Joanna's Scribe Post

Multiplying Integers

January 13, 2014

    There are 4 different kinds of equations that you'll might come across whenever you are multiplying integers.

Here are some examples...

(+2) x (+6)                (+2) x (-6)

These two equations have one important thing in common. Both equations are able to make groups or in other words, you are using repeated addition. 

What is repeated addition?

How do you make groups?

Repeated addition is another way of multiplying. Instead, we add the groups of numbers we need. In this situation, the equation is...

 (+2) x (+6)

Repeated Addition is simple...         (+6) + (+6) = (+12)

As you can see, we are technically adding instead of multiplying. 

The equation asks you for 2 groups of +6 meaning, you should end up with 2 positive 6s'

                      two groups of 6                                                              (+6) + (+6) = 12  

                                     words                                                                                            repeated addition

Here is another equation that relates to making groups

(+2) x (-6) 

This is a different equation because instead of making groups of positive numbers, you are making groups of negatives. The steps are still the same.

You have two groups of (-6)

(-6) + (-6) = (-12)

              two groups of negative six                                                    (-6) + (-6) = (-12)  

                                  words                                                                                                repeated addition

The next equations will be a little different. Instead of making groups, we are removing them.

(-3) x (+3)                        (-3) x (-3)

The trick is to add zero pairs

♫ Whenever something is not there, You must add a zero pair! ♫

(-3) x (+3) 

In words this would be, remove two groups of three

You must indicate the arrows pointing out. This will show that you are removing.

Remove two groups of positive three = owe 9

(-3) x (-3) 

Remove three groups of negative three = have 9

Making groups - join the party

Removing groups - leave the party

Here's a video that I hope will make it easier for you to understand multiplying integers

           

Also, if you feel the need for a game to help you with this topic, try this game out!

http://www.mathplayground.com/ASB_IntegerWarp.html

Thanks For Reading

&

Good Luck!

Joanna's Scribe Post

Subtracting Integers

2 0 1 4

♫ Whenever something is not there,

You must add a zero pair! ♫

             Whenever you're subtracting integers, you may see these types of equations...

6 - (-9) =            (-2) - (-5) =            6 - 7 =          -4 - 6 = 

Everything is combined but subtracting. You must remove when it's an equation with 2 negatives. 

6 - (-9) =        or       (-2) - (-5) = 

Instead of saying, have six and owe 9, you say, have 6 REMOVE owe 9. The positive always stays behind. If you find 2 negatives together, you always have more than what you're owing. For this question, instead of combining have 6 and owe 9, we remove the negatives. By doing so, we add zero pairs. Like this...

6- (-9) = 15

Have 6 remove owe 9 = have 15

            Step 1                 Step 2               Step 3                     Step 4    

              (-9)                Remove         +++++++++         +++++++++ ++++++    =     15

      +++++++++              -9            Add it with your             

      - - - - - - - - -       - - - - - - - - -   positive number

For this next equation, we do the same thing but instead of starting with a positive and a negative number, they will both be negative.

(-2) - (-5) = 3

Owe 2 remove owe 5 = have 3

            Step 1                 Step 2               Step 3                         Step 4    

              (-5)                 Remove            +++++                      ++ +++   = 3 

            +++++                  -5        Combine it with your         - - 

            - - - - -               - - - - -       negative number

These next equations will be different from removing. The next equations will not have 2 negatives together meaning that you'll combine without removing. 

6 - 7 =         or        -4 - 6 = 

6 - 7 = -1

Have 6 and owe 7 = owe 1

              Step 1                                          Step 2           

           ++++++          = -1                 Remove all zero 

           - - - - - -    -                      pairs and take what is left.

-4 - 6 = -10

Owe 4 and owe 6 = owe 10

For this equation, we're doing the same thing but replacing the positive number with a negative number.

               Step 1                                                            Step 2         

      - - - - - - - - - -  = -10                     For this step, you're practically combining

                                             whatever negative numbers you have with the negative sign.

Here is a video that may help you to use different equations through subtraction...

In case you need any practice for subtracting equations, please enjoy this game...

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

Hope you find subtracting easier know that you've read this.

GOOD LUCK!

January 8, 2014

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!

Joanna's Pay it Forward

Pay it Forward 

2 0 1 4

PART I

What is Pay it Forward?

               Pay it Forward is having to do some sort of Act of Kindness for a person or a group of people. It's simple, it doesn't have to be extraordinary or courageous but something that would either help or make someone's day. There are many people who are physically and mentally hurt and Pay it Forward is a great opportunity for people like you and me to help them in a way that's possible. In the movie, Pay it Forward, a boy named, Trevor, was inspired to help three people he had thought needed help or felt like their life had problems. By doing so, his actions would inspire those three people to pay it forward for another group of three people. That's the whole beauty of this idea. Throughout the whole process of making someone's day, we come to the point where more and more people are becoming engaged. 

PART II

What was your Pay it Forward act of kindness?

                 Our group's Pay it Forward act of kindness were four actions; shovelling (money donated to the Philippine Typhoon Relief), designing kitchenware items for our neighbours,  giving out treats for teachers, dropping candy canes with small messages in people's mail boxes, and a box full of candy canes with a letter for a daycare.

Why did we choose this activity?

                 We chose these activities because it was something we were all capable of doing. Throughout the whole process of managing each act of kindness, we learned that the most important part isn't whether how many people we've helped but the most important part was seeing people understand what you're doing and inspiring each individual to make a difference. That's what makes it even better. It's nice to make someone cheer up but how do you know if they learned anything from what you've done? We had also chosen these activities because it was very fair for each person in the group. Watching someone do most of the work while the rest do less lacks the magic of teamwork. This project not only helped us to stretch but to experience more on working as one and what we needed to go through to make a big difference. 

Who did you help? (How did the person or people react?)

                 We had mostly helped people around our community. The most inspiring moment we've gone through during the time we spent on the project was shovelling. Shovelling the sidewalk was probably something we would never forget. At the beginning, we didn't expect to get any money or even anything out of it. We weren't doing this to get money but to help the people and at least save some time for them. Since it was winter break, we had plenty of time to practically do anything we wanted but might as well use most of our time to shovel people's sidewalk. While shovelling one of our neighbour's sidewalk, we unexpectedly saw the lady opening her door with a $20 bill in her hand. We were so thankful but we couldn't accept it. We didn't really need any money since seeing her smile isn't worth any amount of money. We had told her about our project and how we were inspired by the actual movie, Pay it Forward, and we were surprised to hear that she also helps people to move forward. She told us that we could use the money for coffee or food but instead, we told her we would donate it to the Philippine Typhoon Relief. We were so thankful and we couldn't hold the excitement in. After that, we went to the next house. Another lady had opened her door with another $20 bill in her hand! At this point, we felt like tearing up. It was so inspiring and it made us feel like difference makers. She was very surprised about what we did and again, we told her about our project and how the money is used for something good. We felt really honoured for what they've done so we gave them a letter to tell them how thankful we were including the designed kitchenware items.  They will always inspire us to be better people and if little kids shovel our sidewalks in 20 years, we'll do the same thing.

                           

                                                When did you do act of kindness?

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

                                                                                                                                                                

*Here is our video showing what we've done for each activity. We apologize for the length of the video but it was so hard trying to make it shorter because each moment we had was so special that we had no other choice but to add it in. Thank you and Enjoy!*

    

                                                                                                                                                             

PART III

How did your act of kindness go?

                     Our act of kindness had gone differently then we thought but we were still able to stay on the road. Throughout the whole winter break, we had the tendency of changing and tweaking most of the activities. Each action wasn't very easy. Making a difference is harder than it looks but while we wrote letters, designed, wrapped food, and shovelled the snow, we would forget how cold it was outside or how long we've worked for because of the people we've inspired. It removes all the hard work because something great came out of it. Doing these activities makes you want to do more good things.

What happened?      

                    When we shovelled, we planned to have 2 people shovel while the other 2 people captured each moment through videos and pictures. We all took turns to make it fair for each person. There was a time where no one wanted to take videos or pictures and we all wanted to do was shovel. It was more like a fun time and we promised each other that we would do this again before winter ends. After shovelling, we earned $40. The most difficult part was the weather. As long as you had 3 pairs of gloves then you'll be alright. 

                    When we designed the kitchenware items, we used sharpies to create designs on the items. To make the designs from rubbing off, we needed to heat them in the oven. What made this so difficult was to heat it more than once. To heat a batch of items, it took more than 30 minutes. We wanted to design these items because it was something we haven't seen too many people have done. We thought of using kitchenware items because that's what a lot of people would use. Overall, it was a great experience to do something new.

                   The time we had making teachers a letter and wrapping their gift was very fun. It was hard figuring out what each teacher would want or didn't want. Some of the gifts included Hersheys, Reeses, Candy Canes, Nature Valley Bars, and a letter. We were practically walking everywhere in Walmart trying to find the things we needed and we had almost lost each other while we were there! This action was just our way of showing the teachers how special they are to be doing what they do.
                   The idea of giving a gift for a daycare was something we felt was important. If you think about it, some people forget the importance of a daycare. The workers who help and watch the kids are people who take the time to do a simple thing yet a big help. In the letter we had given them, we wrote a little bit about how Pay it Forward works and about the movie. We put a good amount of information for them to fully understand why we're doing this and of course, we told them to pay it forward as well. 

                   Last but not the least was to create a card with candy canes shaped as hearts with a message. We had taped two small candy canes into one heart on the cover and when you open the card, it briefly talks about what Pay it Forward is for and if they have any further questions, they could easily call our school. Some of the messages we had put on the card were, 'Have a Great Day!', 'You are Amazing!' and etc. The hardest part of finishing this activity was giving them out. On the day we gave each card to everyone's mailbox, it was one of the coldest days we had gone out. We were glad that we hadn't shovelled on that day. The first 5 minutes of being outside, your ears and fingers were already frozen. Then again, we knew that all the hard work would be worth it.

How did you feel?

                         After the whole experience, I felt really influenced to do more activities that will for sure make a difference. Personally, this is just the start and even if we work separately in the future, this whole project taught us how to stretch and become independent with actions I thought I couldn't have done. At the end, we gained confidence from one another. That's really important when it comes to stretching because there will be times where you feel hesitant on whether you should help or not but it is never about the journey but the destination.

How did the person or people react?

                      The people had reacted with big smiles. The two ladies that saw us shovelling their sidewalk were very shocked. Honestly, even if we saw people shovelling our sidewalk, we'd all feel this warm feeling in our hearts. After a hard day at work and coming home seeing these group of kids giving time to do something they didn't need to do takes stress off your shoulders. 

Did you ask the person or people to pay it forward?

                       Yes, we did ask the person or people to pay it forward. At first, we were a bit shy since it's our first time doing this project but after awhile, you gain that confidence after talking to all these people. 

PART IV

Why is the idea of Pay it Forward so important?

                       The idea of Pay it Forward is important because we all learn something from it. I think that's what makes us better because if we experience something and we don't fully understand what you've done wrong, how will you ever prevent that mistake from happening again? In this case, we learned how to be more selfless, hopeful, and positive. At the end, the most important thing that matters is the love you've given. It could be family love, friendly love, true love, or etc. You will always be judged on how you treat people. We gain affection and care from this idea. Imagine a world full of people who cared each person, a world with no war, or no madness. Now, imagine a world full of people who hated one another and wore anger for every single day of their lives. It's a simple choice that leads to a big difference. Pay it Forward is the act of kindness that spreads and multiplies. The more people we help and are helped, the more we'll gain experience and pride.  

Has your act of kindness made a difference?

                       I think our act of kindness has made a difference. It may be a small difference but later on in our lives, those differences become bigger and brighter. Our act of kindness not only made a difference for the people we had helped but also for each of our lives. This will be something we could all get used to. 

Acknowledgement  

                      I'd like to thank the teachers for being one of the first people to inspire us to become who we are today. I'm thankful for your help and guidance in completing this project. Thank you for unfolding the importance of Pay it Forward and what comes out of it. I'd also like the thank my cousin for coming with us to buy some of the materials and to design some of the kitchenware items. Last but not least is to thank my parents for allowing us to work on this project. Thank you for having to go through our loud laughs and giggles and yet support us through the days we needed help. 

                                                                                                                                                                

 songs used   

iMovie Theme Music - Simple

Better Together by Jack Johnson

cameras used

Canon EOS T3I

Canon EOS 70D

editing software

Final Cut Pro

Other Group Members

Ceci Zhong                                Pam Joseph                   Allison Concepcion

                                                                                                                                                              

Believe in the magic of Paying it Forward

 2014.

Joanna's Percent Post

What is a percent?

Percent is an equivalent fraction out of 100.
Here is how we find an equivalent fraction out of 100.

  9/10 = 90/100
  9 x 10 = 90                 Why 100%? 100 is used because it's just right. It is also a number that is
  10 x 10 = 100                                                            easily seen.

Percent was made by the French. Per means 'out of' in French and Cent means '100'. Together, they make 'out of 100'. For the percent symbol %, the line symbolizes the 1 while the two little circles represents the two zeros from 100.

Improper or Top Heavy fractions are fractions that have a greater numerator than the denominator.
205/100 = 2 wholes, 205 out of 100, 205%
5/4 = 5 out of 4, 125 out of 100, 125%

100% means all, whole, everything, 100/100, 6/6.
10% means 10/100, 1/10.
50% means half, part / whole, 20/40 or 50/100.
25% means 25/100, 1/4, one quarter.
1% means 1 out of 100, 1/100.

Representing Percents %

a) 180%

                                         












b) 0.6%

c) 12 3/8%

Fractions - Decimals - Percents

Fractions and converting them into decimals and percents...

1) 3/40 

Decimals: 3 ÷ 40 = 0.075

Percents: 0.075 x 100 = 7.5 

               0.075    /     1

       0.075 x 100 / 1 x 100

                7.5    /    100

3/40 --> 0.075 --> 7.5/100

Decimals and converting them into fractions and percents...

2) 0.086

Fractions:               43 / 500 

                                How?

                         0.086 / 1

            0.086 x 1000 / 1 x 1000

                            86 / 1000

                     86 ÷ 2 / 1000 ÷ 2

                          43 / 500

Percents: 43 ÷ 500 = 0.086 0.086 x 100 = 8.6%

0.086 --> 86/1000 or 43/500 --> 8.6%

Percents and converting them into decimals and fractions...

3) 33%

Decimals: 33 ÷ 100 = 0.33

Fractions:     33 / 100

                       How?

                 0.33 / 1

      0.33 x 100 / 100

                  33 / 100

33% --> 0.33% --> 33/100

PERCENT OF A NUMBER

                  1) 20% of 60

Calculator: 20 ÷ 100 = 0.20                            Mental Math:   #   |  %   

0.20 x 60 = 12                                                                           60 | 100  

                                                                                      ÷ 5       12 | 20    ÷ 5

20% of 60 = 12                                                                     12% of 60 = 12

A way of finding a percent of a number is to divide. Of means divide. In other words, you are multiplying 20% to 60, but what is 20% as a number? In order to do that, you have to divide your percent by 100. After that, you multiply your decimal to your number or whatever amount you have.

               2) 0.1% of 40

Calculator: 0.1 ÷ 100 = 0.001                         Mental Math:    #   |   %

0.001 x 40 = 0.04                                                                      40  | 100               

                                                                                ÷ 1000    0.04  | 0.1   ÷1000       

                                                                                             0.1% of 40 = 0.04

Since 0.1% is less than 1 and you know that 1% of 40 is 0.40, you should have something that is less than 0.40.

When dividing by 10, 100, 1000, etc, you move the decimal to the left by how many zeros are in the number. 

60 ÷ 100 = 0.60

          6 0 . 0 = 0.60

                                                                            ^ ^ ^   - move to two place values since 100 has 2               

                                                                                                                 zeros.

                3) 250% of 400

Calculator: 250 ÷ 100 = 2.50                           Mental Math:    #  |   %  

2.5 x 400 = 1000                                                                      400 | 100

                                                                                       x 2     800 | 200   x 2

                                                                                      ÷ 4     200  | 50     ÷ 4

                                                                                            + 1000 | 250

                                                                                        250% of 400 = 1000

Since 250 is greater than 100, you'll end up having more than you total.

             What you do on one side, you do to the other.

Combing Percents %

When you are working with money, you may often see discounts, sale prices, or regular prices...

Discount - What you save

Sale Price - What you pay

When finding the sale price...

Regular Price - Discount = Sale Price

When finding the total price including the taxes...

Step 1) Calculate the total prices of the item(s) that were bought.

4.4 Page 149

7.  A herd of 100 caribou 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.

             a) The population of the herd of caribou was 132. How?

                                

1. For finding the increase of the caribou, first thing's first is to add 100 + 10 since 'increasing' means to end up having more than what you had before. This tells you that for your answer, you should have a number that's more than the regular amount of caribou. 
2. After that, you need to take the percents that were from the question and convert them into a decimal. By doing so, you would have to divide the percent by 100.
3. Last part is to multiply the decimal to the total amount of caribous.

                            100 + 10 = 110                 110 ÷ 100 = 1.10              1.10 x 100 = 110

                                100 + 20 = 120              120 ÷ 100 = 1.2            1.2 x 110 = 132

                     b) The reason why 30% was not used because 100% was changed. From the first photo, the total amount of caribou were 100, but since we needed to make another diagram, the total was not 100 anymore because it was changed to 110 instead.

4.4 Page 148 Show you know

What is the final sale price at each store? Which is a better buy? Explain your thinking.

Store A: 50% off one day only

Store B: 25% off one day followed by 25% off the reduced prince the second day

Store A:

Price - $200 for a guitar

200 ÷ 2 = 100

Why 2? I used 2 because the 2 represents half of the number and in decimals, half equals 0.5.

or

50 ÷ 100 = 0.50              0.50 x 200 = 100 

The final price of the guitar in Store A is $100.

Store B:

Price - $200 for a guitar

25 ÷ 100 = 0.25       0.25 x 200 = 50        200 - 50 = $150 

   25 ÷ 100 = 0.25         0.25 x 150 = 37.5        150 - 37.5 = $112.50

First, you'll need to convert your percent, in this case it is 25%, to a decimal. In order to do that, you'll need to divide your percent out of 100 since percentage is out of 100%. 

25 ÷ 100 = 0.25

Second, you will need to solve what 25% is out of 200. To do that, you need to multiply the decimal to the total which is 200.

0.25 x 200 = $50

Now, you have found what 25% is out of 200 but you do not know how much you pay. Since we are working with money, 25% is what you save. You aren't done till you have your sale price. To find your sale price, you need to subtract 25% of 200 from $200.

200 - 50 = $150

You now have the sale price of the guitar of that one day. Next step is to find another 25% off from the sale price on the second day.

Again, you'll need to convert the percent into a fraction and multiply the given decimal to the sale price, which is 150.

25 ÷ 100 = 0.25                     0.25 x 150 = 37.5 or $37.50 

After that, you will need to subtract 25% of the reduced price and subtract it from the sale price, $150.

150 - 37.5 = 112.5 or $112.50

Which is a better buy? Buying the guitar from Store A is a better buy because you are saving $12.50 if you don't buy it from Store B. The reason why Store A was better than Store B was because of how the total of 100 was changed to 150 which caused it to have a bigger amount. Since Store B has a greater total or all than Store B, it will end up saving less than what Store A is saving.