Ontario MPT flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Division of fractions rule

To divide by a fraction, multiply by its reciprocal: a/b ÷ c/d = a/b × d/c. For example, 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8.

Order of operations (BEDMAS)

Evaluate brackets first, then exponents, then multiplication and division left to right, then addition and subtraction left to right. Example: 6 + 2 × 3 equals 12, not 24.

Grade 9 MTH1W strands

Ontario's de-streamed Grade 9 mathematics course has six strands: Mathematical Thinking and Making Connections, Number, Algebra, Data, Geometry and Measurement, and Financial Literacy.

Elementary mathematics strands (2020)

Ontario Grades 1–8 mathematics organizes expectations into Number, Algebra, Data, Spatial Sense, and Financial Literacy, along with social-emotional learning skills and the mathematical processes.

Mathematical processes

Seven processes woven through Ontario expectations: problem solving, reasoning and proving, reflecting, selecting tools and computational strategies, connecting, representing, and communicating. They are applied within every strand.

Pythagorean theorem

In a right triangle, a² + b² = c², where c is the hypotenuse. Grade 8 students use it to find a missing side length or to check whether an angle is right.

Theoretical probability

Theoretical probability equals favourable outcomes divided by total equally likely outcomes. Experimental probability compares observed favourable outcomes to total trials; the two converge as the number of trials increases.

Mean, median, and mode

Mean is the sum divided by the count; median is the middle value when data are ordered; mode is the most frequent value. Outliers shift the mean much more than the median.

Integer multiplication rules

Two numbers with the same sign give a positive product; two numbers with different signs give a negative product. So (−3) × (−4) = 12 and (−3) × 4 = −12.

Volume of a cylinder

V = πr²h, where r is the radius of the base and h is the height. Volume is reported in cubic units, whereas surface area is reported in square units.

Unit rate

A unit rate expresses a ratio per one unit, such as $3.20 per kilogram. Unit rates let students compare differently sized packages and support proportional reasoning across Grades 5 to 8.

Solving a linear equation

Keep the equation balanced by applying the same operation to both sides, undoing operations in reverse order: 3x + 5 = 20 becomes 3x = 15, then x = 5.

Slope of a line

Slope m = rise ÷ run = (y₂ − y₁)/(x₂ − x₁). In the form y = mx + b, m is the slope and b is the y-intercept where the line crosses the vertical axis.

Ratio versus rate

A ratio compares two quantities of the same kind, such as 3:5. A rate compares quantities with different units, such as kilometres per hour. Both can be written as fractions.

Multiplying fractions

Multiply numerators together and denominators together: a/b × c/d = ac/bd. The product of two proper fractions is smaller than either factor, which students use to check reasonableness.

Surface area of a rectangular prism

SA = 2(lw + lh + wh), the sum of the areas of all six faces. The result is expressed in square units, distinct from volume in cubic units.

Pattern rule to linear relation

A pattern with a constant first difference is linear. The difference becomes the multiplier and the value at term zero becomes the constant: 5, 8, 11 gives 3n + 2.

Grade 3 multiplication expectation

Ontario Grade 3 students develop and use multiplication facts for 2, 5, and 10 and the related division facts; Grade 4 extends to facts through 10 × 10.

Three-part lesson structure

A lesson frame with an activation or minds-on, a problem-solving action phase, and a consolidation where strategies are shared, compared, and named as the mathematical learning.

Success criteria

Co-created, student-friendly statements describing what a successful response looks like. They must be observable and specific enough for students to monitor their own work against them.

Descriptive feedback

Feedback that names what was done well and what to do next, tied to the success criteria. It improves achievement more than marks, grades, or general praise.

Triangulation of evidence

Judging achievement using three sources of evidence: observations, conversations, and student products. No single source or single task should determine a grade.

Concrete-representational-abstract sequence

A teaching sequence moving from manipulatives, to drawings and diagrams, to symbols and algorithms. Skipping a stage can leave conceptual gaps that surface in later grades.

Number talk

A five to fifteen minute routine of mental computation followed by sharing and comparing strategies. It builds fluency and flexibility rather than speed of recall.

Bansho

Organizing student solutions on the board by strategy so the class can compare approaches and build a shared mathematical generalization during the consolidation phase.

Low floor, high ceiling task

A task with accessible entry points but room to extend into sophisticated mathematics, so the whole class can work on the same problem at different levels.

Assessment for learning

Formative assessment used during learning to adjust teaching and provide feedback. It is diagnostic and forward-looking, focused on closing the gap rather than judging performance.

Differentiated instruction

Adapting content, process, product, or environment in response to student readiness, interest, and learning profile, while keeping the same big idea for the whole class.

Math anxiety

A negative emotional response to mathematics, often increased by timed tests, public comparison, and speed pressure. Flexible grouping and multiple entry points help reduce it.

Wait time

Pausing about three to five seconds after asking a question before taking responses. It increases response length and the number of students who participate.

Additive to multiplicative thinking

A progression from 'how many more' comparisons to 'how many times as many'. This shift underpins proportional reasoning in Grades 5 to 8.

Learning goal

A brief statement of the mathematical idea students should understand by the end of a lesson, written in student-friendly language and linked to a curriculum expectation.