## Wednesday, January 22, 2014

### Ian's Dividing Integers Post

The Sign Rule makes integers easier. The Sign Rule is: If the question is a + and a + or a - and a - then the answer is postive. If they are have + and a - or - and a + then the answer is Negative.
++ = Positive
-- = Positive
+- = Negative
-+ = Negative

Question 1:
(+8) / (+4) =
There are 2 ways to answer this question.
1. "Share (+8) into (+4) equal groups."
2. "How many equal groups of (+4) are in (+8)?"

So, first way is to Share 8 into 4 equal groups.

We are simply sharing 8 into 4 equal groups.

The second way, "How many equal groups of 4 are in 8?"

Since there is 2 groups of 4 in 8.

Question 2:
(-8) / (-4) =

First way: "Share (-8) into (-4) equal groups" You can't do the first way because we can't share -8 into -4 equal groups. So we have to do the second way.
Second way: "How many equal groups of (-4) are in (-8)?"
It is a positive because of the Sign Rule. - and - make +.

Question 3:
(-8) / (+4) =
First way: "Share (-8) into (+4) equal groups"
Second way: "How many equal groups of (+4) are in (-8)?" We can't do the second way because there isn't an equal group of +4 in -8.

Question 4:
(+8) / (-4) =
First way: "Share (+8) into (-4) equal groups"
Second way: "How many equal groups of (-4) are in (+8)?"
Both of them are wrong. So there is this thing called "Multiplicative Inverse"
Which is:
(-2) x (-4) = +8

Here is a video about Dividing Integers

## Tuesday, January 21, 2014

### Nicklaus' Integers Post

(If you see any mistakes, please comment)

I will label the 3 columns A,B,C. A is the left column, B is the middle column and C is the right column. I also label the rows 1-11.  I will just put the column letter and the the row number in my questions.

Question (A,4)
(-5) + (-3) = (-8)
(because I am in Mr. Harbeck's class, I need to put the "have" and "owe" on every question. So here I go)

Owe 5 and owe 3 = owe 8

( I also have to put it into integers chips [ i don't know what you call those chips] and or to a number ling)

Nice there are no Zero pairs, I just added all of the negative chips

Question (A,8)
9+(-6)=3
Have 9 and owe 6 = have 3

Since there are zero pairs, i simply circled all of the zero pairs and count how many positive or negative chips there is left which in this case, there are 3 positive chips left.

Question (B,6)

8-(-7)=15
have 8 remove owe 7 = have 15
(sorry i cant do this one on paint because there is not that much space to do this on paints)
+ + + + + + + +            - - - - - - -
+++++++                      +++++++

Question (B,7)
(-6)-9=(-15)
owe 6 owe 9 =owe 15
Question (B,9)
2-(-5)=7
have 2 remove owe 5=7 ( i added because 2 negative makes a positive so - -7 =+7)

Question(C,1)
8-(-2)= 10
Have 8 remove owe 2 =10

### Saansouk's multiplying integer scribe

The Sign rule

• When multiplying integers with the same value (-2) x (-2) = the product will always be positive.
• When the value of integers are different (+2) x (-2) = the product will be negative

The Same Value:
When the first number is a (-) it means that if the the second number was a (-) you would have had to make a zero pairs and then take away the negatives.
Example: (--)(--)--->
(++)(++)

When the first number is a (+) and the second number is a (+) you are basically doing regular multiplication.
Example: (++)(++)
The Opposite Value:
When the first number is a (+) and the second number is a (-) you are multiplying regular numbers just with a negative with it.
Example: (--)(--)

When the first number is a (-) and the second number is a (+) you are going to make a zero pairs but take away the positives.
Example: (--)(--)
(++)(++)--->

Number Lines:
This includes all of the sign rule example all you have to do is put how many arrows the first amount uses and then add to the number line using the second number.
Examples:

0
<-----------+------+--->
-->-->(+4)

0
<---+------+---------->
(-4) <--<--

That concludes this scribe and I hope it was a good one.

## Monday, January 20, 2014

### Dividing Integers Scribe #2

Have ----->(+8)  ÷ (+4) <---- Groups
There are two ways to solve this problem:
1) Share (8) into 4 equal groups
++ ++ ++ ++
2) How many groups of 4 are in 8?
++++ ++++

(-8)  ÷ (-4) =
Share (-8) into (-4) equal groups
We cant do that because we cant share negative into another negative.
How many equal groups of (-4) are in (-8)
---- ----
(-8) ÷ (+4) =
Share (-8) into 4 equal groups
-- -- -- --
How many groups of (-4) are in (-8)?
(+8) ÷ (-4) =
Share (+8) into (-4) equal groups
How many groups of (-4) are in (+8)?
-2 x -4 = 8
^This is called Multiplicative Inverse ^

### Janette's Dividing Integers Scribe Post

(+8) / (+4) = *using a '/' because I don't have a division thing.*

The way to solve this question is in two ways.

1. In the words:
"Share 8 into 4 equal groups."

(I'm gonna put in a picture because I'm lazy.)
So pretty much, this is what it would be separated into. (Answer is obviously 2.)

Now, the second way to say this question would be,
"How many equal groups of 4 are in 8?"
So, the answer would be 2 once again.

NEXT QUESTIONABLE QUESTION THAT MADE ME CRY OK LET'S GO

(-8) / (-4)

Share (-8) into (-4) equal groups.
NO. DO NOT PUT THAT. You can't share negatives into a negative amount of groups. So, we use the other statement.

How many equal groups of -4 are in -8? 2.

This is positive 2, because of the sign rule where it says "an even number of negatives will always result in a positive.".

So..yeah.

(-8) / (4)

Share -8 in 4 equal groups.

For the second way,

How many groups of 4 are in -8
Lol u loser we can't do that.

Question 4 (Final question.)

(8) / (-4) =

Share 8 in -4 equal groups.
No.

How many groups of -4 are in 8?
Nope lol

NOW THIS IS A PART WHERE WE CRY. BECAUSE WE ARE GOING INTO SOMETHING CALLED THE MULTIPLICATIVE INVERSE.

The statement which is the Multiplicative inverse, is "What times ____ gives you ____?"

And there is a new equation for this. Now, it is:

(-2) x (-4) = +8.

Aaaaaand we're done! Yayayayayayayay

## Thursday, January 16, 2014

### Nicklaus' multiplying integers scribe

Question #5
Write each repeated addition as a multiplication.
A)   (+1)+(+1)+(+1)+(+1)+(+1)= 5 * 1 = 5
B) (-6)+(-6)= 2 * -6 = -12

Question #7
Write each expression as a repeated addition.
A)  (+3)*(+8)= (+8)+(+8)+(+8)= (+24)
B)  (+5)*(-6)= (-6)+(-6)=(-6)+(-6)+(-6)= (-30)

Question # 13
Copy and Complete each multiplication statements.
A) (+4)*(+6)= (+24)
B) (+7)*(-2)= (-14)
C) (-1)*(+5)= (-5)
D) (-8)*(-2)=(+16)

Question # 15
An aircraft descends at 3 m/s for 12 s. Use multiplication to represent the situation.  How far does the aircraft descend?

3*12= 36     The aircraft descend 36 m.

Question # 17

An oil rig is drilling 2 m/min. How deep is the well after the first 8 min?
2*8=16    The well is 16 m deep.

### Angel's Multiplying Integers Scribe Post

One way of figuring out a multiplication integer equation is by using a number line.

For example: 6b) (+3) x (-6)

You first have to make a line with arrows facing outward on both ends and place a zero anywhere on the line.

Next you have to make an arrow going left if it's negative and right if it's positive (in our case it's left) and label it -6.

We do this two more times so we have three groups of -6.

Where the arrow has ended will determine your answer which is -18.

Here is a picture showing all the steps:

Another way of figuring out a multiplication integer equation is by using the sign rule.

For example: 8a) (+10) x (+4)

It is best to first multiply the numerals without thinking about the integers so 10 x 4 = 40.

Now look at your integers. If the two integers are the same, then the product is positive. If the two integers are different, they are negative.

In our equation, the integers are both positives so the answer will be +40.

Now let's do this with different integers.

For example: 8c) (-7) x (+5)

First we multiply the numerals: 7 x 5 = 35

Then we look at the integers and since the two integers are different, the product is negative which means the answer is -35.

## Wednesday, January 15, 2014

### Ainsley's Multiplying Integers Scribe

This is my post on how to multiply integers with different signs or the same signs.

The Sign Rule:

• When multiplying integers with the same value (+ or -), or for example (-2) x (-2) = the product will always end up being positive
• When the value of the integers are different (+,-) or for example (+2) x (-3)= the product will always end up being negative.
Another way:

1) When you have an even amount of (-) signs, the product will end up being positive.
(-4) x (-2) x (-1) = -8
|_______|
+8       x (-1) = -8

2) When there is an odd number of (-) signs, the product is negative.
(-2) x (4) = -8                                          <----(++++)   (++++)--->
remove 2 groups of 4 = -8                                 - - - -       - - - -

Now, these are a few questions that I've solved using the sign rule : Math Links 8.2

17. Question: Without evaluating the products, identify the least product. Explain your reasoning.
(+99) x (+82)
(-99) x (-82)
(+99) x (-82)
To answer this question, I chose (+99) x (-82) because if you recognize the sign rule, you know that when you multiply two integers with different signs, you get a negative. In this case, I didn't have to calculate it because I just saw the signs and I already know it's going to be a negative.

9. Question: Determine each product.
a) (-6) x (-6) = +36
I know that because if you multiply 6 x 6, you get 36. Also, they have the same signs and that means they are positive.
b) (+9) x (+6) = +45

c) (-12) x (+2) = -24
I know this because if you multiply 12 x 2, you get 24. Also, they have different integers and based on the "sign law/rule", when there are two different signs they are going to end up being negative.
d) (+11) x 0 = 0

### Denice's Intergers

Question 1:
(+4) + (+7)= (+11)
1) First you would translate it to English
+ = have - = owe
ex.
(+4) + (+7)=11
have4 and have7
2) Second you add 4 and 7 and equals to 11

chips:
++++
+++++++

Number line:

Question 2:
(+9) - (+7)=
1) First you subtract 9 and 7 and equals to 2
2) Second you would find all the zero pairs
(+9) - (+7)= +2
have9 remove have7
Chips:
+++++++
+++++++++

Number line:

Question 3:
(+6) + (-8)= (+14)
Have6 and owe8
1) First make make zero for the -8

chips:
--------
+++++++
2) Now you are left with +8 chips now you will add the +8 and +6 equals to +14
++++++
++++++++

Question 4:
(+8) - (-5)=
Have8 remove owe5
1) First make zero for the -5
-----
+++++

2) Second now subtract +8 and +5and you'll be left with +3
+++++
++++++++

### Jonathan's multiplying integers

The Sign Rule
When you multiply integers with the same value (+ or -) the product  will always be positive. ex. (-5)x(-4)=+20 or 7x9=49
When the value of the integers are different (+,-) the product will be negative. ex. (+2)x(-8)=-16

Here are 3 more examples so you can understand the sign rule a little bit better-
(-4)x(+2)= -8                          since these integers have opposite signs, the answer will be a negative
remove 4 groups of 2
Now we need to make zero pairs because you can't remove -4 groups of 2.
<(++++) (++++)>  you need to circle the groups and make arrows so you know if they are coming/going
- - - - - - - -
Now you are left with -8 which is the answer.

+4x+8= +32                                the numbers have the same sign which means the answer will be positive
4 groups of 8
So all we need to do is make 4 groups of 8
(++++++++) (++++++++) (++++++++) (++++++++)
^                     ^                     ^                ^

(-3)x(-3)= +6                              3x3=6. You need 6 zero pairs
remove 3 groups of -3
+ + + + + +
< ( - -  -)( -  -  -)>
Sign Rule Continue
When you have an even amount of (-) signs the product is positive. ex. (-5)x(+5)x(-5)=+125
When there are odd number of (-) signs the product is negative. ex. (+5)x(-5)x(+5)=-125

Let's do 2 more examples so you know this concept more well-
4x(-2)x(-2)=
4 groups of -2 groups of -2. This looks difficult so lets do this into parts.
4 groups of -2    (--) (--) (--) (--) this is -8  Now lets rephrase the question ( you don't have to do this step)
^     ^    ^     ^
It's now -8x-2= +16                8x2=16=16 zero pairs                      + + + + + + + + + + + + + + + +           remove 8 groups of -2                                            <  ( -  -) ( -  -) (-  -)  (- -)  (-  -)  (-  -)  (- -)  (-  -)>

(-3)x4x1=
remove 3 groups of 4 groups of 1
remove 3 groups of 4                               <( +++)(+++)(+++)(+++)>        = -12
- - - - - - - - - - - -
-12x1=-12
remove 12 groups of 1                        < (+) (+) (+) (+) (+) (+) (+) (+) (+) (+) (+) (+)>
-12 is the answer                                    -     -    -    -     -   -    -     -    -    -    -    -

Thanks for looking at my scribe post. Be sure to comment on my work and give me any suggestions if I made a mistake. Here's a video about the sign rule that will make you a genius.

### Sign Rule Scribe post #2 Patricia A.

The sign rules (short)

When multiplying integers with the same value (+or-) (-2)x(-2) the product will always be positive.

When the value of the integers of (+,-) (+2) x(-3) The product is always negative

Sign rules cont'd
(+4)x(-2)x(-1)=
8 x (-1)=+8
When you have even amount of (-) signs the product is Positive

When there are an odd number of (-) signs the product is negative

http://www.mathgoodies.com/lessons/vol5/multiplication.html

(Don't mind me)
(〜 ≖◡ ≖)〜 (ãƒŽ；Ïƒ □ Ïƒ）ãƒŽ

## Tuesday, January 14, 2014

### Julius' scribe post

Julius' scribe post

Multiplying Integers

first we learned to multiply two positives together. To multiply positives you multiply them. But you have to show your work.

For example:

(+3)x(+4)= +12

to show your work you have to write out: (number) groups of (number)

(+3)x(+4)=+13
3 groups of 4

You also have to model the question. To model you must have a certain number of groups containing a certain number of positives/negatives. But it is not a group unless you circle the groups. Then show that they are arriving

(++++) (++++) (++++)<-------

Multiplying negatives

To multiply negatives you do the same thing except with a negative.
For example:

(2)x(-3)= -6
2 groups of negative 3

(---) (---)<----

If the first number is a negative then the words start with remove

(-4)x(3)= -12
remove 4 groups of 3
to do this we need to have zero pairs
--- --- --- ---
(+++) (+++) (+++) (+++)
then make 4 groups of 3 positives. And then show that the positives/negatives are going away by making a arrow pointing away from the groups.
(+++)----> (+++)-----> (+++)-----> (+++)---->

f you are still feeling confused here is a video

feel free to criticize and correct me

### Zoe's Scribe Post #3

Multiplying integers: Positives and Negatives
Today during class we learned how to multiply integers!
Multiplying positives:
We started off with a very simple question and it was:
(+4) x (+3)= 12
Figuring out the answer is simple if you write the question down first. In this case the question in L.A form would be 4 groups of 3. This means: 3+3+3+3= 12, this is called repeat addition (skip count).
+ + +     + + +     + + +
Even if this is a simple question we have to model the question to show our work.

Lets practice on one more multiplying positive integers question.
(2)x(3)=6
2 groups of 3. 3+3=6

Multiplying with negative and positive integers:
(-4)x(3)=

To make this question easier you must write it down in words.

Negative 4 remove groups of positive 3. To remove something that isn't there you must use zero pairs, in this case you have to use 12 (=4x3).

Positive: Blue
Negative: Red
Now that you have your 4 groups of 3, like in what we wrote later we have to "remove 4 groups of positive 3".

Negative x Negative multiplying.

(-2)x(-3)= +6

Negative 2 remove groups of negative 3= positive 6

Remove 2 groups of negative 3:

## Monday, January 13, 2014

### Gabby's Pay it Forward post.

What is Pay it Forward? (Part 1)

In my opinion, Pay it Forward is a random act of kindness towards someone or many;
It is something that helps  younger (sometimes older) people understand further than just eating, sleeping and playing. It gives us a better understanding of the future and others.

Pay it Forward was planned to spread random acts of kindness throughout our society, to give thanks to people because maybe in the past, present or in the future you may also need someone else' generosity.

My Pay it Forward: (Part 2)

For my first Pay it Forward I decided on giving teachers and neighbors little notes that reminded them that they are important and that they should always keep a smile on there face everyday. I did this assignment on December 13th 2013 (Teachers), and December 22nd 2013 (Neighbors)

My second Pay it Forward assignment  was to donate clothes and non perishable foods to Winnipeg harvest. This was due to the fact that there are millions of people who go homeless without food and need help to get back up on there feet. I did this assignment on January 3rd 2014.

(First)  I picked this assignment to acknowledge the fact that they have helped me understand a life lesson nor an academic lecture. They took part of my life and helped me, which I am very grateful for.

(Second) I picked this other assignment because many kids go starving and with no clothes every year. It's sad to hear that us people in general think that food is an unlimited resources but really it's not.

Did it go well?: (Part 3)

My first Pay it Forward assignment went well and I had a great time. At first I wasn't sure about how they would react (I signed all of the notes anonymous) but they seemed happy and seeing them smile also made me smile.

My second Pay it Forward assignment went well and I found many things that my family and relatives no longer need. We tried our best to gather as much things as we can, and it was a huge success.

What I felt:

I felt a bit sad due to the fact that people are homeless and starving but we take everything we have for granted. We never think about the food we waste and those people who don't have food.

Why is Pay it Forward important to me? (Part 4)

In my opinion Pay it Forward is important because it helped me mature and think about others and not only about myself. It helped me get a better understanding on other people and how I should be taking action. One little action such as giving a person a positive note may brighten up there day.

Pay it Forward gives people a chance to give and not take. To show others that we should all be taking action towards small or rather large crisis' in the world.

### Gabby's scribe post #2

Multiplying integers: Positives and Negatives

Today during class we learned how to multiply integers!

Multiplying positives:

We started off with a very simple question and it was:
(+4) x (+3)= 12

Figuring out the answer is simple if you write the question down first. In this case the question in L.A form would be 4 groups of 3. This means: 3+3+3+3= 12, this is called repeat addition (skip count).

Even if this is a simple question we have to model the question to show our work.
 Remember to group your integer tiles!
Lets practice on one more multiplying positive integers question.

(2)x(3)=6
2 groups of 3. 3+3=6

Multiplying with negative and positive integers:
(-4)x(3)=

To make this question easier you must write it down in words.

Negative 4 remove groups of positive 3. To remove something that isn't there you must use zero pairs, in this case you have to use 12 (=4x3).

Positive: Blue
Negative: Red
Now that you have your 4 groups of 3, like in what we wrote later we have to "remove 4 groups of positive 3".

Negative x Negative multiplying.

(-2)x(-3)= +6

Negative 2 remove groups of negative 3= positive 6
Remove 2 groups of negative 3:

## Julius' pay it forward Part 1: Pay it forward is when you do something nice for 3 three people, and they do it for 3 other people and this chain becomes even bigger. You do this to either make them feel good or help them with something. Part 2a: My pay it forward was babysitting my baby cousin since her parents were shopping for Christmas. My parents couldn't do it because they were picking up my aunt from the airport. I babysat my cousin for an hour until my parents took over. I did this on December 23rd. Part 2b: I chose to do this because my cousin's parents were away and she cries a lot when her parents aren't here and I wanted to hear her laugh not cry Part 2c: I helped my my aunt and my uncle because they were too taken up in the Christmas rush Part 2d: I did this on December 23rd Part 3a: there were a few rough spots here and there, since i haven't babysat anyone, but overall it went very well. Part 3b: When my cousin laughed instead cried it put a big smile on face and it made me feel very nice. Part 4: Pay it forward is something that has probably gone over some peoples head and they just wiped it off as another idea. But this could become something more and if everyone did this the world would feel happier.

### Angie's Pay it Forward

Part 1

What is "Pay It Forward?"
Pay it Forward is a random act of kindness you do to 3 people. Then those 3 people will do a random act of kindness, therefore this will create a ripple effect. You don't really get anything in return, you just feel good about it.

Part 2

What was your "Pay It Forward" act of kindness?
My Pay it Forward act of kindness was to leave a short kind note on the windshield of person's car in hopes to cheer them up or to possibly, put a smile on their face.

Why did you choose this activity?
I chose this activity because sometimes I look out the window to see people sad, tired or maybe in just a bad mood so I really wanted to do something about it.

Who did you help?
I didn't really "help" anybody. The purpose of this was to just make someone smile or to make
someone's day.

What did you do?
I wrote a short note and left it on the windshield of a person's car that was parked along my street. It was literally the only car left parked on my street so I was in luck.

When did you do your act of kindness?
I did my act of kindness on January 5 2014.

Part 3

How did your act of kindness go?/What happened?
My act of kindness went really well. I had really enjoyed doing it. I hoped that the person who received the note appreciated it.

How did you feel?
I felt joy in doing this whole project. I think that it would really make a person smile.

How did the person/people react?
I didn't really see how the person reacted to my note. I waited for a few hours to see if the owner came back to his/hers car. Unfortunately the car was already gone by then.

Did you ask the person/people to "Pay It Forward?"
I actually did write on the note for the person to pay it forward. I also explained what Pay it Forward was all about just in case they were confused.

How did they react to your request?
I'm not sure how the person reacted since I didn't verbally say it to them and by then the person was already gone.

Part 4

Why is the idea of "Pay It Forward" important?
I think that the idea of "Pay it Forward" is important because doing something positive for a stranger could really impact that person or to maybe motivate that person to do something kind to another stranger. Doesn't matter what height you are, what age you are, etc. anyone can do this. Doing this can spread alot of positivity and good vibes from one person to another person.

My act of kindness hasn't really made a difference. Hopefully it will motivate some people to go out and do this type of positive thing. Something so small like a smile from a stranger can make anyone's day.

## Sunday, January 12, 2014

### Janette's Interger Scribe Post

Question 1/8:

10 + (-2) =

First off, I write it down in 'have -- owe --" So, written down it would be 'Have 10 Owe 2', having 'and' in between the two statements is not needed.

As Mr. Harbeck has taught us, the bigger number and it's one-syllable-word-thing wins the little fight. So now we know the answer would be 'Have --"

NOW ONTO ZERO PAIR

You Have 10, so that would be:
++++++++++
- -
You Owe 2, so that would be above this statement. So, where the red signs are it means you have a zero pair!

So, after the zero pairs cross each other out, you are left with have 8 (8 '+'s), which is the answer I got!

Question 2/8:

(-5)+(-3) =

Just like the previous question, you write it out.

Owe 5 and Owe 3 =

Owe 5: -----
Owe 3: ---

Since there are no zero pairs, you add the two numbers together to get owe 8. That's the answer I got anyways.

Question 3/8:

2-(-5) =

This is a little bit different, and it has that little rhyme thing.

What to find what isn't there,
YOU MUST FIND A ZERO PAIR.

Is how I remember it. (Possibly wrong.)

So, how it goes, you write it out.

Have 2 remove owe 5.

Have 2: ++

AND, owe 5:

-----

BUT YOU ADD A ZERO PAIR TO THOSE NEGATIVE HUNY BUNCHES

+++++
- - - - - THEN YOU KICK THEM OUT BECAUSE YOU DON'T WANT THEM ANYMORE.

So now, all that's left is combining the two numbers. Have 2, and have 5.

It equals have 7 okay.

Question 4/8:

(-7) - (-7) =

Owe 7, remove owe 7.

Owe 7: -------

Remove owe 7:

+++++++
- - - - - - - >> bYE

+7 -7 = 0.

Question 5/8

(-8) + (-3) =

Owe 8 Owe 3

Owe 8: --------

Owe 3: ---

-----------

-11. YAY.

(That's the answer by the way.)

Question 6/8

8-8

Have 8, owe 8.

Have 8: ++++++++
Owe 8: - - - - - - - -

These two cross each other out since they are zero pairs, which leaves 0 left. Which is what I got for my answer.

Question 7/8:

0 + 1

Have/Owe 0 have 1

Have 0:

Have 1: +

Question 8/8

9 + (-6)

Have 9, owe 6 = Have (because the bigger number is have) 3

(9-6 = 3)

Have 9: +++++++++
Owe 6: - - - - - -
(zero pairs)

### Ian's Integer Scribe Post

Question 1.
9-1=
For this question, we need to write it in words. Owe = Negative (-), Have = Positive (+)
Have 9 and Owe 1 =
Also you don't need to put the And, It just makes it easier.
Second Step.
You need to do it using Chips.
+ + + + + + + + +

Then you can see that there is 3 Zero Pairs. + and - make a Zero Pair.
So we have to take those out. Just pretend the red ones are removed.
+ + + + + + + + +
-
Now all there is left is Positive 8. So the answer for Have 9 and Owe 1 is Have 8 or 9-1 = +8
You also don't need to put the + sign for the answer since if there is no sign it means it is positive.

If you decide to do a number line for this question this is what you do.
+9
--------->
<----------------------------0------------------------------->
+8 <-
-1
And as Mr. Harbeck told us, Positive on the Number Line go on the top and Negative on the Number Line go on the bottom.

Question 2.
6 + (-7) =
Now you know the concept. Let's do this question.
Write it in words.
Have 6 and Owe 7 =

Second Step, Chips.
+ + + + + +
-  -  -  -  -  -  -
Zero Pairs.
+ + + + + +
-  -  -  -  -  -  -
Left is Negative 1. So the answer for Have 6 and Owe 7 is Owe 1 or 6 + (-7) = -1
This time you need to put a negative sign for the answer because if you don't the answer will be Positive 1 which is wrong.

Number Line.
+6
------>
<-----------------------------0-------------------------------->
-1   <--------
-7
Question 3.
8 - (-2) =
Now this question is different. This time we are REMOVING. If you see a question with  # - ( - #) it means we are removing. The # means numbers.
First we write it in words.
Have 8 Remove Owe 2 =

Second Step, Chips
+ + + + + + + +       - -
We have to turn the Negative into a Positive so we have to do a Zero Pair
+ + + + + + + +      - -
+ +
Then we remove the Negatives. Like I said I'm using Red Font for removing.
+ + + + + + + +
+ +
The answer for Have 8 Remove Owe 2 = Have 10 or 8 - (-2) = +10

Number Line.

+8         +2
--------> --> +10
<----0----------------------------------->

Question 4.
10 + (-2) =
Words.
Have 10 and Owe 2 =
Chips.
+ + + + + + + + + +
-  -
Zero Pairs.
+ + + + + + + + + +
-  -
We have +8 left.
Answer : 10 + (-2) = +8 or Have 10 and Owe 2 = Have 8

Number Line
+10
---------->
<--------0--------------------------------->
+8  <--
-2

Question 5.
10 - 4 =
Words.
Have 10 and Owe 4 =
Chips
+ + + + + + + + + +
-  -  -  -
Zero Pairs.
+ + + + + + + + + +
-  -  -  -
We have +6 left.
Answer : 10 - 4 = +6 or Have 10 and Owe 4 = Have 6

Question 6.
(-8) + (-3) =
Words
Owe 8 and Owe 3 =
Chips
- - - - - - - -
- - -
No Zero Pairs.
We have -11.
Answer : (-8) + (-3) = -11 or Owe 8 and Owe 3 = Owe 11

Number Line

<--------------------------0---->
-11 <--- <--------
-3        -8
Question 7.
0 - 5 =
Zeros are neither Positive or Negatives they are the Middle.
Words
0 and Owe 5 =
Chips
- - - - -
No Zero Pairs.
We have -5.
Answer : 0 - 5 = - 5 or 0 and Owe 5 = Owe 5

Number Line

-5
-5 <-----
<---------0------->
Question 8.
8 - 4 =
Words.
Have 8 and Owe 4 =
Chips
+ + + + + + + +
-  -  -  -
Zero Pairs
+ + + + + + + +
-  -  -  -
We are left with +4.
Answer : 8 - 4 = +4 or Have 8 and Owe 4 = Have 4

Number Line

8+
-------->
<----------------0---------------->
+4 <----
-4
Question 9
9 - (-4) =
Words
Have 9 Remove Owe 4 =
Chips
+ + + + + + + + +      - - - -
Make Zero Pairs
+ + + + + + + + +      - - - -
+ + + +
Remove Negatives.
+ + + + + + + + +      - - - -
+ + + +
We are left with +13.
Answer : 9 - (-4) = +13 or Have 9 Remove Owe 4 = Have 13

Number Line

+9              +4
---------> ----> +13
<--0-------------------------------->
Question 10
(-5) + (-3) =
Words
Owe 5 and Owe 3 =
Chips
- - - - -
- - -
No Zero Pairs.
We have -8.
Answer : (-5) + (-3) = -8 or Owe 5 and Owe 3 = Owe 8

Number Line

<--------------------------0--->
-8   <--- <-----
-3      -5

### Saansouk's Scribe Post

I will be doing a scribe on the first lession we did.

(-6) + (+9) =

Breaking this question down in to words it would have said.

Owe 6 and Have 9 =

The reason this is what it is, it's because the - means that it's Owe and the + means that it's Have.

The job of the brackets these ( and ) are to seperate the numbers.

Finally the + in the middle stands for and it separates the number to tell you that they are what need to be added.

### Sophia's Integer Scribe Post

Question 1:
9-1=

1. First you have to write out the question in words, owe = negative ( - )  have = positive ( + or/ numbers without the + ex. 9 )

For this question the sentence would be:
Have 9 Owe 1= 8
( You don't need an "and" but you it makes it easier for you can put one)

2.We have to put into integer chips ( + and - )

This would be:
+++++++++
-

Since there is a zero pair we take those out and then what ever we have left is the answer. Which is 8 chips ( ++++++++ ) Zero pairs are a positive sign (+) with a negative sign (-) like what we have here in the top.

3. We put it in a number line.
9
----------->
<_______0______8_______________>

<---
-1

Question 2:
6+(-7)=

1. Like what we did on the first one we need to put it in a sentence.

Have 6 Owe 7 = Owe 1

2. Put it into integer chips.

++++++
- - - - - - -

There are zero pairs, so we take them out.

3. Put it in a number line
6
-------->
<_____________-1_0____________>
<----------
-7

Question 3:
(-8) + (-3) =

1. Put in sentences ( owe and have )

Owe 8 Owe 3 = Owe 11

2. Integer chips ( - and + )

- - - - - - - -    - - -

In here we have no zero pairs so we just count what we have and that is the answer.
So, that 11 chips.

3. Number line, like the others we put it in a number line.

<________-11____________0_____>
<------<---------
-3       -8

Question 4:
9 - (-4) =

1. Put it in sentences:
Have 9 negative Owe 4 = Have 14

You see the bold negative we put that because "To remove what isn't there you must add a zero pair"

2. Integer chips:
Since this question is a bit different than other you have to do a little extra work. As before "To remove what isn't there you must add a zero pair"
put into integer chips like so,
- - - -  >>>
++++
Now the negative chips goes away and gets replaced my positive chips.
Then add with positive 9 ( Have 9)
++++++++++ ++++
which makes positive 14 ( Have 14)

3.Make a Number line.

You cannot make a number line for this question, so you need to show your work by using the integer chips.

Question 5:
(-7) - (-7) =

1. Once again put it in sentences.
Owe 7 negative Owe 7 = 0
( remember negative )     :)
( zero is the middle so it doesn't have a positive or negative sign )

2. integer chips:
"To remove what isn't there you must add a zero pair"
So once again,

- - - - - - -  >>>>>>
+++++++

- - - - - - -
+++++++

Then the zero pairs are taken out. The remaining is 0.

3.Make a Number line.

You cannot make a number line for this question, so you need to show your work by using the integer chips.

\

Question 6:
3 + 8 = 12

(Repeat what we did )
1. Write it out!
Have 3 Have 8 = Have 12

2. Integer chips!
+++    +++++++++

3.Number line

Question 7:
0 - 8 =8
(From the top)
1.Write the sentence (owe and have)
0 Owe 8 = Owe 8

2. ( + - )

- - - - - - - - -

3. NUMBER LINE.

Question 8:
(-2) + 3 = 1
1. Sentence:
Owe 2 Have 3= Have 1
2.Chips.
+++
- -
There is a zero pair take it away. You have have positive 1.
3. Numberline.
(make it )

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