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

Appendix on Implementing District Standards

My school follows the California Common Core State Standards for Mathematics (CCSSM). The following standards were touched on throughout this unit:

Quantities (N-Q):

Reason quantitatively and use units to solve problems.

1. Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas…”

Students will be required to label a value’s units when answering word problems in the problem sets.

Seeing Structure in Expressions (A-SSE):

Interpret the structure of expressions.  

1. Interpret expressions that represent a quantity in terms of its context.
   1. Interpret parts of an expression, such as terms, factors, and coefficients.

Students will interpret expressions they create from word problems in Problem Set 1.

Creating Equations (A-CED):

Create equations that describe numbers or relationships.

1. Create equations and inequalities in one variable…and use them to solve problems.

Students will create equations that describe relationships they observe in the problem sets’ word problems.

Reasoning with Equations and Inequalities (A-REI):

Understand solving equations as a process of reasoning and explain the reasoning.

1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to jutify a solution method.

Students will justify solutions by substituting and evaluating their found solutions into the original equations.

Solve equations and inequalities in one variable.

3. Solve linear equations and inequalities in one variable…

Students will create and then solve equations from word problems in the problem sets.