Instructional Shift 5: Take every available opportunity to support the development of number sense.

Chapter 6: Building Number Sense




What should we see in an effective mathematics classroom?

-An unrelenting focus on estimation and justifying estimates to computations and to the solution of problems

  • Facilitate a team discussion: "How can estimation be interwoven into mathematics classroom activities?"
  • When lesson planning, include deliberate questions that have students answer the following: "What do you predict the solution may be?", "Is your answer reasonable and how do you know?" "Why is an unreasonable estimation for the solution?", etc.
  • Encourage teachers to pair up and observe each other, taking note over the course of one week how many times estimation was emphasized in the classroom. Have teacher pairs meet to share results.

-An unrelenting focus on a mature sense of place value

  • Lead a brainstorming session focused around the importance of place value:
    • Why is place value important?
    • How is estimation and place value related?
    • In what real-life situations is estimation and place value critical?

-Frequent discussions and modeling about how to use number sense to "outsmart" the problem

  • Encourage multiple strategies for solving a problem. Have students "demonstrate" their strategy for the class.
  • When necessary, model for students alternate ways to solve a problem.
  • Allow time in team meetings for teachers to experience at least one math task. Have teachers share out strategies they used to solve the problem and how they knew their strategy was mathematically sound. As a follow-up discuss what number sense skills were needed to solve the problem and how these skills could be developed in the mathematics classroom.

-Frequent opportunities to put the calculator aside and estimate or compute mentally when appropriate

  • Periodically begin/end the lesson with a mental math task. Have students solve a problem mentally, then describe their method for solving the problem. Example: Describe how you would subtract 72 - 59 mentally.
  • Have students find the solution to one-step or two-step equations by completing the "I'm Thinking of a Number" game. Example: "I'm thinking of a number that when you multiply the number by 2 then add 3 the result is 11. What is my number?"