Positive-negative

• 10 - (-3)
• 2 - (-7)
• 3 - (-10 )
• 7 - (-2)
• 9 - (-4)
• 4 - (-9)

You must build before you draw!!!

What is the rule for a positive - a negative? What is the justification?  

Class Ideas: 
* Add the two absolute values
*Why: Because you have to add zeros in order to take away negative
*Rewrite the problem into an addition problem.

R-10 All Subtraction Rules

(+) - (+)
Find the difference between the 2 numbers and  if the number you are subtracting from is larger and answer is (+).

(-) -(+)
Add the absolute values of 2 #'s make answer negative.
Justification: Because you add the same # of zero's as the second # because there are no (+) to take away. After you take (+) away, you total (-) and increase by the amount of the second #. 

(+)-(-)

* Add the two absolute values
*Why: Because you have to add zeros in order to take away negative
*Rewrite the problem into an addition problem. 

(-)-(-)
Change the #'s to their absolute value and find the difference. If the larger absolute value is first the answer is (-). If the larger absolute value is second, the answer is (+).
Justification: If you don't have enough (-) to take away, add pairs of zeros until you do. Then take away (-). Remaining is the answer.

How are the rules similar? Can you generalize?  

Rule for Negative - Positive

 How can we figure out -768+324= without using the chips. What rule can we make every time we have a negative and subtract a positive.

Class Rule: Add the absolute value of 2 #'s and make answer negative. 

Rule for Subtracting 2 positives

Positive - Positive

Find the difference between the two numbers and if the number you are subtracting is larger the answer is -, if the number you are subtracting from is larger answer is +.

negative-positive

What do you predict will happen if you have a negative- positive problem?
-closer to zero
-Answer will be negative 
-sometimes +/-
-Depends on absolute value
-Can be anything?

Must build and draw
-4-5

 

-7-3
-9-2
-8-9
-1-5
-7-3

***Cancellation isn't taking away. We need to take away. Not cancel and make sure that we don not change the net value. 


What did we notice? 

* keep spending and your debt gets bigger. 


HW: 
 Must DRAW a model and solve each!!! No model=no credit
L3 pg. 44 
#1-13, #17-19, 27, 31, 35, 36, #48 a, b, c, e, g

Due on Monday 12/15!!!

How are cancellation and subtraction different? (Examples of subtraction problems with chips)

L1 Zeroation/Cancel-Best Definition 
-When a +/- are put into a collection and it's net value doesn't change. The problem's net value doesn't change.


How is this helpful to us? 
-Clear zeros to simplify problem 



When you have zeroation, what does it do to the netvalue?

-It doesn't do anything. It does nothing to the value, it is just zero.


2-7=

Way 1

 

          Step 1                                      Step 2                                     Step 3

Way 2

            Step 1                                                                              Step 2



147-132=

How would I figure out how many zeros I need to add to the pot?

367-147=220
I need 220 zeros

Subtracting Integers

R-65 Subtraction

What are all the types of subtraction problems that we will need to test? ex. for addition its +/+, -/-, +/- 


Must Build and draw first. 

10-3=
2-7=
3-10=
7-2=
9-4=
4-9=

What is the difference between subtraction and cancelling out (zeroation) 

subtraction- taking away
Cancelling-there needs to be a match between a positive and a negative 

Why can I cancel out a positive and negative? But not a positive and positive or negative and negative? 

-They are opposites. They are the same distance away from zero with the same absolute value. They have the same absolute value of zero. 

Adding Integers

What do we think the word zeroation means?
Cancelling out, putting something together to make zeros
examples:
-7+7=0
-8+8=0

Can also be 5+-3

L-62
5+-2=3
5-2=3

How are these the same and different? 
-they both got the same answer.
-for the negative 2, we needed to think of a problem in the real world where you would start with a negative
- -2 will always represent in debt
-when we subtract 2 they don't

example: Noah has 10 candy bars and I take 3 away from him, Mack as 4 candy bars and I give him 3.
-they both have 7.
-Noah feels bad because you took them away
-Is what happened with Zach and Noah different? yes. Did they get the same number?

It matters in real life whether we are adding or subtracting.

Make a prediction...

What happens when you add:

+/+

-/-

+/-



These problems matter in real life and it does make a difference.


2+3=
-3+2=
5+-2=
-4+-5=
-4+9=
-10+3=
2+8=
-3+-7=

Class Public Record:
+/+: Get a bigger positive 

-/-: Get a smaller # and it will always be negative

+/-: 
a. If neg #'s absolute value is bigger answer is negative, if positive #'s absolute value is bigger answer is positive.

b. Answer is The difference between the 2 absolute values

**Need to do both parts a and b