817 Math Blog

In class today, we didn't do very much. We were given a quiz consisting of 10 questions. We were all instructed to show our work. Since we were to hand in the quiz following the completion, I cannot talk about each of the questions. But what I will do is refresh your eager minds about boxing (the "Green" way, and "Blue" way), adding integers, and subtracting integers. I will, because that's what the math quiz that we did was all about.

Do you remember how to add integers? Hopefully, you do. Here is a very simple example.
(+2) + (+3)
Since the integers are both positive, you would use standard math to answer this question. Although, standard math is probably the ideal method to use, but there are other ways to solve questions such as these, as well. The other methods are using integer tiles, number lines, and have and owe.
So, did you figure out the answer ? Yup, I knew you did. The answer is (+5)

Now, let's see if you remember subtracting negative integers, shall we? Here is a simple question. Try solving it. Keep in mind, you never really subtract. When you see a negative sign, you switch the sign to a negative, and the next integer sign to the opposite sign.
(+2) - (+3)
(+2) + (-3)
When subtracting integers, it is useful to use a number line. Remember, a number line has a ZERO in the middle, and infinite positive numbers to the right, and infinite negative numbers to the left. When subtracting integers, you would move that many places to the left. The same rule applies to adding positive integers, except you would move to the right, instead of the left.

Alright now, we should remember this number line method by now. Below, is the Have and Owe method.


Now, I'll be talking about the recent things we have learned, which is multiplying integers.
Remember, when the brackets are touching, they multiply! Keep in mind the ROOM 17 Theorem !
"When you multiply an odd amount of negatives, the product is always negative"
(the amount of positives in the question won't affect the product)

When you multiply a negative, and a negative, the product is always positive.
When you multiply a positive, and a negative, the product is always negative.
When you multiply a positive, and a positive, the product is always positive.
When you multiply a negative, and a positive, the product is always negative.

Here is a fairly simple example.
(2)(-3) = (-6)
The answer is (-6) because a positive and a negative equals a negative, and 2 multiplied by 3 equals 6.

Now, I'll talk about boxing, the BLUE way.
Here is an example using brackets.


Now, I hope that the picture above is helpful to you all. Using the "blue" method, you box out the group of integers, that you will multiply. In the group of integers, you multiply the integers to get 1 answer. Then, once you have your answers for the boxed out integers, you bring down the order of operations.

Now, I'll talk about the Green method. Using the green method, you put a (1) by the order of operations, if its an adding sign. You put a (-1) if its a subtraction sign. Below is a picture explaining the who "Green Method" idea.Sorry if I did the Green Method wrong. I wasn't absolutely sure how to do it...
Karen, I choose YOU ! (as the next scribe)
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Here is a video of adding integers






Here is a video of subtracting integers




Here is a video of multiplying integers