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Teacher/Tutor - Numeracy

Algebra: Patterns and Functions


ReAlgebra includes more than formal methods of equation solving, age problems or lots of X’s and Y’s. 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.

Screen shot from siteThe Domino Problem
Another great problem posed on the Math Forum at Drexel University, this domino problem includes an introduction, building a brick wall (finding patterns), extended project, and technology. Related links and extensions are also included. We’ve found the Math Forum to have well thought out, comprehensive material.

The Locker Problem
Another problem posed by the Math Forum at Drexel University, 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.

Screen shot from siteMillion $ Mission
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.

Screen shot from siteProject Interactivate
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.

Screen shot from siteStressed Out
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.

Screen shot from siteThe 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 teacher’s guide shows ways of extending the activity by looking for patterns, as well as writing the answer algebraically.

To submit ideas and resources for this section, please contact Susan Cowles.