FTCE Middle Grades Math 5-9 (025) study plan

Compute fluently with fractions, decimals, and percents, converting among all three forms without a calculator.

Apply order of operations and integer exponent rules to simplify numeric expressions, including negative and zero exponents.

Classify numbers as rational or irrational and justify each classification with a written reason.

Solve multi-step proportional reasoning problems involving unit rates, scale drawings, and percent change, showing the set-up for each.

Find GCF, LCM, prime factorizations, and divisibility patterns, then use them to simplify and combine expressions.

Convert among standard form, scientific notation, and word form for very large and very small quantities.

Explain in writing two common student misconceptions about fraction operations and the correct reasoning behind each.

Solve absolute value and integer comparison problems set in real contexts such as temperature, elevation, and debt.

Simplify and factor polynomial expressions, including difference of squares and trinomials with a leading coefficient other than one.

Solve linear equations, inequalities, and literal equations, and graph solution sets on a number line.

Compute slope from tables, graphs, and pairs of points, then write equations of lines in slope-intercept and point-slope form.

Solve systems of two linear equations by graphing, substitution, and elimination, and interpret the solution in context.

Graph quadratic functions, identifying vertex, axis of symmetry, and intercepts, and describe transformations from the parent function.

Distinguish functions from non-functions using tables, graphs, and mapping diagrams, and apply function notation.

Convert between radical and rational-exponent forms and perform operations on expressions with integer exponents.

Set up and solve word problems with linear and quadratic models, defining variables explicitly before solving.

Compute perimeter, area, surface area, and volume for polygons, circles, prisms, cylinders, pyramids, and cones.

Apply the Pythagorean theorem and the distance formula to find missing lengths and classify triangles.

Convert units within and across customary and metric systems using dimensional analysis.

Determine similarity and congruence relationships and use scale factors to find missing measures.

Compute experimental and theoretical probabilities for simple, compound, and conditional events, with and without replacement.

Construct and interpret frequency tables, histograms, box plots, and scatter plots, describing shape, center, and spread.

Calculate mean, median, mode, range, mean absolute deviation, and standard deviation, and explain how outliers affect each.

Identify misleading graphs and unsupported statistical claims, justifying each critique in writing.

Design a standards-aligned lesson objective paired with a matching assessment item for a middle-grades math topic.

Compare direct instruction, inquiry, and cooperative learning, matching each strategy to an appropriate objective.

Analyze student work samples to diagnose error patterns and prescribe a specific re-teaching move.

Select and justify formative and summative assessment methods, including rubric design and item-type choices.

Complete two full-length timed practice exams and record total scores plus domain-level breakdowns.

Rework every missed item from the weeks 1-7 error logs until each is solved correctly twice.

Drill the weakest objectives identified by exam data in spaced 20-minute review blocks.

Recite from memory the key formulas and definitions for all five domains.