OSAT Middle Level/Intermediate Mathematics (225) study plan
OSAT Middle Level/Intermediate Mathematics (225) · Give each week a clear focus.
8 weeks · About 7 hours per week
Number Sense and Operations
Compute fluently with rational numbers in all four operations, including signed fractions, decimals, and mixed numbers, without a calculator.
Convert among fractions, decimals, and percents and order a mixed set of ten values from least to greatest.
Apply order of operations and properties of exponents (product, quotient, power, zero, negative) to simplify 20 numeric expressions.
Classify numbers as rational or irrational and place square roots of non-perfect squares between consecutive integers.
Your checkpoint
A timed 25-question number sense quiz scored at 88% or higher, with every missed item rewritten and re-solved correctly.
Number Sense and Operations
Solve multi-step percent problems: percent change, tax, discount, markup, simple interest, and percent error.
Compute with ratios, rates, unit rates, and proportional reasoning, including scale factors and similar-figure side lengths.
Solve problems involving scientific notation, including multiplication and division with exponent rules.
Apply divisibility rules, prime factorization, GCF, and LCM to simplify and combine fractions and radicals.
Your checkpoint
A one-page error log of 15 mixed number-sense problems, each showing the correct method and the specific rule that was initially misapplied.
Algebra and Functions
Solve linear equations and inequalities in one variable, including those with fractions, absolute value, and variables on both sides.
Graph linear equations and inequalities on the coordinate plane and interpret slope as a rate of change.
Write equations of lines given two points, a point and a slope, or a parallel/perpendicular condition.
Solve systems of two linear equations by substitution, elimination, and graphing, and classify as consistent, inconsistent, or dependent.
Your checkpoint
A 20-problem linear-functions set scored at 85% or higher, including at least four word problems translated from context to equation.
Algebra and Functions
Add, subtract, multiply, and divide polynomial expressions, including binomial expansion and factoring of trinomials.
Factor completely using GCF, difference of squares, and trinomial methods, and use factoring to solve quadratic equations.
Apply the quadratic formula and discriminant to determine the number and type of solutions.
Evaluate, compose, and find inverses of functions, and identify domain and range from equations and graphs.
Your checkpoint
A two-page summary sheet of factoring and quadratic techniques with one worked example each, plus a 15-question self-test at 80% or higher.
Geometry and Measurement
Compute perimeter, area, surface area, and volume for polygons, circles, prisms, cylinders, pyramids, cones, and spheres.
Apply the Pythagorean theorem and distance formula to find lengths and verify right triangles.
Use angle relationships (parallel lines and transversals, triangle angle sum, exterior angles, inscribed angles) to find missing measures.
Perform unit conversions within and across measurement systems and compute with significant precision appropriate to the problem.
Your checkpoint
A formula reference card plus a 20-problem measurement set scored at 85% or higher, with units labeled on every answer.
Geometry and Measurement
Transform figures using translations, rotations, reflections, and dilations on the coordinate plane and describe the effect on coordinates.
Prove and apply congruence and similarity criteria for triangles, including ratio of areas and volumes under scaling.
Solve coordinate-geometry problems involving slope, midpoint, and parallel/perpendicular lines.
Analyze three-dimensional solids from nets and cross-sections and compute composite-figure area and volume.
Your checkpoint
A set of six labeled coordinate-plane sketches demonstrating each transformation and a written similarity proof, self-checked against a rubric you write.
Statistics, Probability, and Data Analysis
Compute and interpret mean, median, mode, range, quartiles, and interquartile range, and identify outliers.
Read and construct displays: histograms, box plots, scatter plots, and two-way tables, and describe association and trend.
Compute probabilities for simple, compound, and conditional events, including independent versus dependent events and the complement rule.
Distinguish correlation from causation and evaluate sampling methods and sources of bias.
Your checkpoint
A one-page statistical report analyzing a dataset you choose, including a box plot, a scatter plot with a described trend, and a probability calculation with justification.
Number Sense and Operations & Algebra and Functions & Geometry and Measurement & Statistics, Probability, and Data Analysis
Complete two full-length timed practice tests under exam conditions and record per-domain accuracy.
Re-teach the two weakest domains using targeted drills until each reaches 85% accuracy.
Review all error logs and formula cards, re-solving every previously missed problem without notes.
Practice pacing and calculator-free arithmetic strategies to finish each section with five minutes remaining.
Your checkpoint
A final score report across both practice tests showing per-domain accuracy, with every domain at 80% or higher and a written list of remaining weak spots.
Milestones
Week 2: Score 85% or higher on a 20-question cumulative number-sense test taken without a calculator.
Week 4: Score 80% or higher on a mixed algebra test covering linear, quadratic, and function items, and explain two solution methods aloud.
Week 6: Score 80% or higher on a geometry and measurement test, with correct units on at least 90% of items.
Week 8: Average 80% or higher across both full-length practice tests with no single domain below 75%.