Great Ideas of Primary Mathematics

CONTENTS OF CURRICULUM UNIT 11.06.11

  1. Unit Guide
  1. Overview
  2. Background
  3. Strategies
  4. Activities
  5. Appendix A – Implementing District Standards/Delaware State Standards
  6. Appendix B – Rules of Arithmetic and Rules of Exponents
  7. Appendix C – Sample Problem Sets
  8. Resources
  9. Notes

Boosting Number Sense in High School Students

Nancy Rudolph

Published September 2011

Tools for this Unit:

Resources

Davis, Sue. "Oral and Mental Mathematics." Mathematics Teaching 215 (2009): 45-48., http://vnweb.hwwilsonweb.com (accessed June 25, 2011).

Gardiner, A. Extension mathematics Beta, Gamma. Oxford: Oxford University Press, 200, Problem sets to promote number sense, especially for stronger students.

Gross, Herbert, and Richard Medeiros. "Mathematics As A Second Language.", Mathematics As A Second Language. http://www.adjectivenounmath.com/ (accessed July 20, 2011), Power Point slides available for arithmetic, algebra and calculus lessons.

Howe, Roger , and Susanna Epp. "PMET - Resources: Taking Place Value Seriously.", Mathematical Association of America, http://www.maa.org/pmet/resources/PVHoweEpp-Nov2008.pdf (accessed July 21,2011).

Mcintosh, Alistair, Barbara Reys, and Robert Reys. "A Proposed Framework for Examining Basic Number Sense." For the Learning of Mathematics 12, no. 3 (1992): 2-8., http://www.jstor.org/stable/40248053 (accessed July 17, 2011).

Parrish, Sherry. Number talks: helping children build mental math and computation strategies, grades K-5. Sausalito, Calif.: Math Solutions, 2010., Strategies and sample problems for mental math calculations.

Pitta-Pantazi, Demetra, Constantinos Christou, and Theodossios Zachariades. "Secondary school students' levels of understanding in computing exponents." The Journal of Mathematical Behavior 26, no. 4 (2007): 301-311, http://www.sciencedirect.com (accessed July 13, 2011), Comparison of relative size for exponential expressions.

Rubenstein, Rheta. "Mental Mathematics beyond the Middle School: Why? What? How?" Mathematics Teacher 94, no. 6 (2001): 442-446., Objectives and sample items for number sense, algebra, and Precalculus.

Threlfall, John. "Flexible Mental Calculations." Educational Studies in Mathematics 50, no. 1 (2002): 29-47. http://vnweb.hwwilsonweb.com (accessed July 20, 2011)., Purpose and strategies for teaching mental calculations.

Tirosh, Dina. "Enhancing Prospective Teachers' Knowledge of Children's Conceptions: The Case of Division of Fractions." Journal for Research in Mathematics Education 31, no. 1 (2000): 5-25., http://www.jstor.org/stable/749817 (accessed July 17, 2011), Sources of errors in dividing fractions and how to help children understand division conceptually.

Weinstein, Lawrence, and John A. Adam. Guesstimation: solving the world's problems on the back of a cocktail napkin. Princeton, N.J.: Princeton University Press, 2008., Sets of estimation problems and solutions organized by topic.

Yang, Der-Ching, Robert Reys, and Barbara Reys. "Number Sense Strategies Used by Pre-Service Teachers in Taiwan." International Journal of Science and Mathematics Education 7, no. 2 (2009): 383-403., http://vnweb.hwwilsonweb.com (accessed June 25, 2011).

Comments:

Nathan Hochmuth

November 7, 2013 at 8:34 am

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

December 5, 2013 at 1:04 pm

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

May 5, 2014 at 4:11 pm

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

August 3, 2016 at 8:52 pm

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 gdaymath.com). 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), Joshua--

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