High school math tutor in Montreal, Secondary 1 to 5

What Secondary 1 to 3 math asks of a student

The first three years of secondary school build the tools every later year assumes. The ministry's Progression of Learning describes Secondary 1 and 2 as the years when students “move from arithmetic thinking to algebraic thinking”, and calls proportional reasoning “an essential concept that has many applications both within and outside mathematics.” In practice that means:

• Fractions and signed numbers. Operations on fractions, decimals and negative numbers, the order of operations, divisibility, and switching between a fraction, a decimal and a percentage.
• Proportional reasoning. Ratios, rates and proportions, percentages in discounts and taxes, and telling a directly proportional situation from an inversely proportional one.
• The start of algebra. Writing the rule of a pattern, translating a sentence into an equation, then by the end of Secondary 2 simplifying algebraic expressions, solving first-degree equations with one unknown and checking the solution by substitution.
• Geometry and measurement. Angles and constructions, perimeter and area, arcs and sectors of a circle, and the surface area of prisms, pyramids, cylinders and the solids built from them.
• Statistics and probability. Collecting data without bias, the mean and the range, and counting outcomes with a tree or a table.

Secondary 3 is the last year every student takes the same course, and it is a heavy one: real numbers, the laws of exponents and scientific notation, factoring out a common factor, first-degree inequalities, the linear function with its rate of change and systems of two first-degree equations, the Pythagorean relation, the volume of cones and spheres, and the median, the quartiles and the box-and-whisker plot.

Where marks are usually lost

Rarely on the idea, usually on a step. A fraction calculation done correctly with one sign dropped. An equation solved for the wrong quantity because the sentence was translated too quickly. A problem with the right final number and no visible reasoning.

That last one costs more than parents expect. The Quebec program evaluates three competencies (solving a situational problem, using mathematical reasoning, and communicating in mathematical language), and its criteria for reasoning include the “proper organization of the steps” and the “correct justification of the steps.” A bare answer meets neither. That is why sessions work on why a method works, not only on how to run it.

A gap at this age also does not stay where it started. A student unsure of fractions in Secondary 1 meets them again in algebraic expressions, in equations and in the laws of exponents, so the cheapest time to close it is the year it opens.

Secondary 4 or 5? Read the exam-years page

From Secondary 4 the course splits into three options: Cultural, Social and Technical (CST), Technical and Scientific (TS) and Science (SN). Secondary 4 also ends with the ministry's uniform mathematics exam, which counts for 50% of the final mark for the competency it evaluates. Those two years work differently enough to have their own page: Secondary 4 and 5 math tutoring covers what each option demands, the June exam and how sessions prepare for it. If your teenager is in Secondary 3, that page is also where the choice between CST, TS and SN is set out.

How sessions work

• A written diagnostic first. A short paper separates what is genuinely solid from what only looks solid, so the hours go to the real gap instead of re-teaching what your teenager already knows. In Secondary 2 or 3, that gap can sit a year or two back.
• Practice on the exact topic, marked. If you want work between sessions, it is written for exactly what was covered and marked before the next session, with each error read for what caused it.
• A written recap after every session to whoever books: what was covered, what was handled unaided, what has been assigned and what comes next.
• A record that carries forward. Every student has a standing file: the route through the course with dates, what each session established, and a short list of recurring slips to catch.
• Materials included. Practice problems, summaries and formula sheets for your teenager's course are part of the session rate.

Sessions are one-on-one, in person in Montreal (downtown and at public libraries such as the Grande Bibliothèque) for families in Westmount, Outremont, Town of Mount Royal, Hampstead, Côte-Saint-Luc, NDG, Nuns' Island and the West Island, or online on Zoom with a shared whiteboard. Students come from English and French public and private schools across the city.

When families usually get in touch

• After the first report card, when a math mark comes home lower than the year before. It is early enough to fix the cause rather than the next test.
• In the weeks before a unit test on fractions, proportions or equations, where one missing step shows up in every question.
• At the start of Secondary 1, when operations on negative numbers and algebraic expressions arrive in the same year.
• During Secondary 3, so that the year that sets up CST, TS or SN ends on solid ground.

The free printable worksheets listed below follow the Secondary 1 to 5 program topic by topic and make a fair first check of where your teenager stands; the Secondary 4 and 5 sets are written for SN.

Free practice worksheets

Every practice sheet is free to print, with no sign-up.

• Secondary 1 Math worksheets: 15 sets
• Secondary 2 Math worksheets: 14 sets
• Secondary 3 Math worksheets: 11 sets
• Secondary 4 Math worksheets: 17 sets
• Secondary 5 Math worksheets: 21 sets

For parents

• When to start math tutoring: September, after the first report card, or May?
• “I understood it in class but failed the test”: what’s going on

Common questions

Tutoring at other levels

• Secondary 4 and 5 math tutoring in Montreal
• CEGEP Science calculus and linear algebra tutoring in Montreal
• AP Calculus AB tutoring and exam preparation in Montreal
• University math and science courses