Math tutor in Winnipeg

Grades 1 to 5

Elementary Maths for Grades 1-5

Number sense, operations, fractions and measurement, the skills the Grade 3 numeracy assessment looks at in the classroom.

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Grades 6 to 8

Middle School Mathematics Mastery

Number skills and number sense, integers, ratio and equations, ahead of the Grade 7 assessment and Grade 9.

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Grades 9 to 12

High School Mathematics

Grade 9 math through Grade 12 Applied or Pre-Calculus Mathematics, with trigonometry, logarithms and counting. The school grants every Manitoba credit.

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Grades 7 to 12, contest-minded

Waterloo Math Contests

Original problems in the style of the CEMC contests, for students who want harder questions than the course gives them.

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Browse the course atlas for more than one hundred options and use the coding roadmap to check prerequisites.

Vibe codingAges 13 to 17

Vibe Coding for Teens

Python, web and AI projects where the learner still owns the thinking.

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Python and AICollege and adult

Python Automation Course

Automate the work you already do, then let AI carry part of it.

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AI and MLAges 14 to 18

AI and Machine Learning for Teens

Train a model, read what it learned, and be able to say why it is wrong.

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Agentic codingProfessionals

Codex & Claude Code

Run AI coding agents on real work without losing control of the codebase.

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The early assessments are formative: Manitoba describes them as classroom-based assessment for and as learning, reported to parents to show a child’s strengths and needs. The Grade 12 tests are different. Manitoba says they are administered at the end of each semester, marked locally by teachers according to marking guidelines and training offered by the department, and that they count for 20 per cent of students’ final grades in Applied, Pre-Calculus and Essential Mathematics. Which test a student writes depends on which Grade 12 course they take, so the course choice in Grade 10 and 11 matters.

For comparisons with other provinces, our high school math courses compared across Canada sets Manitoba’s Grade 12 options beside Ontario, BC and Alberta. For younger children, math classes for kids in Canada explains how we teach number sense from age 6.

Question. A Winnipeg street has ten boulevard trees: 5 green ash, 3 elm and 2 linden. (a) Two trees are chosen at random. What is the probability they are the same kind? (b) In how many distinct orders could the ten trees stand along the street, if trees of one kind look alike? (c) If three trees are chosen at random, what is the probability that at least one is an ash?

Step 1, count pairs. There are C(10, 2) = 45 ways to choose two trees. Same-kind pairs: C(5, 2) = 10 ash pairs, C(3, 2) = 3 elm pairs and C(2, 2) = 1 linden pair, 14 in all. The probability is 14/45, about 0.311, much higher than the city-wide 0.110 because this street is mostly ash.

Step 2, arrange with repeats. If all ten trees were different there would be 10! orders. Swapping two ash trees changes nothing you can see, so divide by 5! for the ash, 3! for the elm and 2! for the linden: 10! / (5! 3! 2!) = 2,520 distinct orders. This is the permutations with repeated elements idea that trips students who reach for 10! straight away.

Step 3, use the complement. “At least one ash” is the opposite of “no ash”. Choosing three non-ash trees from the five others can be done in C(5, 3) = 10 ways, out of C(10, 3) = 120. So the probability of no ash is 10/120, and of at least one ash, 1 minus 10/120, about 0.917.

Step 4, connect to the data. The city-wide figure of 0.0716 for two green ash trees comes from exactly the step 1 method, with 81,895 in place of 5 and 305,969 in place of 10. The arithmetic is bigger; the idea is identical.

Try it yourself. (1) Add one bur oak to the street and redo part (a). (2) How many distinct orders are there now? (3) Using the city table, estimate the chance that three random Winnipeg trees include no green ash. Bring your answers to the free lesson and we will check them together.

For most Winnipeg students, a group class at one level gives steady progress and regular practice. One to one earns its cost in short, specific bursts: the weeks before the January or June provincial test, a unit such as logarithms or combinatorics that will not click, or a move from Applied to Pre-Calculus Mathematics. Many families use both, in that order.