Class 9 maths tuition: the year answers stop being enough

Proof. Geometry stops being about measuring and starts being about justifying, and a proof is marked step by step on the reasons rather than on the conclusion. Nothing in Class 8 prepares a child for that kind of writing.

The content grows, certainly - cubics, circle theorems, irrational numbers. But content growth is normal and children absorb it. What is not normal is a change in what an answer is.

Until Class 8, an answer was a value. You found x, or the area, or the percentage, and the working showed how you got there. Marks followed the answer.

From Class 9, an answer can be an argument. 'Prove that the diagonals of a parallelogram bisect each other' has no number in it at all. The marks are for the sequence of justified steps, and a child who writes the conclusion without them has written nothing the examiner can credit.

This is why a child who was comfortable in Class 8 can drop sharply in Class 9 without their effort or ability changing at all.

In two columns, in effect: what you claim, and why you may claim it. Every statement needs a reason beside it - a given, a theorem, a property or a previous step - and the figure comes before either.

The routine below sounds mechanical because it is, and mechanical is exactly what a child needs here.

1. Draw the figure and label it. Large, and labelled to match the question. Most failed proofs fail here.
2. Write what is given, in symbols, from the question.
3. Write what is to be proved, in symbols. Now you know where you are going.
4. Then the steps, each with its reason - 'AB = CD (given)', 'angle 1 = angle 2 (vertically opposite angles)'.

A child who follows those four in order rarely writes a proof worth nothing, even when the proof is incomplete - because partial proofs with reasons earn partial marks, and conclusions without reasons do not.

Algebraic identities and factorisation, completely and without revision. Polynomials is the first chapter that matters, and it is unusable without both.

Class 9 does not open with revision. It opens with polynomials, which assume that expanding a bracket and factorising an expression are automatic.

So the first useful thing any Class 9 family can do costs ten minutes: ask your child to expand (x + 5)(x - 3), factorise x² - 49, and factorise 2x² + 7x + 3. Hesitation on any of the three is a Class 8 gap that Class 9 will keep charging for, and closing it takes a fortnight in September and a term in January.

Proof as a writing skill rather than as a topic, and any Class 8 algebra gap closed before polynomials rather than during them. The first session checks both.

Most Class 9 tuition teaches theorem by theorem. That is reasonable and it treats the symptom - the child learns each proof and cannot construct one they have not seen.

We teach the format first and the theorems inside it. Figure, given, to prove, steps with reasons - drilled on easy theorems until it is automatic, then applied to hard ones. A child who owns the format can attempt an unseen proof and score most of it; a child who has memorised twelve proofs can score on twelve.

See Class 9 tuition, maths tuition Class 1 to 10, our free Class 9 maths worksheets, and fees published by class. The free assessment is 20 minutes.