Algebra
National Council of Teachers
of Mathematics
Standards 2000
URL: http://standards.nctm.org/document/chapter6/alg.htm
For all grades, NCTM standards focus
on students being able to: "understand patterns,
relations, and functions; represent and analyze
mathematical situations and structures using algebraic
symbols; use mathematical models to represent
and understand quantitative relationships; analyze
change in various contexts "
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In grades 6–8 all students should— |
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represent, analyze, and generalize a
variety of patterns with tables, graphs,
words, and, when possible, symbolic
rules; |
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relate and compare different forms of
representation for a relationship; |
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identify functions as linear or nonlinear
and contrast their properties from tables,
graphs, or equations; |
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explore
relationships between symbolic expressions
and graphs of lines, paying particular
attention to the meaning of intercept
and slope; |
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use symbolic algebra to represent situations
and to solve problems, especially those
that involve linear relationships; |
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model and solve contextualized problems
using various representations, such
as graphs, tables, and equations; |
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use graphs to analyze the nature
of changes in quantities in linear
relationships.
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Earthquake I-IV
(click on image for larger view)
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The Problem: Students determine
the location of the epicenter of an earthquake
using seismographic data. simulations
and dynamic graphs involving rate, time
and distance, and the speed of P and S
waves in a seismograph.
Where's the Math: Students explore
rate, time and distance relationships,
generating hypothesis from graphs and
simulations.
NCTM Standards: Algebra, measurement
Components: Simple world, swing
slider, simple graph, simple function,
simple clock, time label, text editor,
Sketchpad, number entry
Earthquake 1
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Click on the links above to learn more
about the problem series, the math involved,
sample solutions, and developers' assessment
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Galactic Exchange
(click on image for larger view)
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The Problem: Students discover
the exchange rates among different types
of alien currency, and use this information
to find out the amount of money needed
to "buy" certain types of food.
Where's the Math: This problem
allows students to investigate ratio and
proportion, by discovering the exchange
rate between different alien currencies
(i.e. 7 circles have the same value as
3 triangles, etc.). By manipulating these
exchange rates algebraically, students
can come up with equations which represent
the money needed to buy certain products.
The use of symbols for coin types encourages
a symbolic or alphabetic representation
of each type of currency.
NCTM Standards: Algebra, number & operations
Components: Custom bean, number entry field, button panel
Learn
more about the problem, the math
involved, sample solutions, and developers'
assessment
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