Modeling Integer Operations
Well, we have to model these equations using these chips. (Red= negative, Yellow=positive) So these are our models and explanations for them for them.
(Model and explain)
6 + -4 = Positive 2
So we start out with 6 and we have to add 4 negatives. When you add one positive and one negative together they cancel each other out. So when you add -4 to +6 then it basically takes away 4 from 6, and in the end you end up with 2.
(Model and explain)
4 - -3 =
We start out with 4, and we need to take away -3. However 4 has no negatives to take away. SO in order to get those negatives you need to add in some zero pairs (zero pairs equal 0, so you are not actually adding any more value)! Now you have some negatives to take away, but when you take them away you still have the positives left. So because of that it actually adds onto the original number you were taking away from.
-4 * -2 =
SO basically you have to get two negative groups of negative 4 in order to do that you need to first get two groups of -4. Then after that since negatives are the opposite of positives then you just change the answer of -4*2 (-8) into it’s opposite (+8) and that's your answer.
-84 =
Since it starts out -8. You first need to get 8 negative chips. Then, since you are dividing by 4, you need to split the negative 8 into 4 different groups. You are left with negative 2 in each group so the answer is negative 2.
Rules for adding, subtracting, multiplying and dividing integers: (Clearly explain the rules as you understand them here. Use math language.)
Adding & Subtraction - When you add positives, you add on top of each other. Adding positive moves you right on the number line, subtracting positives moves it left. The opposite is for negatives, adding moves you left, subtracting moves you right.
Multiplication - If you love to love you’re a lover + * + = +
If you hate to hate you’re a lover - * - = +
If you hate to love you’re a hater - * + = -
If you love to hate you’re a hater + * - = -
Division- Dividing is basically splitting it up into equal groups. So dividing a positive into another positive will always result in a positive. Dividing a negative into positive groups is also the same, just splitting it into how many groups of the positive. Dividing a negative by a negative, you think, how many groups of this number is in this negative.
Dividing a positive by a negative, you have to rephrase it like a multiplication problem
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It's a little messed up so here is the link:
https://docs.google.com/document/d/1ZjHZ7YwpMxrEql8Vt3lphB-XYu4FfwULTHZuU3eaQl8/view
It's a little messed up so here is the link:
https://docs.google.com/document/d/1ZjHZ7YwpMxrEql8Vt3lphB-XYu4FfwULTHZuU3eaQl8/view
