Mathematical Practice 8

Look For and Express Regularity in Repeated Reasoning

Teacher Behavior

  • Engage students in discussion related to repeated reasoning that may occur in a problem's solution
  • Draw attention to he prerequisite steps necessary to consider when solving a problem
  • Urge students to continually evaluate the reasonableness of their results

"I can notice when calculations are repeated. Then, I can find more efficient methods and short cuts."

Student Behavior

  • Notice repeated calculations and look for general methods and shortcuts
  • Continually evaluate the reasonableness of immediate results (comparing estimates)
  • Make generalizations based on findings


Fourth Grade Example Video

In 4th grade, students work on a number talk asking them to evaluate the reasonableness of a two-digit problem and solution--to see if the problem is true or false without solving. As students discuss e rationales for determining why 62+ 78 is or is not equal to 238. Various students offer responses that the numbers are "too small" or "would have to be bigger." Students eventually conclude that adding two two-digit numbers cannot, no matter what, equal more than 198.