From Arithmetic to Algebra: Variables, Word Problems, Fractions and the Rules

CONTENTS OF CURRICULUM UNIT 17.05.03

  1. Unit Guide
  1. Introduction and Rationale
  2. Polya’s Method
  3. A Brief History of Singapore Math
  4. Model Method
  5. Whole Group Discussion
  6. Taxonomy of Word Problems
  7. Activities
  8. Sample Collection of Problems 
  9. Bibliography
  10. Additional Resources for Teachers and Students
  11. Appendix A: Implementing District and National Standards
  12. Common Core Standards
  13. Endnotes

Understanding Problems: Using Bar Models with Common Core Taxonomies

Valerie J. Schwarz

Published September 2017

Tools for this Unit:

Endnotes

  1. G. W. Melvin, “Polya’s Problem Solving Techniques,” https://math.berkeley.edu/~gmelvin/polya.pdf.
  2. http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/index.shtml
  3. V. Schwarz, “Dr. Word Problem – Solving Word Problems with the Four Operations Using Singapore Bar Models,” The Yale National Initiative, last modified July 2007. http://teachers.yale.edu/curriculum/viewer/initiative_07.06.05_u
  4. Common Core State Standards Initiative, “Mathematics Glossary Table 1 & Table 2” http://www.corestandards.org/Math/Content/mathematics-glossary/Table-1/ http://www.corestandards.org/Math/Content/mathematics-glossary/Table-2/
  5. G.W. Melvin, “Polya’s Problem Solving Techniques,” https://math.berkeley.edu/~gmelvin/polya.pdf.
  6. B. Kaur, “The model Method: A tool for representing and visualizing relationships,” http://www.umac.mo/fed/ICMI23/doc/Proceedings ICMI STUDY 23 final.pdf
  7. G. W. Melvin, “Polya’s Problem Solving Techniques,” https://math.berkeley.edu/~gmelvin/polya.pdf.
  8. B. Kaur, “Evolution of Singapore’s school mathematics curriculum,” Curriculum in Focus: Research Guided Practice 29 June to 3 July 2014.
  9. B. Kaur, “The model Method: A tool for representing and visualizing relationships,” 449. http://www.umac.mo/fed/ICMI23/doc/Proceedings ICMI STUDY 23 final.pdf
  10. S.F. Ng and K. Lee, “The Model Method: Singapore Children’s Tool for Representing and Solving Algebraic Word Problems,” 296.
  11. IBID, 291.
  12. IBID, 291.
  13. IBID, 291.
  14. IBID, 291.
  15. IBID, 296-297.
  16. L. Englard, “Raise the Bar on Problem Solving,” 157.
  17. S.F. Ng and K. Lee, “The Model Method: Singapore Children’s Tool for Representing and Solving Algebraic Word Problems,” 283.
  18. IBID, 282.
  19. Y.K. Cheong, “The Model Method in Singapore,” 2002.
  20. S.F. Ng and K. Lee, “The Model Method: Singapore Children’s Tool for Representing and Solving Algebraic Word Problems,” 283.
  21. S.F. Ng, K. Lee, S.Y. Ang, & F. Khng, “Model Method: obstacle or bridge to learning symbolic algebra,” 227-242.
  22. C.K. Looi and K.S. Lim, “From bar diagrams to letter-symbolic algebra: a technology-enabled bridging,” 358.
  23. IBID, p358.
  24. IBID, p 261
  25. http://www.corestandards.org/Math/Content/mathematics-glossary/Table-1/

Comments:

Grace Laz

March 29, 2021 at 6:40 am

Can bar method be applied to complex word problems?

Hi. I am an educator to my 11 year old daughter. We has been using Singaporean math books for her year 5 and came across this bar method. Do you think the bar method can be applied to complex word problems? Thank you.

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