Over, Around, and Within
Over, Around and Within

Everyone has some experience with geometry and measurement. In this unit, students:

  • Build upon their knowledge as they encounter increasingly complex dilemmas about the nature of shapes, the measures of perimeter, area, and volume, as well as linear, square, and cubic unit measurements, both metric and U.S. customary
  • Learn to speak the language of geometry as they share 'secret' designs and become increasingly familiar with shape attributes
  • Learn about angles, and in particular right (90°) and straight (180°) angles, as they explore optimum reading angles and the use of protractors
  • Investigate perimeter, area, and volume
  • Explore similar shapes, scale, and units of measure
  • Examine surface area and volume

Assessments involve general review as well as practical applications of knowledge where, for instance, students plan to redecorate their classroom or are asked to design a box fitting established criteria.

With its heavy emphasis on hands-on activities and mathematical discourse, Over, Around, and Within offers a welcoming context in which students develop a firmly grounded understanding of:

  • Angle relationships
  • Unit differences and conversions
  • Interplay of dimensions in determining perimeter, area, and volume measures

Gradual shifts in emphasis allow students to move from intuitive to formal methods of measuring and comparing shapes and objects. No one memorizes formulas. Everyone understands them. Students will never see the world and its objects in the same way after completing this unit.

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.