Ontario MPT key terms

One of the broad organizing categories of the Ontario mathematics curriculum - Number, Algebra, Data, Spatial Sense, and Financial Literacy - each of which contains overall and specific expectations across the grades.

A broad curriculum statement describing the knowledge and skills students are expected to demonstrate by the end of a grade or course, elaborated in detail by a set of specific expectations.

A detailed curriculum statement that breaks an overall expectation into teachable, observable skills, often accompanied by examples, sample tasks, and teacher supports in the published curriculum documents.

Seven interrelated processes threaded through Ontario mathematics learning: problem solving, reasoning and proving, reflecting, connecting, communicating, representing, and selecting tools and computational strategies.

A set of skills embedded in the Ontario mathematics curriculum - identifying emotions and managing stress, keeping an open mind, persevering, seeking help, and identifying personal strengths - that support learning mathematics.

Understanding of quantity, place value, magnitude, and the relationships among numbers and operations, forming the foundation for computation, estimation, and later algebraic work.

Understanding of how the four operations work, how they relate to one another, and how to choose and apply them, including mental math and estimation strategies, appropriately in context.

Reasoning about multiplicative relationships between quantities, including ratios, rates, percentages, and scale, requiring comparison by multiplication rather than by adding a constant difference.

Understanding of shape, location, movement, and measurement, including geometric properties, transformations, and the measurement of length, area, volume, and angles.

Recognizing, describing, extending, and generalizing regularities found in numbers, shapes, and everyday contexts, serving as a bridge toward algebraic thinking and generalization.

A mathematical phrase that combines numbers, variables, and operations without an equals sign, used to represent a quantity or a generalized relationship between quantities.

A relationship between two variables whose graph is a straight line and whose equation can be written in a form such as y = mx + b, showing a constant rate of change.

The ability to collect, organize, represent, analyze, and interpret data, and to use that evidence to make informed decisions and judgements in a variety of contexts.

Knowledge and skills relating to money, budgeting, spending, saving, and financial decision-making, taught in Ontario mathematics through realistic contexts such as costs, interest, and planning.

Writing and interpreting precise sequences of instructions that a computer can execute, used in the Ontario mathematics curriculum to develop problem-solving skills and algebraic reasoning.

An instructional progression in which a concept is first explored with physical materials, then with drawings or diagrams, and finally with symbols and abstract notation.

A physical object such as counters, base-ten blocks, or fraction tiles that students handle and arrange to build understanding of mathematical ideas and relationships.

Presenting the same mathematical idea through diagrams, tables, graphs, symbols, words, and physical models so that students can connect and compare different forms of the idea.

The ongoing gathering of evidence about student learning during instruction, used to adjust teaching and provide feedback rather than to assign a grade.

Assessment of learning carried out at the end of a period of instruction to judge achievement against curriculum expectations and to report results to students and parents.

Assessment carried out before instruction to identify students' prior knowledge, misconceptions, and readiness, so that teaching can be planned to match learner needs.

Specific, actionable information given to a learner about what was done well and what to do next, connected to clear learning goals and shared success criteria.

A short, student-friendly statement of what students are expected to learn in a lesson or sequence of lessons, written in language learners can understand and use.

Co-created, observable descriptions of what successful work looks like, which help students monitor their own progress and evaluate the quality of their mathematical work.

Planning and adapting content, process, products, and learning environment in response to student readiness, interests, and learning profiles so that all students can access the curriculum.

A planning framework that builds multiple means of engagement, representation, and action and expression into lessons from the outset so that diverse learners can succeed.

Temporary supports such as models, prompts, guided questions, or partially worked examples that help a learner complete a task and are gradually withdrawn as competence grows.

The range of tasks a learner can accomplish with guidance from a more knowledgeable person but cannot yet manage independently, marking where instruction is likely to be most productive.

The purposeful effort students expend on challenging but attainable mathematics, which builds persistence and deeper conceptual understanding rather than encouraging quick answer-getting.

Structured classroom conversation in which students explain, justify, and compare mathematical strategies and reasoning, building shared understanding and increasingly precise mathematical language.

A brief, routine whole-class activity in which students solve computation problems mentally and then share, compare, and discuss the different strategies they used.

A lesson structure consisting of a minds-on activation, an action phase in which students work on a rich problem, and a consolidation phase that makes the intended mathematics explicit.

Different versions of a problem that share the same learning goal but vary in difficulty, numbers, or context, allowing students to work simultaneously and discuss common mathematics.

A problem that is accessible to a wide range of learners at entry while still offering extension into deeper or more complex reasoning for students who are ready.

A stable, often reasonable but incorrect idea a student holds that must be surfaced and addressed through discussion and evidence, rather than simply corrected by restating a rule.

Grasping the meaning and connections underlying mathematical procedures - knowing why an algorithm or relationship works, not only how to carry out the steps.

The ability to carry out mathematical procedures accurately, efficiently, and flexibly, including choosing an appropriate strategy and estimating to check whether a result is reasonable.

Assessment in which students monitor their own learning, set goals, and use self-assessment and reflection to become metacognitive, self-regulating learners of mathematics.

A feeling of tension or fear experienced when engaging with mathematics that can interfere with working memory and lead students to avoid mathematical tasks and courses.

A change in how a student accesses learning or demonstrates learning without altering the curriculum expectations, such as extra time, a quiet setting, or access to a calculator.