Sample Curriculum

EIGHTH GRADE ALGEBRAIC FUNCTIONS (SEPT-NOV EXCERPT)
Algebraic study, the “science of comparison and reduction,” begins in early grades and ends with a formal study in the eighth grade year. Such study includes work with variables, expressions and equations, transformation of equations, polynomials, linear and quadratic equations, Cartesian planes, and set theory.

Common Core Standards
Expressions and Operations

• Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

• Define appropriate quantities for the purpose of descriptive modeling.

• Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

• Interpret parts of an expression, such as terms, factors, and coefficients. *Limited to linear, exponential, and quadratic functions.

• Interpret complicated expressions by viewing one or more of their parts as a single entity. *Limited to linear, exponential, and quadratic functions.

• Interpret expressions that represent a quantity in terms of its context. *Limited to linear, exponential, and quadratic functions.

• Use the structure of an expression to identify ways to rewrite it. *Limited to linear, exponential, and quadratic functions.

Equations and Inequalities

• 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 justify a solution method.

• Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

• Create equations and inequalities in one variable and use them to solve problems. *Linear, quadratic, and exponential (integer inputs only)

• Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. *Linear, quadratic, and exponential (integer inputs only)

Transformation and Congruence

• Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

• Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

• Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

Desired Understandings

Students will understand that expressions and equations are powerful abstractions. They will understand that equations contain within them all their solutions, but hidden and disguised.  The “science” is the set of skills and procedures that lead from the original equation to a clear and simple reading of the solution.  

Students will understand that an equal sign is a serious and important statement of an important fact.  (They will understand that it does not mean:  “and my next step is…” or “and the answer is…”

Students will understand that the Algebra is the writing of sequential, strategic, logical steps.