Ontario MPT cheat sheet

Ontario Grades 1–8 mathematics (2020) is organized into five strands - Number, Algebra, Data, Spatial Sense, Financial Literacy - plus Social-Emotional Learning skills and seven mathematical processes.

The de-streamed Grade 9 course MTH1W (2021) has six strands: A Mathematical Thinking and Making Connections, B Number, C Algebra, D Data, E Geometry and Measurement, F Financial Literacy.

The seven mathematical processes are problem solving, reasoning and proving, reflecting, selecting tools and computational strategies, connecting, representing, and communicating; they are embedded in every strand, not taught separately.

Fraction rules: a/b × c/d = ac/bd; a/b ÷ c/d = a/b × d/c (multiply by the reciprocal); a common denominator is required only for addition and subtraction.

Order of operations: evaluate brackets, then exponents, then multiplication and division left to right, then addition and subtraction left to right.

Proportional reasoning tools: unit rate = total ÷ number of units; part = percent × whole; a/b = c/d is solved by cross-multiplication (ad = bc).

Grade-band anchors: Grade 3 multiplication facts for 2, 5, 10 and related division; Grade 4 facts through 10 × 10; Grade 8 Pythagorean theorem and linear relations; Grade 9 slope, equations, and connections to financial contexts.

Measurement formulas: triangle A = ½bh; circle A = πr² and C = 2πr; cylinder V = πr²h; any prism V = area of base × height; rectangular prism SA = 2(lw + lh + wh).

Data summary measures: mean = sum ÷ count; median = middle value of ordered data; mode = most frequent value; range = maximum − minimum. Outliers affect the mean far more than the median.

Three-part lesson structure: activation (minds on) → action (a rich problem solved by students) → consolidation (selecting, sequencing, and comparing student strategies) → practice.

Assessment purposes: assessment for learning (formative, feedback-driven), assessment as learning (student self-monitoring), assessment of learning (summative); evidence is triangulated from observations, conversations, and products.

Success criteria must be co-created, specific, observable, written in student-friendly language, and directly aligned with the stated learning goal.

Concrete–representational–abstract (CRA) sequence: manipulatives first, then drawings and diagrams, then symbols and algorithms; skipping a stage leaves conceptual gaps that surface later.

Differentiation decision rule: adapt content, process, product, or environment in response to readiness, interest, and learning profile, while keeping the same big idea for all students.

Open tasks with a low floor and high ceiling allow the whole class to work on one problem at different levels; solutions are then selected and sequenced on the board (bansho) to build a shared generalization.

Number talks run 5–15 minutes: mental computation followed by strategy sharing, with emphasis on efficiency and flexibility rather than speed.

Descriptive feedback tied to success criteria and to the task (not the learner) improves achievement more than marks or praise; wait time of three to five seconds increases participation and response length.

Math anxiety is reduced by flexible grouping, untimed assessments, multiple representations, and norms that treat errors as information rather than failure; timed public comparisons increase anxiety.