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:
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Symbols are used to represent quantities that are unknown or that vary.
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Mathematical phrases and real-world relationships can be represented using symbols and operations.
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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.
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The relationship between the variables of a function can be represented visually by a graph.
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Functions can be represented in multiple, equivalent ways.
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Rate of change describes how one quantity changes with respect to another.
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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:
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Function rules describe the quantitative relationships between variables.
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Linear functions are characterized by a constant rate of change.
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Linear functions can be represented in multiple, equivalent ways.
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Function families share similar graphs, behaviors, and properties.
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Systems of equations (or inequalities) contain functions that share the same set of variables.
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A solution simultaneously makes each function rule in a system of equations (or inequalities) true.
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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.
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Quadratic equations can be solved by rearranging the equation into an equivalent forms.
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Quadratic functions are distinguished by a power of 2.
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Equivalent representations of a function highlight different properties.
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Functions within a family are transformations of the parent function.
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Quadratic functions have 0, 1, or 2 real roots.
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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: