The Coordinate Plane

Above you will see an example of the coordinate plane.  The coordinate plane is a two dimensional surface on which you can plot points to create lines and curves.  

The plane is constructed by two axes - the x-axis and the y-axis.

The x-axis is the horizontal (left/right) scale or number line with negative numbers two the left of zero and decreasing in value and positive numbers to the right of zero increasing in value.

The y-axis is the vertical (up/down) scale or number line with negative numbers two the below zero and decreasing in value and positive numbers to the above zero increasing in value.

Where the x and y axes cross is called the origin and is noted as (0,0).

The x and y axes also create four separate sections on the plane and are called quadrants.  Quadrant I has both positive coordinates.  The rest of the quadrants are numbered in counter clockwise order. (See image above)

You plot points using a value of x (horizontal) and a value for y (vertical).  You need both values to plot a point and they are written as (x,y).  They can be called coordinates or ordered pairs.

Features to Think About

• You can tell whether a point lies on the x or y axis by looking at the coordinates
• If the y coordinate is zero then the point lies on the x axis
• If the x coordinate is zero then the point lies on the y axis
• This should make sense because if there is no value for y, for example, the point will be neither above or below the x-axis.
• Because of what was mentioned in the previous bullet, not all points will be placed in one of the four quadrants.  Some points will lie on either the x or y axis or on the origin iteself

Help Hints (Reasons for the Names)

• If you break the word COORDINATE into the prefix CO and the root ORDINATE, know that the prefix CO means 'together' and the root ordinate means 'place in orderly rows or regular fashion.'
• Think of ORIGIN is the beginning or a starting point
• Look at the word QUADRANT, 'quad' signifies 'four'
• To remember the order of your coordinates, think about why they are called ORDERED PAIRS.  Notice that they are written in alphabetical order (x,y).

Uses for the Coordinate Plane

• Navigation
• Business and Statistics to track and understand trends
• Scientists and Economists to analyze relationships

Image From:  http://www.learningwave.com/lwonline/algebra_section2/alg_coord.html

Plotting Practice

Click on the link below for a list of interactive resources you can use to practice plotting points on a coordinate plane.

http://www.internet4classrooms.com/skill_builders/coordinate_plane_math_sixth_6th_grade.htm

I personally like this Stock the Shelves game to increase your speed and accuracy.

Pep Talk

Integers and the Coordinate Plane Pretest

Integers and the Coordinate Plane Pre-Test

Absolute Value

Absolute value simply means the amount of "jumps" made on a number line.  It is a measurement of distance moved from one place on a number line to another.  Because it is measuring distance and not direction, absolute value is always positive.  The absolute value of a number is noted between two absolute value bars.

|-5| = 5

|7| = 7

If we take the absolute value of |-6|or|6| or and look at it as the distance from zero on the number line, you can see that in either direction you have moved six spaces.  You either move or you don't.  This is way the value is always positive.

Important to Remember: Absolute value bars are also considered grouping symbols.  Like parentheses, whatever operations occur inside the absolute value bars are done first in order of operations.

|5-2*6|=|5-12|=|-7|=7

Number Line Image taken from www.mathisfun.com

Integers & Rational Numbers

Welcome to the new unit on Integers and the Coordinate Plane.  In class we talked about two categories of numbers.  Integers are any positive or negative whole number including zero.  Essentially any whole number and its opposite is considered an integers (for example 4 and -4 are opposites).  The other category is called rational numbers.  Rational numbers are numbers that can be converted into fractions.  Decimals that repeat in consistent patterns or that terminate can be converted into fractions.  Numbers like pi or phi can not be converted into fractions because the decimal does not terminate and there is no consistent pattern with the digits.  These numbers are called irrational.

One clue to remember what a rational number is to look at the word rational itself.  RATIOnal.  Notice the root of the word is ratio.  Remember ratios are the comparison of one quantity to another (numerators as compared to denominators) and are typically written in fraction form.

A set of integers ordered least to greatest may be {-5, -1, 0, 4,  10}

A set of rational numbers ordered least to greatest may be {-3/5, -.25, 1, 1/2, .4444....} 

Fractions, Decimals, and Percent Conversions

Click on the link to go to the Math is Fun website to review your understanding of fraction, decimal, and percent conversion.  There is a great interactive manipulative for you to use.  My only issue with this page is when it explains how to convert decimals into percents and back into decimals again, it does not explain why you move the decimal two places.

Remember: converting a decimal to a percent requires you to multiply by 100 (percent means for every hundred).  You are moving the decimal to the right because you are multiplying by a number greater than one.  You are moving it twice because 100 is equivalent to 10 to the 2nd power which is equivalent to two place values.  Moving from a percent to a decimal requires you to divide by 100.  It should make sense that you would move the decimal to the left now because you number should get smaller.