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

CONTENTS OF CURRICULUM UNIT 17.05.07

  1. Unit Guide
  1. Overview and Rationale
  2. The Wrong Path Taken by Past Curricula
  3. Description of The Multiple Unit Approach and Progression of Learning
  4. Major Implemented Strategies
  5. Problem Sets
  6. Activity List
  7. Appendix
  8. SMP 
  9. Additional Resources
  10. Bibliography
  11. Notes

Introduction of the Variable by Forming and Interpreting Expressions

Jeffrey Rossiter

Published September 2017

Tools for this Unit:

Appendix

Sixth Grade

Students are expected ‘apply and extend previous understandings of arithmetic to algebraic expressions.’ This leaves the door open for multiple deficiencies in content knowledge.

CCSS.Math.Content.6.EE.A.1 Write and evaluate numerical expressions involving whole-number exponents.

CCSS.Math.Content.6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers.

CCSS.Math.Content.6.EE.A.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

CCSS.Math.Content.6.EE.A.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

Seventh Grade

CCSS.Math.Content.7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

CCSS.Math.Content.7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.

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