Math+7


 * **//__Math 7__//**

Use this space to discuss what we did today including any assignments. Also, summarize your learning here. Use text, examples, any diagrams or pictures to help you with your explanation. Aug.29/07 __Number system Naturals:__ 1,2,3,4...counting numbers __wholes:__0,1,2,3,4... __Integers:__ ... -4, -3, -2, -1, 0,1,2,3 __Rationals:__ fractions, decimals, any number written a/b 1/2 __Irrationals:__#, nonrepeat __Complex:__ imaginary numbers

Aug. 30/07 quitent divident divisor

Remainder

Aug. 30/07 __- power numbers__ 2 times 2 times 2 times 2= 2 4 - scientific calculator 4 times 4= 4 2

Aug. 31/07 We learned how to take numbers and say them in word form 3 962 000 000 = Three billion nine hundred sixty two millon 8 86 000 000= Eight hundred eighty-six million ||


 * billions || hundred millions || ten millions || millions || hundred thousands || ten thousands || thousands || hundreds || tens || ones || tenths || hundredths || thousandths ||
 * 4 || 4 || 9 || 7 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 ||

Two ways to write this number are: 3 893 046= 3.893 million or 4 million

Round to the nearest hundred: 8463= 8500 Round to the nearest tenth: 14.439= 14.400 Round to the nearest tenth: 14.983= 15.0

Sept. 4/07 __Place value__ Round to the nearest hundred: 2467.481= 2 500 Round to the nearest thousand: 2 467.481= 2 000 Round to the nearest thousandth: 2467.4819=2467.482
 * billion || hundred million || ten million || million || hundred thousand || ten thousand || thousands || hundreds || tens || ones || tenths || hundredths || thousandths || ten thousands || hundred thousands ||
 * 2 || 9 || 8 || 4 || 5 || 6 || 7 || 1 || 2 || 3 || 6 || 1 || 2 || 4 || 5 ||

Expanding numbers(whole numbers) nimbers can be expressed in 2 ways: a) standard form b) expanded form __**Estimating**__ 8623-5799 es) 9000-6000=3000 49x37=1843 es) 50x40=2000 2736/48 = 57 es) 3000/50 = 60 numbers that are divisible by 2 are even ex) 2, 4, 6, 8 , 10 a number that is divisible by 5 is a number that ends in a 0 or a 5 ex) 50, 55, 60, 65, 70, 75 a number that is divisble by 10 is a numbe that ends in 0 ex) 10, 20, 30, 40, 50 for any 3 digit number to see if its divisible by 4, see last 2 digits. If the last 2 digits are divisible by 4 then the whole # is divisble by 4. ex) 532/4=133, 328/4=82 all multiples of 1000 are divisible by 8. For any whole number with 4 or more digits, we only need to check the last 3 digits to find out if the number is divisible by 8. A number that is divisible by 8 is also divisible by 2 and 4 ex) 8=2x4 any whole number with 4 or more digits we only need to check the last 3 digits and see if they are divisible by 8 ex) 2048/8 another way si to divide by 4 or if the quotient is even, then the number is divisible by 8. we use divisibly rules to find the factor of a number such as 100. any __**Lesson 2**__ //**2.1 Representing Integer**// To add negative intergers you add the numbers then add the negative sign before your answer To add positive and negative integers use tiles and circle the zero pairs. What is left over is your answer.
 * __multipication__**
 * __division__**
 * __divisibility : to be able to be divided into a number__**
 * **Negative Integers**
 * -are numbers that are below zero
 * **Positive Integers**
 * -Are Numbers above Zero
 * ex.+34 degrees celcius
 * We can use tiles to represent positive and negative integers
 * 1 negative and 1 positive integers are called a zero pair (they equal 0)
 * integers can be expressed in many different ways
 * 1 yellow tile can represent +1
 * 1 Red tile can represent -1
 * //2.2 Adding Integers With Tiles//**
 * **//Adding Positive Integers//**
 * Add The Numbers like normal
 * (+4)+(+5)=+9
 * take away the + signs and the brackets like this
 * 4+5=9
 * **Adding Negative Integers**
 * **Adding Positive and Negative Integers**
 * 2.4** **Subtracting Intergers with Tiles**
 * To subtract integers we do the reverse of adding integers (remove tiles from the group).
 * When we subtract integers we can use zero pairs if we need to
 * You can change - signs to + if they are beside each other only separated by a bracket.
 * To use tiles to subtract integers we model the first integer then take away the number of tiles indecated by the second integer.
 * We add zero pairs without changing the value.


 * 2.5 Subtracting Intergers on a Number line**
 * Step One: Use tiles to subtract.
 * Step Two: Model each subtraction with tiles on a number line.
 * Step Three: Use any method.
 * Step Four: Check your pattern use other integers.
 * Oposite integers are numbers that are the oposite of each other. Example: -6 +6
 * __Decimals__ March 13/08**

__A decimal is a part of a number or a whole number and part of a number ex: 1.5 or 0.8__ __//Dividing//__ If you divide by 10 or 100 or 1000, etc the decimal goes to the left by the amount of zeros there are and when you multiply the decimal goes to the right. ex:25.4\100=0.254 25.4\1000=0.0254 __//Multiplying//__ Multiply a number then count from right side back the number of the decimal places. ex:25.4x10=254 25.4x100=2540 //__Adding__// 82.635 325.680 __53.47__ 461.785 //__Subtracting__// 7836.25 -__4532.78__ 3303.47 //__Repeating Decimals__// _ ex:__1__=0.09 11 The line over nine means repeating decimal //__Terminating Decimals__// The decimal stops ex:0.1 or 0.25 __**B**__rackets __**E**__xponents __**D**__ivide __**M**__ultiply __**A**__dd __**S**__ubtract __March 10,2008__ An expression is an equation that doesn't give you an answer. ex 9-n ~an expression needs a number and a __variable.__ A variable is any letter that represents number.
 * Expressions and equations:**

An equation gives you an answer. ex 9-n=2. ~ To solve an equation you need to find out what the n represents. To find out what the n represents, you take the 2 and subtract it from the 9. 9-2=7. 7 is your variable, that n represents. Area of a Circle** __Radius-__ distance from the center of the circle to the outside of the circle __Diameter__- the longest line that passes through the center of the circle __Circumference__- area aroung a circle (perimeter) R=radius D=diameter C=circumference A=area A=pi. R² R=D divided by 2 D=2xR D-2r Radius of any circle is about 3. C divided by D=R=aprox.3 C divided by R=D C=Distance around C divided by D aprox. 3.14 C divided by D = pi pi= aprox. 3.14 C= pi. x D A=area B=base H=height A=BxH divided by 2 A=BxH
 * //__UNIT 4__//
 * Area of a Triangle**
 * Area of a Rectangle**

__To Add Fractions:__ 1. Find a common denominator. 2. Add numerator numbers together. 3. Place over common denominator. 4.Reduce to lowest terms.
 * __January 7, 08__**

__**January 14, 08** To Subtract Fractions:__ 1. Find a common denominator. 2. Subtract numerators. 3.Place numerator over common denominator. 4. Put in Lowest terms.

__Adding with Mixed Numbers:__ You can use models of circles to help you when adding mixed numbers. You could: Color ONE WHOLE circle and 5/6 so color 5 slices and leave one slice not colored that models 1 5/6

__Subtracting With Mixed Numbers:__ We can use Cuisenaire rods to model fractions and mixed numbers. Suppose the dark green rod is 1 whole, then the red rod is 1/3. so, seven red rods is 7/3 or 2 1/3.

Before we subtract the fraction parts of two mixed numbers, we must check the fractions to see wich is grater. When the second fraction is greater than the first fraction, we cannot subtract directly.

__**January 28, 08**__ //Variable- is the number we choose.//

5x+2=27 5x+2-2=27-2 5x=25 5x divided by 5 = 25 devided by 5 x=5

__Expression__ __Equations__ n-9 n-9=6

Multiply <-> Divide Add <--> Subtract

The mean is a number that can represent the center of a set of numbers. AKA average The mode is a number that occurs most often. MEAN- EX: 23, 32, 45, 45, 56, 67, 78, 89, 90 the mean is 58 MODE- EX: 23, 32, 45, 45, 56, 67, 78, 89, 90 the mode is 45 because that is the number that shows up the most.
 * __MEAN AND MODE 7.1__**

The median is the middle number when the data are arranged in order. The range of a data set tells how spread out the data are. ( difference between the greatest and least numbers). MEDIAN-EX: 23, 32, 45, 45, 56, 67, 78, 89, 90 the median is 56, because that is the middle number. RANGE-EX: 90 - 23= 73 the range is 73, because that is the difference. A number in a set of data that is significantly differents from the other numbers is called and outlier. An outlier is much less or much greater than most of the numbers in the data set Outliers sometimes occut as a result of error in measurement ot recording. In these cases, outliers should be ignored. Sometimes an oulier is an important piece of imformation that should not be ignored. For example if one student does much better or much worse than the rest of the class on a test. Outliers may not always be obvious. Identifying outliers is then a matter of choice. 23 24 24 26 78 The outlier is 78. The mode is the number that occurs most often. There can be more than one mode. For example if there are 2 numbers that occur the same amount then there is 2 modes.
 * __MEDIAN AND RANGE 7.2__**
 * __7.3 The Effects of Outliers on Average__**
 * __7.4 Applications of Averages__**

When the outcomes of an expirement are equally likely, the probability of an event occuring is: number of possible outcomes**
 * __7.5 Different ways to Express Probability__**
 * __number of outcomes favourable to that event__

A probability can be written as a ratio, percent, and as a fraction.

Ex of probability: At the pet store, Bob buys 100 biscuits for his dog, Ping-Pong. He buys 75beef-flavoured biscuits, 15 cheese-flavoured, and 10 chicken-flavoured. The clerk puts them all in one bag. When Bob gets home he shakes the bag and picks one bicuit out randomly. The probability that is an **impossible event** will occur as 0 or 0% The probability that a **certain event** will occur is 1, or 100. All other probabilities lie between 0 and 1.
 * **What is the probability that Bob pulls out a cheese biscuit?** ...__ the probability would be 15:100, 15/100, and 15% because there is 15 biscuits that are cheese flavoured out of 100. __
 * **What is the probability of pulling out a vegetable flavoured biscuit?** **...**the probability would be 0:100, 0%, and 0/100 because there are not any vegetable flavoured biscuits.



__**7.5 Different ways to exspress probabilty**

number of outcomes favourablt to that event__ number of posible outcomes

A probality can be written as a ratio, fraction, or as a percent The probabilty that an impossible event will occur is 0 or 0% The probility that a certain event will occur is 1 or 100% All other probabilities lie between 0 and 1

EX: At the pet store Benny buys 100 biscuits for his dog ping-pong. He buys 75 beef flavoured biscuits,

When there is an odd number of data, to find the middle number: add 1 to the number of data then divide by 2. This gives the position of the middle number.

Probibility is the chance of something happening EX:If you have heads or tails there is 1:2 or 50% or 0.5 or __1__ 2 there are 4 different ways to express probibility witch are fractions, ratios, percenteges, or decimals. impossible events- 0% chance certain events- 100% chance
 * __7.5 Probability__**

all other possibilities lie between 1 and 0 independent event- the result of one event does not depend on the result of another event EX: coin outcomes= heads or tails EX: If a person spins a spinner labeled white, black, striped, and dotted and if that person then tosses a coin that is labeled heads and tails, here is a tree diagram that shows the outcomes the independent events ( Spinning a spinner and tossing a coin) __Spinner Coin Outcomes__ White Heads White and Head Tails White and Tails Heads Black and Heads Black Black and Tails Tails Heads Striped and Heads Striped Tails Striped and Tails

Heads Dotted and Heads Dotted Dotted and Tails Tails

__**8.2 Perpendicular Lines**__ Perpendicular LInes are lines that make a 90 degree angle. Some examples of this are a window corner or a picture frame. A 90 degree angle is a right angle that is square, such as an L shape. This is an example.
 * __8.3 Constructing Perpendicular Bisectors__**

A bisector is a line that divides a line segment into 2 equal parts A perpendicular bisector divides a line into 2 equal parts at a 90 degree angle. There are 4 four ways to bisect a line. 1.) With a ruler 2.) With a compass and ruler

3.)By paper folding: Fold a paper in half in the middle of the line segment. 4.)With a protractor: line up protractor middle to thr line, on the edge draw a line bisecting the line segment __Lesson 8.5__ Y axis-> Vertical X Axis-> Horizontal Coordinate grid- vertical number line and horizontal number line intersects at 90 Degrees Origin (0,0) Quadrant divide plane into 4 (+,+) quadrant 1 (-,+) quadrant 2 (-,-) quadrant 3 (+,-) quadrant 4

__Lesson 8.6__ April 29/08 Translation- when you slide a shaoe up, down, left, or right Reflection- where a shape is flipped ( it is like looking in a mirror) Reflecting on x-axis: Change the y value to the oppisite integer( + or -) ex: (1,3)=A-original (1,-3)=A'- reflected on the x-axis Reflecting on y-axis: change the x value to the opposite interger ex: (3,2)=A-original (-3,2)=A'-reflected