MTLE Mathematics (Grades 5-12) study plan
MTLE Mathematics (Grades 5-12) · Give each week a clear focus.
8 weeks · About 6 hours per week
Algebraic Relationships and Functions
Review the function concept (domain, range, notation, multiple representations) and classify parent functions by their key features
Solve and graph linear equations, inequalities, and systems in two variables, including contextual word problems
Factor polynomials of degree two and higher and use factoring to solve polynomial equations
Build fluency with exponent and radical rules by simplifying 30 mixed expressions without notes
Set up a personal error log that records the misconception behind each missed item
Your checkpoint
A 25-item self-made mixed algebra quiz (linear, systems, polynomials, exponents) scored and annotated with an error-log entry for every miss
Algebraic Relationships and Functions
Analyze quadratic functions in standard, vertex, and factored forms and connect each form to its graph
Derive and apply the quadratic formula and the discriminant to classify roots
Perform operations on rational expressions and solve rational equations, checking for extraneous solutions
Compose functions and find inverse functions, verifying inverses algebraically and graphically
Interpret and transform exponential and logarithmic functions in growth and decay contexts
Your checkpoint
A one-page function-family reference sheet you author yourself (equation, graph shape, key features, transformations, a worked example each) for linear, quadratic, polynomial, rational, exponential, and logarithmic functions
Algebraic Relationships and Functions & Number Sense and Operations
Sketch and interpret graphs of absolute value, piecewise, and step functions, including domain and range restrictions
Solve absolute value equations and inequalities and justify solutions on a number line
Apply real number properties and the order of operations to simplify numeric expressions with signed numbers, fractions, and nested grouping
Convert fluently among fractions, decimals, and percents and use proportional reasoning in multi-step problems
Classify numbers within the real number system and explain why each classification holds
Your checkpoint
A written solution set of 20 problems mixing absolute value, piecewise functions, and rational-number operations, each with a one-sentence justification of the method chosen
Number Sense and Operations & Geometry and Measurement
Apply integer exponent and scientific notation rules to compute with very large and very small quantities
Use ratio, rate, and percent change to solve consumer and measurement problems, including percent error
Compute perimeter, area, surface area, and volume of standard two- and three-dimensional figures, choosing correct formulas from a formula sheet
Solve problems involving circles (circumference, arc length, sector area) and composite figures
Convert within and between measurement systems using dimensional analysis
Your checkpoint
A timed 40-minute, 20-question number-sense and measurement practice set completed under exam conditions, with a scored breakdown by subskill
Geometry and Measurement
Prove and apply triangle congruence and similarity criteria to find unknown lengths and angles
Apply the Pythagorean theorem and right-triangle trigonometric ratios to solve applied problems
Use coordinate geometry to verify properties of lines and polygons, including slope, midpoint, and distance
Identify and apply transformations (translation, rotation, reflection, dilation) and describe their effects on coordinates
Analyze properties of circles, including inscribed angles, chords, tangents, and central angles
Your checkpoint
A portfolio of 10 fully worked geometry problems, at least three of which require a two-column or paragraph proof, each diagram redrawn by hand from the problem text
Statistics, Probability, and Data Analysis
Compute and interpret measures of center and spread and choose the appropriate measure for a given distribution
Construct and read displays (histogram, box plot, scatterplot, two-way table) and describe shape, center, spread, and outliers
Analyze scatterplots for association and fit and interpret a line of best fit
Compute probabilities for simple, compound, and conditional events and distinguish independent from dependent events
Design and critique sampling methods and identify sources of bias in data collection
Your checkpoint
A statistics mini-project using a real dataset of at least 30 values that includes a hand-built histogram and box plot, computed summary statistics, and a written paragraph interpreting the distribution and one possible bias
Mathematical Reasoning, Problem Solving, and Communication & Pedagogical Content Knowledge and Instructional Practice
Select and apply problem-solving strategies (make a table, work backward, find a pattern, guess and check) and justify the choice
Write clear mathematical explanations and construct viable arguments and critique flawed reasoning in sample student work
Analyze student misconceptions in number sense, algebra, and geometry and plan an instructional response
Apply assessment principles by writing items aligned to a stated learning objective and a cognitive-demand level
Differentiate instruction for diverse learners, including English learners and students with IEPs, using appropriate scaffolds
Your checkpoint
A written analysis of three sample student solutions to the same problem, identifying each misconception, prescribing an instructional intervention, and drafting one aligned follow-up assessment item
Pedagogical Content Knowledge and Instructional Practice & Mathematical Reasoning, Problem Solving, and Communication & Algebraic Relationships and Functions & Number Sense and Operations & Geometry and Measurement & Statistics, Probability, and Data Analysis
Synthesize all domains through two full-length timed practice exams, simulating test-day conditions
Review every missed item from the practice exams and reclassify each error as content gap, misread, or time pressure
Re-teach your three weakest subskills using self-generated explanations and worked examples
Rehearse instructional-scenario questions by articulating a rationale for each selected response
Finalize a one-page formula and concept sheet you can review in the 48 hours before the exam
Your checkpoint
Two completed full-length practice exams with a scored error analysis and a finalized one-page personal formula and concept sheet
Milestones
Week 2: Score at least 80% on a self-made 20-item algebra quiz covering functions, quadratics, and rational expressions, and confirm every error-log entry names a specific misconception rather than a topic
Week 4: Complete the timed number-sense and measurement set at or above 75% accuracy within 40 minutes, with no more than two formula-recall errors
Week 6: Earn at least 80% on a 25-item mixed set spanning Domains 1 through 4, and submit the statistics mini-project with all required components present
Week 8: Score at least 80% on both full-length practice exams and demonstrate that at least 70% of previously logged errors are resolved on a targeted re-quiz