A mathematics class should not require every child to complete the same work at the same speed.
At Academia Discovery, each new topic is taught through a clear, carefully structured lesson. Students first receive a simple explanation of the rule, with worked examples that show exactly how and why it works. They then practise through five levels of gradually increasing challenge.
A student usually works through the 20-24 questions at their own levels. A full lesson contains 60–90 questions in total, so that every level has enough material — no child is expected to complete them all.
Levels A and B: Building the Foundation
Levels A and B focus on one new skill at a time. The questions are clear, guided, and carefully sequenced, and they give a student the chance to make an important foundation secure before moving ahead.
This is not a place where a child stays. Most students move beyond these levels within the first few weeks of consistent study.
Level C: Grade-Level Mastery
Level C is the main grade-level pathway. Students apply the new skill more independently and begin combining it with ideas they have already learned.
Level C also includes spiral review, so students regularly return to important knowledge from earlier lessons and units. Mathematics is not learned once and forgotten; it is revisited until it becomes secure.
Levels D and E: Extension and Advanced Thinking
Students who are ready move to Levels D and E.
Here the questions require deeper reasoning, connections between several rules, and non-routine problem-solving that reaches beyond the standard grade-level curriculum. This is the work that prepares students for mathematics contests such as the Waterloo CEMC competitions, and for university-level mathematical thinking later on.
Students who begin at Level C often move quickly to Level D. Level E is deliberately demanding, and students may need teacher guidance as they learn to approach unfamiliar and more complex problems.
How Do We Know Which Level Is Right?
Students who are ready move to Levels D and E.
Here the questions require deeper reasoning, connections between several rules, and non-routine problem-solving that reaches beyond the standard grade-level curriculum. This is the work that prepares students for mathematics contests such as the Waterloo CEMC competitions, and for university-level mathematical thinking later on.
Students who begin at Level C often move quickly to Level D. Level E is deliberately demanding, and students may need teacher guidance as they learn to approach unfamiliar and more complex problems.
How Do We Know Which Level Is Right?
During the first two lessons, the teacher observes each student’s knowledge, confidence, speed, and problem-solving approach. Review lessons provide further evidence.
The teacher then selects the level of work that fits the child. This is the heart of what we call Find the Missing Piece: rather than repeating a whole topic, the teacher identifies the exact idea a student has not yet secured and works on that.
The decision is not fixed. If the work is too easy, the student moves up. If a student is missing something, the teacher moves the student down to rebuild it and then brings them back up. Both directions are normal, and both are progress.
Our small class sizes are what make this possible. The teacher can make these decisions carefully and respond quickly. Strong students are not held back by unnecessary repetition, and students who need support are not left confused in the middle of a large class.
How Students Are Assessed
The levels govern practice, not grading. Tests and assessments are common to the whole class and are marked against the Ontario curriculum expectations for that grade, so every student is measured against the same standard.
If you would like to know which level your child is working at, your child’s teacher can tell you at any time.
Extra Help After School
Students who need extra support can attend our Math Club, which runs [days] from 3:00 to 4:00 p.m.
A student may come with a single question, get help, and leave. Another may stay for 15, 30, or 45 minutes when more explanation or practice is needed.
This means a child does not have to wait until the next lesson, or until a small problem becomes a large one. Help is available early, personally, and regularly.
Our Goal
We do not expect every child to reach the same level at the same time.
Our goal is to find each child’s true starting point, supply the missing piece when one is there, provide the right level of challenge, and help every student produce their strongest possible work.
No child is left without help. No strong child is left without challenge.