MTEL 65 study plan
MTEL 65 · Give each week a clear focus.
8 weeks · About 7 hours per week
Number Systems and Operations
Classify 30 numbers as natural, whole, integer, rational, irrational, or real, and justify each classification with a definition.
Apply order of operations and number properties to simplify 25 expressions containing exponents, radicals, absolute value, and grouped operations.
Convert among fractions, decimals, percents, and scientific notation across 40 items, including repeating decimals and numbers greater than one million.
Solve 20 ratio, proportion, and percent application problems, labeling the unknown and checking reasonableness of each answer.
Your checkpoint
Completed 60-item Number Systems diagnostic with a written error log identifying at least 8 error types and corrected worked solutions for each miss.
Number Systems and Operations & Algebra and Functions
Execute integer and rational operations, including negatives and fractions, in 30 mixed problems without a calculator.
Use prime factorization to compute GCF and LCM and to simplify 15 radical expressions.
Translate 15 verbal relationships into algebraic expressions or equations, then verify each translation by substitution.
Solve and graph the solutions of 20 one- and two-step linear equations and inequalities on a number line.
Your checkpoint
A 45-minute timed mixed set of 30 Domain 1-2 problems scored at 80% or higher, with every miss reworked and annotated.
Algebra and Functions
Identify slope, intercepts, domain, and range from 15 linear equations, tables, and graphs.
Solve 12 systems of two linear equations using graphing, substitution, and elimination, and classify each system as consistent or inconsistent.
Factor 15 polynomials and solve 10 quadratic equations by factoring and by the quadratic formula.
Distinguish functions from non-functions using 20 mappings, tables, graphs, and equations.
Your checkpoint
A one-page function toolkit containing definitions, slope procedures, and factoring steps, plus 25 solved practice items scored at 90% or higher.
Number Systems and Operations & Algebra and Functions
Complete 50 mixed cumulative problems under 75-minute timed conditions.
Categorize every missed item by domain, skill, and error type, then re-teach the two highest-frequency weak skills.
Write 10 original worked examples that combine number sense with algebra, such as percent growth, rational equations, and rate problems.
Explain in writing three common traps: negative exponents, distributing a negative, and extraneous solutions.
Your checkpoint
A full-length 50-item cumulative assessment with score, item analysis, and a revised two-week remediation list targeting the weakest skills.
Geometry and Measurement
Apply angle relationships for parallel lines, triangles, and polygons to solve 25 missing-angle problems.
Use the Pythagorean theorem, congruence, and similarity to solve 20 problems, including indirect measurement.
Compute perimeter, area, surface area, and volume for 20 composite two- and three-dimensional figures.
Convert units within and across measurement systems in 15 multi-step problems, preserving appropriate precision.
Your checkpoint
A formula sheet with 20 labeled hand-drawn diagrams and 30 solved geometry problems scored at 85% accuracy or higher.
Geometry and Measurement & Statistics, Probability, and Data Analysis
Interpret 12 data displays, including dot plots, histograms, box plots, and scatterplots, by describing center, spread, shape, and outliers.
Compute mean, median, mode, range, interquartile range, and mean absolute deviation for 10 data sets, then choose the most appropriate summary for each context.
Solve 20 probability problems involving sample spaces, compound events, and expected value.
Distinguish experiments, observational studies, and samples, and identify potential bias in 10 scenarios.
Your checkpoint
A statistics portfolio with 5 constructed or cited data sets, each including a display, summary statistics, and a one-paragraph contextual interpretation checked against an answer key.
Statistics, Probability, and Data Analysis & Number Systems and Operations & Algebra and Functions & Geometry and Measurement
Complete 30 mixed probability and statistics items, including conditional probability and counting techniques.
Analyze scatterplots for association, line of fit, and prediction, and explain correlation versus causation in 5 written prompts.
Review geometry and measurement formulas through 20 applied mixed problems.
Build a 10-question Domain 4 quiz with complete answer explanations.
Your checkpoint
A timed 40-item Domains 3-4 assessment scored at 80% or higher, with written explanations for 10 missed or flagged items.
Number Systems and Operations & Algebra and Functions & Geometry and Measurement & Statistics, Probability, and Data Analysis
Take two full-length timed practice tests or equivalent 100-item mixed sets under simulated testing conditions.
Classify every missed item by domain, skill, and error type, and rank the remaining weaknesses.
Re-solve 25 previously missed problems without notes until reaching 90% correct.
Create a one-page test-day reference of key formulas, definitions, and decision rules.
Your checkpoint
Two timed full-length practice scores, a final error-analysis sheet, and a one-page formula-and-strategy card.
Milestones
Week 2: Score at least 80% on the 30-item timed Domain 1-2 mixed set and submit an error log with 15 corrected worked items.
Week 4: Score at least 75% on the 50-item cumulative Domain 1-2 assessment and list the three highest-frequency error patterns with a corrective action for each.
Week 6: Complete the 5-data-set statistics portfolio and score at least 80% on a 20-item Domain 3-4 quiz.
Week 8: Score at least 80% on one full-length practice test and at least 90% on the reattempted set of 25 previously missed problems.