Negative-Negative

What do you think will happen when you have a negative- negative?



You must build, draw, and then come up with an answer.

• -3 - (-7)
• -9 - (-4)
• -2 - (-5)
• -6 - (-1)
• -8 - (-7)
• -4 - (-7) 

Public Record: Change the #'s to the absolute value and find their difference. If the larger absolute value is first the answer is negative.

R-10 All the Subtraction Rules!

R-10 All the Subtraction Rules!

 (+)-(+)
Find the difference between two #s and if the # you are subtracting from is larger, answer is +.


 (+)-(-)
Add together the absolute value of the 2 numbers to get the answer.
-Justification: Why does this work?

* I you do not have negatives to take away, you have to zeroate so you do not change the net value, but you get the negatives you need.

(-)-(-)

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

(-)-(+)
Add absolute value of #'s and convert answer to negative. 

The class made 2 Rules: 

Different Sign
1.  (-)-(+) and (+)-(-) Add the absolute value. If the first # is (-), make the answer negative.

Same Sign
2. (+)-(+) and (-)-(-) Find the difference of the absolute value if the bigger # is first, the answer is positive.
 

Positive -negative

8-7=1
7-8=-1

Difference between the numbers
1st numbers smaller=>-
1st numbers bigger =>+

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


Class Rule: 

What is the difference between subtracting and zeroation?

What is the difference between subtraction and zeroation/cancellation? 


4-7= 




















3-9=

















***The difference between each subtraction problem was how many zeros we added 

154-268=

268-154=

154+114=268
Now I have enough to take away. 

Subtracting Integers

R-67 Possible Subtraction Problems
(big -) - (small +)=
(-) - (-)=or (big -) - (big -)

Multiple numbers to subtract: 
(Small +) - (bigger +)=
(big +) - (small +)=

(+) - (-)=

positive - (opp)


L Page
(Small +) - (bigger +)=
(big +) - (small +)=

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

Adding Integers

Class definition for Zeroation:

-When +/- integers cancel each other out and doesn't affect the net value
-The chips being cancelled out have to have the same absolute value
-A way to solve a problem visually-doesn't affect answers.


The class made predictions:

What happens if you add:

2 positives
*Bigger number  +
*Greater absolute value

1 negative and 1 positive
*Maybe 0
*Depends if + or - has greater absolute value which ever is greater is the sign of the answer.
*First zeroation than leftovers is answer

2 negatives
*negative answer
*answer smaller
*absolute value bigger
(Answer further from 0)

Show with the red and black chips:
2+3=
-3+2=
5+-2=
-4+-5=
-4+9=
-10+3=
2+8=
-3+-7=

Let's make some generalizations. Could we write a rule?

1. The sign of the number that has the larger absolute value
2. Difference between those 2 positive numbers

Public Record for Adding

positive  plus positive
-Get a bigger positive

negative plus negative
-Get a bigger negative or smaller number or bigger absolute value. 

positive plus negative 
-convert both numbers to positive and find their difference. The answer ad the sign of the # with the longer absolute value. 

-4+3=>3+-4
             3-4

Commutative property-

Black and red chips

What do we think zeroation is?
-They cancel each other out

Hans's Zeroation-































The value of the bottom collection is -5. What happens after I do zeroation? There are a certain number of blacks and reds that get removed. It takes it away and has no effect on the net value.

L page

Write your own personal definition for zeroation?