more than formal methods of equation solving, age problems
or lots of Xs and Ys. Conceptual understanding,
algebra as a means of representation, and algebraic methods
are all problem-solving tools. Algebraic reasoning allows
us to think about and express patterns, relations, and functions
that ultimately give us access to technology.
Be sure to look
at the different set of resources
listed at the Student/Learner webpage for this topic.
Another great problem posed on the Math Forum at
this domino problem includes an introduction, building a brick
wall (finding patterns), extended project, and technology.
Related links and extensions are also included. Weve
found the Math Forum to have well thought out, comprehensive
Another problem posed by the Math Forum at
this version of the locker problem includes an introduction,
using a manipulative (locker boards), using technology, displaying
data, extending the activity by looking for patterns, and
solving the problem algebraically.
The problem posed in this site immediately grabs the attention
of most students (it deals with money!). However, it is the
extensions that are fascinating. Exponential growth, patterns,
and exponentials are all areas of further exploration. The
Teachers Notes, like those in all of Cynthia Lanius
lessons, are extremely helpful.
Interactive lessons, discussion, and activities enable
the teacher to extend hands-on activities in the classroom
and provide new content and practice in four areas: Number
and Operation Concepts, Geometry and Measurement Concepts,
Function and Algebra Concepts, and Probability and Data Analysis
Concepts. Each activity comes with supplementary pages that
can be accessed from the activity page. "What" gives
background, "How" gives instructions, and "Why"
gives curriculum context. Function and Algebra Concepts
include an introduction to functions, linear functions, graphs
and the coordinate plane, and reading graphs. Lesson plans
and resources for the teacher are also available.
This site looks at slope as rate of change, using performance
relative to stress. Another of Cynthia Lanius lessons,
it is of high interest and includes great teachers notes.
Traffic Jam problem
"There are seven stepping stones and six people.
On the three left-hand stones, facing the center, stand three
of the people. The other three people stand on the three right-hand
stones, also facing the center. The center stone is not occupied."
The challenge is to have the people change places in the minimum
number of moves. This website has a student page and a JAVA
Applet to simulate the problem. The teachers guide shows
ways of extending the activity by looking for patterns, as
well as writing the answer algebraically.