Transitions in the Conception of Number: From Whole Numbers to Rational Numbers to Algebra

CONTENTS OF CURRICULUM UNIT 23.03.07

  1. Unit Guide
  1. Introduction
  2. Student and School Background Information
  3. Content Objectives
  4. Teaching Strategies
  5. Classroom Activities
  6. Resources
  7. Annotated Bibliography
  8. Appendix on Implementing District Standards
  9. Notes

Improving Proportional Reasoning = Improving High School Math Success

Julie Skrzypczak

Published September 2023

Tools for this Unit:

Resources

Rules of Arithmetic22

  1. Commutative Property for Addition: for any two numbers a and b,

    2. a + b = b + a

  2. Associative Rule for Addition: for any three numbers a, b, and c,

    3. (a + b) + c = a + (b + c)

  3. Existence of Additive Identity (aka Zero): there is a number 0 such that for any number a,

    4. 0 + a = a

  4. Existence of Additive Inverse (aka “the negative” and “the opposite): for every number a, there is another number, called the additive inverse or negative of a, and denoted by -a, such that

    5. -a + a = 0

  5. Commutative Rule for Multiplication: for any two numbers a and b, we have

    6. a X b = b X a

  6. Associative Rule for Multiplication: for any three numbers a, b, and c,

    7. (a X b) X c = a X (b X c)

  7. Existence of Multiplicative Identity (aka One): there is a number 1 such that for any number a,

    8. 1 X a = a

  8. Existence of Multiplicative Inverse (aka “the reciprocal”): for every non-zero number a, there is another number, called the multiplicative inverse or reciprocal of a, and written as 1⁄a(or sometimes also as a-1), such that

    9. Equation

  9. Distributive Rule: for any three numbers a, b, and c,

    10. a X (b + c) = a X b + a X c

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