Seeking Patterns, Building Rules
Seeking Patterns, Building Rules

This unit demystifies basic algebra, as students explore the meanings revealed by tables, graphs, verbal rules, and equations. Students learn to connect algebraic representations with the linear (and sometimes nonlinear) patterns or functions they describe by investigating patterns in:

  • Their own lives
  • In-Out tables
  • Banquet table and patio tile arrangements
  • Calorie-burning tables, graphs, and equations
  • The relationship between diameter and circumference
  • Pay and accumulated earnings
  • Gas price increases
  • Cell phone use-cost patterns

They see that algebraic tools and symbols serve to describe and interpret a situation; the situation itself is always central. Early lessons introduce students to ways of 'reading' tables, graphs, and equations through construction of these representations. Graph, table, verbal rule, and equation conventions become familiar through varied and meaningful use.


  • Gradually gain proficiency in representing situations graphically and symbolically
  • Deepen their understanding as they explore concepts and representational conventions related to rates of change
  • Come to recognize equivalent expressions and to compare expressions
  • Grasp what a y-intercept, flat-line graph, straight- or curved-line graph, or a point of intersection reveals about situations

All of this learning occurs in a lively, practical way that takes the fear out of approaching algebra and replaces it with a sense of wonder and mastery.

The Teacher Book is an essential component of the EMPower program. It is designed to be used in conjunction with the Student Book. The Teacher Book includes:

  • Suggestions for facilitating class discussions
  • Open-ended questions designed to keep the math on track
  • Math Background sections to help teachers deepen their understanding of a concept
  • Lesson in Action sections with examples of student work and comments that illuminate the underlying mathematics
  • Examples from the authors' and pilot teachers' classroom experiences

Download sample chapters from the student and teacher books.

EMPower is part of the Adult Numeracy Center at TERC.
Developed and field tested by the Educational Research Collaborative at TERC with support from the National Science Foundation.