Class 8 maths tuition: the last year the syllabus forgives a gap

Algebra stops being a topic and becomes the language. Identities, factorisation and equations are no longer chapters to finish - they are the tools every later chapter is written in, and Class 9 assumes them without revision.

Up to Class 7, algebra was one chapter among several. In Class 8 it becomes the thing the rest of the syllabus is written in.

Three chapters carry disproportionate weight: linear equations in one variable, algebraic expressions and identities, and factorisation. Between them they account for most of Class 9's opening term and a good deal of Class 10.

The rest of Class 8 is comparatively self-contained. Mensuration, data handling and quadrilaterals return later but are retaught. Algebra is not, which is why a family with limited time should spend it on the three chapters above rather than spreading it evenly.

Because Class 9 polynomials and Class 10 quadratic equations are built on them entirely. A child who cannot factorise fluently cannot do either, and neither year sets aside time to teach it again.

There are three identities in Class 8 and they are worth knowing the way a child knows their tables:

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• (a + b)(a - b) = a² - b²

Memorising them is the easy part and is not what the paper tests. What it tests is recognition - seeing that x² - 49 is the third identity in disguise, or that a question can be done in one line with an identity and in six without. That recognition only comes from doing enough of them, which is why this is the chapter where practice genuinely cannot be substituted.

Factorisation then needs an order rather than trial: take out a common factor first, look for an identity second, try grouping third, and split the middle term last. A child working through those four in order rarely gets stuck; a child guessing gets stuck constantly.

Because it is usually taught as a formula. A child who has never seen that the interest of one year is added to the principal of the next has no way to check whether their answer is sensible.

Compound interest is the one Class 8 chapter where a formula is handed over before the idea, and it shows in the errors - answers smaller than the simple interest, or periods and rates not adjusted for half-yearly compounding.

Two minutes fixes most of it. Work out one year's interest, add it to the principal, and do the second year on the new amount. Once a child has done that by hand once, the formula stops being arbitrary and their answers become checkable, which matters more than the formula does.

By weighting the three chapters that Class 9 assumes and treating the rest normally. Where a Class 7 gap exists, we close it inside the Class 8 chapter that needs it rather than as separate revision.

Most Class 8 tuition covers the syllabus evenly, which is fair and not what a family with two hours a week should buy. Identities and factorisation deserve more of the year than the textbook's page count suggests, because their return is spread over the next two years rather than this one.

The first session is a short diagnostic: expand a bracket, factorise three expressions, solve an equation with a variable on both sides. Ten minutes, and it usually shows whether the problem is Class 8 at all - a Class 8 difficulty is very often a Class 7 sign rule or a Class 6 fraction that never became automatic.

See Class 8 tuition, maths tuition Class 1 to 10, our free Class 8 maths worksheets, and fees published by class. The free assessment is 20 minutes and is exactly the diagnostic above.