Teaching Algebra I at home

Prepare before the lesson

1. Read the unit's main idea and work through an example. Identify the earlier skill the method relies on.
2. Choose a short practice set that includes both a familiar example and a changed case. Have paper, a diagram or a number line ready when useful.
3. Locate the worked steps and common mistakes. Decide which step the learner should attempt before you offer a hint.

Teach, discuss and check

1. Ask for a prediction or estimate and a representation before starting an algorithm.
2. Explain one worked step and why it is valid. Let the learner complete the next step with less support.
3. Use an incorrect solution to discuss the reasoning, then give a changed problem without the model in view.
4. Check the result by substitution, units, another representation or an estimate. Ask when the method applies.

Judge the reasoning

Use these discussion criteria with the unit’s own marking guidance. They are a feedback framework, not a universal numerical grade.

• Chooses a suitable representation or relationship.
• Uses valid steps and carries the necessary units or conditions.
• Explains why the method answers the question.
• Checks the result and can adapt to a changed case.

Keep one worked example, one corrected error and one independent changed-case solution. Solving a practice question after retries is progress, but does not by itself establish independent mastery.

When the learner needs support

• When a procedure is memorized without meaning, return to a diagram or a small numerical example.
• When a prerequisite is missing, revisit the matching earlier unit rather than repeating a harder set unchanged.
• Separate an arithmetic slip from a misunderstanding of the relationship, and choose feedback accordingly.

Plan this course

Regents Algebra I — the Grade 9 course, and the same course accelerated students take in Grade 8: expressions and equations, linear relationships and data, exponential and quadratic functions, radicals, and statistics.

This math course has no authored weekly timetable in the Parent Center. Schedule its units or your own activities at a pace you choose.

No authored weekly timetable is available here. Schedule individual units and outside activities at your chosen pace.

Materials and records

Use paper, a suitable diagram or manipulatives, and the worked examples in the existing course.

Use the course assessments

Keep one worked example, one corrected error and one independent changed-case solution. Solving a practice question after retries is progress, but does not by itself establish independent mastery.

Read the full course guide

Units and teaching goals

• Unit 1 · Expressions, Structure & Units

  Before you manipulate an expression, read it. Its structure tells you what it means and what you are allowed to do.

• Unit 2 · Solving Equations & Literal Equations

  Every step you take must keep the two sides equal. Say which property justifies it, and the algebra never drifts.

• Unit 3 · Linear Inequalities

  Solve it like an equation, with one extra rule: multiplying or dividing by a negative reverses the sign.

• Unit 4 · Slope & the Forms of a Line

  Three ways to write the same line. Each one is best at answering a different question.

• Unit 5 · Writing & Transforming Linear Functions

  Once a linear model is written, every question about it — rate, starting value, prediction, shift — is a short calculation.

• Unit 6 · Systems of Equations & Inequalities

  Two conditions at once, solved three ways — graph, substitute, or eliminate. The shaded overlap is the answer for inequalities.

• Unit 7 · Bivariate Data & Correlation

  Fit a line, read its slope in context, and judge how well it fits — then resist the urge to claim a cause.

• Unit 8 · Exponential Functions & Growth

  Linear growth adds the same amount each step. Exponential growth multiplies by the same amount — and always wins in the end.

• Unit 9 · Sequences, Explicit & Recursive

  A sequence is a function whose inputs are the counting numbers. Describe it from the start, or from the term before.

• Unit 10 · Polynomial Operations

  Add and subtract by collecting like terms. Multiply by making sure every pair meets exactly once.

• Unit 11 · Factoring

  Factoring is multiplication run backwards. Always pull out the common factor first — it makes everything after it easier.

• Unit 12 · Graphing Quadratics

  Every parabola has a vertex, an axis of symmetry, and up to two roots. Find those and the graph draws itself.

• Unit 13 · Solving Quadratic Equations

  Four methods, one goal. Factoring is fastest when it works; the quadratic formula always works.

• Unit 14 · Radicals & Rational Exponents

  A root is a fractional power. Once you accept that, every exponent rule you know still applies.

• Unit 15 · Absolute Value, Piecewise & Step Functions

  Some functions change their rule partway along. Work out where the rule changes, then treat each piece separately.

• Unit 16 · Statistics: Centre, Spread & Displays

  Report a centre, a spread, and the shape. One number on its own has almost never told the whole story.