GACE Middle Grades Mathematics (4-8) (704) study plan

Classify the real number system (natural, whole, integer, rational, irrational) and place benchmark values on a number line without a calculator.

Compute fluently with rational numbers in fraction, decimal, and percent form, including signed operations and order-of-operations chains.

Convert between fractions, decimals, and percents and justify which representation is most useful in a given comparison problem.

Apply ratio, rate, unit rate, and proportional-reasoning setups to multi-step word problems.

Apply integer-exponent and scientific-notation rules to simplify and compare very large and very small quantities.

Solve percent-change, tax, tip, discount, and simple-interest problems using a single algebraic setup.

Identify and generate equivalent expressions using prime factorization, GCF, LCM, and divisibility rules.

Explain, in writing, why a common student misconception about negative numbers or exponents is wrong.

Translate verbal relationships into linear equations, inequalities, and systems, and identify the meaning of slope and intercept in context.

Solve multi-step linear equations and inequalities, including those with variables on both sides and absolute value.

Graph linear functions from slope-intercept, point-slope, and standard forms and interpret the graph in a real-world scenario.

Solve systems of two linear equations by graphing, substitution, and elimination, and verify solutions algebraically.

Add, subtract, multiply, and factor polynomials, including difference of squares and simple trinomials.

Solve quadratic equations by factoring, completing the square, and the quadratic formula, and interpret the discriminant.

Identify key features of quadratic graphs (vertex, axis of symmetry, intercepts) and connect them to the algebraic form.

Distinguish functions from non-functions using tables, graphs, and mappings and evaluate function notation correctly.

Apply exponent rules and basic operations on exponential and rational expressions, and recognize linear vs. exponential growth from a table or graph.

Set up and solve geometry problems using perimeter, area, surface area, and volume formulas for composite figures.

Apply the Pythagorean theorem and distance formula, including converse reasoning to classify triangles.

Convert within and across measurement systems and judge the reasonableness of a computed measurement.

Apply angle relationships (parallel lines with a transversal, triangle sum, exterior angle) to find unknown measures with justification.

Compute and interpret mean, median, mode, range, and standard deviation, and predict how outliers shift each measure.

Read, construct, and compare displays (histogram, box plot, scatter plot, two-way table) and identify the story each display tells.

Distinguish correlation from causation and evaluate the appropriateness of a sampling method.

Solve basic probability problems using sample spaces, the addition and multiplication rules, and complements.

Compute conditional probability from a two-way table and interpret independence correctly.

Apply transformations (translation, rotation, reflection, dilation) and identify congruence versus similarity.

Evaluate a real-world claim for bias, misleading graph scaling, or an unsupported inference.

Select and justify a problem-solving strategy (make a table, work backward, find a pattern, use a model) for unfamiliar multi-step tasks.

Construct and evaluate mathematical arguments, including identifying errors in a flawed student solution.

Explain a mathematical procedure clearly enough for a middle-grades learner to follow.

Complete a full-length timed practice test under exam conditions and analyze results by domain.