Teaching Grade 7 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

A traditional sequence: number systems and exponents, then algebra, measurement and geometry, finishing with data, Pythagoras and functions.

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 · Exponents & Scientific Notation

  An exponent counts how many times you multiply, not what you multiply by. That one idea explains every rule.

• Unit 2 · Problem Solving

  A hard problem is rarely beaten by cleverness. It is beaten by a method: understand it, pick a strategy, carry it out, then check.

• Unit 3 · Squares & Square Roots

  Squaring and taking a square root undo each other. A root asks: what number, times itself, gives this?

• Unit 4 · Real Numbers

  Every number you meet this year is either rational — a fraction — or irrational. Knowing which tells you how it behaves.

• Unit 5 · GCF and LCM

  Prime factorisation answers both questions at once: shared factors give the GCF, and everything needed gives the LCM.

• Unit 6 · Positive & Negative Rational Number Operations

  Negative numbers are directions, not just "less than nothing". Subtraction is adding the opposite, and sign rules come from patterns you can see.

• Unit 7 · Representing Other Algebraic Relationships

  Not everything is proportional. Learn to read a pattern, name the rule, and write it as an expression you can trust.

• Unit 8 · Solving Equations

  Undo what was done, in reverse order, doing the same thing to both sides every time.

• Unit 9 · Measurement

  Every conversion is a multiplication by one. Write the unit you want on top, the unit you have on the bottom, and the wrong units cancel themselves.

• Unit 10 · Circles

  Every circle has the same ratio of circumference to diameter. That ratio is π, and it drives both formulas.

• Unit 11 · Volume & Surface Area of 3-D Figures

  Volume fills the inside — base area times height. Surface area wraps the outside — add up every face.

• Unit 12 · Proportional Reasoning with Rates

  A rate compares two different kinds of quantity. Turn it into a unit rate and you can compare anything.

• Unit 13 · Proportional Relationships

  A proportional relationship is y = kx: a straight line through the origin, with one constant ratio running through every pair.

• Unit 14 · Reading Graphs & Estimation

  A graph is an argument. Read the scale before the shape, or you will believe whatever it wants you to believe.

• Unit 15 · Sampling, Inferences & Comparing Populations

  You cannot measure everyone, so you measure some. A random sample lets a small group speak honestly for a large one.

• Unit 16 · Probability of Simple Events

  Probability is a fraction: what you want over everything that could happen — as long as every outcome is equally likely.

• Unit 17 · Probability of Compound Events

  Two or more things happening: multiply along a path, add across paths, and watch whether the first event changes the second.

• Unit 18 · Pythagorean Theorem

  In any right triangle, the two legs squared add to the hypotenuse squared. It turns a right angle into arithmetic.

• Unit 19 · Functions

  A function is a machine: one input goes in, exactly one output comes out. The rule is the machine.