Boosting Number Sense in High School Students

byNancy Rudolph

Many students reach high school having received high grades in math because they learned the algorithms, but using algorithms does not guarantee conceptual understanding. Many students lack number sense. In this unit, number sense is defined by three characteristics: understanding Number Systems, Mathematical Operations, and Flexibility in Mathematical Situations. The Number Systems refer to the different types of numbers, place value and the relative magnitude of numbers. Mathematical Operations are addition, subtraction, multiplication, division and the relationships between them, the Rules of Arithmetic that govern them, and the effect of these operations on different types of numbers. Flexibility is being able to recognize multiple ways to work with numbers and identify the most efficient method with which to proceed. This unit encompasses Roger Howe's Great Ideas in Primary Mathematics, which build number sense, in the form of calculator-free, daily warm-up/bell-ringer activities for one semester, focusing on one topic per week. Throughout the unit, students are expected to describe and defend their thought processes to their classmates. Although this unit is written for upper-level math students, many of the ideas are basic enough to be used for younger students.

(Developed for Pre-Calculus, grades 11-12; recommended for Pre-Algebra and Pre-Calculus, grades 7-12)

Comments (4)

    Nathan Hochmuth (Shoreland Lutheran High School, Somers, Wi)
    Subject taught: Math
    Appendix C
    I was wondering if you had the resources available listed under Appendix C. I would like to incorporate number talks in the high school level, and would like to see some examples.

    Thank you
    Ingrid Nilsson Anderson (Palisade High School, Palisade , CO)
    Subject taught:
    Appendix C
    I would greatly appreciate a copy of Appendix C as number talk is something I want to incorporate in my teaching.
    Janet Zegna (Thurgood Marshall Elementary School, Newark, DE)
    Subject taught: all, Grade: 1
    Boosting Number Sense in High School Students
    \"Flexibility in Mathematical Situations\" Boy, is that missing from our instruction in 1st grade! We have so little time to really delve into what numbers mean before we expect our little ones to \"use\" them or perform operations with them. This is exactly why I wanted to participate in DTI. While I stopped reading your unit after your Background section, I am sure that it will help me to develop a similar unit for the lower elementary grades :) Thanks!
    Joshua Hornick (Four Rivers Charter Public School, Greenfield, MA)
    Subject taught: Math, Grade: 11
    How has it been going.
    Hi Nancy,
    I\'m playing with how to improve the number sense of my 11th grade Algebra 2 students. I have played some with number talks and I\'m a big proponent of James Tanton\'s exploding dots curriculum (easy to find at I also play with Fermi problems.
    I don\'t know when you posted this and I don\'t know if you\'ve tried it. If you have, I\'d like to know what results you\'ve experienced.
    Please let me know if you or any one else has played with this curriculum. What has worked and what hasn\'t? Or has it all worked? :-)
    Thanks (and thanks for sharing what you put together),

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