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Curriculum map
A single sequence for students sitting both the Grade 8 State Test and the Algebra I Regents. Overlapping standards are consolidated.
Primary sources: NYS Next Generation Mathematics Learning Standards (PDF) · Algebra I Regents (NYSED)
Unit 1
The Number System & Roots
Irrational numbers, rational approximations, and square and cube roots. Algebra I later uses these properties when classifying sums and products.
Essential question: How do we locate and compare numbers that never terminate or repeat?
Unit 2
Exponents & Scientific Notation
Integer exponent properties and scientific notation for very large and very small quantities — a Grade 8 focus that supports Algebra I quantitative reasoning.
Essential question: How can exponent rules compress enormous (and tiny) quantities?
Unit 3
Slope, Rate of Change & Linear Equations
The shared spine of both exams: slope as unit rate, y = mx + b, and constructing linear models. Taught once, assessed on both tests.
Essential question: What does a constant rate of change look like in a table, graph, and equation?
Unit 4
Solving Linear Equations & Inequalities
Grade 8 solving in one variable is extended in Algebra I to inequalities, literal equations, and modeling constraints.
Essential question: When does an equation have one solution, none, or infinitely many?
Unit 5
Systems of Linear Equations
Graphing, substitution, and elimination. Grade 8 introduces systems; Algebra I requires fluency and the f(x) = g(x) intersection view.
Essential question: How can two conditions be true at the same time?
Unit 6
Functions & Function Notation
Grade 8 defines functions; Algebra I adds domain, range, and f(x) notation. Taught as one progression, not two separate units.
Essential question: What does it mean for a relationship to be a function?
Unit 7
Transformations, Congruence & Similarity
Rigid motions, dilations, and similarity. Algebra I later reuses these ideas as function transformations.
Essential question: Which moves preserve size and shape, and which only preserve shape?
Unit 8
Pythagorean Theorem, Distance & Volume
Right triangles, distance on the coordinate plane, and volume of cylinders, cones, and spheres.
Essential question: How does the relationship among three lengths unlock distance and space?
Unit 9
Bivariate Data
Scatter plots and lines of best fit appear on both exams; Algebra I adds correlation and residual thinking.
Essential question: What does a cloud of points tell us about a relationship?
Unit 10
Exponential Functions
Growth and decay, geometric sequences, and distinguishing linear from exponential change.
Essential question: When does a quantity change by a constant factor rather than a constant amount?
Unit 11
Quadratic Functions
Standard, vertex, and factored forms; graphs, roots, vertex, and axis of symmetry.
Essential question: How do three equivalent forms of a quadratic highlight different features of the same parabola?
Unit 12
Polynomials, Modeling & Comparison
Polynomial arithmetic and choosing among linear, exponential, and quadratic models.
Essential question: Which function family best tells the story of this situation?