Pam's Scribe Post

integers lesson

 

When multiplying integers, here is the basic lesson.
Here's an example:
(+7) x (+2)=
In words, this would be seven groups of positive 2.
In repeated addition: (+2) + (+2) + (+2) + (+2) + (+2) + (+2) + (+2) =
You could use integer chips as so:

The red symbolizes positive.

You can also represent this equation as a number line, either vertical or horizontal.

And you'll have your answer, which is (+14).

Here's something new:

scribe rule

 

When the integers have the same value (+ or -), the product is positive.

When the integers have different values (+, - ), the product is negative.

 

Let's apply this rule.

(+5) x (+4) =

Just multiply and then see whether or not the signs match or not.

5x4= 20

both positive, so the answer is positive.

(+ 5) x (+4) = +20)

 

(-6) x (+2)=

Multiply, 6x2= 12

They have different signs, meaning it's negative.

 

(-7) x (-8)=

Find the answer of 7x8, = 56

Then to see whether 56 or the answer is positive or negative, check the signs.

The two signs are the same, meaning the answer is going to be positive.

= (+56)

 

sign rule part 2

 

When multiplying integers , count the negative signs. When the number turns out to be an even number, it is going to be a positive product, and an odd number while counting equals to a negative product.

 

For example: (+4) x (+6) x (-7) x (-1) =

count the negative signs, and there are 2.

2 is an even number, therefor the answer will turn out to be a positive product.

 

To solve it, just do order of operations.

 

(+4) x (+6) x (-7) x (--1) =

(+24) x (-7) x (-1) =





(-168) x (-1)=
(+168) = answer. :)
See, it's a positive product.

Let's try this again.
(-4) x (-1) x (-3) x (+2) =
by following the same rule from before, this must be a negative product since there are 3 negative signs, and 3 is odd.

(-4) x (-1) x (-3) x (+2) =
(+4) x (-3) x (+2) =
(-12) x (+2)=
(-24) = answer
                                       
Let's try with more factors.
(-4) x (+2) x (-1) x (+1) x (-5) x (+1) =
There are 3 negatives, and 3 is an odd number meaning that the answer is going to be a negative product.

(-4) x (+2) x (-1) x (+1) x (-5) x (+1) =
(-8) x (-1) x (+1) x (-5) x (+1) =
(+8) x (+1) x (-5) x (+1) =
(+8) x (-5) x (+1) =
(-40) x (+1) =
(-40)= answer.
See it wasn't that bad.
If you're having problems with multiplying integers, please refer to the video below,




















P
Please feel free to play this game, and apply the sign rules to your answers. :)


Integer Multiplication Game

Have fun, and Good Luck! :)

Pam's Scribe Post

 today's lesson:

January 8, 2014
 (all answers at the end of explanation)
 

       Integers not only have adding in them, but subtracting, or removing. A rule you must know is "Whenever something is not there, you must add a zero pair"
A stragety you can use when you want to recongnize when to say "and" (add or combine) or "remove" is when the equation is a double negative or it's a negative and a negative, if not, then always combine unless you remove a negative (negative and negative). When you have a negative and a negative, you must add a zero pair since that negative isn't there.

negative minus negative (with brackets)

 



For example, (-5) - (-6) =
For the words, it would be :
Owe 5 Remove Owe 6.

Since you are trying to remove (-6), you can't since there isn't so you do a zero pair.

++++++
- - - - - -     <--- This evens them out and then you remove the (-6) so you are left with positive 6.

Here  you would remove the (-6) since it's part of the equation.
Then you combine (-5) since integers is all about combining.

+ + + + + +
-  -  -  -  -

You have one positive left over, therefore, the answer is (+1) or have 1.

 

positive minus negative (no brackets)

 

And example for a positive minus negative equation is:

9 - 1 =

This may seem like a regular subtracting question, but it really is like saying (+ 9) - (-1).

The minus sign actually is part of the one since it means that the one is negative.

A way this might be easier is to say the equation out loud or put it in words like so:

             have 9, owe 1.

To show this you would have 9 positives (have is positive), and 1 negative (owe is negative).

 

+ + + + + + + + +

 -



The zero pair cancels one of the positives and one of the negatives, leaving behind only 8 positives. The answer would be (+8) or have 8.

negative minus negative ( first one has no brackets)

 

This may seem different from the first one, but it's all about how you look at it.

An example of this type is : -4 - (-6) =

The only difference for this is that the negative 4 doesn't have brackets.

In words this would be : Owe 4 REMOVE Owe 6.

In pictures or in integer chips this would be 6 zero pairs, removing the minus, and you add the positives with the negative which is negative 4.

 

-  -  -  -  -  -

+ + + + + +

 

Then COMBINE the positive 6 with the negative 4.

 

+ + + + + +

-  -  -  - 

 

Then you have 2 positives left over which gives you your answer of (+2). 

 

It goes with positive minus negative, example: 4-(-6)
 

positive minus negative (with brackets)

 

 

An example of positive minus negative would be:

7-(-6) =

In words this would be have 7 REMOVE owe 6. This a double negative, since there are two negatives together.

+ + + + + +
-  -  -  -  -  -

Then you combine the 6 positives together with the 7 positives, which equals 13.

 

Calculate with the zero pairs and you're done. You have one positive left over, and you answer is (+1) or have 1.

if that didn't work, here's a video. 



 

 







here's some more fun with subtracting integers (game)

 

 

Integers Subtracting Game

(if that didn't work try copying this link)

http://www.sheppardsoftware.com/mathgames/integers/FS_Integer_subtraction.htm

 

 

 

Good luck on your learning!

Ceci's Pay it Forward

PAY IT FORWARD 

2014 :)

BY: CECI ZHONG

    JOANNA BABADILLA

    PAM JOSEPH

    ALLISON CONCEPCION

Part 1 

What is pay it forward?

 Paying it forward is a way to thank our society by helping other people, we can do some simple things that can help others or make their days. the boy named Trevor in the movie <pay it forward>, he came up with the idea of paying it forward, it starts with one person to help 3 three other people to do something big , and these 3 people have to help 3 other people, and more...it spreads out, more people will involve to this activity, you can make a huge difference to the world just by doing something kind to others. These actions does not have to be huge, but just do something that can make them feel happy and warmth.

Part 2

What was your pay it forward act of kindness?

Our pay it forward act of kindness was to shovel the sidewalk of the street and walkway for our  neighbors; designing kitchenware items for our neighborhoods; giving out treats to teachers, putting candy canes (made in heart shape) with a small messages into people’s mail boxes and also we had also given a box of candy canes with a letter that has information of pay it forward to a day care.

Why did you choose this activity?

We choose these activities because its something that are helpful to them, and can make them happy. Shoveling the street snow, and neighborhoods walkway were very helpful to them. Because its hard to walk on thick cold snow, also it wastes a lot of time just to shovel a small area of snow, we did it for them so, they don’t have to come out to this very cold weather and shovel when they should have a rest or have a nice warm dinner with their family. We designed kitchenware items because, kitchenware items are useful to family, every family needs kitchenware items efforts that were putted in the designing shows how much we care about them, I am sure that you can feel the warmth when you look at it. We had given treats to teachers because we really want to thank them, they had helped us a lot, not only knowledge for school also knowledge for life. We dropped off candy canes with a small messages and information of pay it forward into peoples mail boxes, the main point of this activity was making their day by a candy cane and a small message, also we want them to know and understand what are we doing and what is pay it forward, so they can spread the information of pay it forward to other people or they can get started on pay it forward. The last thing that we did was giving a box of candy canes with a letter to the day care because, we wanted to let the teachers know what are we doing so they can teach kids about pay it forward, so in their heads, they have some ideas of pay it forward, candy canes also made them feel happy!

Who did you help?

We helped people around us, 

Teachers, 

Kids

Neighborhoods

(etc)

When did you do your act of kindness?

We did our act of kindness on December, 29th and December 30th .2013  

here is  our video ...

            

Part 3

How did your act of kindness go?

Our act of kindness was not going like what we had planned, a lot of thing are not as easy as we thought of, but we still tried our best to do it. Things that we really can’t do it such as, giving kitchenware items to the elderly home, we could not do it because they have to confirm with our teacher, but we don’t have our teachers’s number, so we decided to give these kitchenware items to our neighborhoods. Also it was hard for us to shovel snow in a very cold day for more than 2 hours. Even though our actions were not easy but when we see their smile, everything worth it .

What happened?(how did the person or people react? Did you ask them about pay it forward...)

Our group decided to go to one of our member’s house (BABADILLA) to work on our project. On the first day, we went to Walmart to buy all the materials that we need, then got back to Joanna’s house to get our shovels and get ready to shovel the sidewalk and neighborhoods’s snow. We planned two people to shovel and two people to take pictures and videos (rotated). When we were shoveling the first neighborhoods houses, a woman came out ans she was very appreciated what we did, she said “thank you” so many times, and gave us 20 dollars, we told her that we are doing this for “pay it forward” we don’t want to receive her money, when she heard we said we were doing this for paying it forward, her reaction was very surprised, she told us that she loves the movie pay it forward, but she wants us to receive the money so she has a chance to pay it forward. And after we received more money, we decided to donate these money to the Philippine Typhoon Relief. After we shoveled snow, we started to work on writing cards, designing kitchenware items, rapping gifts, and editing, it took us a lot of times to do it, after we go out again and dropped off candy canes, kitchenware items to people’s houses and mail boxes. 

How did you feel...? What did you learn?

I felt very satisfied and happy after I helped people and made them smile. Even though I always knew that its a good thing to help other people but I don’t experience it a lot, I didn’t really understand the main of helping, after I did this project, i will never ever forget the moment when people had a big smile on their face when they received our help, it was so beautiful, their smile lift up the whole world, at that moment you feel like the sun is shining on you, you can feel the heat even though you are standing in a temperature of -40co, you feel like you are the happiest person in the world! While working on this project I had learned how teamwork is very important because, if we don’t work as a team, we don’t cooperate each other, we would have a lot of disagreements, we wouldn’t be able to finish this project.

Why is the idea pay it forward important ?

Pay it forward is important because it makes people become more selfless from selfish, more positive from negative and it lets you experience the fun of helping others. while we were doing these act of kindness, we learned to be more selfless, we learned to think about other people, our community and the whole world. We work harder and have a big smile rather than complaining. Also we had fun while helping others.

Did your act of kindness make a difference?

I think our act of kindness did make a difference, because I could see people were touched by our action, this little “touched” might not make a big difference but it will spreads out, it will grow bigger and bigger, stronger and stronger.

Acknowledgment...

Thanks to all our grade eight teachers for always there to help us !

Thanks to Joanna’s family for letting us to work at their house!

Thanks to Joanna’s cousin who helped us to buy materials and helped us to make the kitchenware items!

Pam's Pay it Forward

our group:
Joanna, Allison, Ceci, and Pam 

PART 1

 

           What is Pay it Forward? Paying it forward is an action that basically spreads out like wildfire. It is started by one simply act of kindness, and after just say, pay it forward. In the movie "Pay it Forward" Trevor, decided to contribute to helping people's lives by doing a kind act for three people. These three people would pay it forward, and then next thing you know, you got thousands of people doing it too!

 

 

PART 2

 



 

            Our Pay it Forward act of kindness was:

• Shovelling sidewalk, and some parts of our neighbour's walk (money raised goes to Typhoon Haiyan)
• Giving out candy canes shaped as a heart with a small message such as "Have a Great Day!" or "You're awesome!", and a small sentence explaining pay it forward
• Small Gifts for teachers to show that we care about their hard work with our education
• Kitchenware such as mugs and cups that we designed, given to the neighbours who had given us money
• A box of candy canes for the daycare beside the school

      We chose this activity because we thought that all these activities were very simple and we thought that we should do many simple activities rather than doing one complex idea. We chose to shovel our neighbours' walk and also the sidewalk so they would save time and see how much we wanted to help. We are younger, and we can do it, and hopefully, we also want someone to do this to us when we are older and uncapable. We chose to give out candy canes shaped as a heart with a small message to brighten up their day. A very simple yet big message. When they get home from doing anything, hopefully, they'll feel better and turn a bad day into a good day, also, they'll wonder about Pay it Forward. We designed mugs, cups, etc. to give to the neighbours who had given us money although we had rejected.  We chose to do this because we wanted them to know that we did the shovelling for not just the money, but to make a difference. We gave the box of candy canes to the daycare near our school so that the children could have a little treat, and also, so show that we support them and the hardwork put into taking care of all the children.

        We helped the community by shovelling the sidewalk, and we also helped the neighbourhood with the candy canes given out.  Another group we had encouraged were our teachers, giving a card and a little treat to show that we appreciate their hard work. We also helped the neighbours by sending a basket with mugs and cups we had designed. We also supported the daycare beside the school and the victims of Typhoon Haiyan by donating $40.

          We did our act of kindess or our Pay it Forward activity during the winter break we were given. We did this around the days of December 29-30th.

PART 3

 



         I think our act of kindess went well. I wouldn't say it was perfectly done, no mistakes, because we did have a few bumps in our road. We couldn't shovel the whole neighbourhood (two sidewalks) because it was a very cold day, also, we had planned to give the mugs and etc. to the elderly home near Cookatoos, but when we called, we still had a problem since it had to go through more security measures, and etc. Another problem was that we couldn't create enough candy canes shaped as a heart and re-writing every single thing over and over again, and we didn't have a printer available.

         With my mindset before, I thought the whole plan over and the overall process and activity was unexpected. When we shovelled the sidewalk, I thought that it would be easy, but it was very difficult with the weather and everything else. By accident, we shovelled our neighbours walk, but since we started, we can't just stop and we kept going. The snow was about or above our knees and it wasn't easy, finally, something unbelieveable happened. The neighbour opened their door and came and wanted to talk to us. They said how much time we saved for them and they wanted to thank us. This happened with two of our neighbours! We rejected, but they insist we kept the money. After thinking, we thought we should donate the money! We gave a letter to our neighbours and said how we gave the money received to charity so that they know where their money is going. With the mugs and cups, it was very difficult. We had to think of a design, draw it with a sharpie, and layer the sharpie 2-3 times so it had layers of sharpie. After that, we baked them to insure that the permanent marker would stay put. It was a very difficult process since we were just experimenting and we were scared that the mugs might shatter inside the oven which could be a very dangerous procedure to clean.

        I felt like I've changed. I felt that this project was going to be very hard and was going to take plenty of days, but it only took 2. It wasn't the most simpliest project, but it was very productive. We tried everything and we improvised for the best. I felt so appreciated when we shovelled and talked to the neighbours. They had thanked us and we can tell by their big grins that we made their day and made them happy. All the cold air went away when talking to them, until it came back again. :)  I felt different, like I'm not myself anymore, since I haven't shovelled for others. But I have to say, we had an urge to stretch at that point.

        The neighbours reacted with great smiles and amazed eyes. They were freezing but they had to talk to us even if their door was half open and it's freezing outside. We did the rest of the activities being anonymous. We felt that they might not be there, or we didn't need to name names to receive credit. The main objective is to pay it forward.

         We asked the neighbours that we shovelled sidewalks for to pay it forward, and one of them said that they loved that movie. That person had a job for inspiring people and being a difference maker. We also wrote very tiny notes to indicate to pay it forward and a brief summary of what pay it forward was for the candy canes.

PART 4 

 

         The idea of Pay it Forward is very critical for creating a kinder society. This spreads out just like a viral video. This helps brighten anyone's day, it's not very hard at all (you could do the simplest things such as open the door), and the best part, it goes on and on and on.

 

         

          Hopefully, our act of kindness has touched one heart and has spread around. Our act of kindness  has made a difference to their persepective on the world and how there are very supportive people in the world.

 

 

a video to show our activities

 

Pam's Percent Post

Notes:

• Percent means/is an equivalent fraction that is out of 100.

ex. 9/10 x 10/10 = 90/100 or 90%.

• Percent is out of 100 because "It's just right" and it's "easily seen", and it could also be a friendly number.
• The percent symbol (%) includes two zeros and the division sign. The division sign is the 1__ and the two zeros are _00 making it 100.
• In French, the word percent is split into two parts, "per" being "out of" and "cent" being "100".
• You may be asked, is 205% still a percent? even though it's past 100? It still can be. It's 205/100.
• Percent can be an "improper fraction" meaning that the numerator is greater than the denominator in a fraction. Another word for this could be "Top Heavy". ex. 5/4

100%- means all, whole, everything.

50% - means half, part/whole, 20/40 or 50/100

   %    |  apples
  100  |   40
    50  |   20
*We divided both sides by 2.

10% - is 10/100

   %    |  apples
  100  |   40
   10   |    4

25% means 25/100 or 1/4
 
   %    | apples   
 100   |    40
   25   |    10
*We divided both sides by 4.

1% - means 1 out of 100 or 1/100
*To find 1% of something, divide the number by 100.

   %    | apples
   100 | 40
     1   | 0.4
*We divided by 100 on both sides (what you do to one side, to do to the other).

Representing Percent

180 %







____________________________________________________________________________

0.6%

__________________________________________________________________________

    12 3/8 %

____________________________________

FRACTION - DECIMAL - PERCENT

3/40   Numerator ÷ Denominator = Decimal
                           3 ÷ 40 = 0.0.75  x 100   =   7.5  or 7.5%
                                            1     x 100        100
_____________________________________________________________________________________               

DECIMAL - PERCENT - FRACTION

0.0064    0.0064  x 100      0.64  or 0.64%    →    0.0064
                   1       x  100     100                             10000

_________________________________________________________________________

PERCENT - DECIMAL - FRACTION

0.3% ÷ 100  =  0.003  →   3     
                                         1000

_________________________________________________________________________

                                                PERCENT OF A NUMBER

MENTAL MATH                                                                     CALCULATOR

20% of 60 -             %  |  #                                                    20   20 ÷ 100 = 0.2
                             100  | 60                                                  100
                (÷ 5)       20  | 12                                                
                                                                                             0.2 x 60 = 12

* 0.2 is 20% and you must find the decimal of 

the percent by dividing the percent by 100.

                                                                                                                                                        

0.1% of 40  -          %   |  #                                                  0.1     0.1 ÷ 100 = 0.001
                              100 | 40                                                100
              (÷ 1000)   0.1 | 0.04
                                                                                            0.001 x 40 = 0.04
* when dividing 10, 100, 1000, etc, you
move the decimal place by how much zeros
there are in the number you are dividing by.
When there is no decimal, the decimal is always
on the right side of the ones place value.
     
                                                                                                                                                        
250% of 400 -        %  |  #                                                  250           250 ÷ 100 = 2.5
                             100 | 400                                               100
                     (x2)  200 | 800
       (÷ 2 from 100)    50 |  200                                              2.5 x 400 = 1000

800 + 200 = 1000

                           
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5.                                                 COMBINING PERCENT                                                     

Question 7 -page 149                                                            

                                                                                             

A herd of 100 caribou was moved to a new 

location. The population increased by 10%

the first year and then increased by 20% the

second year.

a) Find the population after the second 

year.

b) Explain why there was not a 30% increase

in population over the two years.

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WORK :

first year

                  - The caribou population (the whole or 100%) was increased by 10%, meaning that 10% was added to the whole, so you could just find 110%.

   

            100%         - caribou

            + 10%        -increase in population

            110%

             110            110 ÷ 100 = 1.10
             100                                            1.10 x 100 = 110

    second year

- This is now the new percent since you are trying to find

a percent of a percent. You try to find 20% of 110 caribou

instead of the original 100 caribou. The 20% must be added into

the 100% (110 caribou)

or only use one step:

             100%             120 ÷ 100 = 1.20    1.20 x 110 = 132

            + 20%                                    1

             120%               On the second year, there were 132 caribou.

explanation

There was not a 30% increase over the years because if it was

30% increase, it would of been 130 caribou. This was not the same

and we did not get the same answer as a 30% increase because in the process

of finding 20% of 110 caribou and adding the 20%, we also had a new 100% or

a new all. This is finding a percent of a percent.

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Show You Know pg. 148

What is the final sale price at each store? Which is a better buy?

Explain your thinking.

Store A : 50% one day only

Store B : 25% off one day followed

by 25% off the reduced price the

second day

example price for both BAGS : $50

Store A

for one day:

50% off (discount ) of $50.

Since this is the discount, the discount is what you save, while the sale price is what

you pay. You could just find the sale price but since this is 50%,

you could just half the number at this point.

50÷2 = 25

$25 is the reduced price, or the amount you are now paying (not including taxes).

Store B

first day:
25% off of $50

 25       25 ÷ 100 = 0.25
100

0.25 x 50 = $12.50

Since this price is the discount, we try to find the sale price. The
sale price is 75% (subtracting 25 off of 100).
Then we subtract $12.50 from $50 = $37.50
You pay $37.50.

* You could have just found 75% of $50 rather than finding 25%
then subtracting that number from the regular price.

second day:
25% off of $37.50 (new 100%)

 25      25 ÷ 100 = 0.25
100

0.25 x 37.50 = $9.38

$37.50 - $9.38 = $28.12

conclusion

In conclusion to this math problem, store a would have been the better buy.

Store A is offering $25 for a bag while Store B is offering $28.12 on the second day.

If you choose Store A over Store B, you'll save $3.12 compared to Store B's price.

Again, for Store B, it's different from Store A because Store B includes you to find

a percent of a percent meaning there will be a new 100%.

 Overall, Store A has a better buy.

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