Math Word Wall

PERIMETER measures the distance a closed figure. It is the sum of the side lengths of the figure.
 
Perimeter of a rectangle:
P=length+width+length+width
P=(Length+Width)x2

Perimetre of a square:
P=Sidex4 

Perimeter of a pentagon:
P=Sidex5


A Area Model Is A different way to show multiplication.
For this example I used 7783 x 69.
Area Model Shown Below  V V Instructions to make a area model is under the example.
 7000 x 60 =
420 000

700 x 60 =
42 000

80 x 60 =
4 800

 
 3 x 60 =
180

 7000 x 9 =
63 000
 700 x 9 =
6 300

80 x 9 =
720

 3 x 9 =
27


Then we add 420 000+42 000+4 800+180+63 000+6 300+720+27
Which equals 537 027
How To Make a Area Model
1. Build A Rectangle
2. Draw VERTICAL line(s) in the rectangle NOTE You should ONLY draw as many lines as the highest amount of digits(In my case I had a 4 digit number: 7783 so I would only make 3 lines because with 3 lines you get 4 spaces and with 4 lines you will get 5 spaces) ALSO Make the biggest digit have the biggest space so first block gets the most space and the last block gets the least.
3. Draw HORIZONTAL line(s) in the rectangle. NOTE Make only one Horizontal line if you have a 2 digit number, 2 lines for 3 digit etc etc.... Also make the top have a bigger space then bottom(So the line wouldn't be straight across the middle)
4. Basically add the expanded form of the number, so in each block write the expanded form of the largest number(by that I mean you put 7000 in the first then 700 in second 80 in third and 3 in fourth).
5. Now you have your 69 left over(or whatever your number is) so now 69 in expanded form is 60 and 9 so now in the top row of boxes you put the highest value(hundreds tens thousands etc) and multiply it by the value that is already in that box. For the second row of boxes you put the lowest(or whatever comes next) value and multiply it by the same value.
6. Now multiply every box equation, so 7000 x 60, 700 x 9 etc..
7.Now add all of the sums and there's your answer!

Factor Trees
A factor tree is just like a table. But It is spread into a tree. After The Example I will show you, what a factor tree is.

Example Number: 64(our class), make a factor tree for that number.(If question says make all possible factor trees you probably should make more than one)
          64                  OR             64
         /   \                                   /   \
        8 x 8                                2 x 32
      /  \  /  \                               |   /  \
     4x2x4x2                             2x2x16
    / \  |  / \ |                              |  |   /  \
   2x2x2x2x2x2                                   2x2x2x8
                                              |    |   |  / \

                                             2x2x2x2x4
                                             |   |   |  |   / \
                                            2x2x2x2x2x2

How to make a Factor Tree/What it Is
Okay so, basically since you already know this(I will make sure its detailed if you do not know) you have a base number or the "top" number in this case I have the number 64. The point of a factor tree is to list all the factors branched in to the factors of a certain number(base number). What I mean by "list all the factors branched into factors of a certain number" is that if you have the number 64 you can only include its factors in its Factor Tree for example, 19 is not a factor of 64 so it is not included in its factor tree.
There is also the Prime Factorization(Prime Factors). Well I bet you're saying,Whats a prime factorization?! Well a Prime Factorization is the last equation of the factor tree. That means the last row of numbers are all prime, that's the "Prime" part of it, the factorization comes because even though they are all prime numbers they are still factors. So that sums up to be: The last equation of the Factor tree is made from prime numbers. It is called the Prime Factorization.

Long Division
All of you know what Long Division is so I'm not going to take my time to explain that to you. But what I am going to explain to you is long division Method #2. I will show you an example then explain. Example Number :9462÷29.
               
29) 9462  | 300
    -8700  |
     0762  | 20
    -0580  |
      182  | 6
    - 174  |      
         8    326         
... 9462 ÷ 29 = 326 29 or 326 R 8

So basically It's really simple.
On the left of the line is your division on the right is your addition.

NOTE: DO NOT PUT A 3 DIGIT NUMBER IF THE DIVIDEND IS A 5-DIGIT NUMBER! FOR 5-DIGIT YOU WILL NEED TO START WITH THE 4-DIGIT NUMBERS. SAME RULE IS APPLIED IF IT GOES TO 6-DIGIT OR 7-DIGIT.
 
1. Make a long division symbol with a line going down the end.
2. Find a number 3 digit number ending with two zero{s}(EX.100, 200, 300, DO NOT PUT: ex. 846 999 522)[If your reading this from step 7 make that 3-digit number a two digit number with one 0]
3. Multiply that number with your divisor.
4. Put the 3/2 digit number ending with two/one zero(s) on the right side of your line
5. Subtract the answer from step 3 from your dividend(Do just as you'd do in a normal long division equation)
6. Now Make the 3-digit number into a 2-digit number ending in one 0.
7. Repeat steps 2-5
8. Make the two digit number a one digit number with no 0's
9. Find the number.
10. Subtract it with your left over dividend.
11. Put that one-digit number on the right side of the line.
12. Add the right side of the line
13. If there is a remainder make it into a fraction or decimal.
14. You have just completed Method # 2 of division. Enjoy.

A composite number is a whole number with more than two factors.

Examples:12 is a composite number. It's factors are 1,2,3,4,6 and 12.
                35 is a composite number. It's factors are 1,5,7 and 35

A prime number is a number that has only two factors:1 and itself.

Examples:5=5x1     17=17x1

Factors - numbers that are mulitiplied to get a product
Product - the result obtained by multiplying two factors
Dividend - the number to be divided
Divisor - the number by which another number is divided
Quotient - the number obtained by dividing one number into another

A proper fraction is a common fraction that names a number less than 1. The numerator is less than the denominator.    1/2  2/3  6/7

An improper fraction is a common fraction that names a number equal to or greater than 1. The numerator is equal to or greater than the denominator.   3/2   6/5   6/6

A mixed number has a whole number and a fractional part. The fractional part may be a common fraction or decimal amount.  2 1/2 = 2.5    3 4/5 = 3.8   4 3/5 = 4.6

Perimeter - measures the distance around a closed figure. It is the sum of the side lengths of the figure.
Perimeter of a rectangle - P=lengthx4
Perimeter of a square - P=lengthx4

When solving perimeter problems, show all your work and remember to include the unit of measurement in your final answer.

Probability is the likelihood , or chance, that a given event will take place. Probability is represented by a fractional number(1/2 or3/5 etc.) or a decimal number between 0 and 1 or a percentage(0-100%).
The closer to 1, the more likely it is that the event will take place.
The closer to 0, the less likely it is that the event will take place

Examples - The probability that the sun will rise tomorrow is 1.
                  The probability that it will snow in Honolulu is 0.
                  The probability that a tossed penny will land on heads is 0.5 or1/2 or 50%.

Experimental probability is based on the results of an experiment. An example of experimental probability would be drawing a red object from a a bag of multi-coloured objects.
For theoretical probability, all outcomes are equally likely. It is not necessary to conduct experiments. An example of theoretical probability would be drawing a red card from a full deck of cards.


Polygon - a closed figure with three or more straight sides; named by the number of it's sides;for example, a five sided polygon is a pentagon
Quadrilateral - a figure with 4 sides
Parallelogram - a quadrilateral with both pairs of opposite sides parallel
Rectangle - a quadrilateral with 2 pairs of equal oppisite sides and 4 right angles
Square - a quadrilateral with equal sides and angles, each angle is a right angle
Rhombus - a quadrilateral with all sides equal and 2 pairs of parallel sides
Triangle - a polygon with 3 sides
Equilateral Triangle - a triangle with all sides equal
Isosceles Triangle - a triangle with 2 sides equal
Scalene Triangle - a triangle with no sides equal
Right Triangle - a triangle with one right angle
Acute Triangle - a triangle with all angles less than 90 (all angles acute)
Obtuse Triangle - a triangle with one angle greater than 90 and less than 180


A ratio is a comparison of to quantities with the same unit.
Part to part ratios are ratios that compare one part to another part
A ratio that compares a part of a set to the whole set is a fraction.

A rate is a ratio that compares two items measured in different units. Rate problems can be solved using pictures, tables, graphs and calculations.

Examples - A tortoise travels 0.2 km/h
                 A cheetah can run 70 km/h

                 In 3 hrs, the tortoise will travel 0.6km.(0.2x3).
                 In 3 hrs, the cheetah can cover a distance of 210 km(70x3).

Mean:is the average of 15 in this case!
Ex. 13+18+13+14+13+16+14+21+13  divided by 9
       =135 divided by 9
       =15

Median:the middle value
Ex. 13,13,13,13,14,14,16,18,21  The middle value is 14 because it's the middle number.

Mode: the number repeated more often than any other.
Ex. 13,13,13,13,14,14,16,18,21   13 is repeated often.

Range:The smallest value subtracted by the largest value. If we use the numbers we have been using in the                      previous examples the range would be  21-13=8. So the range would be 8.

Outlier:The number that is not close to the rest
           Ex:13,18,13,14,76,13,16,14,15,13

Circle Graph(Pie Graph):This type of graph displays data using a circle divided into sectors that shows parts of a                                       whole. It is usually colour coded and labelled show the different parts.

Broken Line Graph: This type of graph shows data using line segments to show trends or patterns. They usually go up and down a lot. Points are also connected by line segments. Broken Line Graphs show changes over a period of time.

Stem and Leaf Plot: This graph consists of a stem;left hand column that contains the tens digits and a leaf;right                                  hand column that contains the ones digits. This graph is used to show place value.

Pictograph: This type of graph uses picture/symbols to represent the data. The pictures/symbols can represent more than one object. They key also tells what the picture represents. It shows quantities or amounts. It is usually in the form of a t-chart or bar graph. Not all the pictures show the same value.

Bar Graph: This type of graph is usually colour coded and displays data using vertical or horizontal bars. It                             represents two different groups, places or values.

Double Bar Graph: This is a like a bar graph but with two bars per choice instead of one. It usually compares two                                sets of information or data.

Scatter Plots: This type of graph shows data using the form of dots. The Scatter Plot Graph is usually very messy                      with dots all over the place. It also compares two different topics. The points are also not connected.

Interpreting: Interpreting a graph means to state a sentence that is shown in the graph

Inferring: Infering is a conclusion drawn by reasoning.

Area, Surface Area and Volume

Area of Square: A=2(L+W)
Area of Rectangle:A=2(L+W)
Area of Parallelogram : A=b x h
Area of Triangle:A=b x h divided by 2

Surface Area of Cube                    l       Find the area of all the faces
Surface Area of Rectangular Prism l                  and then add them together
Surface Area of Triangular Prism    l

Volume of Cube:V=L x W x h
Volume of Rectangular Prism:V=L x W x h
Volume of Triangular Prism:V=L x W x h divided by 2
                                            Base Area x h divided by 2
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