Math101 · Independent Ontario learning library
Math101learn.math101.caWelcome to Math101
Math101 is a connected reference and practice library, not a sequence that every learner must read from page one.
Welcome to Math101: a connected lesson library for finding one skill, learning it actively, checking it, and choosing a sensible next step.
Intuition and core definition
Math101 is a connected reference and practice library, not a sequence that every learner must read from page one. Each lesson isolates one idea, names its prerequisites, develops meaning before procedure, and ends with checks and practice. The useful unit of progress is a skill you can explain and apply without copying a model.
Notation, language, and conditions
Lesson titles in double brackets, such as Fractions, are internal links. Displayed formulas use mathematical symbols; callout boxes labelled intuition, example, warning, and teacher signal different purposes. “Featured” identifies a publication-ready lesson, but it does not mean the lesson is automatically the right starting point for every learner.
Why this idea matters
A precise route through the library saves time because it connects a learner's immediate obstacle to one prerequisite and one useful next step.
A dependable method
- Name the exact task you want to learn, such as adding unlike fractions, rather than choosing a whole subject.
- Open that lesson and note any unfamiliar prerequisite words or linked ideas.
- Read the intuition and worked example, then close or cover the example.
- Attempt the practice independently and use the checks before viewing answers.
- Follow a related-topic link only after you can state what you learned in one sentence.
Worked example
Representations and interpretation
Think of the library as a map with concepts as places and related-topic links as roads. A learning path is not determined only by grade; it is determined by the prerequisite that is missing between the current skill and the intended destination.
Reasoning about variations
If Maya could solve equations but confused negative-number arithmetic, the best next link would be Integers, not a harder equations lesson. If she solved correctly but could not explain the balance principle, she would revisit the intuition instead of doing twenty more identical exercises.
Common mistakes
How to check your work
- After a session, explain the target idea aloud without the page open.
- Solve one altered example whose numbers or representation differ from the model.
- Use the original conditions, units, graph, or substitution to verify the mathematical answer.
Practice
- A learner understands percentages but cannot set up a percent increase. What should the learner identify first?
- After reading a worked solution, what action supplies evidence of learning?
- When should a learner follow a related-topic link?
Answers and brief solutions
Show answers
- The precise missing skill: translating a percent increase into a multiplier A focused skill points to the relevant lesson and prerequisite; “all of percent” is too broad.
- Solve a comparable problem without viewing the model Independent retrieval distinguishes usable knowledge from familiarity.
- When it addresses a prerequisite or a sensible next skill Links serve a learning goal; following them randomly can fragment attention.
Synthesis and transfer
Suppose a learner can solve linear equations but stalls when a denominator contains a variable; locating the missing restriction skill is more productive than restarting all of algebra.
The search should move backward only until the first broken dependency is found. If factoring and restriction tracking are both secure, the learner can enter rational expressions directly; if factoring fails, that earlier skill becomes the short detour. A useful learning path therefore branches according to evidence rather than subject labels. After the missing step is repaired, one mixed problem should test whether the learner can recognize when to use it without being told. That final transfer attempt decides whether to advance, review once more, or choose a neighbouring lesson. The result is a route that is short enough to sustain momentum but explicit enough to prevent a hidden prerequisite from causing repeated failure.
Related topics
Teaching and accessibility note
Try it yourself
Hints are part of learning. Open one whenever it makes the next step feel possible.
A learner understands percentages but cannot set up a percent increase. What should the learner identify first?
- A focused skill points to the relevant lesson and prerequisite; “all of percent” is too broad.
End of lesson
Nice work making it this far.
Understanding grows through return visits. Save this lesson, try the practice, or continue when you are ready.
