841Angelic+M


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This is **my** g.8 Math Portfolio. There are a total of 4 sections that I will be guiding you through: Mean, Median, and Mode, Square Roots, Percentages, and our most recent unit, Ratios and Proportions. Each section has 3 sub sections, 2 of which are included in this page. Just to give you a little overview, I will be teaching you about these units and then you will be using that knowledge to solve a few questions. I have provided a link after every question so that you could verify your answer after attempting to solve it. Good luck! =)

How do you calculate the...

Also known as "__the average__". And there you have it =)
 * 1) Rewrite the data in numerical order, **ASCENDING** or **DESCENDING** (eg. __a f b e d c__ becomes __a b c d e f__ -or- __f e d c b a__).
 * 2) Add up all the numbers in a set of data. This equals the **SUM OF ALL DATA.**
 * 3) Count up how many **PIECES OF DATA** there are. This will be known as the **AMOUNT OF DATA.**
 * 4) Divide the **SUM OF ALL DATA** by the **AMOUNT OF DATA.**

Also known as "__the number in between__" If there's and **ODD** amount:
 * 1) Rewrite the data in numerical order, **ASCENDING** or **DESCENDING** (eg. __a f b e d c__ becomes __a b c d e f__ -or- __f e d c b a__).
 * 2) Make **PAIRS** (eg. [[image:http://i19.tinypic.com/47m7rb7.png width="100" height="32"]]).
 * 3) Then the middle number becomes the median (eg. [[image:http://i12.tinypic.com/2jac3uf.png width="100" height="32"]]).

If there's and **EVEN** amount:
 * 1) Do steps 1 and 2 above.
 * 2) Find the **TWO** middle numbers and **INDICATE** that they are in some way. (eg. [[image:http://i15.tinypic.com/2ik5wt1.png width="100" height="32"]])
 * 3) **ADD** them together (eg. c + d)
 * 4) **DIVIDE** the **SUM** by 2.

Also known as "__the most popular number__" or "__the number showing up the most__".
 * 1) Rewrite the data in numerical order, **ASCENDING** or **DESCENDING** (eg. __a f b e d c__ becomes __a b c d e f__ -or- __f e d c b a__).
 * 2) **FIND** the number that shows up the **MOST**.
 * 3) You can have **MORE THAN 1** (eg. [[image:http://i16.tinypic.com/49j4h38.png width="96" height="21"]]).
 * 4) You can have **NONE** (eg. [[image:http://i5.tinypic.com/2vd1kzp.png width="74" height="24"]]).

Find the **MEAN**, **MEDIAN**, and **MODE**:

=//78, 45, 45, 78, 60, 75//=

Give up? Want to know the answer? Click here.

What is a **PERFECT SQUARE**?

Any square with equal sides and NO decimals or fractions is a perfect square (eg. l x w = 6 x 6). Below is a **PERFECT SQUARE CHART** up to 10. It will be useful to you later on =). See, no **FRACTIONS** or **DECIMALS**.

What is (ignore the blue underline =P)?

is the sign for **SQUARE ROOT**. A square root is a number produced when you multiply a number by itself (eg. the square root of //121 equals// //11², which equals// //11 x 11//). Unlike **PERFECT SQUARES**, square roots could have decimals and fractions. On a calculator, all you have to do to find the square root is type in the number and push the "" button.

I will show you an easy way to get the without using a calculator. We will use mixed fractions! Of course it won't be completely accurate but it wil be pretty close. It'll probably be with one to two tenths of the way.

The...

is the first number you should find out. (**__1__**¾)
 * 1) Find the **PERFECT SQUARES** on either side of the number you are trying to find the square root of. You can use the **PERFECT SQUARE CHART**. Example: [[image:http://i16.tinypic.com/2qiqx5y.png align="center"]]
 * 2) Find the **SQUARE ROOTS** of the adjacent perfect squares. (eg. [[image:http://i19.tinypic.com/2hz24cz.png]]= 5 and [[image:7sqrootsANGELIC.PNG width="82" height="26"]]= 6)
 * 3) Take the square root of the first number. This is the whole number for the number you are trying to solve.

is the top number or part section of a fraction (1 **__3__**/4). Let us continue on...
 * 1) This step is really easy... Subtract the "original number" from the first perfect square. (eg. 27-25=**__2__** <- the numerator).

is the bottom number or total section of a fraction (1 3/**__4__**). Now for the second last step..
 * 1) Another easy step. All you need to do is subtract the lesser perfect square from the greater perfect square (eg, **36**-**25**=**11**).

All that's left to do now is combine them. (eg. **5 2/11**)

//Find the square root of// //**78**. You are allowed to use the perfect square chart below (click to enlarge).//

Give up? Want to know the answer? Click here.



A percentage is a fraction out of 100. It can be more than 100 though. For example, if you were to draw out 150%, it would look like the image below.



Remember a percent is out of 100. 1 square equals 100. The NUMERATOR is 150. 150 - 100 = 50, so you need to colour 50 more squares. Think of it as making too much soup. You wouldn't try to shove it all into one bowl right? Now let's see if you can answer this question...

Is taking 15% off an item, then taking away 10% the same as taking away 25%?

Give up? Want to know the answer? Click here.



We learned that in questions like "//What percent of 50 is 25?//" we are __always__ given **3** numbers, leaving us with one more to solve. In this case the numbers are **25** as the first part, **50** as the first total, and **100**. Remember that a percent is __always__ out of 100. **__Per__**//cent// = **__out of__** //100//. In Term 2, we learned how to solve ratio and proportion questions using **CROSS MULTIPLYING**, **RATIO TABLES**, **XKY CHARTS**, and **EQUIVALENT FRACTIONS**. Let me show you how to use three of these simple methods using instructions and diagrams. I will be showing you the ones I use the most...

(PT table) A ratio table has 2 parts, one for the part and one for the total. Our example question will be...//If Paulo can eat **45** chips in __25__ seconds, how many can he eat, **__500__** seconds//? Ilustrations are after all the steps =)

1. Find the "part" or numerator of the question. It's the smaller number. Put it in the first section. In this case we will rename the part section **SECONDS** because it is the lesser value. 2. Find the "total" or denominator. Obviously, it's the larger number. Put it in the second section. Using the example question, we will rename the total part to **CHIPS**. 3. From here I find the **UNIT RATE**. The unit rate is the smallest value. Divide the first section (or the seconds section) by itself. 4. What you do to one side, you __have__ to do to the other side. Now you can find any value using this. Remember what you do to one side, you must do to the other.

Ilustrations:

media type="custom" key="27229"

An xky chart has 3 parts as you might've guessed. The first is for **object A**. The middle is used to show **what number you multiply** the value of object **A** by t**o** get the value of object **B**. The final section is to show the value of **object B**. I will be using **FINDING THE MISSING MEASURE** as an example.



1) Decide what to lable the x and y sections. If you're doing **FIND THE MISSING MEASURE**, I would label it __shape A__ and __shape B__. You could just call it __A__ and __B__ for short. 2) Get the parts (the length or width, depending on which one is missing) of the two things you are comparing and put them in the appropriate columns. In this case, we are comparing the widths first because the both areas are not missing it's measurement. 3) Divide section B by section A. Put the answer in the K section. 4) Put the remaining pieces of information into the appropriate sections. 5) Depending if A is **larger** or //smaller// than B, **divide** or //multiply// it (you should be able to pick out what to do). Put the answer in the blank section.

And there you have it! Ilustrations: media type="custom" key="27245"

Equivalent fractions are made up of usually 3 fractions. One is a word fraction and the other two are what you are comparing.
 * 1) Decide on a word fraction. For a question like "//68 is 90% of what number?//" it would be **PART** over **TOTAL**.
 * 2) Put the information that you already know in place. I'll use the example question from #1 again... [[image:http://i16.tinypic.com/34o37uo.png width="95" height="49"]]. //*Do you remeber how I got the 100?*//
 * 3) Compare the two pieces of information that we already know (part to part -or- total to total) such as we do when we use **XKY CHARTS**. Now you have figured out the relation between those two numbers. This would count for multiplying the number. Example: [[image:http://i17.tinypic.com/4bnvcbb.png width="243" height="26"]]
 * 4) Remember the rule, what you do to the top, you must do to the bottom. Depending on whatever value is missing it could be the other way around. Example: [[image:http://i16.tinypic.com/2a85g5k.png width="134" height="25"]]

Now you have found the missing value! Are you ready to solve some questions?

//Use// //**EQUIVALENT FRACTIONS** to solve this question. Jacob has a record of winning **2** boxing matches for every **5** he loses. If he had **49** boxing matches during the last year, how many did he win?//

//Use a// **//RATIO TABLE//** //to solve this question: On average, Eva runs about **23** laps in **30** minutes around the school. How long does it take her to run 100 laps?//

Give up? Want to know the answer? Click here.

Marking Rubric:
 * || **Question 1** || **Question 2** || **Question 3** || **Question 4** || **Question 5** ||
 * Question for parent to do || 2/2 || 2/2 || 2/2 || 2/2 || 2/2 ||
 * Answer with explanation || 2/2 || 2/2 || 2/2 || 2/2 || 2/2 ||
 * Parent Notes explaining topic || 2/2 || 2/2 || 2/2 || 2/2 || 2/2 ||
 * Extra work to further explain topic, bubbleshare, pictures etc. || 3/3 || 3/3 || 3/3 || 3/3 || 3/3 ||
 * Extra links to math blog sites || **5/5** ||  ||   || **Total** || **50/50** ||