starting point on this map of the world?
2. How is this map different than a number line? How is it like a number line?
Where in the world are you?
Compare the map above to this graph. Do you see how they are similar now? What do you notice?
When we put points on a graph we get two sets of "directions" about where a point is. We get directions for where we move to on the x-axis and the y-axis. You know how x comes before y? Well, they always give us the x directions first.
How would I get to the black point on the graph?
Step 1: Become a dot.
Step 2: Start at ________ on the ___-axis.
Step 3: Move two spaces to the right, staying on the x-axis.
Step 4: Once you have moved to the right spot on the x-axis, you worry about your directions for where to go on the y-axis. Move ___ spaces ____. You final location is (2, 1), which could also be written as (+2, +1).
Compare the map above to this graph. Do you see how they are similar now? What do you notice?
When we put points on a graph we get two sets of "directions" about where a point is. We get directions for where we move to on the x-axis and the y-axis. You know how x comes before y? Well, they always give us the x directions first.
How would I get to the black point on the graph?
Step 1: Become a dot.
Step 2: Start at ________ on the ___-axis.
Step 3: Move two spaces to the right, staying on the x-axis.
Step 4: Once you have moved to the right spot on the x-axis, you worry about your directions for where to go on the y-axis. Move ___ spaces ____. You final location is (2, 1), which could also be written as (+2, +1).