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Grade 7: The Learning Equation Math
21.02 Graphing Relations 

Learning Outcomes:
The student will:
You need to understand a graph before you can interpolate or extrapolate a
graph on a Cartesian plane. The Cartesian
plane was introduced to mathematics by René Decartes
(15961650). 
 Review the parts of the Cartesian Plane.


 Cartesian Plane  grid for identifying points on a plane using two axes
 xaxis  horizontal axis on the coordinate plane
 yaxis  vertical axis on the coordinate plane
 origin  the intersection point of the x and yaxis. It is
usually the point (0, 0) on the cartesian plane.
 quadrants  one of the 4 regions formed by the x and yaxis
 interpolate  to determine a data value on a curve between two known
values
 extrapolate  to determine a data value by following a pattern outside
of a curve of known values

In the previous activity you reviewed the part of the grid or Cartesian
Plane. The plane is made up of points. The xaxis () and yaxis (  )
provide the location (coordinates) of each point. Ordered pairs written (x,y)
provide a simple way to write the location of each point on the plane. 
source: Simple
Cartesian Coordinates 
Move the mouse over the grid (white area) on the left.
Study the changes in the ordered pair name as you move your mouse. What
happens to the ordered pair as you move the mouse left, right, up, and down.
Check your responses by clicking on the buttons below.

Graphing Ordered Pairs
Instructions:
 Take any ordered pair of the form (x, y). Example: (3, 4)
 Use the mouse arrow to find that point on the graph.
 Click on the point.
 The coordinates you have clicked on will be given to you.
 Did you find the point you were looking for?
source: http://www.accessone.com/~bbunge 
Locating Points
Click your mouse on the corresponding ordered pair on the graph.
source: NSUMath 1030 Unit
4 Section 2 Author 
Your turn, find the solution in each of the
following problems (note: some browsers don't update properly, if the point doesn't change
you need to convince the browser to redraw everything, the easiest way is to scroll up
until the picture is off the screen and then scroll down again):
source: NSUMath 1030 Unit
4 Section 1 Author
Now you are ready for two new games. If you understand negative
numbers, then the second game will be more challenging. 
Interpolation requires a set of data points:
How much will the student make after:
Interpolation requires one to determine a data value on a
curve between two known values.
Maze
Game  Interpolate  all Quadrants 
Extrapolation requires a set of data points:
If the temperature of the water continues at the same rate, how long will
it take the water to reach:
Extrapolation requires one to determine a data value by
following a pattern outside of a curve of known values. 

Graphing Instructions
for ClarisWorks and MS Word
Java Bar and Line Graph
Simple
Plot

Review: Simple
Plot
Positive
Coordinates Game
Coordinates
Game
Funbrain.com 
What's the Point?
Shoot Balls

 Enrichment:
 The Cartesian plane was introduced to mathematics by René Decartes (15961650).
Instructions:
 Click "New Problem" to get an equation of the form y = mx + b.
 Find the yintercept on the graph. Click on that point. Keep trying until your answer is
correct.
 Using the slope (m), find any other point on the line. Click on that point. Keep trying
until your answer is correct.
 Any time you wish to see the line, click on "Draw the Line".
 Can you find the correct points before you see the line?
source: http://www.accessone.com/~bbunge 
Instructions:
 This applet will help you graph equations of the form y = mx + b.
 "m" is the slope of the line.
 "b" is the yintercept.
 This program only works for integer values of m and b (no fractions or decimals 
sorry!).
 Type your values into the text fields. Then click on "Enter".
source: http://www.accessone.com/~bbunge 
Instructions:
 Click on a point.
 Click on another point.
 Drag the mouse between the points to make a line segment.
 The coordinates of each endpoint are displayed at the right, along with the slope (m)
of the line segment.
 Can you calculate the slope without the computer's help?
Source: http://www.accessone.com/~bbunge 
Graph It!  functions
Algebra
Graphs Applet
Graph Sketcher
 functions
Slope Version 2
Linear
Equation  move the sliders

relations, table, graph, xaxis, yaxis, ordered pair, coordinate,
interpolate, extrapolate

Prerequisite
Skills:
Patterns and Relations: Grade 7 Lesson
21.01
Graphing Relations: Grade 7
Lesson 21.02
Cartesian Plane

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