Integers: The set of whole numbers and their opposites. Remember, the integers are the numbers we normally see on a number line.
The arrows on each end of the number indicates that the number line goes on and on in each direction...so the number line does not stop with -5 and 5!
Modeling Integers
We can model integers using chips. For our example we will use red and green chips.
We are going to let the red chips represent 1 negative number and the green chip represent 1 positive number.
Look at the following examples:
Now let's combine positive with negatives!
What if I have one positive and one negative? It would look like this:
1 + (-1) (remember, we do not need to put the "+" in front of positive numbers) There is a property that tells us that if we add a number and it's opposite we get ZERO! Can you name the property? THEREFORE, when we have one positive and one negative they cancel each other because their value is ZERO. These are called zero pairs. |
Let's look at another example:
NOW LET'S LOOK AT YOUR 'MODELING INTEGERS' NOTES
In your notes, a solid circle represents +1 and an open circle represents -1 (just like our green and red chips above).
In the first 4 questions you are asked to write the number the model represents. Remember to cross out zero pairs if you can.
In the first 4 questions you are asked to write the number the model represents. Remember to cross out zero pairs if you can.
Try and fill in #3 and #4 on your own.
We can also model integer expressions. Look at #5 in your Notes. It looks like this:
Try #6 and #7 on your own.
HINT for #7: Rewrite -3 - 4 to -3 + -4.
HINT for #7: Rewrite -3 - 4 to -3 + -4.
We can also model expressions on a number line. Look at #8 in your Notes which looks like the image to the right.
What integer equation does the model represent? In order to find the answer to this question we start with the dotted line that begins at zero. Do you see it? ALWAYS START WITH THE LINE THAT BEGINS AT ZERO! This line moves from zero in the positive direction to 15. The second dotted line on top of the first starts where the previous line left off and goes in the opposite direction (negative direction) 5 units (notice that the number line is numbered by 5's) So we can write this as 15 - 5 = 10 . Notice - the answer to our equation above is 10 - it is where the second line ends! |
When there are multiple line on the same level (all dotted lines are side by side) this is a multiplication problem. When you multiply, you can think of it as grouping. For example, take the problem
3 x 2 That is 3 groups of 2, or 2+2+2 = 6. Now look at the example to the right (#9 in your Notes). On this number line there are 4 groups of -5. This number line models 4 x -5 = -20 Again, notice how the last line ends at -20. |
Try and do #10 on your own. REMEMBER, start with the line that starts at ZERO!
When you are done, grab some earphones and click on the button below to watch a video.