Anabelle's Algebra Post

Algebra- writing mathematical phrases using letters to represent numbers

Variable- a letter that represents a number in an algebra equation or expression

Constant- integer in an algebra expression or equation

Equation- only has one answer and has an equal sign

Expression- has a pattern, many answers
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Adding and Subtracting

Whether we are adding, subtracting, multiplying, or dividing we start off by isolating the variable.

Let's start off with an addition problem.

v+8=26

How we isolate the variable is to make a zero pair to cancel out the constant. Try not to think of +8 as add eight, but instead think of it as positive eight. To cancel a positive eight we need a negative eight.



Remember, what we do to one side, we do to the other side.


Then what we have left is the v on one side and 18 on the other.

The same rules apply for a subtraction problem, but instead we cancel the constant with a positive integer.

The only thing left to do is verify to check.

Plug in the number in place of the letter.

Then show equality.


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Multiplying and Dividing

10n=40

To be able to isolate the variable of a multiplication problem we will divide and do the same to the other side.


Next, verify to check.


x/2= 5

Isolate variable.
Cancel using opposite.

Then, verify to check.




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Integer Tiles

Now, we will solve these problems using integer tiles.



*NEVER USE ALGEBRA TILES TO VERIFY TO CHECK

x+2=3

Start by changing the problem to what it would look like using integer chips.


Using the same concept we'll cancel the constant using zero pairs. In the case we cancel two +1 tiles using two -1 tiles. With what's left is how much the x tile is worth.


x2=6

1. Zero pair
2.Simplify
3.Answer


-2x=4
1. Zero pair
2.Simplify

We need to switch the final answer around by multiplying -1 on both sides.


x/2=5

When representing x you'll cut it in half .

You then add the other half making the x complete, and remember the rule of equality. You add another half then you add another set of tiles.

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Solving 2 step equations

2x+1=7

1.Isolate the variable starting off with with the addition/subtraction part
2.Cancel constant
3.Balance
4.Simplify the variable
5.Balance

6.Verify


x/2+2=6

1.Isolate the variable starting off with with the addition/subtraction part
2.Cancel constant
3.Balance
4.Simplify the variable
5.Balance

6.Verify to check


If you're still having trouble have a look at this video.

Adding mixed fractions

Anabelle's Great Big Book of Integers

Chapter 1: Grade 7 Integer review

From last year I learned that integers are positive and negative whole numbers. Integers can be represented using integer chips (2 different colored chips representing positive and negative integers) and with a number line as well.

Here are the pictures of the two:

(number line)


(integer chips)



Questions:

-3-(-7)


-3-7


3-7


3+7

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Chapter 2: Multiplying Integers

(+2) x (+3)=

or two groups of +3

(+2) x (-3)=

or 2 groups of -3

(-2) x (+3)=

or remove 2 groups of +3

(-2) x (-3)=

or remove 2 groups of -3

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Chapter 3: Dividing Integers

Partitive division: a problem where you know the total number of groups, and you are trying to find the number of items in each group.

6÷2= 3

-6÷ (-2)= (-3)


Quotative Division: a problem where you know the number of items in each group and are trying to find the number of groups

(-6)÷2= (-3)


Sign rule:

6÷2= 3
The answer will be positive because the integers are the same sign.

-6÷ (-2)= 3
The answer will be positive because the integers are the same sign.

(-6)÷2= (-3)
The answer will be negative because the integers have different signs.

6÷(-2)= (-3)

The answer will be negative because the integers have different signs.
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Chapter 4: Order of Operations with Integers

(+5) x (-3) + (-6) ÷ (+3)=

For this problem you will probably only need the DMAS in BEDMAS.


I've got to admit, this video made things really easy to understand:

Term 2 Reflection

In Term 2 We learned about Percents, Surface area, and Volume. For the most part, I though that I did well on all three of them. Surface Area and Volume were a bit harder due to the many formulas and units we had to remember in order to solve and get full credit for quizzes and tests. Percents were easier because of my previous teachings and knowledge on the subject. Next term, I will try to keep up with blogging. I think I should comment more and make my opinions and suggestions more helpful, by suggesting sites and videos. I also think I should read my questions more carefully, and to check over my tests to see if I’m missing anything.

I learned about how to convert percents and how to use percents in our daily lives. At this point along the way we enhanced our problem solving skills. For surface area, we learned about how to calculate the total surface of different prisms and cylinders. For volume we learned how to calculate the volume of prisms and cylinders. This is basically how much is in or how many units the shape is made of. That’s also the difference between surface area and volume. Surface area is finding how much is around the shape and volume is how much a shape is made of or can hold.

Winnipeg Harvest Visit- Make Manitoba Hunger Free 8-14

1.What did I learn about Winnipeg Harvest?

I learned how important Winnipeg Harvest is to many people and how big the part it plays in the community. To think, without Winnipeg Harvest many people would be left to starve, and without the countless and generous donations they receive, Winnipeg Harvest would be out of food within a week. Almost none of the donations are wasted. When they come across something they can not send or use they try to compose waste material and most of the leftovers, even sending some unusable bread to be sent to feed animals, such as horses.

2.Who does Winnipeg Harvest Help?

Winnipeg Harvest helps anyone who is in need of food. On average, 56 000 people use Winnipeg Harvest every month. Sad to say, half of the people are under the age of 18. While on my tour I could tell that the clients are very grateful to them when I saw a few lending the Harvest a hand. Behind each client is their story. Each have a reason for not having the money for food. Some being the need for medical attention, but do not have the money for both. Whatever it is Winnipeg Harvest will care to their needs the best they can, even making sure you get the nutrition you need through the basic nutrition kits.

3.Where does Winnipeg Harvest get the food it supplies to its users?
Winnipeg Harvest gets the food they supply from many generous agencies. Even the trucks they use were kindly given to them to help with the relocation of food. Many stores, other food banks, businesses companies and schools across the province help Winnipeg Harvest. Some examples being Sobey's, Superstore, Safeway, and of course, donations from the public. You may also find bins at Superstore and Safeway to drop off donations.

4.What are the top 10 items needed in Winnipeg Harvest?

The top ten items needed in Winnipeg Harvest are:

Canned fish and poultry
Canned fruit and vegetables
Canned stew, chili, brown beans
Peanut Butter (light)
Baby Food
Whole grain pasta/whole wheat pasta
Rice
Canned spaghetti sauce or tomatoes
Cereal
Canned soup

As you can see these are items anyone can get a hold of. All you need to do is go out and donate them. I know that they'll really appreciate it.

5. When you volunteered what do you remember about your job?

What I definitely remember the most was the vast amount of food they had. While touring I saw countless piles of pasta, bread, cereal and pretty much anything else you could imagine. Afterward I remember having to wash a bunch of bins. It was a bit gross, (especially the last bin I had to wash), and I almost fell into them countless times, but it was a great experience. I was glad to be of some help, and I'm sure they really appreciated it. While moving around the warehouse I found that the volunteers were really close to each other. Seeing them talk and joking around, and it was truly very heartwarming to see. Next was pasta sorting. It was not as easy as I had once thought. There were so many varieties of pasta, some that I've never heard of. I had a hard time deciding where I would place some, and just when I think I get it, I find a new kind of pasta. Luckily, I was assigned to label boxes instead. Our teamwork was great, and we managed to fill quite a few boxes. I really learned a lot from this trip to Winnipeg Harvest, and I was really happy to have come.

For more info check out their website: here

Math textbook: pg. 250-253 #2,5,8,10

No, it does not matter.
Take this rectangular prism for example (the proportions are probably strange, but you get the idea.)

v=area of base x height
v=50cm² x 4cm
v=200cm³

v=area of base x height
v=20cm² x 10cm
v=200cm³
As you can see the volume is the same.



v= area of base x height
v=12cm² x 5cm
v=60cm³

v= are of base x height
v= 15cm² x 4cm
v=60cm³



v= are of base x height
v=120cm² x 8cm
v=960cm³

v=are of base x height
v=48cm² x 20cm
v=960cm³



So, basically one centimeter cube would look like this:

And if you were to make one layer or a base out of the fifteen centimeter cubes used, it should look like this:

The area of the top of this one layer should be 15cm² so we will use that as our base.

Since the prism is made of 5 layers of those 15 centimeter cubes we will use that as our height.

v= area of base x height
v= 15cm² x 5cm
v=75cm³



Though worded differently it is basically asking for it's volume.

v= area of base x height
v= 1250cm² x 100cm
v= 125 000cm³

Here's a link to calculating volume.

And two videos explaining both rectangular prisms and cylinders:




Cylinder Volume and Volume Problems


v=π x r x r x h
v=(3.14 x 12 x 12) x 15
v= 452.16cm^2 x 15 cm
v= 6782.4 cm^3

6782.4/4= 1695.6cm^3

Assume that 1/4 of the cheese was cut.


Cylinder one:
r= d/2
r =10/2
r= 5m

v= π x r x r x h
v= (3.15 x 5 x 5) x 30
v= 78.5 m^2 x 30m
v= 2355m^3

Cylinder two:
r= d/2
r= 8/2
r=4

π x r x r
(3.14 x 4 x 4)
50.24 m^2

2335m^3/ 50.24m^2= 46.5 m

I pray that I made any sense.

Final Percent Post

In general percents are a way to represent numbers as a fraction out of one hundred. In this chapter we learn how to represent percents, how to write it as a decimal or fraction, how to find the percent of a number, and how to combine percents. Percents are essential to learn for it appears in our lives daily, like when we shop.

Representing percents:
Percents are used to represent numbers with a fraction out of 100. To show percent we used hundred grids, and filled them depending on the number we are representing. for example:

Fractions, Decimals, and Percents:
Percents can also be represented as fractions or decimals and can be used to represent numbers in different situations.


Percent of a number:
Using various mental math strategies, ratio tables, and changing the percent to a decimal and then multiply by the number you can find the percents of numbers.



Combing Percents:
Percents can be combined by adding to solve problems.



Here's a link to one of my older posts.
Also, a website I found useful.
And lastly, a video:

Anabelle's Percent Review Video

Percent is used as a way to express a number out of 100, and can also be written as a decimal or a fraction. Percents are essential to learn, for it is used in every day life. Like, shopping, and business.

Here's my video:

Anabelle's Pay it Forward

Part1:

(Movie summary)
Trevor, is a young boy who through a project given to him by his teacher Mr. Simonet has effected the lives of countless people. He was able to see the goodness in human nature, and so came up with an idea, that he at first thought had failed. He would do a favour to 3 other people, and they would each do a favour to another 3.

(My take on Paying it Forward)
Paying it forward is when you do a favour for someone else and not get anything in return. Instead, that person must help another person, and so on and so on. So, Instead of it being a endless cycle of favours between two people, it will be a chain of acts of kindness effecting many.

Part 2:
My act of kindness will be to look after my cousins puppy, Hiro, for the weekend. I chose this activity because after they got the puppy I noticed that they have not been getting a lot of free time for themselves. With both parents working and my two cousins in university, they're very busy people.




Part 3:
My act of kindness went pretty well. I've been bitten a few times, but I survived the day, and my cousins are quite grateful.

I spent most of my day, following Hiro around, playing fetch, and taking him outside. As simple, as it sounds it isn't. Take your eyes off him for one second and he's gone. Not only that he's teething and prone to biting people, ie. me. Even putting a leash on him is tedious. Though cute and fuzzy, he has also attacked my brother one or two times, and has also chewed up my camera strap as seen in the film.

After a long day I actually feel quite proud of myself. I mean, even my cousins questioned whether or not I could handle him. It feels really good to do something nice for someone.

They were surprised about the favour, stating it might be a little much to consider it as one, but they were very happy. They were also hesitant at first, but they let me take care of him.

I did explain to them the concept, and asked them to pay it forward after they tried offering me money. Though taken aback by the request they said they would think about it.

part 4:
It is important, because one good deed can effect many people. Sometimes even save lives, like the ones in the movie. The woman who was ready to jump, and the little girl who needed medical attention were both saved, and Trevor didn't even know them.

My act of kindness may or may not have made a difference. I suppose it depends whether or not the people I've helped are willing to pay it forward. If not, I could always try paying it forward again, and again until it does.

Math textbook: Pg.135-136 #1,3,6,7,9

Jordon is correct. When converting a decimal to a percent you multiply the decimal by 100 or move it up 2 place values.
0.003x100=0.3


I'm not all that sure about this one, but yes they can be both correct. Let's pretend the other team scored a total of 10 points. 500% of 10 would be 50. 5 times as many would also be 50.
(Check out Mark873's scribe. He has the same answer, but he explained it differently.)

(The answers for the following questions are highlighted and the shown work isn't.)

6.Convert each decimal to a percent and a fraction.


7.Change each decimal to a percent and a fraction.


9. Express each percent as a decimal and a fraction.



If you are having trouble understanding here's a link to a site you may find useful. It has a short exercise at the end to make sure you get what they were explaining. You can also take it to refresh your skills.

And of course, a video. This one is only percent to fraction, but I'm sure you'd find the other videos in the suggestions on youtube. Feel free to send me a link to another video,(because honestly, I don't like the monotone in their voices. It's not very enjoyable to sit through.)