Math in Grade 8

In their final year, students at Stephen Decatur Middle School 35 are afforded the opportunity to take the Algebra I Regents Examination which makes them eligible for credit towards high schools graduation.  During this time students continue to engage in the Mathematical Practices in order to gain a thourough understanding of the concepts they are learning.  The units of study are as follows:

Unit 1: Foundations of Algebra

Students build on their prior knowledge of algebra through reinforcement of the following ideas:

  • Symbols are used to represent quantities that are unknown or that vary. 

  • Mathematical phrases and real-world relationships can be represented using symbols and operations. 

  • Numbers and operations comprise a system that share a set of common properties.

Unit 2: Solving Equations

Unit 3: Solving Inequalities

Unit 4: An Introduction to Functions

In units 2-4 students continue to build on their knowedge of algebra by emphasizing the following ideas: 

  •  A solution is a value that makes a function rule true.
  • The relationship between the variables of a function can be represented visually by a graph.

  • Functions can be represented in multiple, equivalent ways.

  • Rate of change describes how one quantity changes with respect to another.

  • A function’s rate of change and initial value determine its other properties and behaviors.

Unit 5: Linear Functions

Unit 6: Systems of Linear Equations and Inequalities

Unit 7: Exponents and Exponential Functions

Students begin to deepen their knowledge of functions as they progress through units 5-7 by focusing on the following ideas:

  • Function rules describe the quantitative relationships between variables.

  • Linear functions are characterized by a constant rate of change.

  • Linear functions can be represented in multiple, equivalent ways.

  • Function families share similar graphs, behaviors, and properties.

  • Systems of equations (or inequalities) contain functions that share the same set of variables.

  • A solution simultaneously makes each function rule in a system of equations (or inequalities) true.

  • The solution to a system of equations (or inequalities) can be represented in multiple, equivalent ways.

Unit 8: Polynomials and Factoring

Unit 9: Quadratic Functions and Equations

Unit 10: Radical Expressions and Equations

Unit 11: Rational Expressions and Equations

Students further deepen their knowledge of functions in units 8-11 as they explore these ideas: 

  • Quadratic expressions can be written in multiple, equivalent ways.
  • Quadratic equations can be solved by rearranging the equation into an equivalent forms.

  • Quadratic functions are distinguished by a power of 2.

  • Equivalent representations of a function highlight different properties.

  • Functions within a family are transformations of the parent function.

  • Quadratic functions have 0, 1, or 2 real roots.

  • Quadratic functions can be represented in multiple, equivalent ways.

Unit 12: Data Analysis and Probability

Students end the year by focusing on these two essential ideas in unit 12:

  • Measures of center are used to interpret univariate data.

  • Visual models illustrate the correlation of bivariate data.