Using Benchmarks
Using Benchmarks

Fractions may be interpreted many ways. In Using Benchmarks, students focus on the concept of fractions as representations of part/whole relationships. This opens the door for them to compare fractional quantities and make useful estimations about the size of amounts in a wide array of real-world situations.


  • Develop their understanding of the benchmark fractions—1/2, 1/4, 3/4 and 1/10—as they count and draw objects and answer: "What’s the whole?" "What’s the part?"
  • Learn to use drawings and objects to support their reasoning and communication with others as they move flexibly between finding a fractional part of an amount as well as finding the whole when the part or fraction is known
  • Use benchmark fractions, decimals, and percents as fundamental tools
  • Gain the dexterity necessary to explore the larger world of rational numbers
  • Acquire flexibility, as well as fluency, with the use of benchmark terms as the connections between the benchmark fractions and their decimal and percent equivalents are reinforced continually
  • Learn to consider the part counted and the part remaining as complements that make a whole, so 3/4 is first introduced as the part left over when 1/4 is used and 9/10 is seen as the remaining amount when 1/10 is taken
  • Encounter deep mathematical ideas related to rational numbers through a well-sequenced series of accessible lessons
  • Cement an understanding of the crucial and frequently used benchmark fractions

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.