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Ontario MPT overview

Ontario MPT study guide: key rules on all 9 topics

Free Ontario MPT study guide: 74 key points from the The Ontario Curriculum: Mathematics (Grades 1–8, 2020; Grade 9, 2021) in plain words, organised by topic, each topic linked to its practice questions.

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  • 9 topics
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This study guide collects our notes on every topic of the Ontario Mathematics Proficiency Test for Teachers (MPT) on one page: 74 short points in our own words, grouped by topic and by handbook section. Read it from top to bottom before your first practice test, or jump to a topic from the list below.

Each topic ends with a link to its practice questions, so you can check what you just read straight away, and a link to the official chapter for the full wording. The notes summarise the The Ontario Curriculum: Mathematics (Grades 1–8, 2020; Grade 9, 2021) from the Education Quality and Accountability Office (EQAO), for the Ontario College of Teachers; they do not replace it, and where our notes and the official source differ, the official source wins.

Study these notes as flashcards →

MPT requirement, format and scoring

Who must pass the Mathematics Proficiency Test for Ontario certification, the two components, the 70% standard on each in the same attempt, cost, retakes, booking and test windows.

Practise MPT requirement, format and scoring questionsFlashcardsOfficial chapter

EQAO MPT page and FAQ (2026)

  • MPT reinstated as a certification requirement for teachers certified in Ontario as of February 1, 2025.
  • Multiple-choice; two components: mathematics (Grades 3–9 content, some no-calculator and some calculator items) and pedagogy (curriculum, assessment and evaluation, learning for all).
  • Optional identity questionnaire and Mathematics Attitude and Perceptions Survey (not scored).
  • Pass: 70 % or higher on each component in the same attempt.
  • Sessions in person at approved test centres or online with remote proctoring; booked first come, first served.
  • No limit on attempts; one registration or waitlist spot at a time; register again after results.
  • Applicant Report (Successful / Not Yet Successful) within 10 days; successful results sent to the College.
  • Windows: fall Oct 1 – Nov 14, 2026; winter Jan 28 – Mar 20, 2027; spring Apr 13 – May 29, 2027.

Mathematics Proficiency Test

  • Requirement for most applicants for a general Certificate of Qualification and Registration as of Feb 1, 2025.
  • Not required: members holding a general CQR on Feb 1, 2025; IETs certified before that date; Labour Mobility applicants; graduates of Lakehead ILTD and Nipissing TILSL programs.
  • No cost, including repeated attempts.
  • IETs certified after the start must pass within two years of initial certification, or the certificate expires.
  • Curriculum section (Grades 3–9) is at least 70 % of the MPT.

Number: fractions, decimals, percents and ratios

Place value, operations with fractions, decimals and integers, percents, rates and ratios, exponents and square roots, and proportional reasoning from the Grades 3–9 Number strand.

Practise Number: fractions, decimals, percents and ratios questionsFlashcardsOfficial chapter

Ontario Curriculum, Number strand (Grades 3–8 B; Grade 9 B)

  • Place value and decimals; ordering decimals (more digits does not mean larger).
  • Fractions: equivalent fractions, operations; dividing by a fraction = multiplying by its reciprocal.
  • Percents, fraction–decimal–percent equivalence (1/8 = 0.125 = 12.5 %).
  • Integers and rational numbers on a number line.
  • Powers, square roots (√50 between 7 and 8), scientific notation (first factor 1 ≤ a < 10).
  • Factors and multiples: GCF, LCM.
  • Proportional reasoning: unit rates, ratios, percent change on different bases.
  • Common misconceptions used as distractors: adding numerators and denominators; counting decimal places; additive instead of multiplicative reasoning.

Algebra, patterns and coding

Patterns, variables and expressions, solving equations and inequalities, linear relations and their graphs, and reading simple code that uses loops and conditions.

Practise Algebra, patterns and coding questionsFlashcardsOfficial chapter

Ontario Curriculum, Algebra strand (Grades 3–8 C incl. coding; Grade 9 C)

  • Patterns: repeating cores (use remainders), growing patterns with rule an + b.
  • Variables and expressions; substitution; simplifying with distribution and like terms.
  • Equality as balance (equal sign means "same value as").
  • Solving linear equations and inequalities; systems by elimination.
  • Linear relations: slope (rate of change) and initial value; y = mx + b.
  • Distance–time graphs: horizontal segment = no movement.
  • Coding is part of the Algebra strand from Grade 1 (ontario.ca); loops repeat instructions; conditionals choose a branch.

Data and probability

Reading and choosing graphs, mean, median, mode and range, sampling and bias, and the probability of simple and compound events.

Practise Data and probability questionsFlashcardsOfficial chapter

Ontario Curriculum, Data strand (Grades 3–8 D; Grade 9 D)

  • Qualitative vs quantitative data; sampling and bias; representative samples.
  • Graph choice: histogram (intervals), circle graph (parts of a whole), line graph (change over time), scatter plot (relationship).
  • Mean, median (average of the two middle values for an even count), mode; outliers affect the mean most.
  • Misleading graphs: axis not starting at zero exaggerates differences.
  • Correlation (positive/negative) does not prove cause.
  • Probability: theoretical = favourable ÷ total; experimental = observed ÷ trials; sample space by tree or table (die and coin = 12).

Spatial sense: geometry and measurement

Angles and polygons, the Pythagorean relationship, transformations, area, surface area and volume, metric unit conversions and circles.

Practise Spatial sense: geometry and measurement questionsFlashcardsOfficial chapter

Ontario Curriculum, Spatial Sense strand (Grades 3–8 E; Grade 9 E)

  • Triangle angles sum to 180°; polygon interior sum (n − 2) × 180°; supplementary = 180°.
  • Quadrilateral properties (rhombus: four equal sides).
  • Pythagorean relationship a² + b² = c².
  • Area: parallelogram bh; trapezoid (a + b)h ÷ 2; circle πr²; 1 m² = 10 000 cm².
  • Volume: prism lwh; cylinder πr²h; surface area of a prism.
  • Transformations on a grid: reflection in x-axis (x, −y); translations.
  • Similar figures: scale factor.
  • Triangular prism: 5 faces, 9 edges, 6 vertices (Euler: F − E + V = 2).

Financial literacy

Budgets, unit prices and best buys, simple and compound interest, sales tax and discounts, and exchange rates as taught in the Financial Literacy strand.

Practise Financial literacy questionsFlashcardsOfficial chapter

Ontario Curriculum, Financial Literacy strand (Grades 1–8 F; Grade 9 F)

  • Financial literacy is its own strand from Grade 1 (ontario.ca): coins and bills, needs vs wants, budgets.
  • Unit price comparisons; percent of income.
  • Simple interest I = Prt; compound interest A = P(1 + r)^n.
  • Discounts and sales tax (Ontario HST 13 % used in examples).
  • Exchange rates: when 1 unit of foreign currency = r CAD, divide a CAD amount by r to get the foreign amount.
  • Debit (own money) vs credit (borrowed; interest on unpaid balance; monthly ≈ annual rate ÷ 12).

Pedagogy: the mathematics curriculum

How the Ontario math curriculum is organized: strands, overall and specific expectations, the seven mathematical processes, social-emotional learning skills, coding and culturally responsive teaching.

Practise Pedagogy: the mathematics curriculum questionsFlashcardsOfficial chapter

Ontario Curriculum, Grades 1–8 Mathematics (2020), front matter; ontario.ca summary page

  • Six strands: A Social-Emotional Learning Skills in Mathematics and the Mathematical Processes; B Number; C Algebra; D Data; E Spatial Sense; F Financial Literacy.
  • Strand A is taught and assessed within the context of the other five strands.
  • Seven mathematical processes: problem solving; reasoning and proving; reflecting; connecting; communicating; representing; selecting tools and strategies.
  • SEL skills include identifying and managing emotions; recognizing sources of stress and coping with challenges; maintaining positive motivation and perseverance; building relationships and communicating effectively; developing self-awareness and a sense of identity; thinking critically and creatively.
  • Coding is in the Algebra strand from Grade 1; financial literacy from Grade 1.
  • Overall expectations = general knowledge and skills by the end of the grade; specific expectations = the detail.
  • Culturally responsive and relevant teaching: students see themselves in math.
  • Grade 9 Mathematics MTH1W (2021): a single de-streamed course.

Pedagogy: assessment and evaluation

Growing Success: assessment for, as and of learning, the achievement chart's four categories and four levels, learning goals and success criteria, descriptive feedback and how grades are determined.

Practise Pedagogy: assessment and evaluation questionsFlashcardsOfficial chapter

Growing Success (2010)

  • Primary purpose of assessment: improve student learning.
  • Seven fundamental principles (fair, transparent, equitable; support all students; planned to expectations and learning goals; communicated clearly; ongoing and varied; descriptive feedback that is clear, specific, meaningful, timely; develop self-assessment).
  • Assessment for learning (diagnostic before, formative during; descriptive feedback, coaching), assessment as learning (students monitor own progress, set goals, reflect), assessment of learning (evaluation for reporting).
  • Share learning goals and success criteria at the outset.
  • Evidence from observations, conversations and student products.
  • Achievement chart: four categories — Knowledge and Understanding, Thinking, Communication, Application.
  • Levels: 1 much below standard (limited, 50–59 %), 2 approaches (some, 60–69 %), 3 provincial standard (considerable, 70–79 %), 4 surpasses (high degree/thorough, 80–100 %).
  • Criterion-referenced, not norm-referenced.
  • Learning skills and work habits (reported separately): responsibility, organization, independent work, collaboration, initiative, self-regulation.
  • Grades reflect the most consistent level of achievement, with special consideration for more recent evidence.
  • Secondary: 70 % evaluation throughout the course, 30 % final evaluation.

Pedagogy: learning for all students

Learning for All: universal design for learning, differentiated instruction, the tiered approach to prevention and intervention, and planning from each student's strengths and needs.

Practise Pedagogy: learning for all students questionsFlashcardsOfficial chapter

Learning for All, K–12 (2013)

  • Three approaches: Universal Design for Learning (UDL), differentiated instruction (DI), the tiered approach to prevention and intervention.
  • UDL: broad principles for planning instruction and environments accessible to all (ramp example; assistive technology that helps everyone).
  • DI: addresses specific skills and difficulties; can differentiate content, process, product and affect/environment.
  • Readiness = current knowledge, understanding and skill for a particular learning sequence, not general ability.
  • Learners need a safe environment, appropriate challenge (neither too hard nor too easy) and connections to prior knowledge.
  • "Necessary for some, good for all."
  • Tiered approach: early identification and ongoing monitoring; Tier 1 universal, Tier 2 targeted, Tier 3 clinical/intensive.

Written in our own words from: The Ontario Curriculum: Mathematics (Grades 1–8, 2020; Grade 9, 2021)

FAQ

Ontario MPT study guide: common questions

What is the best way to use this Ontario MPT study guide?

Read one topic, then answer that topic's practice questions while the rules are fresh. Note the questions you miss, re-read those notes, and finish with a full practice test across all 9 topics.

Is this the official Ontario MPT handbook?

No. It is our own summary of the The Ontario Curriculum: Mathematics (Grades 1–8, 2020; Grade 9, 2021). Use it to review, and use the official handbook when you need the exact wording of a rule.

Can I print the study guide?

Yes, with your browser's print command. For practice questions on paper with an answer key, use our printable questions and answers page instead.

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