Understanding Graphs
Graphing holds a central place in algebra. It connects the algebraic statement
to a geometric representation. These resources begin at the beginning—plotting points—then move on to examining slope and the graphs of linear and
nonlinear functions. Lots of opportunity for experimenting with graphs!
Here is a game for those just learning the Cartesian coordinate system. An
applet allows players to name the coordinates of a house placed on the grid by
the computer, or input their own coordinates for the house. A brief history of
Descartes' invention and a good discussion on plotting points are provided,
but, unfortunately, no game rules are included. Your students will enjoy
inventing their own. MSP full record
The game is to move a robot from the bottom corner of an x-y grid to the top
right corner, but mines block the way. To move the robot, players have to give
the coordinates of the next point; one mistake and BAM! Students can request up
to 30 mines and, after a little experience with the game, will probably want
that many. Good practice on locating and naming x-y coordinates. MSP full record
In these two lessons, students use an online simulation of one or two runners
along a track. Students control the speed and starting point of the runner,
watch the race, and examine a graph showing time versus distance. Students can
use the activity to come to conclusions on the distance, speed, and time
relationship. They can also use it to consider the graphical representation and
the concept of slope.
A story and a graph begin this activity. The graph shows how performance is
related to stress; questions ask students to analyze the graph in terms of the
story situation. Students then consider a graph of speed over time, and are
asked to create their own graph showing "a direct relation between the rate of
change of a function and the slope of its lines." This activity is part of
Mathematics Lessons That Are Fun! Fun! Fun! MSP full record
You are traveling through space. You must find the coordinates of four planets
and then write the equation of the line you have created. This game is part of
the Maths File Game
Show. MSP full record
A chameleon named Joan helps illustrate how to graph linear equations, first
using only two points that are solutions to an equation, then gradually
introducing the idea of slope, and building to the slope-intercept form of the
equation. The goal is to visualize the concept of slope and understand the
reasoning behind the standard formulas. MSP full record
Using this simulation, students can manipulate a linear function of the form
f(x)=mx+b and explore the relationship between slope and intercept in the
coordinate system. They can see the slope of the line change as they change the
value of m. MSP full record
An interactive tool for practicing graphing or for visualizing functions!
Students can graph one to three functions, of different colors, in the same
window. Functions can be written with absolute value, square roots, exponents,
or algebraic fractions, and the domain can be restricted. MSP full record
This simulation tool allows students to graph not only linear but also
exponential and polynomial functions. Students create the function, see it
graphed, and can then change the constants, noting the effects visually and
immediately on the graph. MSP full record
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Copyright
June 2006 — The Ohio State University. This material is based upon work
supported by the National Science Foundation under Grant No. 0424671. Any
opinions, findings, and conclusions or recommendations expressed in this
material are those of the author(s) and do not necessarily reflect the views of
the National Science Foundation.
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This work is licensed under a
Creative Commons License.
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