NYSTCE Multi-Subject: Middle Childhood (Grades 5-9), Part Two: Mathematics (232) Practice Tests

Competency 0001 makes up about 15% of the 232 score. It covers: number and operations; ratios and proportional relationships; rational and real number systems.

• Number and operations: Operations and the relationships among them; representing the four operations with integers; Writing and interpreting numerical expressions; generating and analyzing patterns; Place value, computational algorithms and equivalent fractions, and justifying them; Multiplication as scaling; operations with decimals, fractions and rational numbers, including the distributive law; Number theory: primes, divisibility, factors, LCM, GCF; Arithmetic and order of operations extended to algebraic expressions, equations and inequalities; Analyzing assessment data to plan number and operations instruction
• Ratios and proportional relationships: Ratio and rate reasoning with tables, tape diagrams, double number lines, equations and coordinate graphs; Unit rates, percents and percent problems; unit conversion; Constant of proportionality in multiple representations; equations and graphs of proportional relationships; Multistep ratio and percent problems: simple interest, commissions, percent change, percent error; Connections among proportional relationships, lines and linear equations; similar triangles and slope
• Rational and real number systems: Opposite signs, ordering and absolute value of rational numbers; Irrational numbers and rational approximations; repeating decimals; Integer and rational exponents; rewriting radicals; Square and cube roots; scientific notation; Using units to solve multistep problems

Competency 0002 makes up about 35% of the 232 score. It covers: algebra; functions.

• Algebra: Properties of operations and equivalent expressions; Vocabulary and structure of expressions; equivalent forms: factoring quadratics, completing the square; Polynomial arithmetic, zeros and factors, polynomial identities and the binomial theorem; Rewriting rational expressions; Creating and solving one-variable equations and inequalities (linear, quadratic, simple rational, exponential); Multivariable equations and graphs; pairs of simultaneous linear equations; systems of equations and inequalities as constraints; Solving as a reasoning process; solving graphically; Analyzing assessment data to plan algebra instruction
• Functions: Concept of a function: domain, range, function notation; Interpreting functions in context: intercepts, increasing intervals, maxima and minima, zeros, asymptotes, end behavior; Analyzing linear, quadratic, square root, piecewise, polynomial, exponential and logarithmic functions across representations; Building functions that model relationships; effects of f(x + k), composition, inverses; Constructing and comparing linear, quadratic and exponential models; interpreting parameters in context

Competency 0003 makes up about 30% of the 232 score. It covers: measurement and geometry; data, statistics and probability.

• Measurement and geometry: Attributes of polygons and circles; lines and angles; Measurement and unit conversion; relating perimeter, area and volume to number operations; Angle measure, perimeter, area, surface area and volume, including cones, cylinders and spheres; Congruence and transformations in the coordinate plane; Pythagorean theorem and coordinate distance; Proofs of theorems about lines, angles, triangles and parallelograms; Similarity and scale factors; trigonometric ratios for right triangles; Analyzing assessment data to plan instruction
• Data, statistics and probability: Statistical variability and describing distributions: dot plots, histograms, box plots; Random sampling and informal comparative inferences using center and variability; Chance processes and probability models (independent and dependent events) with lists, tables, tree diagrams and simulations; Bivariate data: scatter plots, linear models, two-way tables; Inferences from surveys, experiments and observational studies

Competency 0004 makes up about 20% of the 232 score and is the constructed-response item. It covers: constructed response.

• Constructed response: Analyze student work samples and assessment data to monitor progress and identify strengths and needs; Identify and analyze errors and misconceptions; Describe content-specific strategies or interventions for identified needs, such as skill deficits or low motivation; Generate real-world scenarios that illustrate mathematical concepts; Justify the effectiveness of the selected strategies